ࡱ> 69/012345 bjbj΀ p  IIIIId])\xN :A A A &&&MMMMMMMPRTM9I&&^&&&MIIA A T2N555&@IA IA M5&M55@|wBA  3-{AMHN0xNA S4 S$wBwB SID &&5&&&&&MM5&&&xN&&&& S&&&&&&&&& :  AWARENESS OF LEARNING STYLES AND MATH VOCABULARY INSTRUCTION Except where reference is made to the work of others, the work described in this thesis is my own or was done in collaboration with my Thesis Chair. This thesis does not include proprietary or classified information. Janice Wearden Certificate of Approval __________________________ _____________________________ Donald R. Livingston, Ed.D Sharon M. Livingston, Ph.D. Thesis Chair Thesis Advisor Education Department Education Department AWARENESS OF LEARNING STYLES AND MATH VOCABULARY INSTRUCTION A Thesis by Janice Wearden to LaGrange College in partial fulfillment of the requirement for the degree of MASTER OF EDUCATION in Curriculum and Instruction LaGrange, Georgia May 5, 2011 Abstract This study investigated the role of addressing learning styles when teaching math vocabulary to fifty-three fifth grade students at a small elementary school in West Central Georgia. Research shows vocabulary mastery influences success in math. Various activities addressing different learning styles were implemented with the treated group while the untreated group wrote definitions. Quantitative data analysis revealed there were no significant statistical differences between the post-tests of the treated and untreated groups. The qualitative data showed an improvement in the attitudes of both the students and the teacher. The results of this study serve as a foundation for future research on whether addressing students learning styles can improve the mastery of math vocabulary leading to higher test scores. Table of Contents Abstract..........iii Table of Contents........iv List of Tables ..........................v Chapter 1: Introduction...........1 Statement of the Problem.....................1 Significance of the Problem.....................2 Theoretical and Conceptual Frameworks....................3 Focus Questions.......................6 Overview of Methodology.......................6 Human as Researcher.......................7 Chapter 2: Review of the Literature................8 The Vocabulary of Mathematics......................8 Learning Styles....................9 Opposing Views on Learning Styles......................11 Student Learning Outcomes...................12 Attitudes of Students and Teachers....................15 Summary....................16 Chapter 3: Methodology.......17 Research Design.....................17 Setting....................17 Subjects and Participants..............................18 Procedures and Data Collection Methods.................... .20 Validity, Reliability and Bias Measures................................23 Analysis of Data....................26 Chapter 4: Results.........29 Chapter 5: Analysis and Discussion of Results........40 Analysis.....................40 Discussion......................45 Implications........................47 Recommendations for Future Research.....................48 References.......,.50 Appendixes...........54 List of Tables Tables Table 3.1. Data Shell.20 Table 4.1 Pre/Pre Independent t-test...................................................................31 Table 4.2 Treatment Group Pre/Post Dependent t-test.......32 Figure 4.3 Untreated Group Pre/Post Dependent t-test.33 Figure 4.4 Post/Post Independent t-test....34 Figure 4.5 Untreated Group Chi Square ......................35 Figure 4.6 Treatment Group Chi Square......................36 CHAPTER ONE: INTRODUCTION Statement of the Problem According to the recent Georgia state CRCT results, 18% of the fifth grade students did not meet the state standards in mathematics (Georgia Department of Education [GADOE], 2008). This amounts to a significant number of fifth graders, in the state of Georgia, who did not master the necessary math concepts for advancement to middle school. Consequently, educators must continue to seek alternate teaching strategies during math instruction to engage all students. A large part of math is vocabulary. Vocabulary should be the scaffold that lessons are developed around. Greenwood (2006) clearly states that the practice of looking up words in the dictionary and writing sentences with them is pedagogically useless. According to Carter and Dean (2006) students must be able to decode and comprehend word problems and textbooks in addition to making sense of specialized mathematical vocabulary in order to communicate and think mathematically. Students with a greater vocabulary can use it to gain new knowledge. Improving the vocabulary of all students, especially children who come from low socio-economic groups or who are learning English, will help them understand the concepts being taught (Spencer & Guillaume, 2006) This study investigated whether the use of methods addressing different learning styles in the acquisition of math vocabulary would improve understanding of mathematical concepts among students. The Georgia Department of Education states in their Performance Standards Framework that teachers should present vocabulary and concepts to students with models and real life examples thus causing students to be able to recognize and demonstrate these concepts with words, models, pictures, or numbers. Pierce and Fontaine (2009) maintain that the depth and breadth of a childs mathematical vocabulary will influence a childs success in math. The comprehension of math specific terms and ambiguous, multiple-meaning words could assist students in understanding problems on the CRCT thus leading to higher scores. Significance of the Problem Georgias minimum percentage of students passing math to meet Adequate Yearly Progress rose from 67.6% for 2010 to 75.7% for 2011. Students often struggle when test questions contain words that are not specific and have more than one meaning. Technical words have a very specific mathematical meaning. Sub-technical words have a common meaning that students usually already know; however, they also have a less common mathematical meaning with which students may not be familiar. Pierce and Fontaine (2009) assert that teachers are aware of the need to teach the meaning of technical vocabulary words, yet often do not realize that sub-technical vocabulary also needs to be taught as well. The National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics, includes Communication as a process strand. It states that students should use the language of mathematics to express mathematical ideas precisely. The Georgia Performance Standards (GPS) repeat exactly what the NCTM standard states about expressing ideas with precision. Pierce and Fontaine (2009) state that a childs knowledge of mathematical vocabulary is an important indicator of how successful a child will perform in math. The purpose of this study was to determine if there will be an increase in math vocabulary test scores and ultimately the Georgia CRCT math test by using methods that address all learning styles when teaching vocabulary. Theoretical and Conceptual Frameworks This study relates to the social constructivist theory in the fact that it seeks to show how creating learning environments in which learning is both enjoyable and rigorous can be effective (LaGrange College Education Department, 2008, p. 3). In the article, The Good, the Bad, and the Ugly: The Many Faces of Constructivism, Phillips (1995) examines the views of various constructivist authors. Overall, constructivists do not believe that humans are born with cognitive data banks of empirical knowledge, but that they construct knowledge through inquiry and experiences (Phillips, 1995, p. 7). Piaget proposes that humans do not immediately understand and use information they are given; instead humans must construct their own knowledge (Powell, & Kalina, 2010, p. 242). Tomilinson suggests that teachers should be learning facilitators rather than dispensers of information and they should create learning environments in which students can be actively involved in the teaching and learning process (LaGrange College Education Department, 2008). Domain Three of the Georgia Framework for Teaching states that teachers should create learning environments that encourage positive social interaction, active engagement in learning, and self motivation. Teaching math concepts and vocabulary should be both enjoyable and rigorous in addition to being learner focused. This thesis relates to both Tenets One and Three of the LaGrange College Education Departments (2008) Conceptual Framework. Tenet One involves the learner being enthusiastically engaged in learning. Teachers must know their learners, so that they construct knowledge in a context of social relations. No one has the same background experiences. Because approximately 87.5% of the students at the school in this study participate in the free and reduced lunch program, many may lack experiences that would make understanding vocabulary easier. The teacher needs to be aware of this. This thesis is related to the Knowledge of Learners subgroup under Tenet One of the LaGrange College Education Departments (2008) Conceptual Framework and Domain Two of the Georgia Framework for Teaching. Teachers need to know about their students abilities, needs, and interests in order to provide them with curriculum that is meaningful to them (LaGrange College Education Department, 2008). The Georgia Framework for Teaching reports that teachers should understand how learning occurs and adapt their lessons based on students stages of development, multiple intelligences, learning styles, and areas of exceptionality (LaGrange College Education Department, 2008, p. 2). When teaching students from high-poverty backgrounds, the teacher should take a holistic approach and use a wide variety of strategies. The teacher must understand how students lives and learning are influenced not only by what happens at school, but also outside the school setting. The teacher must have high expectations for the students and believe that these students can learn at a high level. (LaGrange College Education Department, 2008) On the national level, the National Board for Professional Teaching Standards (NBPTS) Core Assumptions; Knowledge of Learners can be directly linked with Proposition One. This proposition, Teachers are committed to student learning states, They act on the belief that all students can learn. They treat students equitably, recognizing the individual differences that distinguish one student from another and taking account of these differences into their practice (NBPTS, 2002). This is also included in Domain 2 of the Georgia Framework for Teaching. The teachers of high poverty students must hold these principles in order to accomplish desired outcomes. The LaGrange College Education Departments (2008) Conceptual Framework , using the work of Delpit and Kincheloe, places importance on teachers linking the content taught in their classrooms to the life histories of their students, so that students can make meaningful personal connections. Tenet Three of the LaGrange College Education Departments (2008) Conceptual Framework is also relative to this thesis. This third tenet focuses on the professional dispositions that teachers need to develop and demonstrate in their work with students, families, professional colleagues, and members of the larger community (LaGrange College Education Department, 2008, p. 8). The third cluster suggests that teachers should take action and advocate for changes in curriculum and instructional design. Teachers need to improve the learning environment to support the diverse needs and high expectations for all students. In order for teachers to advocate public changes, Jenlink and Jenlink recommend that they must first learn to become self-critical practitioners who use research in their teaching (as cited by LaGrange College Education Department, 2008, p. 8). Paulo Freire states in Pedagogy of the Oppressed, teacher educators are asked to take actions that will overcome injustice and inequalities that hinder the development of children (LaGrange College Education Department, 2008, p.8). Domain Six of The Georgia Framework for Teaching states that teachers should reflect and extend their knowledge of teaching and learning to be able to improve their own teaching practices. Implementing effective strategies and curriculum, in addition to establishing a well rounded learning environment should be the goal of all those in the teaching profession. Proposition Four in the NBPTS (2002) Core Assumptions is that teachers need to think systematically about their practice and learn from their experience. Teachers seek to encourage lifelong learning in their students due to their engagement in lifelong learning themselves. They aim to strengthen their teaching and adapt their teaching to new findings, ideas, and theories (NBPTS, 2002). Focus Questions Factors that affect the 5th grade math CRCT scores will be researched in this study. There are many factors that could affect student learning in the area of math. This study focused on three specific areas and the factors within those areas. The following focus questions will be used to guide the research for the study: What is the process