Who Uses Math? Upper Elementary Children s Perceptions of the Uses of Mathematics. Gwenanne M. Salkind. George Mason University

Transcription

1 Running Head: WHO USES MATH? Who Uses Math? Upper Elementary Children s Perceptions of the Uses of Mathematics Gwenanne M. Salkind George Mason University EDRS: Problems and Methods in Educational Research Instructor: Dr. Margo A. Mastropieri Qualitative Method Section November 9, 2005

2 Who Uses Math? 1 Research Questions Research has found that children in grades kindergarten through grade 3 primarily define mathematics in terms of number and/or mathematical operations. They have limited awareness of the use of mathematics in the context of everyday life (Perlmutter, Bloom, Rose, & Rogers, 1997). No research has been done about how children in upper elementary grades define mathematics and perceive its real life uses. This study therefore, is intended to replicate and extend the work of previous researchers by asking the following research questions: 1. How do children in the upper elementary grades define mathematics? 2. Do children in the upper elementary grades feel confident in their mathematics ability? 3. What are the views of children in the upper elementary grades of the uses of math in real life? 4. How do children in the upper elementary grades think adults use math in real life? 5. How do children in the upper elementary think children use math in real life? Method Design This study will use an ethnographic design to investigate the perceptions of children in upper elementary grades of the uses of mathematics in real life. Four schools will be involved in the study. Schools will be purposefully chosen to participate based upon similar demographic characteristics. In order to guarantee an equal number of male and female participants, stratification will be used. Two levels of random selection will be used. Two classes at each grade level (3-5) will be randomly selected from the classes at the four schools. Permission will be obtained from the teachers, the parents, and the children in those classes. Two girls and two

3 Who Uses Math? 2 boys will be randomly selected from the children whose parents have given permission from each of the two classes. Participants The subjects in this study will be 24 children in grades three through five. Two girls and two boys will be chosen at random from each of six classrooms from four schools in a large suburban district in the eastern United States. The participants will include students from a range of racial and ethnic backgrounds as well as socio-economic status. Specific demographic information will be collected and reported (i.e., age, gender, racial/ethnic background, socioeconomic status, and achievement level). Demographic information of the sample population will be compared to demographic information of the entire population of the four schools to determine if the sample is representative of the total population. Settings Classroom settings. Classrooms will be representative of typical regular education classrooms in the district. A typical classroom is one in which mathematics instruction occurs for about an hour each day. Teachers use one of three approved mathematics textbooks as resources to teach the district and state curriculum. Both large and small group instruction is provided. Students explore mathematical ideas through the use of manipulatives and paper-and-pencil activities. Interview settings. The researcher will interview students individually in private rooms in the schools away from the students classrooms. The interviews will be audio and video taped. Researcher Background and Perspective I have worked in the field of elementary education for 20 years. I spent 11 years as a classroom teacher of grades one, two, and three. For the last nine years, I have provided

4 Who Uses Math? 3 mathematics professional development to school-based elementary mathematics resource teachers and classroom teachers. In my work in elementary education, I have come to believe that children should learn mathematics in context and understand how mathematics is part of everyday life. Part of the mathematics instruction that I provide students is to help them see the mathematics in the world around them. We talk about math happenings or mathematical events that occurred outside of the school setting. Children might describe a trip to the grocery store with their parents. They might talk about setting the table at home or planning for a party. I ve noticed that children don t seem to find the mathematics in the world around them naturally, but they can see it once it is pointed out to them. This study will help me to look at how children view mathematics in their world. I hope to be able to determine how children define mathematics, how they think adults use mathematics, and if they can tell how they, themselves, use mathematics in their daily lives. Data Collection Methods A semi-structured interview will be conducted with each child in the study midway through the school year. Interview protocol is shown in the Appendix. The researcher will meet with the children in their classroom several times before the actual interviews in order to establish rapport. These meetings may take the form of the researcher assisting the teacher in mathematics class or playing mathematics games with the students. No mention of real life mathematics will be made during these interactions. Children will be interviewed individually in a private room in the school away from the classroom. The interviewer will progress from general open-ended questions such as, Who uses math? to more structured questions about specific uses of mathematics, like How do people

