1. 1 Overview of Class #7 Comments about course Continue work with base ten blocks – modeling decimals Analysis of student thinking using samples of students’ written work Wrap up

2. 2 Why are we working on this? Modeling place value, numeration, computation; moving into decimals and upper elementary content: –Learning to produce clear explanations, make meaning visible, help students make solid connections –Filling in what teachers’ guides will not provide –Teaching this content well will give you leverage as a beginning teacher in about 3/4 of the elementary curriculum Learning to make judgments about students’ mathematical proficiency –Diagnosis, to be able to match focus to where students are is absolutely crucial to effective teaching –Communicating clearly, and backing up with examples and evidence, about students’ progress (parents, other teachers, specialists, students themselves) is essential to professional work a a teacher

3. 3 Base Ten Blocks Trading model Highlights geometry of number and number relationships Little cube, rod, flat, big cube Micro-, mini-, super-, mega- as prefixes for extending the blocks Unit can change Expensive Flexible across K - 8 and beyond

4. 4 Modeling with Base Ten Blocks #1 1002 - 483

5. 5 Modeling with Base Ten Blocks #2 5.3 5.03 0.53 0.8 0.08 0.4 0.40 How can using the blocks help students compare and order decimals?

6. 6 Modeling with Base Ten Blocks #3 2.4631.9 + 1.57 + 18.47 33.0210 - 19.71 - 3.83 DISCUSS AND THEN REFLECT IN NOTEBOOK: How would you explain to students why we “line up the decimal points” in the standard algorithms for adding and subtracting decimals?

7. 7 Our Work on Student Thinking We’ve been focusing on: eliciting listening probing interpreting We’re now shifting to: evaluating responding using

8. 8 Analysis of Third Grade Quiz 1.Answer each of the questions on the quiz yourself. 2.Use handout to analyze particular questions (#9, #10, #8, then your choice): What is the purpose of the question and the core mathematical ideas addressed? What are examples of “good” answers at the third grade level?

9. 9 Analysis of Student Work Read each of the three student responses to a particular question (starting with #8, #9, and #10). For each question discuss the following: 1.What does each student’s response tell you about his or her mathematical understandings? 2.What follow-up questions would you like to ask each student?

10. 10 Reflection What stood out to you about looking at this quiz and the sorts of questions it posed to students, and what those enabled you to see, and not see, about the children’s thinking?

11. 11 Analyzing Student Work Samples For each question: 1.Answer the question yourselves. 2.Analyze the question: –What is the purpose of the question and the core mathematical ideas addressed? –What are examples of “good” answers at that grade level? 3.Read the student responses to that question: –What does each student’s response tell you about his or her mathematical understandings? –What follow-up questions would you like to ask each student?

12. 12 Wrap Up Assignments –this week’s on website this afternoon –can pick up assignment #5 next week Office hours changed next two weeks: –Wednesday, Oct. 22 & 29, 3:15 – 4:15 Collect notebooks Questions or comments?

13. 13 Assignments Reading –Lampert, Chapters 5-6 Midterm Course Comments –Part 1: anonymous feedback about course –Part 2: questions about your field placement