of teaching math vocabulary to address different learning styles of individual students? How do test scores compare between traditional methods of teaching vocabulary and vocabulary taught by addressing different learning styles? How do teacher/student attitudes change about vocabulary when different learning styles are addressed? Overview of Methodology This action research study was designed to determine if there was a difference in scores when math vocabulary was taught by addressing the different learning styles that students possess as opposed to traditional methods such as copying the definition from the dictionary/glossary. This was a mixed-methods research study that incorporated both quantitative and qualitative data. Assessment data in the form of pre/post tests were collected to evaluate the success of addressing different learning styles of individual students. The pre/post surveys were analyzed quantitatively using a chi square. Qualitative data were collected with a reflective journal that was coded for recurring, dominant, and emerging themes. The school where this study took place is located in a county in west central Georgia. The subjects were the students in my 5th grade math class. Human as Researcher The qualifications of the researcher are important to know for this study. I teach 5th grade in a high-poverty school in Troup County. With 25 years teaching experience, I have taught in both self-contained and departmentalized settings. I have taught math each year whether just to my class or all classes on a particular grade level. I feel that the teachers passion or lack of, in teaching math can influence students performance. Creating an environment where students feel comfortable and safe is very important when teaching math. Another belief is that teachers should hold every student, no matter his economic status, up to high academic standards. This may also influence math scores. CHAPTER 2: REVIEW OF THE LITERATURE Many school improvement plans place an emphasis on increasing student achievement. In order to make gains in these areas, improvement in standards-based instruction, curriculum alignment, teacher quality, and the overall learning environment is often the focus (Beecher & Sweeny, 2008). The No Child Left Behind Act (NCLB), places the responsibility on states to raise student performance and meet Adequate Yearly Progress (AYP), which is measured for all students by state standardized, high stakes tests (Tajalli & Opheim, 2005). According to Fore, Boon, and Lowrie (2007), the ability to read and vocabulary knowledge in the content areas are essential for school success. For this study, the focus was on the effect of teaching math vocabulary to address different learning styles of individual students. The Vocabulary of Mathematics According to Pierce and Fontaine (2009), the depth and breadth of a childs mathematical vocabulary is more likely than ever to influence a childs success in math. Research has shown that teaching mathematical vocabulary enhances a students performance on math tests. Students with difficulty reading often have limited vocabularies which hinder their ability to relate new terms and concepts to previous knowledge especially in content areas such as mathematics (Fore, et al., 2007). The National Council of Teachers of Mathematics (NCTM, 2000) Principles and Standards for School Mathematics now includes Communication as a process strand. Students are expected to be able to explain their problem-solving methods orally and in written form, both in the classroom and on high-stakes tests. Studies have shown that mathematical thinking skills of both general and special education students improved through an effective use of vocabulary instruction (Fore, et al., 2007). Math contains a lot of specialized vocabulary that is specific to the subject of mathematics. Some words such as divisor, rectangle, and place value are used only in mathematics. Other terms are used in math and in the non-math world with about the same meaning, such as measure, half, and tally. There is another group known as multi-meaning words like prime, odd, and right. These words have a math meaning and other meanings outside the math context (Cunningham, 2009). Pierce and Fontaine (2009) refer to two categories of mathematics vocabulary as technical and sub-technical. Technical words have a precise mathematical denotation that must be specifically taught to students. These are words that are often defined in math textbooks. Sub-technical words have a common meaning that students generally already know; however, they also have a less common mathematical denotation that students may be less familiar with. If you teach the general meaning of these words along with the mathematical meaning, you can use the familiar meaning to connect to the mathematical meaning. Learning Style One of the most enduring effects on education has been the search for individual differences that can explain and predict variation in student achievement. This led to the hope that learning opportunities can be designed that will maximize the attainment of these individual differences (Scott, 2010). Though all human beings have common characteristics in the learning process, ways of giving meaning and acquiring information may vary. Learning styles is defined as the different ways used by individuals to process and organize information or to respond to environmental stimuli. It is important to take into account the characteristics, abilities and experiences of learners when planning to teach a lesson. Teachers should select and organize methods and strategies, classroom environment, and teaching materials according to learning styles rather than expecting the student to adapt to the existing organization (Yilmaz-Soylu & Akkoyunlu, 2009). Jensen (1998) refers to it as a sort of way of thinking, comprehending and processing information. Haas (2003) states that auditory-sequential learners tend to do well in school where the curriculum, materials, and teaching methods are predominantly sequential and presented in an auditory format. Auditory-sequential learners are easily able to remember their math facts, memorize the steps to complete equations, answer homework questions correctly, and earn good grades in math without ever truly understanding the underlying mathematical concepts. Auditory-sequential instruction of math often separates the number from what it represents. Visual-spatial learners would also miss the underlying mathematical concept and they may not be able to remember math facts, nor readily be able to memorize the steps to complete equations. They might not be able to correctly answer homework problems leaving them with a lowered self-esteem and a perceived deficit in mathematical ability. Silverman (2005) suggests that the visual learner needs to see the information rather than hear it in order to make sense of it. They have to change the information to visual images if any true learning is to occur. If a teacher is presenting information in an auditory manner, the visual-spatial learner is listening to the words, and then creating an image in their brain. This takes additional processing time, which leaves the visual-spatial learner behind. According to Rapp (2009) when teaching auditorally, use visualization strategies that allow the learner to create a picture in their head. Historically, vocabulary instruction has consisted of looking up a word in a dictionary or glossary. This method has been proven to be a useless practice because retention of the knowledge is not achieved (Bromley, 2007). Students blindly copy the definitions and forget about them. Beck, McKeown, and Kucan (2002) assert that becoming interested and aware of words is not a likely outcome from having students look up definitions in a dictionary or glossary. More effective strategies are being developed to enhance vocabulary lessons (Bromley, 2007). For teachers, the idea of being able to use an individuals learning styles as a diagnostic, predictive, or pedagogical tool for the purposes of improving academic performance at school is an appealing one (Sharp, Bowker, & Byrne, 2008). Cunningham (2009) states that adding strategies to address visual, auditory, and kinesthetic (VAK) styles while teaching math vocabulary maximizes the potential for learning in that subject area. Opposing Views on Learning Styles The idea that individual differences in academic abilities can be partly ascribed to individual learning styles has tremendous appeal especially when looking at the number of learning style models or inventories that have been devised 170 at the last count and rising. The disappointing result of this entire endeavor is that, on the whole, the evidence time and again shows that modifying a teaching strategy to account for differences in learning styles does not result in any improvement in learning outcomes (Geake, 2008). While it is commonly believed that learning styles cannot be overlooked in education, there is still substantial disagreement over the perceived status of learning styles in teaching and learning and how the different styles should be addressed in the classroom. Most educators know that individuals of all ages approach different tasks in diverse areas of their work in different ways, learn at different rates, and apply what they learn with different degrees of confidence and success. They know that learning styles is only one of a great many variables which influence academic performance (Sharp, et al., 2008). Concentrating on one sensory modality contradicts the brains natural interconnectivity. The input modalities in the brain are interconnected: visual with auditory; visual with motor; motor with auditory; visual with taste; and so on. To many educators VAK has become mixed-modality pedagogy where material is presented in all three modes. According to Kratzig and Arbuthnott (as cited by Geake, 2008) research has shown that there is no improvement of learning outcomes with VAK above teacher enthusiasm. Student Learning Outcomes Engaging students in active hands-on lessons for the purpose of acquiring vocabulary is one method that can be used to achieve vocabulary comprehension. Giving students the opportunity to design a picture definition is an example of a hands-on strategy that can be used to motivate students and keep them involved in the lesson (Greenwood, 2006). These picture definitions produced by the students can be posted in the room or in the hall. Bull and Whittrock (as cited by Sadoski, 2005) found that when students wrote a verbal definition and drew a picture to represent the definition, the students retention was significantly better than when they wrote the definition alone, or were provided with the definition and an illustration as in a textbook. Good readers make the non-verbal images automatically as they read. Readers who fall at the lower end of the ability spectrum end up calling words and not seeing the pictures in the text (Hibbing & Rankin-Erickson, 2003). Using a graphic organizer keeps a strong focus on the relationship among the definition of a concept, one or more illustrative examples of the concept, and characteristics of the concept that the word represents. These three sections correspond to Rector and Hendersons (1970) three ways of teaching a concept. When a teacher talks about the properties or characteristics of the object named by a term, they employ the connotative use of the term. When teachers give examples, they use the term in a denotative manner and when they define the term, they employ the implicative use of the term (Gay, 2008). Learners need multiple opportunities to interact with words in order to truly know them. Vocabulary cards based on the Frayer model encourage learners to think about new vocabulary through definition, contrasts, and visual representations. Typically they are developed using a five-by-seven-inch index card divided into four quadrants (Frey & Fisher, 2009). The learning cycle is a teaching method that uses visualization to teach vocabulary. There are four phases of this cycle: engage, explore, develop, and apply (Spencer & Guillaume, 2006). Imagery in the engage phase involves teacher centered introduction of words with pictures. According to Spencer and Guillaume (2006), using pictures increases student interest in the subject. Drawing is a suggested technique for the exploration phase. The students are encouraged to make picture maps in their notes. An added benefit of drawing at this stage is that the teacher can easily spot misconceptions and correct them while looking at a drawing. In the development phase of the learning cycle, students can group pictures of words to illustrate comprehension. In the final stage, application, students can use knowledge gained in the previous three steps in a unique way, enabling multiple exposures to the word. Some examples of application are creating poetry, plays, songs, or multi-media presentations that display the students enduring understanding of the word (Spencer & Guillaume, 2006). Another powerful way to help students build vocabulary is by using word dramatizations. The students in groups use skits or pantomimes to present their words to their classmates. At the end of the skit or pantomime, have