Investigating Students Understanding of Place Value

Investigating Students Understanding of Place Value

ED 411/518 Teaching Children Mathematics

Fall 2006

Student Thinking Interview:

Investigating a Student’s Understanding of Place Value

ASSIGNMENT DESCRIPTION

Overview of assignment

The purpose of this assignment is to help you learn more about how to figure out what students know and can do. This is an essential part of teachers’ work. In this assignment, as an instance of this work, we are probing how students understand and use ideas about place value. To carry out the assignment, you will establish a setting in which you can assess one student’s thinking by:

  • carefully analyzing, organizing, and using mathematical tasks;
  • and practicing asking good questions, listening carefully, and interpreting what you see and hear.

You will use the information you are able to collect to make thoughtful claims about what your individual student seems to know, understand, and know how to do with respect to place value. After conducting your interview, you will have an opportunity to discuss your student's performance with colleagues to gain insight into your student from what others notice. You will then write a memo to your cooperating teacher about your student’s knowledge of and skill with place value. Overall, the skills you develop in this assignment will help you engage more proficiently in many typical teaching situations, such as working one-on-one with students as they complete their daily work or communicating with parents about their child’s progress in mathematics.

An important aspect of the work on the student thinking interview is the opportunity to see and use the course principles in new ways. As you prepare for your interview, you will analyze tasks to understand their core mathematical points so that you can maintain the mathematical focus and the mathematical integrity of the interview. As you engage in the interview your goal is to create a productive environment for you to learn about your student’s knowledge, skills, and dispositions. Developing skill in assessing what students know and are able to do will help you improve the achievement of all students. Finally, working with peers and instructors to better understand what students say and do, as well as to hone your questioning techniques and use of math tasks are aimed at the improvement of practice. As a set, the course principles can inform and enhance your interview work.

Detailed description of assignment

There are three parts to the student thinking interview. In Part 1, you will prepare to meet with one student, analyzing and organizing a sequence of tasks that will help you learn how your student thinks about and understands place value. In Part 2, you will conduct your interview and prepare to talk in class about what you found. In Part 3, you will write a memo to your cooperating teacher — a brief, probing description of what happened in your interview and your interpretation of what the student knows and is able to do in the area of place value that you explored. Specifics about each part of the assignment are explained below.

Part 1 — Select a student and plan your interview

(a) Make arrangements at school. Consult with your cooperating teacher and arrange to meet with a student in your field placement between October 23 and 27. Plan to spend approximately 20 to 40 minutes on the session, depending on the age of the student.

Consider carefully whom you select. You may want to meet with a student with whom you have not yet made a connection, or who is quiet in class. Or you might pick a student who has said intriguing things in class about which you were unsure. Think about what you can learn as you make your selection.

Send me an email by 9 pm on October 19 with a brief description of the student you selected, your reason for selecting this student, and when you will meet with him or her. Use a pseudonym for your student, to protect confidentiality.

(b) Study and select tasks. In class on Thursday, October 19, you will be given a set of place value tasks organized for students of different ages. You will spend time working through them in class, and also on your own, to select tasks that you think will help you learn how your particular student understands and uses ideas of place value. For each task selected, you will think about the mathematical ideas it involves, anticipate what your student might say, and prepare for how you could probe your student's thinking. The more you have thought through possibilities, the more likely the interview will be rewarding for you and the student.

(c) Make a plan for your interview. Assemble the tasks you have selected, and add annotations about the purposes you have for those questions, your anticipations of what your student might do or say, and what you will ask or do. Be sure to also plan how you will open and close your session. You may use the template that will be provided in class or design your own. If you would like feedback on your plan, please email it to me at least three days before you conduct your interview.

Part 2 — Conduct your interview and prepare preliminary assertions about your student’s understanding of place value

Conduct the interview with your student on the date you selected. Make a digital audio recording of your interview. Be sure to also keep written notes and collect any student work.

After the interview, carefully work through your data and formulate two or three clear and justifiable assertions about your student's understanding of place value — ideas, procedures, and ways of reasoning. Your assertions should explain what the child seems to know, understand, and know how to do. Find specific examples and quotes from the interview to illustrate your claims.

Come to class on Thursday, Nov. 2 prepared to describe what your student did and to discuss your assertions with others in our class. Be sure to bring your notes and any student work from the session. You should also prepare an “assertion sketch” that clearly states your 2-3 draft assertions and briefly lists the supporting evidence for each. Please bring a hard copy of your assertion sketch for each member of your group and email me an electronic version before you come to class. I will provide feedback that you can use to prepare your memo in Part 3.

Part 3 — Write a memo to your cooperating teacher

Type a one-page memo to your cooperating teacher reporting about your student’s understanding of place value. (I will provide sample memo templates to help you with formatting.) Your memo should convey an open-minded and thoughtful analysis of your interview. It should demonstrate your ability to connect your impressions with specific evidence from your investigation, as well as professional resources and learning opportunities from the course.

Begin your memo with an introductory paragraph describing your interview. In this introduction, briefly explain the mathematical focus on the interview (e.g., math topics, processes, or dispositions) and the main tasks you posed. In addition, comment on your student’s disposition toward the interview tasks.

Next, write two clear and justifiable assertions about your student's understanding of place value — including ideas, procedures, or ways of reasoning. For each assertion, state it clearly and succinctly, and explain what you mean and why you make it. Substantiate each assertion with specific examples or quotes from the interview. You should also connect your assertions to the strand/s of mathematical proficiency to which it is related.

Your memo should be submitted to me electronically by Thursday, November 9. I expect you will use the feedback on this memo to create a final version to give to your cooperating teacher.

Mathematics Methods Planning GroupPage 1 of 3

University of Michigan