Nadine Bezuk and Rachelle Feiler San Diego State University CMC-S 2004 November 5, 2004

1. Addressing Assessment in an Elementary Mathematics Methods Course: Helping Prospective Elementary Teachers Use a Variety of Assessments to Enhance Children’s Mathematics Understanding Nadine Bezuk and Rachelle Feiler San Diego State University CMC-S 2004 November 5, 2004

2. Context of Our Classes • Elementary (K - 6) mathematics methods course • Fifth-year credential program • Most students are also student-teaching while taking the methods course

3. How We Address Assessment in Our Course • Purposes of assessment • Types of assessment • Using assessment to guide instruction

4. California Teacher Performance Expectations Addressed • TPE #3: Interpretation and Use of Assessments • TPE #8: Assessing Individual Students’ Skills • TPE #9: Instructional Planning • TPE #13: Evaluates and Reflects on Practice

5. What Our Students Believe About Assessment • “It’s not fair to assess if they (children) haven’t been taught it.” • “If they (children) don’t do well on an assessment, it’s either because they haven’t been taught it or because they don’t get it--it’s not the teacher’s fault.” • Students “have a difficult time just listening to what kids have to say without any input” during an interview--they think their job is to TEACH.

6. Your Turn • What successes and/or challenges have you experienced in helping prospective elementary teachers learn how to assess children’s mathematics understanding?

7. Our Embedded Assessment Assignment • This assignment was developed collaboratively with our colleagues, including: Judy Bippert, Lisa Clement, Vicki Jacobs, Carole Manderson, Kate Masarik, and Randy Philipp.

8. Overview of Embedded Assessment Assignment • Whole-Class Assessment • Individual Student Interviews

9. Embedded Assessment:Whole-Class Assignment • Consult with classroom teacher to choose whole-class assessment from the ones we provided; • Administer assessment (approx. 10 min.); • Write up the results, including data summary and conclusions; and • Select two children to interview and explain why those students were chosen.

10. Algebraic Reasoning • Are these number sentences true or false? • (Circle TRUE or FALSE for each number sentence) • 1. 5 + 4 = 9 TRUE FALSE • 2. 7 = 3 + 4 TRUE FALSE • 3. 8 + 2 = 10 + 4 TRUE FALSE • 4. 8 = 8 TRUE FALSE • 5. 7 + 4 = 14 - 3 TRUE FALSE • 6. 7 + 4 = 11 - 2 TRUE FALSE • 7. 6 + 5 = 6 + 5 TRUE FALSE • 8. What number can you put in the box to make this a true number sentence? • 8 + 4 = + 5

11. Fraction Comparison and Computation • 1) For each of the following, circle the larger or write “=” if they are equal. a) 1/6 1/8 c) 3/6 1/2 • b) 1/7 2/7 d) 4/3 1 • 2) Choose the best estimate for the sum of 9/10 + 6/7 : • a) 1 b) 2 c) 15 d) 17 e) None of these • 3) Change 4 1/3 into an improper fraction. • 4) 1/2 + 1/3 = 5) 4 – 1/8 = 6) If you had 4 pizzas, and you ate 1/8 of one pizza, how much pizza would be left?

12. Fractions - Identify One Half

13. Computation and Place Value 143 789 +256- 463 435 294 +169 - 157 • 365 519 • +743-242 • 296 403 • +754- 124

14. Identifying Triangles

15. Identifying Rectangles

16. Completed Table for Rectangle Task

17. Items Organized by Percent Correct

18. Embedded Assessment: Interview Assignment • Provide student with a blank copy of the assessment and ask the student to explain her/his thinking while completing the assessment again, or • Use follow-up questions or tasks we provided. • Ask questions to extend/explore student thinking.

19. Embedded Assessment: Interview Assignment • Describe what happened during the interview; • Analyze student understanding; • Compare what you learned in the interviews with what you learned from the whole-class assessment; • Reflect on what you learned about assessment from this assignment; and • Discuss specific next steps for instruction based on the assessment (whole class and interviews).

20. What Our Students Learned From This Assignment • Children’s thinking • Assessment • About themselves

21. What Our Students Learned About Children’s Thinking • “From the whole-class assessment, I assumed that Jenny knows everything about a standard triangle except for triangles coming in different sizes. However, after doing the interview I learned that she does not know that the base of a triangle can be in any direction and still be a triangle.”

22. More About Children’s Thinking • “It was interesting to learn that the students considered factors such as size and orientation on the page when deciding if an item was or was not a rectangle. Prior to administering the assessment, I had not anticipated that third grade students would rely on that type of reasoning to form an answer.”

23. What Our Students Learned About Assessment • “I liked seeing how all the data came together and it made much more sense of what they all were thinking. I thought the hardest thing about interviewing students was getting them to give me more descriptive details about their criteria for triangles.”

24. More About Assessment • “After doing this [interview] assessment, I learned not to make assumptions based on the whole-class assessment.” • “From doing the interviews I learned that sometimes assessments do not truly reveal a child’s capabilities. It was a revelation that abilities may be measured through many different ways.”

25. More About Assessment • “After conducting both the whole-class assessment and the individual student interviews, I saw the importance of both. The whole-class assessment provided an overview of what the class understands conceptually and what they need further instruction on. The one drawback of this type of assessment is that it does not explain exactly how the students are thinking and the strategies they use to answer the questions. This on the other hand is the number one benefit of individual interviewing time. [It] allowed me to identify strategies like the ‘folding over’ method that students used to recognize one-half.”

26. More About Assessment • “I think whole class assessments are a great tool for teachers to use when they want to get a big picture of what their class knows about a particular concept, but they should constantly check in with their students and monitor their mathematical thinking.”

27. More About Assessment • “If the items on the assessment are chosen carefully to represent a range of difficulty, a teacher is able to get a good general view of what conceptions the students have heading into a unit of study. However, while it is possible to see general trends, it is quite difficult to understand why students choose the answers they do. There is no place for them to explain their thinking.”

28. More About Assessment • “The whole group class assessment . . . allows a teacher to get an idea of what in general the class needs help on and what they do all understand. . . It does not provide proof of what they were actually thinking, though. The individual interviews allowed me to find out more specifically what they were thinking. It also allowed me to see the steps they followed to answer a question, instead of just seeing the result of it.”

29. What Our Students Learned About Themselves • “I think this type of assessment would help me to better structure my lessons and manage time wisely.” • “I learned . . that I was rooting for everyone to succeed. In fact, I felt some disappointment when some children did not do well.”

30. More About What Our Students Learned About Themselves • “As a result of this assignment I learned that it is extremely difficult for me to not assist a student when he or she does not understand a concept. I really had to force myself to not give obvious clues to help D__ and J__ reach the correct answer. This realization actually made me even more excited to teach due to the confirmation of my desire to help students learn."

31. Reflections on Assignment: Modifications • Share classroom data and conduct separate interviews • Extend to include planning, conducting, and reflecting on a lesson based on assessment

32. Reflections on Using This Assignment in Our Course • Surprised at how much modeling students need • Still working on finding/creating more assessment tasks (e.g., more choices for lower primary students)

33. Your Turn Again • What ideas from this session might you implement in your classes? • What potential barriers might you encounter, and how might you overcome them?