the students guess what the word was that was being presented to them. It is important to have the students relate the word acted out to their own experience. This type activity provides students with real experience with many words. They remember these words because of this real experience and because they enjoy acting and watching their friends act (Cunningham, 2009). According to Gailey (1993), using childrens literature to make connections between mathematics and literature can increase students mathematical knowledge and understanding. Mathematics and language skills can develop together as students listen, read, write, and talk about mathematical ideas. Of the thousands of childrens books published every year, a number can be used to introduce, reinforce, or develop mathematical concepts. Matz and Leier (1992), believe a student must be both proficient in reading and skilled at mathematics to solve a word problem. The methodology and activities teachers have developed in other curriculum areas to teach vocabulary can be just as appropriate for the mathematics lesson. Attitudes of students and Teacher Research has shown that the results of integrating different methods of teaching vocabulary into math classes has led to a growth in teachers confidence, mathematics and literacy knowledge, and enthusiasm to continue discovering and exploring different ways to increase students vocabulary knowledge (Phillips, Bardsley, Bach, & Gibb-Brown, 2009). A. Susan Gay (2008) affirms that by raising teachers awareness of the critical role of mathematics vocabulary, they begin to realize how important it is for them to use the correct word when describing a mathematical object. Teachers must understand that even though we know what we are talking about, all of the concepts are new to our students and must be explained very clearly and precisely. Cunningham (2009) asserts that you will be amazed at how students vocabularies and enthusiasm for words will grow by allowing them to experience different ways of learning words. Because students are usually enthusiastic about art, music, and physical education, using these experiences increases students enthusiasm about learning new vocabulary. Children usually love to act or watch their friends acting; therefore, using pantomime or dramatization causes the interest in learning new vocabulary to grow (Cunningham, 2009). Fore, et al. (2007) concluded from their study of instructional models for teaching vocabulary that students were very satisfied when given different approaches to learning vocabulary. They noted that enthusiasm also increased among students who were taught with methods other than the traditional looking up words in the dictionary or glossary. Less than interesting instruction is not a problem just because we want students to enjoy classroom activities. It is much better for students to develop an interest and awareness in words beyond school assignments in order to build their own vocabulary inventory. Students become interested and enthusiastic about words when instruction is rich and lively and they are encouraged to notice words in environments beyond the classroom (Beck, et al., 2002). Summary The purpose of this review of literature was to provide background information that was essential for understanding what was explored in this action research study. The literature review completed in Chapter 2 influenced the methodology used to carry out this study. The focus questions supplied the organization for the review of literature and also framed the methodology that followed. The research design, setting, subjects, data collection methods, validity and reliability methods, and analysis of data of the action research are described in the next chapter. CHAPTER THREE: METHODOLOGY Research Design This was an action research study because it focused on a particular problem in pedagogy (Fraenkel & Wallen, 1990). This action research study was conducted in my classroom. My four class periods were grouped to form a Treatment Group and an Untreated Group. First and third periods received the treatment over a three week period. The untreated group, second and fourth periods, received instruction as provided in previous years. Both quantitative and qualitative methods of data collection were used assessment data, surveys, and a reflective journal. Assessment data in the form of pre/post tests were collected to evaluate the success of addressing different learning styles of individual students. A pre-post survey was administered to students to document student attitude changes about vocabulary. Qualitative methods were also used to evaluate the research. A reflective journal was kept and coded for themes. As Hendricks (2009) suggested, the information from this journal was a valuable tool for assessing the progress of the study, recording new ideas that came about from the study, and aided in finding patterns that developed during the research. Setting Green Elementary School, a pseudonym, was located in a small town in a county in West Central Georgia. The population of this town was 2,739. At the time of the study, there were 398 students enrolled at Green Elementary School in grades pre-K through fifth grade. Green Elementary School made Adequate Yearly Progress (AYP) for eight consecutive years and was recognized as a Title I Distinguished school for six consecutive years. The ethnic backgrounds of the students were 61 percent White, 30 percent African-American, 6 percent Inter-Racial and 3 percent Hispanic. 87.5 percent of the students were economically disadvantaged receiving free and reduced lunches. Written permission was obtained from the school system, the principal, and LaGrange Colleges Institutional Review Board to conduct this research project at this location. This setting was chosen because it is where I work Subjects and Participants Fourth and fifth grade students at Green Elementary were departmentalized. I taught the fifth grade math classes. The study involved four fifth grade classes of approximately 14 students each. All of these classes had similar populations. Class A consists of 9 boys and 5 girls. There were 5 African-American, 6 Caucasian, 1 Hispanic, and 2 Inter-Racial in Class A. Class B consists of 7 boys and 7 girls. There were 5 African-American students and 9 Caucasian students in class B. Class C had 6 boys and 8 girls with 6 who were African-American, 6 Caucasian, and 2 Hispanic. Class D had 9 boys and 5 girls with 6 being African-American and 8 Caucasian. At Green Elementary School, 87.5 % of the students participated in the Free/Reduced Lunch Program. Class A had 89%, Class B had 84 %, Class C was 88% and for Class D, 84% participated in the Free/Reduced Lunch Program. The fifth grade students were not ability-grouped for math, but were heterogeneously grouped. All four groups had students with very similar ability levels. Classes A and C were the Treatment group and Classes B and D were the Untreated Group. I chose these groups because I did not want both treatment groups to be before lunch and the untreated groups to be after lunch. This way I had a morning and afternoon class for both the treatment and untreated groups. These students were chosen because they were my students. The instructional plan for this research study was evaluated by two peer teachers at Green Elementary School. The first participant, Peer Teacher A, taught fifth grade and had 18 years of teaching experience. She had been at Green Elementary School for 12 years at the time of the study. She had taught music, third grade, first grade, and fifth grade. She was also an Upper Literacy Coach for two years while Green Elementary was participating in the Americas Choice - Georgias Choice Program. Peer Teacher A was also chosen as the Teacher of the Year to represent our elementary school. The second participant, Peer Teacher B, was new to Green Elementary School at the time of the study. She currently taught all of the fourth grade math classes, but in previous years she taught seventh grade math at the middle school Green Elementary students attend. She had 13 total years teaching experience. She taught seventh grade math for three years in a neighboring system and then moved to the middle school in our system. She taught seventh grade math in this system for the past 9 years. For the 2010-2011 school year, she requested to be transferred to the elementary school where she taught all the fourth grade math classes. She has been a team leader and was the first teacher at the middle school to have her classroom equipped and labeled as a twenty-first century classroom. She was also chosen as Teacher of the Year twice while teaching at the middle school in our system. Both of these teachers were asked to evaluate my instructional plan because of their knowledge and experience with the subject matter and grade level. Procedures and Data Collection Methods This was a mixed-method action research study. One reason for using mixed methods to collect data is that it adds scope and breadth to the study (Cresswell, 1994, p. 175). Both quantitative and qualitative methods of data collection (see Table 3.1) were used to determine if the teaching strategies employed were significantly effective for the acquisition of math vocabulary by students. The quantitative data were in the form of pre-test and post-test scores for both the treatment and the untreated group. The pre/post-surveys were used to assess students attitudes about math vocabulary. The use of a teacher reflective journal allowed for the recording of student observations as well. Table 3.1. Data Shell Focus QuestionLiterature SourcesType: Method, Data, ValidityHow are data analyzed? RationaleFQ1: What is the process of teaching math vocabulary to address different learning styles of individual students?Beck, McKeown, &Kucan,(2002). Bromley,(2007) Cunningham ,(2009) Pierce & Fontaine, (2009) Type of Method: Instructional Plan rubric and interview Type of Data: Qualitative Type of Validity: ContentCoded for themes recurring dominant emerging  Looking for categorical and repeating data that form patterns of behaviorsFQ2: How do test scores compare between traditional methods of teaching vocabulary and vocabulary taught by addressing different learning styles? Beck, McKeown, & Kucan, (2002). Cunningham, (2009) Frey, & Fisher, (2009) Greenwood, (2009) Spencer & Guillaume, (2006)Type of Method: Teacher made- Tests, quizzes Type of Data: Quantitative Interval Type of Validity: ContentDependent T-test Effect Size Independent T -testTo determine if there are significant differences Measure the magnitude of a treatment effect FQ3: How do teacher/student attitudes change about vocabulary when different learning styles are addressed?Beck, McKeown, & Kucan, L.(2002). Cunningham, (2009) Fore, Boon, & Lowrie, (2007) Gay, (2008) Phillips, Bardsley, Bach, & Gibb-Brown, (2009)Type of Method: Reflective Journal Surveys Type of Data: Qualitative Ordinal Type of Validity: ConstructCoded for themes: recurring dominant emerging Chi Square Cronbachs AlphaLooking for categorical and repeating data that form patterns of behaviors To find what questions are significant The treatment designed for use in this research study started with an instructional plan being written (see Appendix A) and evaluated by two peer teachers using a rubric (see Appendix B). A separate interview with both teachers was tape recorded to preserve the suggestions each person made for improving the plan. An attitudinal survey (see Appendix C) was administered to the students in both the control group and the treatment group prior to the unit being taught. The survey measured the attitudes of the students toward math and in particular math vocabulary. The information gathered in the survey provided insight into how students feel about math and math vocabulary. At the end of the instructional unit when different learning styles had been addressed, the students were given the same survey again to see if there were any changes in attitudes towards math and especially math vocabulary. Both the treatment and the untreated group were administered a pre-test (see Appendix D) before anything in the instructional unit was addressed. Different learning style approaches were used to teach the instructional unit to the treatment group and a post-test identical to the pre-test was administered. To answer the first focus question in the study about the process of teaching math vocabulary to address different learning styles of individual students, the students were introduced to Geometry vocabulary by using, art, music, and drama. They made vocabulary cards which included pictures they drew, as well as, the definition, and examples. By using art, they were able to visualize the meaning of the word, thus addressing the visual learners. They were given the opportunity to create songs or raps with their vocabulary words and perform them for their classmates. Using music allowed the students with strong auditory learning to use their strengths. The students also were given the chance to pantomime or perform a skit using their words. They were put into small groups and each group performed their word for their classmates. This addressed those students who are kinesthetic learners. To answer