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

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

How We Address Assessment in Our Course

Purposes of assessmentTypes of assessmentUsing assessment to guide

instruction

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

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.

Your Turn

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

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.

Overview of Embedded Assessment Assignment

Whole-Class Assessment

Individual Student Interviews

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.

Algebraic ReasoningAre 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

Fraction Comparison and Computation1) 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?

Fractions - Identify One Half

Computation and Place Value

143 789+256 - 463

435 294 +169 - 157

365 519 +743 -242

296 403 +754 - 124

Identifying Triangles

Identifying Rectangles

Completed Table for Rectangle TaskStudent 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total Percent

CorrectSofiya 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 13 87%Daniel 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 13 87%Kevin 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 13 87%Jacob 1 0 0 1 1 0 0 0 1 0 1 1 1 1 1 9 60%Erica 1 0 0 1 1 0 0 0 1 0 1 1 1 0 1 8 53%Erin 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1 8 53%Will 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 11 73%Alex. 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 10 67%Sami 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 10 67%Cameron 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 10 67%Spencer 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 11 73%Michael 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 5 33%Taylor 1 0 0 0 1 0 0 1 1 0 1 1 1 0 1 8 53%Nicole 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 9 60%Vanessa 1 0 0 1 0 0 0 1 1 0 1 1 1 0 1 8 53%Martha 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 7 47%Ian 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 5 33%Caleb 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 13 87%Total Correct 17 1 6 17 12 4 0 12 18 4 17 17 15 14 18Percent Correct 94% 6% 33% 94% 67% 22% 0% 67% 100% 22% 94% 94% 83% 78% 100%

Task: Geometry Assessment (Identifying Rectangles)

Items Organized by Percent Correct

Percent Correct Item Number

100% 9

100% 15

94% 1

94% 4

94% 11

94% 12

83% 13

78% 14

67% 5

67% 8

33% 3

22% 6

22% 10

6% 2

0% 7

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.

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).

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

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.”

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.”

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.”

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.”

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.”

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.”

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.”

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.”

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.”

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."

Reflections on Assignment: Modifications Share classroom data and conduct

separate interviews Extend to include planning, conducting,

and reflecting on a lesson based on assessment

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)

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?