Unit 2: Learning and Understanding Mathematics: Fractions, Decimals, and Percents

Class Topics Readings due (before class) In-class activities

Interviewing workshop #1

Fraction concept activities Building assessment into Assessment principles discussion 5. Sept instruction; VdW chapters 5 and 15 and activities 29/30 Developing fraction concepts Due for the next class: prepare all materials for your interview, videotape yourself conducting an interview with an adult

VdW chapters 16 and 17

Article: Ellemor-Collins, D. & Interviewing Workshop #2: Bring Wright, R.J. (2008). Assessing Developing your interview materials and a student thinking about arithmetic: strategies for movie file of your practice Videotaped interviews. Teaching fraction interview Children Mathematics, 15(2), 106- 6. Oct computation; 111. 13/14* developing Fraction computation activities concepts of (This article can be downloaded on decimals and Decimal and percent activities our course website. Look under percents "Class Resources.")

Also prepare for your interview by re- reading the relevant sections of Van de Walle

Interview debriefing: Bring your 2 videorecorded interview files. Meet with partners, watch videos, 7. Oct Proportional start paper VdW chapter 18 20/21 reasoning proportional reasoning activities

Group paper due on Oct 23 30 Major assignments

Inquiry into Children's Mathematical Thinking: Child Interview paper (due October 23 30: 20%)

This assignment was based largely and sometimes directly on the ideas that came out of the Integrating Mathematics and Pedagogy (IMAP) Project, a federally funded project at San Diego State University. Principal Investigators were Randolph Philipp and Judith Sowder.

For this project, you will interview two children in your classroom in order to learn about their mathematical thinking. Along with a partner, you will analyze the thinking of your interviewees and you will report on your findings in a group paper. You will videorecord each interview so that you can thoroughly analyze the children's thinking. All of the interviews will be based on number concepts (counting, place value, and fractions). You will be provided with the appropriate interview protocol that you will use to conduct your interview. Here's an itinerary of the assignment:

Class 5 (Sept 29/30)

 Interviewing Workshop #1: large and small group discussions about characteristics of good interviews, watch sample video clips of interviews  Pairs (and some triples) formed, based on school sites and grades  Interview protocols provided  Before class 6: prepare materials for their interview, videorecord yourself conducting an interview with a friend/relative

Class 6 (Oct 13/14)

Interviewing Workshop #2: Bring ALL materials required for your interview, Watch partners' videotaped interviews; discuss "What if..? "scenarios; practice interviews; watch additional videos in large and small groups

In classrooms: Conduct 2 interviews after Class 6 but before Class 7

Class 7 (Oct 20/21)

Debriefing Workshop: Meet with partners, watch one another's videos, start paper (You will be turning in 1 paper as group. You may want to consider composing it on Google docs.) Guidelines for the paper

The purpose of this assignment is for you to experience the spirit of inquiry in relation to children as mathematical thinkers. We want you to learn, grown, and wonder about how children can and do think about mathematics. Your work will be evaluted on the thoughtfulness of your comments--not on the expertise of your interviewing! So have fun!

You and your partner will write a 4-8 page paper analyzing the mathematical thinking of the children you interviewed. Throughout your analysis, keep in mind the following general question: What did you learn about the children's mathematical thinking? To help you answer that question, you may want to consider some of the following issues:

 what you learned that relates to your experiences in MTHED 420;  what you would do next if you were this child's teacher;  anything that surprised you.

It is not necessary for you to discuss how each child answered every question. Instead, you should choose which questions helped you learn the most about each child's thinking. Furthermore, it is up to you how you want to present your analysis. You may decide to discuss each child individually or you may decide to compare each child with the others throughout the entire paper. In either case, you are required to discuss at least one aspect from each interview (do not leave any children out of the paper!).

*You are required to relate your analysis to the ideas in our textbook. That is to say: you must make reference to Van de Walle whenever appropriate.

You do not need to write a lengthy introduction or conclusion. Your introduction can simply provide background information (including the grade levels of the interviewees). The concluding paragraph can simply be final thoughts that you and your partner want to share as a reflection on the experience.

Reminder: Please protect your students' identities; do not refer to them in your paper by their actual name.

A caution about your write-ups: Please do not include an assessment of the child’s overall personality (e.g., happy, self-confident, or nervous child) or overall ability level (e.g., smart or slow child), because those statements do not provide useful information for our purposes. You may want to comment on a child’s performance in solving a particular problem (e.g., child was very confident with her solution strategy to problem x), but please avoid generalities.

A note about writing a paper as a team :Each team member will have an opportunity to provide feedback about the relative contributions of each team member. An indication of one team member failing to "pull his or her own weight" may result in a reduction of grade. Unit 2 blog entries (due Oct 30: 5%)

For these blog entries, you will respond to a prompt given after each class. This prompt will be given by the instructors either at the very end of class or the day after class on the class website. You will write a 1-2 paragraph response to the prompt (more detailed instructions will be given with each prompt). You must write this response by (gray- Thursday; maroon-Friday) at 5:00pm. Then you will visit 2 of your classmates' blogs and write a comment in reaction to their original response. You will write these reactions by 1:00 on the day you have class (Tuesday for gray; Wednesday for maroon). On each of these 2 comments, you will write at least 1 paragraph in which you discuss what you found interesting, surprising, or unclear in your classmate's entry.

Each week in class you will be assigned not only the prompt but the 2 classmates' to whom you will be responding that week. It is your responsibility to find their blog site.

At the end of this unit, you will have written 3 blog entries on your own site, and a total of 6 reactions to your classmates' entries.