the second focus question about how do test scores compare between traditional methods of teaching vocabulary and vocabulary taught by addressing different learning styles? Both groups were given a vocabulary pre-test (see Appendix D). The strategy of incorporating different learning styles into learning math vocabulary was implemented in Classes A and C. The students vocabulary cards were put on display in the classroom. Each student had to present two of their cards to the class and explain the visuals and how they used the drawing to define the word. The students also had the opportunity to create songs or raps, and pantomime or create a skit using their words. Classes B and D, the untreated group, only received the traditional method for teaching vocabulary. They were given the list of words and instructed to copy the definitions from their math glossary. After the activity and the unit of study were concluded, the same test that was administered at the start of the unit was given as a post-test. The second part of this study had the purpose of answering the third focus question: How do teacher/student attitudes change about vocabulary when different learning styles are addressed? At the beginning and end of the research study, the same survey was administered to the untreated group and the treatment group to identify their feelings about math and math vocabulary. Validity, Reliability and Bias Measures Validity, reliability/dependability, and lack of bias were ensured in this study through the use of specific methods of research and data collection. As a researcher, there are exclusive proceedings that must take place to increase the dependability and consistency of the data. For focus question one of this study concerned with pedagogy the data collection were qualitative. An instructional plan rubric and interviews were used as the method of data collection. The instructional plan used for this study was focused on Geometry lessons. There is a large quantity of vocabulary that must be mastered in order to grasp the concepts taught in Geometry. This made it ideal for comparing the use of learning styles to more traditional methods of teaching vocabulary. The plan includes lessons on lines, angles, polygons, circles, and solid figures. The instructional plan was evaluated by two peer teachers for content validity. The objectives of the plan were directly related to the fifth grade Georgia Performance Standards that were tested on the Georgia CRCT. Popham (2008) asserts that content validity refers to the adequacy with which the content of a test represents the content of the curricular aim being measured. These interviews were the primary source of qualitative data collection for focus question one. Because the interviews were recorded and detailed notes of interviewees responses were taken from the recordings soon after the interviews took place dependability has been assured. Each peer teacher checked the transcribed interviews to ensure accuracy in what was written. Both peer teachers examined the instructional plan looking for any unfair or offensive bias. Popham (2008) states that bias refers to the qualities of an instrument that offend or unfairly penalize a group of students because of students gender, race, ethnicity, socioeconomic status, religion, or other such group-defining characteristics. The second focus question of this study was: How do test scores compare between traditional methods of teaching vocabulary and vocabulary taught by addressing different learning styles? To maintain reliability, I used quantitative interval data to compare scores obtained from pre-test and post-tests. The pre-test and post-tests were compared by independent t-tests to determine if there were significant differences between means from the untreated group and the treatment groups pre/post tests. Both tests were also analyzed using dependent ttests to determine if there were significant differences between means from one group tested twice. The data collected from the interval level of measurement as stated by Salkind (2010), is where a test or an assessment tool is based on some underlying continuum such that we can talk about how much more a higher performance is than a lesser one (p. 140). The data collection and treatment will be consistent with a controlled setting. The content validity will assess whether a test reflects items in a certain topic (Salkind, 2010). The test questions in this study demonstrate content validity because they are representative of the curriculum being taught (Popham, 2008). The pre-test and post-test used were both examined by different faculty members to look for any evidence of bias. The third focus question of this study was concerned with how teacher/student attitudes change about vocabulary when different learning styles are addressed. The data gathering methods used for focus question three was pre and post attitudinal surveys and a teacher reflective journal. The data collected from the surveys will be on the nominal level of measurement. As per Salkind (2010) the nominal level is specified by the aspect of an outcome that adapts to only one class or category. The last method of data collection was a daily reflective journal kept by me. Each entry was guided by a set of reflective journal prompts (see Appendix E) designed to give consistency to the journal. Keeping detailed documentation of behaviors observed, statements made, and attitudes displayed allowed me to plan a program that would incorporate the positive aspects while revising those that were not useful or productive. This valuable information will be utilized to modify future pedagogy. Evidence was collected from the student surveys to gauge interest and motivation, showing construct validity by using the information shown by the literature review to develop the series of statements students read. I was mindful of a limitation on the student attitudinal survey, that students might circle answers they think will please the teacher. To account for this, I pointed out to the students to answer the survey according to their own attitudes and feelings. The survey was checked for bias to increase awareness of how the results may be affected negatively or positively. The construct validity will be strong and it will correlate the survey with a theorized outcome (Salkind 2010). The type of reliability demonstrated is stability reliability as both the control and treatment groups rated their attitudes about math and math vocabulary using the same survey before and after the instructional plan was taught. Stability reliability, also called test re-test reliability is the agreement of measuring instruments over time. To determine stability, a measure or test is repeated on the same subjects at a future date. The results are compared and correlated with the initial test to give a measure of stability. The data collection was composed and evaluated for internal consistency, scale reliability or average correlation using Cronbachs Alpha. The teacher reflective journal I kept while the strategies were being implemented was coded for specific themes, attitudes, and feelings. A set of predetermined journal prompts were used to record how I felt about the lesson, assessments, and to reflect upon the materials that were used. Entries into the reflective journal were recorded daily to review the progress of the study. Using consistent prompts daily creates boundaries and makes it easier to analyze the results. Analysis of Data To answer focus question one about what is the process of teaching math vocabulary to address different learning styles of individual learners. I wrote a detailed instructional plan. Two peer teachers were given the plan and a rubric that was developed for evaluation purposes and to provide feedback. The feedback on the instructional plan was analyzed qualitatively. In addition to the rubric, the two peer teachers agreed to participate in a recorded interview in which they provided detailed feedback about the plan. The two interviews were examined to look for recurring, dominant, or emerging themes. Focus question two about how test scores compare between traditional methods of teaching vocabulary and vocabulary taught by addressing different learning styles. The method used was quantitative because interval data from pre-tests and post-tests was statistically compared for both the control group and the treatment group. A dependent t-test was used to determine if there are significant differences between means from one group tested twice. The null hypothesis is that there is no significant difference between the pre-test and post-test results. The decision to reject the null hypothesis was set at p < .05. An independent t-test was also used to determine if there were significant differences between means from two independent groups, i.e. the untreated and treatment groups. The null statement was stated that student test scores were not influenced by addressing the different learning styles of students. The decision to reject the null hypothesis was set at p < .05. To measure the magnitude of a treatment effect, the Effect size was also calculated. Unlike significance tests, these indices are independent of sample size. Effect size can be measured in two ways: Cohens d for independent groups and Effect size r for paired data such as a dependent t-test. Focus question three was about how teacher/student attitudes change about vocabulary when different learning styles are addressed? A Likert scale survey consisting of seven statements and four questions about students feelings and attitudes toward math and math vocabulary was administered to the students before and after the treatment. . The surveys Likert responses were quantitatively analyzed by performing a Chi Square to find which questions were significant and which were not. Significance was reported at the p < .05, p < .01, and p < .001 levels. The survey was checked for internal consistency reliability by computing Cronbachs Alpha. By keeping a reflective journal during this study, I was also able to code it for recurring, dominant, and emerging themes. I could examine not only my feelings, but also keep a record of attitudes and feelings noticed in the students. Because the journal entries were made up using prompted questions by me, the threat of bias was evident. In order to minimize differing, experimental and background bias of the journal entry, the prompts were reviewed by faculty members (Popham, 2008). The literature review of this thesis is an epistemological validation of the research and remains consistent with the type of research that was implemented in the study (Lather as cited by Kinchloe & McLaren, 1998). Denzin and Lincoln (1998) describe the cycling back to the literature review as epistemological validation, a place where the researcher convinces the reader that they have remained consistent with the theoretical perspectives they used in the review of the literature. Eisner (1991) recommends Consensual Validation, therefore, the research methods will also be reviewed by the LaGrange College faculty to ensure that the description, interpretation, evaluation, and thematic are right. If other teachers understand and perceive that the use learning styles in the instruction of vocabulary is a successful strategy because of this research, the research has referential adequacy because they will use it in their lessons. The findings of this study may be applied to subjects other than math. Catalytic validity (Lather as cited by Kincheloe & McLaren, 1998) is the degree to which researchers anticipate their study to shape and transform their participants, subjects, or school. Catalytic validity is an expected outcome of this study. The next chapter reports the information obtained from the data gathered during duration of this study. CHAPTER 4: RESULTS The results displayed in Chapter Four are organized by focus question. Focus question one in this study is about the process of teaching math vocabulary to address different learning styles of individual students. A peer reviewed instructional plan was developed and followed during the course of this study. Two peer teachers evaluated the plan using a rubric. The peer teachers agreed to be interviewed about their thoughts on the plan. This recorded interview was transcribed and checked for accuracy by each interviewee. Peer teacher A responded very positively on the rubric. Upon closer examination of the instructional plan, she did point out that the learners might not be able to determine what they should know and be able to do from the way it was worded in the plan. She suggested clarifying this by having a written synopsis of what the students need to understand as a part of the plan. Each teacher has a grid on their board that contains information about the lessons being taught that day. It has a space for the Georgia Performance Standard, essential question, concept, vocabulary words, and homework. She suggested quickly going over this grid verbally before beginning the lesson for the day. Another suggestion was to have a plan for reviewing information previously taught to check for any weak areas in the content. If there were any, they could be re-taught before the new content was taught