Addressing Assessment in an Elementary Mathematics Methods Course: Helping Prospective Elementary Teachers Use a Variety of Assessments to Enhance Children

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Addressing Assessment in an Elementary
Mathematics Methods Course Helping Prospective
Elementary Teachers Use a Variety of Assessments
to Enhance Childrens Mathematics Understanding

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

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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

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How We Address Assessment in Our Course

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

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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

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What Our Students Believe About Assessment

• Its not fair to assess if they (children)
  havent been taught it.
• If they (children) dont do well on an
  assessment, its either because they havent been
  taught it or because they dont get it--its not
  the teachers 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.

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Your Turn

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

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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.

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Overview of Embedded Assessment Assignment

• Whole-Class Assessment
• Individual Student Interviews

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Embedded AssessmentWhole-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.

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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
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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?

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Fractions - Identify One Half
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Computation and Place Value

• 143 789
• 256 - 463
• 435 294
• 169 - 157
• 365 519
• 743 -242
• 296 403
• 754 - 124

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Identifying Triangles
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Identifying Rectangles
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Completed Table for Rectangle Task
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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
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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.

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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).

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What Our Students Learned From This Assignment

• Childrens thinking
• Assessment
• About themselves

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What Our Students Learned About Childrens
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.

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More About Childrens 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.

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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.

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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
  childs capabilities. It was a revelation that
  abilities may be measured through many different
  ways.

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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.

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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.

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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.

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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.

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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.

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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."

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Reflections on Assignment Modifications

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

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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)

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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?