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

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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

- Elementary (K - 6) mathematics methods course
- Fifth-year credential program
- Most students are also student-teaching while taking the methods course

- Purposes of assessment
- Types of assessment
- Using assessment to guide instruction

- TPE #3: Interpretation and Use of Assessments
- TPE #8: Assessing Individual Students’ Skills
- TPE #9: Instructional Planning
- TPE #13: Evaluates and Reflects on Practice

- “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.

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

- This assignment was developed collaboratively with our colleagues, including: Judy Bippert, Lisa Clement, Vicki Jacobs, Carole Manderson, Kate Masarik, and Randy Philipp.

- Whole-Class Assessment
- Individual Student Interviews

- 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.

- Are these number sentences true or false?
- (Circle TRUE or FALSE for each number sentence)

- 1.5 + 4 = 9TRUE FALSE
- 2.7 = 3 + 4TRUE FALSE
- 3.8 + 2 = 10 + 4TRUE FALSE
- 4.8 = 8TRUE FALSE
- 5.7 + 4 = 14 - 3TRUE FALSE
- 6.7 + 4 = 11 - 2TRUE FALSE
- 7.6 + 5 = 6 + 5TRUE FALSE
- 8.What number can you put in the box to make this a true number sentence?
- 8 + 4 = + 5

- 1)For each of the following, circle the larger or write “=” if they are equal.
a)1/61/8c) 3/61/2

- b)1/72/7d) 4/31
- 2)Choose the best estimate for the sum of 9/10 + 6/7 :
- a) 1b) 2c) 15d) 17e) 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?

143 789

+256- 463

435 294

+169- 157

- 365 519

- 296 403

- 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.

- 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).

- Children’s thinking
- Assessment
- About themselves

- “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.”

- “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.”

- “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.”

- “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.”

- “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.”

- “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.”

- “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.”

- “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.”

- “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.”

- “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."

- Share classroom data and conduct separate interviews
- Extend to include planning, conducting, and reflecting on a lesson based on assessment

- Surprised at how much modeling students need
- Still working on finding/creating more assessment tasks (e.g., more choices for lower primary students)

- What ideas from this session might you implement in your classes?
- What potential barriers might you encounter, and how might you overcome them?