for that day. Another teacher should be able to take the instructional plan and teach it to their class; however, it was suggested that more detail be added to the vocabulary card activity on day 2. She stated that, You know exactly what you mean, and are planning to do because you have a lot of experience with it, but someone else would not necessarily know what to put in each of the four sections of the card. Peer teacher B also responded very positively to the plan. She had the same suggestion for specific prompts for the days the Writing to Win Journals would be used. The only other negative thing she found in the plan was that day twos essential question and activity did not match. She thought that the detailed listing of vocabulary for each day was impressive. Vocabulary is very essential to the understanding of math concepts. As a math teacher, she asserted that she could take the plan with those revisions and use it with her classes. She declared, It is well written and very clear. I think it would be easy to pick it up and follow it. It is obviously standards based and covers the objectives for this instructional plan. Focus question two of this study was about how test scores compare between traditional methods of teaching vocabulary and vocabulary taught by addressing different learning styles. Classes A and C made up the treatment group. This group was provided with different opportunities to work with vocabulary that focused on meeting different learning styles. The use of art, poetry, and drama was implemented to help them remember the definitions. Classes B and D made up the untreated group. They were taught the vocabulary using traditional methods from previous years. They did activities like looking up the definitions in the glossary of their math text. Data from both groups pre-tests were compared in an independent t-test to determine if addressing different learning styles increased student learning as opposed to writing definitions. The results of the independent t-test (see Table 4.1) show that t (38) = 1.49, p > .05. This means that the obtained value found in this test of 1.49 was less than the critical value of 1.685. Therefore, the null hypothesis that there is no significant difference between students learning when different learning styles are addressed in math vocabulary lessons and when students write definitions from the text must be accepted proving there is no significant difference between the two groups (Salkind, 2010). This provided a level playing field for both groups when this study began. A Cohens d effect size of 0.21 is considered a medium effect size. Table 4.1 Pre/Pre Independent t-test INDEPENDENT t-test: Two-Sample Assuming Equal Variances  Pre-Test A Pre-Test B Mean 16.0689655222Variance 119.137931278.7826087Observations 2924Hypothesized Mean Difference 0 df 38t Stat -1.495708314P(T<=t) one-tail 0.071494646t Critical one-tail 1.685954461P(T<=t) two-tail 0.142989293t Critical two-tail 2.024394147 t(38) = 1.49, p > .05 Data from the pre-test and post-test when the students were given opportunities to participate in activities that address different learning styles were analyzed with a dependent t-test to determine if significant learning occurred. The null hypothesis in this case that there is no significant increase in student learning when students participate in activities that address different learning styles was rejected. The results of the dependent t-test (see Table 4.2) show that t (28) = 14.83, p < .05. This means that the obtained value found in the test, 14.83 was greater than the critical value of 1.70 rejecting the null hypothesis demonstrating that there is significant learning when different learning styles are addressed when acquiring new vocabulary. Effect size is a name given to a family of indices that measure the magnitude of a treatment effect. The treatment groups pre/post test comparison resulted in a large effect size r = 0.84. Table 4:2: Treatment Group Dependent t-test DEPENDENT t-test: Paired Two Sample for Means  Pre Test Post Test Mean 16.068977.8965Variance 119.137931621.8103448Observations 2929Pearson Correlation 0.435403015Hypothesized Mean Difference 0 df 28t Stat -14.83182787P(T<=t) one-tail 4.32463E-15 t Critical one-tail 1.701130908P(T<=t) two-tail 8.64925E-15 t Critical two-tail 2.048407115 t(28) = 14.83, p < .05 Data from the pre-test and post-test when the students only wrote the definitions were also analyzed in a dependent t-test to determine if significant learning occurred. The null hypothesis in this case that there is no significant increase in student learning when students copy definitions from the text was rejected. The results of the dependent t-test (see Table 4.3) show that t (23) = 11.51, p < .05. This means that the obtained value found in the test, 11.51 was greater than the critical value of 1.71 rejecting the null hypothesis. In both cases significant learning occurred. The untreated groups pre/post test comparison resulted in a large effect size r = 0.73. Table 4.3 Untreated Group Dependent t-test DEPENDENT t-test: Paired Two Sample for Means  Pre Test Post Test Mean 2269.83333333Variance 278.7826087701.7101449Observations 2424Pearson Correlation 0.639550005 Hypothesized Mean Difference 0 df 23t Stat -11.50644519P(T<=t) one-tail 2.54318E-11t Critical one-tail 1.713871517P(T<=t) two-tail 5.08635E-11t Critical two-tail 2.068657599 t (23) = 11.51, p < .05 Data from both post-tests were compared in an independent t-test to determine if addressing different learning styles increased student learning as opposed to writing definitions. The results of the independent t-test (see Table 4.4) show that t (48) = 1.13, p > .05. This means that the obtained value found in this test of 1.13 was less than the critical value of 1.677. Therefore, the null hypothesis that there is no significant difference between student learning when different learning styles are addressed in math vocabulary lessons and when students write definitions from the text must be accepted and the test results cannot be considered significant (Salkind, 2010). A Cohens d effect size of 0.31 is considered a medium effect size. Table 4.4 Post/Post Independent t-test INDEPENDENT t-test: Two-Sample Assuming Equal Variances  Post Test A Post Test B Mean 77.8965517269.83333333Variance 621.8103448701.7101449Observations 2924Hypothesized Mean Difference 0 df 48t Stat 1.132639183P(T<=t) one-tail 0.131496016t Critical one-tail 1.677224197P(T<=t) two-tail 0.262992031t Critical two-tail 2.010634722 t(48) = 1.13, p > .05 Focus question three from this study about whether teacher and student attitudes change about vocabulary when different learning styles are addressed was analyzed through the use of student pre/post surveys and a reflective journal I kept during the study. The chi-square test statistic was calculated to compare what was observed on the pre/post surveys to what would happen by chance (Salkind, 2010). Tables 4.5 and 4.6 below show the results of the chi-square tests for the student pre/post surveys. Table 4.5 Untreated Group Survey Survey Items n = 11(2 Pre-Survey(2 Post-SurveyI am good at math 13.18** 15.4**I like to answer questions asked by the teacher in math class.13.71**10.6*I am comfortable asking questions in math if I dont understand something.13.8**13.27**I am comfortable sharing my math ideas with the class.9.8*10.6*I understand the vocabulary we use in math.11.93** 10.6* I think I learn better when I understand the vocabulary in math.15.13**14.16**It is easy for me to use the vocabulary in math.11.22*11.67**Which of these best describes you as a math student?6.9613.8**Which of these best describes how a friend would describe you as a math student?9.6*12.73**How often are you asked to explain your answer using math vocabulary?15.27**19.84***How easy is it for you to use math vocabulary to explain your answer?11.93**10.96**p<.05, **p<.01, ***p<.001 The results of the chi-square statistic for the untreated group pre-surveys highlighted several significant questions. Survey items 1, 2, 3, 5, 6, 10, and 11 were all found to be significant when p < .01, meaning that there was a high percentage of students that answered a certain way on these questions. However, item 10 was not significant at all, which means there was no significant difference on this question between what was observed in the answer and what would have been expected to happen by chance. Table 4.6 Treatment Group Survey Survey Items n = 11(2 Pre-Survey(2 Post-Survey1. I am good at math 18.33**13**2. I like to answer questions asked by the teacher in math class.15.67**20.47***3. I am comfortable asking questions in math if I dont understand something.10.87*13**4. I am comfortable sharing my math ideas with the class.17.98***12.64**5. I understand the vocabulary we use in math.19*** 15.13**6. I think I learn better when I understand the vocabulary in math.22.6***18.33***7. It is easy for me to use the vocabulary in math.13**10.16*8. Which of these best describes you as a math student?10.69*10.87*9. Which of these best describes how a friend would describe you as a math student?14.07**12.64**10. How often are you asked to explain your answer using math vocabulary?16.2**26.64***11. How easy is it for you to use math vocabulary to explain your answer?14.42**15.13** *p<.05, **p<.01, ***p<.001 The results of the chi-square statistic for the treatment group pre-survey shows that questions 4, 5, and 6 were all found to be greatly significant at the p < .001 level, meaning that there were a high percentage of students who answered a certain way on these questions. The results of the chi-square statistic for the treatment group post-survey shows that questions 2, 6, and 10 were all found to be greatly significant at the p < .001 level, meaning that there were a high percentage of students who answered a certain way on these questions. Question 2, about answering questions in math class, had 15 students to agree and 5 who strongly agreed. Question 6, about learning with better understanding of vocabulary, had 16 students to strongly agree and 11 who agreed. Question 10, about how often you use vocabulary to answer questions, had 10 who said more than half the time and 14 who said less than the time. To determine the internal consistency reliability of the items on the surveys given to the students, the Cronbachs Alpha test was conducted using the survey responses for each groups pre/post surveys. The purpose of this test was to compare the score for each item with the total score for each student in order to make sure the items measured only what they were intended to measure (Salkind, 2010). For the untreated group pre-surveys, the Cronbachs Alpha was  = 0.82. For the treatment group pre-surveys, the Cronbach s Alpha was  = 0.86. The untreated group post-surveys had a Cronbach s Alpha that was  = 0.83 and the treatment group was  = 0.86. Therefore, both of these surveys showed a high level of reliability using the results of the Cronbachs alpha test as well. To determine whether my attitudes as the teacher and those of the students changed during the study, a reflective journal was kept by me during the action research of this study. I wrote in the journal daily to record my attitudes as well as those of the students. The journal was coded for recurring, dominant, and emerging themes. A recurring theme throughout the study was the positive response of the treatment group to the different activities they participated in. Student 1 stated, I didnt know learning vocabulary could be such fun! Student 2 added that, Drawing a picture on the cards really makes it easier for me to remember what the word means. Student 3 said, I wont ever forget how that group acted out their word! The Untreated Group had an opposite response. When told to write the words and copy the definitions from the glossary, there was much grumbling and complaining. Many of the students in the untreated group were apathetic towards the assignments they were given. The enthusiasm and excitement of the treatment group was not evident at all. I observed that the lower achieving students in the treatment group were much more involved and interested in the activities. Using these different strategies really helped level the playing field for these students to be successful and the resulting work was of a much higher quality than previously displayed. The students in the treatment group were much more willing to take risks when trying to solve problems and more willing to share with the class what they were thinking as they worked through the process. The untreated group really didnt score much differently on this unit of study than any other previously taught this year. The grades on the tests and quizzes were pretty typical of what they had accomplished all year. I did notice the lower achieving students in the treatment group were very proud of their successes. One parent commented on how her son got in the car at car riders so excited to show her the 100 he had made on a math quiz. She said he told her, This is the first time Ive ever made a grade this good. I found myself feeling much more enthusiasm when working with the treatment group. They were excited and it made me feel that way too. I wrote in my journal the day they