5 Who Uses Math? 4 use math in cooking? When children do not respond or give vague answers, the interviewer will probe for more information. Interviews will be audio and video taped. Data Collection Procedures Permissions from the George Mason University and school district Human Subjects Review Boards will be obtained. Four schools with similar demographic characteristics will be selected from the elementary schools in the district. Permissions from building principals will be obtained. Two classes at each grade level (3-5) will be randomly selected from the regular education classes at the four schools. Permission will be obtained from the teachers, parents, and children in those classes. Two girls and two boys from each class will be randomly selected from the pool of children whose parents have given permission. This will result in a group of 24 children who will be interviewed by the researcher. The researcher will establish rapport with the children prior to conducting the interviews. The researcher will work in the students classrooms either by assisting the teacher during a mathematics lesson or by playing math games with the students in a small group setting. Rapport will be established during the first semester of the school year. A semi-structured interview will be conducted with each child midway through the school year. The interview will be held in a private room in each child s school away from the regular classroom setting. The interviews will be audio and video taped. The researcher will follow the interview protocol (see Appendix). Before conducting each interview, the researcher will describe the research project, telling the student about the purpose of the study, the sources of data being collected, what will be done to protect the confidentiality of the student, and how long the interview will take. The student will reaffirm assent of willingness to participate.

6 Who Uses Math? 5 During the interview, the researcher will progress from general open-ended questions to more structured questions. When children do not respond or give vague answers, the researcher will probe for more specific information. At the end of the interview, the interviewee will be thanked for participating. Proposed Data Analyses Interviews will be transcribed so that analysis can be done. Data will be analyzed for broad themes and categories. The researcher will read through the data, initially, to gain a general sense of the data and perform a preliminary exploratory analysis. The text will be divided into segments and coded. An effort will be made to reduce overlap and redundancy of codes. The codes will be collapsed into five to seven themes that address the major research questions. Themes will be interpreted and connections among themes will be identified. In order to determine how children s perceptions change over the years, student interview data will be combined by grade level. Data will be coded according to identified themes. Initial themes that will be looked at include categories that are built into the interview protocol. Questions seven, nine, and ten ask about the students confidence levels and feelings toward mathematics. Question one asks for a definition of mathematics. Question five asks about the real world math that the student has done. The other questions ask about how other people use mathematics in the real world. Themes will be reduced to five to seven by examining codes that the participants most frequently discussed, were expected by the researcher, or were unique or surprising. A detailed report will be written to describe these themes.

7 Who Uses Math? 6 Appendix Interview Protocol Time of Interview: Date: Place: Interviewer: Interviewee: (Main questions are in bold. Examples of follow-up questions are in parentheses.) I am going to ask you some questions about numbers and math. How old are you? When is your birthday? 1. Tell me about math. What is math? (What are numbers for? What else is math besides numbers?) 2. Who uses math/numbers? (What kind of people use math?) 3. What do people use math/numbers for? (How do people use math in their real life?) 4. Have you ever seen your parents use math? (Tell me about it.) How do your parents use numbers/math? 5. Did you use math for anything today? (What about yesterday or earlier this week? What did you do? Tell me about it.) 6. How do you learn math? (Do your teachers teach you? Do your parents teach you? Do you learn math from your friends? What things in your class help you learn math?) 7. Is it hard or easy to learn math? 8. Why do you need to learn math? 9. Do you like doing math? 10. Are you good at doing math? (How did you get to be good at math? How could you learn it better?) 11. Does your mom like math? (Your dad, your sister, brother) 12. Tell me about? What kinds of things to people? Adding/subtracting: Why to people need to know how to add and subtract? (Would you need to add and subtract in a story? Why?) Measuring: Do people use math when they are cooking? (Do people measure when they cook? Why?) Counting: What kinds of things do people need to count? (Would you need to count in a store?)

8 Who Uses Math? 7 References Perlmutter, J., Bloom, L., Rose, T., & Rogers, A. (1997). Who uses math? Primary children's perceptions of the uses of mathematics. Journal of Research in Childhood Education, 12(1),