acted out the words, It was very noisy, but I observed a lot of enthusiasm and a lot of learning taking place. It took a couple of days before I really felt comfortable with the noise they were making as they learned new concepts and vocabulary. I felt bad that the treatment group had so much fun, while the untreated groups activities were pretty boring. Examining the results of the survey questions was very eye opening for me. I never realized so many were uncomfortable asking questions or sharing in class. I found myself wondering if the ones who were uncomfortable were the same ones who struggle in math class. As you read Chapter Four, you have probably noticed certain discrepancies between the qualitative and quantitative data that were produced as a result of the action research study. While the qualitative data, which was gathered through student surveys and my reflective journal, show positive and significant effects from using motivational teaching strategies that reach the different learning styles of individual students, the quantitative data, or pre/post tests, did not produce significant results to reflect these observations. The data in this chapter will be further analyzed and reflected upon in Chapter Five in order to determine the possible causes for the observed inconsistencies, as well as provide recommendations for future research. CHAPTER FIVE: ANALYSIS AND DISCUSSION OF RESULTS Analysis The first focus question of this thesis was about the process of teaching math vocabulary to address the different learning styles of individual students. The data collection for focus question one, concerned with pedagogy, was qualitative. A peer reviewed instructional plan was developed and followed during the course of this study. The large quantity of vocabulary that must be mastered in order to grasp the concepts taught in the Geometry Unit made it ideal for comparing the use of learning styles to the more traditional methods of teaching vocabulary. Two peer teachers evaluated the plan using a rubric to assure content validity. The interviews with the peer teachers were recorded and detailed notes of interviewees responses were taken. Each peer teacher checked the transcribed interviews to ensure accuracy in what was written. These interviews were the primary source of qualitative data collection for focus question one. I took their recommendations and adjusted the plan accordingly. Both of the peer teachers had positive things to say about the plan. They only made a couple of suggestions to make it better, mainly adding a little more detail to a vocabulary card activity so someone else could easily use my plan. The suggestion was made to do a quick review/assessment at the beginning of each lesson to assure that the content previously covered was mastered. Both teachers agreed that the plan was directly related to the fifth grade Georgia Performance Standards that would be tested on the Georgia CRCT. They also said there were activities included in the unit of study that addressed several different types of learning styles. During this unit of study, the students in the treated group were introduced to the Geometry vocabulary by using art, music, and drama. They made vocabulary cards that included pictures and diagrams that they drew, as well as, the definition, and examples. By using art, they were able to visualize the meaning of the words, thus addressing the visual learners. Students also had the opportunity to create songs or raps with the different vocabulary words. By using music, the students with strong auditory learning styles were able to use their strengths. To address the kinesthetic learners styles, the students were allowed to pantomime or perform a skit using their words. They performed these for their fellow classmates. Yilmaz-Soylu & Akkoyunlu (2009) state that it is important to take into accounts the characteristics, abilities, and experiences of learners when planning to teach a lesson. Teachers should organize lessons according to the learning styles of the students rather than expecting the student to adapt to the existing organization. Rapp (2009) suggests when teaching auditorally, use visualization strategies that allow the learner to create a picture in their head. The second focus question of this thesis about how do test scores compare between traditional methods of teaching vocabulary and vocabulary taught by addressing different learning styles was addressed with dependent t-tests and an independent t-test. All students were given a pre-test on Geometry vocabulary. The pre-tests from both the treatment group and the untreated group were analyzed using an independent t-test. The obtained value found in this test of 1.49 was less than the critical value of 1.685. Therefore, the null hypothesis that there is no significant difference between students learning when different learning styles are addressed in math vocabulary lessons and when students write definitions from the text must be accepted proving there is no significant difference between the two groups (Salkind, 2010). This provided a level playing field for both groups when this study began. The treatment group received instruction that addressed different learning styles, but the untreated group received only traditional activities from previous years. The pre/post tests from both groups were compared using a dependent t-test. The obtained value for the treatment group was 14.83 with a P < .05, a great amount of significance is evident. The obtained value for the untreated group was 11.05 with a P < .05, a great amount of significance is also evident for this group. The post-tests from both the treatment and untreated groups were analyzed with an independent t-test. The obtained value was 1.13 with a P < .05, which was less than the critical value l.68 showing that the null hypothesis that there is no significant difference between student learning when different learning styles are addressed in math vocabulary lessons and when students write definitions from the text must be accepted and the test results cannot be considered significant. The post-test mean score of the treatment group was 77.89 and the mean score of the untreated group was 69.83. Content validity was maintained because the pre-test and post-test were identical. Research in this area supports the findings of this study. Pierce and Fontaine (2009) found that a childs success in math is influenced by the depth and breadth of their mathematical vocabulary. According to Fore, et al. (2007), students who struggle with reading often have limited vocabularies which hinder their ability to relate new terms and concepts to previous knowledge especially in mathematics. The Learning Cycle is a method that teaches vocabulary using visualization. The cycle has four phases including engagement, exploration, development, and application (Spencer & Gilliam, 2006). In the first phase, engagement, pictures were used to introduce the words and the students were hooked. The exploration stage involved drawing. In the development stage the students group pictures of words that are related, the last stage application, requires the students to use all the previous phases in a unique way, such as a poem, song, or play ensuring enduring understanding of the words. One group of students from the treatment class made up a song about the different kinds of lines. This is a good example of application in the treatment group. Cunningham (2009) states that adding strategies to address visual, auditory, and kinesthetic (VAK) styles while teaching math vocabulary maximizes the potential for learning in that subject area. The students in the treatment group showed a significant growth in vocabulary knowledge according to the dependent t-test that compared the means of the pre-test and post-test scores affirming the literature. Significant learning also occurred in the untreated group based on the dependent t-test that compared the means of the pre/post test scores. The treatment group had 7 students that scored below 70 on the post-test and the untreated group had 9. When the post-test scores were compared using an independent t-test between the treatment group and the untreated group there was no significant difference between the two. The obtained value of 1.13 was less than the critical value of 1.68 and the Cohens d statistic, 0.3136 is a medium effect size. This does not align with most of the literature; however, it was supported by those opposed to using learning styles. Geake (2008) posits that, on the whole, the evidence time and again shows that modifying a teaching strategy to account for the differences in learning styles does not result in any improvement in learning outcomes. Most educators know that learning styles is only one of a great many variables which influence academic performance (Sharp et al., 2008). Geake (2008) cites the research of Kratzig and Arbuthnott showing that there is no improvement of learning outcomes with VAK above teacher enthusiasm. This finding does not modify or disprove the literature because only one test was used for comparison. Focus question three was about whether the attitudes of the teacher and students change when different learning styles are addressed. I observed my fifth grade students in the treatment and untreated group as the Geometry unit was implemented. I coded a journal for two themes, positive comments and reactions to the lesson, and negative comments and reactions to the lesson. I was looking for categorical and repeating data that formed patterns of behaviors. I found that out of twenty-nine interactions during the lessons when vocabulary cards were produced including pictures, twenty-six were positive and three were negative. Ninety percent of the reactions to the lesson were positive. When we did the dramatic presentations of the words, I found that twenty-seven out of the twenty nine students had very positive comments. Ninety-three percent of the reactions to this activity were positive. I noted that the students were very engaged in sharing their words with each other and most of the conversations between students were about their vocabulary words. Every student completed the assignment; even though two students were reluctant to participate at first, they were convinced by their peers that they could do it. Greenwood (2002) indicated that engaging students in active hands-on lessons to learn vocabulary is a way to improve vocabulary comprehension, and that creating picture definitions can motivate students and keep them involved in the lesson. According to Paivios Dual Coding Theory (As stated by Hibbing and Rankin-Erickson, 2003), memory is accomplished by fluctuation between mental imagery and language processing. Use of mental imagery improves reading comprehension (Hibbing & Rankin-Erickson, 2003). Sadoski (2005) explains the keyword theory which demands that the student relate new vocabulary to previously learned words that are key parts of the new word. To do this the student creates an image that relates to something they already know. One student created a picture for the word irregular polygon, which is any polygon that does not have congruent sides and angles. Her picture showed a regular square, triangle, and hexagon with a circle surrounding each with the slash mark diagonally across meaning prohibited or negative. She knew what a regular polygon was and used it to show she understood irregular polygon. This student demonstrated the use of the keyword method without being told. Discussion In reflection, the findings of this action research study produced both predictable and unpredictable results. Visuals are a major part of our society. It is important that we teach students to interpret visuals because of the internet, television, and new teaching methods, such as power points and movie maker. Everyone is required to have a word wall in their classroom. Using visuals along with the word wall make it a valuable teaching tool. This activity is easy to implement giving the study referential adequacy. Other teachers in the school are already implementing the strategy giving the study a high degree of catalytic validity. One interesting result that occurred due to this research involved the pictures that the students were asked to draw for each of the vocabulary words. When presented with a list of the vocabulary words and pictures without written definitions, the students in the treatment group were very successful at matching the word to the picture. Twenty-eight of the twenty-nine students in the treatment group successfully matched the pictures to the vocabulary word with a minimum accuracy rate of eighty percent while the twenty-four students in the untreated group only had fifteen students with an eighty percent or higher accuracy rate. This supports the evidence from much of the literature which states that learning occurs when students create visuals. The qualitative part of this study demonstrates structural corroboration because triangulation of the journal observations and student observations was an accurate measure of the student engagement during the lessons. Both positive and negative responses were recorded to ensure the fairness of the study. The student behavior during the lessons supports the rightness of fit of the research. The evidence of active engagement was overwhelming for the treatment group in the journal themes and observations. The quantitative studies of this action research study did not produce significant results supporting the use of addressing learning styles when teaching math vocabulary. This research is credible because the assessments used to pre-test and post-test the students were the same test. Doing this helps to ensure that there are no other variables to cloud the research. Even though the comparison of the data showed that the students did not score significantly higher on the post-test in which learning styles were addressed to teach math vocabulary than they did on the post-test in which the instruction followed traditional methods used in previous years, that was only one test involving a sample size of only fifty-three students. This was a small sample, which decreased the chances that the outcome of the study would be significant. On the test in which traditional methods from previous years were used, the mean of the pre-test scores was 22, and the mean of the post-test scores was 70. When those scores were compared to the pre-test mean (16) and the post-test mean (78) of the test when different learning styles were addressed when teaching math vocabulary, it can be seen that there was more improvement with the treatment group. Further evidence can be found in the literature that learning occurs when different learning styles of students are addressed. Comparing the test results of the treatment and untreated groups proved that both groups made significant gains from the pre-test to the post test. There is evidence in the literature to support that written definitions are not the best teaching tool. Bromley (2007) states the practice of writing definitions has proven to be useless. Students blindly copy the definition and forget it. Beck, McKeown, and Kucan (2002) assert that becoming interested and aware of words is not a likely outcome from having students look up definitions in a dictionary or glossary. Bromley (2007) insists more effective strategies are being developed to enhance vocabulary lessons. Implications Because the sample size was small used in this study, the results of this research cannot be generalized to the larger population. The students in the treatment group were highly engaged in the lessons while there was large amount of disengagement among those in the untreated group. A lesson that promotes active engagement of elementary school students that is easily implemented is already being used by other teachers in the school. Incorporation of the methods used in this research into the lesson plans of my peers gives the research referential adequacy and catalytic validity. The most interesting thing that happened as a result of this research affirms the catalytic validity of this study. One of my students created vocabulary cards for a science vocabulary test using pictures to help remember the word. This proved that he had applied the concept of creating picture definitions to another subject. When several of the other students saw his vocabulary pictures, they too drew pictures to help them in the same way. I will definitely address different learning styles when teaching math vocabulary in the future because of this study and I will share these activities with other teachers in my school. According to Fore et al. (2007), the ability to read and vocabulary knowledge in the content areas are essential for school success. As the bar continues to be raised for schools to make Adequate Yearly Progress (AYP), which is measured by state standardized tests, vocabulary knowledge in all content areas is critical. Addressing students learning styles keeps them actively engaged in the lessons; therefore, leading to an increase in knowledge. I believe that students who have a firm understanding of the vocabulary of math have a better chance of performing higher on not only classroom assessments but also on the state CRCT. Recommendations for Future Research If I could change anything about this study, I would conduct more tests with the different methods for teaching vocabulary, so that I could have a more reliable benchmark with which to compare them. If the sample size was larger I think the results would be different. I would like to see if there would be significant gains when comparing the post-tests when addressing different learning styles to more traditional methods previously used. If the students consistently used pictures, music, poetry, and drama to learn new vocabulary, would they score higher on the state mandated CRCT. It would also be interesting if these same students could be assessed at the beginning of the next school year to see how much of this Geometry vocabulary they retained. I would also like to see if the math scores would be impacted by not only learning content math vocabulary but also the testing language used on the state tests. References Beck, I.L., McKeown, & Kucan, L. (2002). Bringing words to life: Robust vocabulary instruction. New York: The Guilford Press. Beecher, M., & Sweeny, S. (2008). Closing the achievement gap with curriculum enrichment and differentiation: One schools story. Journal of Advanced Academics, 19(3), 502-530. Retrieved October 3, 2010, from ERIC database. Bromley, K. (2007). Nine things every teacher should know about words and vocabulary instruction. Journal of Adolescent & Adult Literacy, 50(7), 528-537. Retrieved September 25, 2010, from ERIC database. Carter, Tamara and Dean, Emily. (2006). Mathematics intervention for Grades 5-11: Teaching mathematics, reading, or both? Reading Psychology, 27(2&3), 127-146. Retrieved September 25, 2010, from ERIC database. Cresswell, John W. (1994). Research design: Qualitative and quantitative approaches. Thousand Oaks, CA: Sage Publications. Cunningham, P. (2009). What really matters in vocabulary: Research-based practices across the curriculum. Boston: Pearson. Denzin, N., & Lincoln, Y. (1998). The fifth moment. In N. Denzin & Y. Lincoln (Eds.), The landscape of qualitative research: Theories and issues (pp.407-430). Thousand Oaks, CA: Sage Publications. Eisner, E. (1991). The enlightened eye. New York: MacMillan. Flanigan, K. & Greenwood, S. (2007). Effective content vocabulary instruction in the middle: Matching students, purposes, words, and strategies. Journal of Adolescent & Adult Literacy, 51(3), 226-238. doi:10.1598/JAAL51.3.3 Fore, C., Boon, R., & Lowrie, K. (2007). Vocabulary instruction for middle school students with learning disabilities: A comparison of two instructional models, Learning Disabilities: A Contemporary Journal, 5(2), 49-73. Retrieved July 23, 2010, from ERIC database. Fraenkel, J., & Wallen, N. (1990). How to design and evaluate research in education. New York, NY: McGraw-Hill Companies, Inc. Frey, N., & Fisher, D. (2009). Learning words inside and out: Vocabulary instruction that boosts achievement in all subject areas. Portsmouth, NH: Heinemann. Gailey, S. K. (1993). The mathematics/childrens literature connection. Arithmetic Teacher, 40(5), 258-261. Retrieved August 12, 2010, from ERIC database. Gay, A. S. (2008). Helping teachers connect vocabulary and conceptual understanding, Mathematics Teacher, 102(3), 218-223. Geake, J. (2008). Neuromythologies in education, Educational Research, 50(2), 123-133. Retrieved November 11, 2010, from ERIC database. Georgia Department of Education (2008).Mathematics Georgia performance standards (GPS), 1-16. Atlanta, GA: Author. Retrieved from HYPERLINK "http://www.georgiastandards.org"http://www.georgiastandards.org on June 23, 2010. Greenwood, S. (2006). Making words matter: Vocabulary study in the content areas. The Clearing House, 75(5), 258-63. Retrieved July 28, 2010, from ERIC database. Haas, S.C. (2003). Algebra for gifted visual-spatial learners. 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Retrieved November 2, 2010, from ERIC database. LaGrange College Education Department. (2008). Conceptual framework. LaGrange, GA: LaGrange College Matz, K.A. & Leier, C. (1992). Word problems and the language connection. Arithmetic Teacher, 39(8), 14-17. National Board of Professional Teaching Standards [NBPTS]. (2002, August). The five core principles. Retrieved June 23, 2010 from the NBPTS Web Site HYPERLINK "http://www.nbpts.org"http://www.nbpts.org National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for School Mathematics. Retrieved July 2, 2010, from HYPERLINK "http://www.nctm.org/standards/content"http://www.nctm.org/standards/content Phillips, D. (1995). The good, the bad, and the ugly: The many faces of constructivism. Educational Researcher, 24(7), 5-12. Pierce, M., & Fontaine, L. (2009). Designing vocabulary instruction in mathematics. The Reading Teacher, 63(3) 239-243. doi:10.1598/RT.63.3.7 Phillips, D.C., Bardsley, M.E., Bach, T., & Gibb-Brown, K. (2009). But I teach math! the journey of middle school mathematics teachers and literacy coaches learning to integrate literacy strategies into the math instruction. Education, 129(3), 467-472. Retrieved July 3, 2010, from ERIC database. Popham, W. (2008). Classroom assessment: What teachers need to know (5th ed.). Boston: Pearson, Allyn, & Bacon. Powell, K & Kalina, C. (2010). Cognitive and social constructivism: Developing tools for an effective classroom. Education, 130(2), 241-250. Retrieved August 12, 2010, from ERIC database. Rapp, W. (2009). Avoiding math taboos: Effective math strategies for visual-spatial learners. Teaching Exceptional Children Plus, 6(2), 2-12. Retrieved September 10, 2010, from ERIC database. Rector, Robert E. and Henderson, Kenneth B. (1970). The relative effectiveness of four strategies for teaching mathematical concepts. Journal for research in mathematics education, 1(2), 69-75. Retrieved September 29, 2010, from ERIC database. Sadoski, M. (2005). A dual coding view of vocabulary learning. Reading and Writing Quarterly, 21, 221-238. Retrieved October 14, 2010, from ERIC database. Salkind, N. J. (2010). Statistics for people who (think they) hate statistics (Excel 2nd Ed.). Thousand Oaks, CA: Sage. Scott, C. (2010). The enduring appeal of learning styles. Australian Journal of Education, 54(1), 5-17. Retrieved November 2, 2010, from ERIC database. Sharp, J.G., Bowker, R., Byrne, J. (2008). VAK or VAK-ous? Towards the trivialization of learning and the death of scholarship. Research Papers in Education, 23(3), 293-314. Retrieved November 2, 2010, from ERIC database. Silverman, L. K. (2005). Teaching mathematics to non-sequential learners. HYPERLINK "http://www.gifteddevelopment.com"www.gifteddevelopment.com Spencer, B., & Guillaume, A. (2006). Integrating curriculum throughout the learning cycle: Content based reading and vocabulary instruction. The Reading Teacher, 60(3), 206-219. Retrieved August 15, 2010, from ERIC database. Tajalli, H., & Opheim, C. (2005). Strategies for closing the gap: Predicting student performance in economically disadvantaged schools. Educational Research Quarterly, 28(4), 44-54. (ERIC) Document Reproduction Service No. EJ718119) Retrieved August 14, 2010 from ERIC database. Yilmaz-Soylu, M., Akkoyunlu,B. (2009). The effect of learning styles on achievement in different learning environments. Turkish Online Journal of Educational Technology TOJET, 8(4), 43-50. Retrieved November 2, 2010, from ERIC database. Appendix A Geometric Figures Instructional Plan DayStandardsEssential QuestionResources/Materials ActivitiesVocabularyAssessmentHomeworkDay 1Concepts and Skills to Maintain: Characteristics of 2D and 3D shapes.How can I identify different types of line relationships and angles?Text: Harcourt Math Rulers Write to Win Journals Harcourt Mega Math Ice Station Exploration Polar Planes (computer lab throughout unit)Preview Voc. Discuss wds. and look for examples in classroom. Find examples in figures. Write to Win Journal entry: Today in Math I learnedPoint, line, ray, line segment, plane, angle, parallel lines, perpendicular lines, intersecting lines, acute, obtuse, right, straight, angles, protractorPre-test Voc. Pre-test Write to Win Journal Practice Workbook lesson 19.1 1-12Day 2Concepts and Skills to Maintain: Characteristics of 2D and 3D shapes.How can I use a protractor to measure angles?Text: Harcourt Math Rulers 5X7 Index Cards Crayons, Markers, Colored PencilsMake Voc. Cards   Word, definition, picture, non-example Use protractors to measure anglesPoint, line, ray, line segment, plane, angle, parallel lines, perpendicular lines, intersecting lines, acute, obtuse, right, straight, angles, protractorVocabulary CardsDay 3Concepts and Skills to Maintain: Characteristics of 2D and 3D shapes.Why does the protractor have 2 different scales? Text: Harcourt Math Protractors TR 26 (Sheet with angles) Write to Win JournalsReview types of angles & how to categorize them. Discuss and examine Protractor and how to use it to measure anglesPoint, line, ray, line segment, plane, angle, parallel lines, perpendicular lines, intersecting lines, acute, obtuse, right, straight, angles, protractorTeacher Observation: Actually using a protractor to measure anglesPractice Workbook Lesson 19.2Day 4Concepts and Skills to Maintain: Characteristics of 2D and 3D shapes.How can I use angles to classify and measure polygons?Text: Harcourt Math 5X7 Index Cards Isometric dot paper Polygon Figures List of polygon names based on sides up to 100 sidesReview angles Make Voc. cards for new Voc. Use text to identify regular and irregular polygons Polygon, regular polygon, irregular polygon, congruent, triangle, quadrilateral, pentagon, hexagon, octagon, decagon Vocabulary Cards  StandardsEssential QuestionResources/Materials ActivitiesVocabularyAssessmentHomeworkDay 5Concepts and Skills to Maintain: Characteristics of 2D and 3D shapes.How can I give the missing angle measure for a triangle and quadrilateral?Text: Harcourt Math Write to Win Journals Review polygons (voc) regular and irregular. Use text to find the missing angle measure of triangles and quadrilaterals. Write to Win: I am a triangle what is my area?Polygon, regular polygon, irregular polygon, congruent, triangle, quadrilateral, pentagon, hexagon, octagon, decagon Write to Win JournalPractice workbook: 19.3Day 6M5G2 Students will understand the relationship of the circumference of a circle, its diameter, and pi ( QUOTE   = 3.14)How can I identify and measure parts of a circle?Text: Harcourt Math Rulers 5X7 Index Cards Crayons, Markers, Colored Pencils Protractor Review parts of a circle (radius, diameter, chord, circumference, central angle) Make voc. cardsCircle, diameter, radius, chord, pi, circumference, central angle Vocabulary CardsPractice workbook 19.4Day 7M5G2 Students will understand the relationship of the circumference of a circle, its diameter, and pi ( QUOTE   = 3.14)What is the relationship between the circumference of a circle and the radius?Rulers Poster board Various size cans Chart paper calculatorGroups will use different size cans to measure radius and circumference, Make a chart, graph, and discuss resultsCircle, diameter, radius, chord, pi, circumference, central angleChart & Graphs Day 8M5G2 Students will understand the relationship of the circumference of a circle, its diameter, and pi ( QUOTE   = 3.14)How can I use angles to classify and measure polygons?Text: Harcourt Math 5X7 Index Cards Isometric dot paper Polygon Figures List of polygon names based on sides up to 100 sidesWrite to Win: discuss relationship between circum., diameter, radius Unknown angle measure in a circle Circle, diameter, radius, chord, pi, circumference, central angle Write to Win JournalPractice Workbook Lesson 19.5 DayStandardEssential QuestionResources & MaterialsActivitiesVocabularyAssessmentHomeworkDay 9Concepts and Skills to Maintain: Characteristics of 2D and 3D shapes.How Can I classify triangles?Chapter 19 Posttest Isometric dot paper Text: Harcourt Math Protractors 5x7 index cardsChap. 19 Posttest Discuss/review triangles Make voc. cardsIsosceles triangle Scalene triange Equilateral triangle Acute triangle Obtuse triangle Equilateral triangleGeometry Posttest Part 1(Ch 19 Voc. CardsDay 10Concepts and Skills to Maintain: Characteristics of 2D and 3D shapes.How Can I classify triangles?Text: Harcourt Math 5x7 index cards Protractors Write to Win JournalChapter 20 Pretest Discuss triangle classifications Practice with text pgs. 385-387 Write to Win Journal: What I thought you taught about triangles.Isosceles triangle Scalene triange Equilateral triangle Acute triangle Obtuse triangle Equilateral triangleWrite to Win JournalsPractice Workbook Lesson 20.1Day 11Concepts and Skills to Maintain: Characteristics of 2D and 3D shapes.How can I classify quadrilaterals?Text: Harcourt Math 5x7 index cards Polygon figuresMake Voc. cards Discuss classifications of quadrilaterals Use text 389-393Square, rectangle, trapezoid, parallelogram, rhombus, congruent, parallelVoc. Cards Teacher Observation Practice Workbook Lesson 20.2 Day 12M5G1: Students will understand congruence of geometric figures and the correspondence of their vertices, sides, & anglesHow can I identify similar and congruent figures?Text: Harcourt Math 5x7 index cards 1cm. grid paper Make Voc. cards Draw figures that are similar and congruentSimilar, congruence, corresponding vertices, Corresponding angles, Corresponding sidesVoc. Cards Teacher ObservationPractice Workbook Lesson 20.3 DayStandardEssential QuestionResources & MaterialsActivitiesVocabularyAssessmentHomeworkDay 13M5G1: Students will understand congruence of geometric figures and the correspondence of their vertices, sides, & anglesHow can I identify corresponding vertices, angles, and sides?Text: Harcourt Math 0.5 cm Grid Paper Write to Win JournalDraw figures and locate corresponding sides, vertices, and angles Write to Win Journal: Acrostic Voc: CONGRUENCESimilar, congruence, corresponding vertices, Corresponding angles, Corresponding sidesWrite to Win Journal Figures drawn on grid paperDay 14Concepts and Skills to Maintain: Characteristics of 2D and 3D shapes.How can I identify solid figures?Solids Text: Harcourt Math 5x7 index cards Examine & discuss solid figures Why 3D? Make voc. cardsPolyhedron Prism, base, faces, Cube, cylinder, cone, sphereVocabulary Cards Teacher ObservationPractice Workbook Lesson 20.4Day 15Concepts and Skills to Maintain: Characteristics of 2D and 3D shapes.How can I identify solid figures?Text: Harcourt Math Solid figure patterns Write to Win JournalMake Solid figures from patterns. Text 394-397 Table for prisms (sides, vertices, faces, edges)Polyhedron Prism, base, faces, Cube, cylinder, cone, sphereWrite to Win Journal Prism Table Solid figures that were constructedReview voc. cards for games tomorrowDay 16Concepts and Skills to Maintain: Characteristics of 2D and 3D shapes.How can I identify solid figures?Vocabulary Cards from chapter 19-20Vocabulary Bingo (ch. 19-20 terms) Jeopardy game for reviewPolyhedron Prism, base, faces, Cube, cylinder, cone, sphereBingo Game Jeopardy GameStudy for chapter 20 posttest and Voc. posttest DayStandardEssential QuestionResources & MaterialsActivitiesVocabularyAssessmentHomeworkDay 17Chapter 20 Posttest 2 Vocabulary Posttest Posttests Writing to Win: Free Write- My favorite part of this Geometry unit is Geometry Posttest Part 2 Vocabulary Posttest Appendix B Rubric for Evaluating Instructional Plan Beginning 1Developing 2Accomplished 3Exemplary 4Score Instruction Goals and Objectives Instructional goals and objectives are not stated. Learners can not tell what is expected of them. Learners can not determine what they should know and be able to do as a result of learning and instruction.Instructional goals and objectives are stated but are not easy to understand. Learners are given some information regarding what is expected of them. Learners are not given enough information to determine what they should know and be able to do as a result of learning and instruction.Instructional goals and objectives are stated. Learners have an understanding of what is expected of them. Learners can determine what they should know and be able to do as a result of learning and instruction.Instructional goals and objectives clearly stated. Learners have a clear understanding of what is expected of them. Learners can determine what they should know and be able to do as a result of learning and instruction. Instructional Strategies Instructional strategies are missing or strategies used are inappropriate.Some instructional strategies are appropriate for learning outcome(s). Some strategies are based on a combination of practical experience,theory, research and documented best practice.Most instructional strategies are appropriate for learning outcome(s). Most strategies are based on a combination of practical experience,theory, research and documented best practice.Instructional strategies appropriate for learning outcome(s). Strategy based on a combination of practical experience,theory, research and documented best practice. Assessment Method for assessing student learning and evaluating instruction is missing.Method for assessing student learning and evaluating instruction is vaguely stated. Assessment is teacher dependent.Method for assessing student learning and evaluating instruction is present. Can be readily used for expert, peer, and/or self-evaluation.Method for assessing student learning and evaluating instruction is clearly delineated and authentic. Can be readily used for expert, peer, and/or self-evaluation. Technology Used Selection and application of technologies is inappropriate (or nonexistant) for learning environment and outcomes.Selection and application of technologies is beginning to be appropriate for learning environment and outcomes. Technologies applied do not affect learning.Selection and application of technologies is basically appropriate for learning environment and outcomes. Some technologies applied enhance learning.Selection and application of technologies is appropriate for learning environment and outcomes. Technologies applied to enhance learning.Materials NeededMaterial list is missing.Some materials necessary for student and teacher to complete lesson are listed, but list is incomplete.Most materials necessary for student and teacher to complete lesson are listed.All materials necessary for student and teacher to complete lesson clearly listed.Organization and PresentationLesson plan is unorganized and not presented in a neat manner.Lesson plan is organized, but not professionally presented.Lesson plan is organized and neatly presented.Complete package presented in well organized and professional fashion.Total Points Appendix C Pre/Post Student Survey Strongly AgreeAgreeDisagreeStrongly DisagreeI am good at math.I like to answer questions asked by the teacher in math class.I am comfortable asking questions in math if I dont understand something.I am comfortable sharing my math ideas with the class.I understand the vocabulary we use in math.I think I learn better when I understand the vocabulary in math.It is easy for me to use the vocabulary in math class. Circle your answer. Which of these best describes yourself as a math student? Struggling Ok Good Very Good Which of these best describes how a friend would describe you as a math student? Struggling Ok Good Very Good How often are you asked to explain your answer using math vocabulary? Never Less than the time More than the time Always How easy is it for you to use math vocabulary to explain your answer? Very Hard Hard Ok Easy Appendix D Geometry Vocabulary Pre/Post-test Name ________________________ __________________________ is an exact location in space, usually represented by a dot. __________________________ is a flat surface that extends without end in all directions. __________________________ is a straight path of points in a plane, extending in both directions with no endpoints. __________________________ is a part of a line; it begins at one endpoint and extends forever in one direction. _________________________ are lines in a plane that do not intersect. _________________________ are lines that cross each other at exactly one point. _________________________ is part of a line between two endpoints. _________________________ is a figure formed by two rays that meet at a common endpoint. _________________________ are two lines that intersect to form right angles. ________________________ is an angle whose measure is greater than 90 and less than 180. _______________________ is an angle that has a measure less than a right angle. ________________________ is an angle that measures 180. _______________________ is a special angle formed by perpendicular lines and equal to 90. _______________________ is a unit for measuring angles. ________________________is having the same size and shape. ________________________is a tool used for measuring or drawing angles. ______________________________is a closed figure with all points on the figure the same distance from the center point. __________________________ ____is a closed plane figure formed by three or more line segments. __________________________ ___is a line segment that passes through the center of a circle and has its endpoints on the circle. _____________________________ is a line segment with one endpoint at the center of a circle and the other endpoint on the circle. _____________________________is a line segment with endpoints on a circle. _____________________________is the angle formed by two radii of a circle that meet at its center. _____________________________is the distance around a circle. ____________________________is the relationship of the circumference to the diameter of a circle; an approximate decimal value is 3.14. ____________________________is a polygon in which the sides are not congruent and the angles are not congruent. ____________________________is a polygon in which all sides are congruent and all angles are congruent. WORD BANK acute angle diameter plane angle intersecting lines point central angle irregular polygons polygon chord line protractor circle line segment radius circumference obtuse angle ray congruent parallel lines regular polygon degree perpendicular lines right angle pi straight angle Appendix E Reflective Journal Prompts What were three main things I learned from this session? What did we not cover that I expected we should? What was new or surprising to me? What have I changed my mind about, as a result of this session? 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