Mathematics Constructed Response

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Mathematics Constructed Response
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Session Goals

• Participants will
• acquire a process for successfully (efficiently
  and reliably) scoring math constructed responses
• develop a better understanding of the rubric(s)
  used in the scoring of math constructed responses
• determine the attributes of a thorough
  constructed response

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Constructed Response Purposes

• Writing elicits student thinking. Students are
  forced to reflect on what has been learned.
  Research on metacognition suggests that thinking
  about thinking helps to cement ideas and concepts
  into memory. It also helps to clarify ideas.
  Writing in math also strengthens writing in
  general.
• Terry Coon, 6th-grade math teacher
• Mathematics Teaching in the Middle School, 2004

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Constructed Response Format

• Step A - Assess student understanding of the
  content skill/concept
• Step B - Assess student ability to communicate
  process or reasoning

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Step A

• Is scored right or wrong
• Is scored for the content standard which it
  addresses
• Any work that is put in this area can be used for
  Part B- Tell students to write all of their work
  here and not on scrap paper

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Step B

• Is scored using the Rubric 2/1/0 for BCR or
  3/2/1/0 for ECR
• Is scored for Processes of Mathematics
• When scoring Step B, the answer to Step A is
  also considered.
• Step A, however, whether right or wrong does not
  dictate the score to Step B.

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How Questions

• How questions ask children to explain the
  procedures/processes they use in finding their
  answer to Step A.
• Students should follow a pattern of First IThen
  I Finally I
• Have students focus on Can the reader of my
  answer walk away from the problem and follow the
  directions/procedures that I wrote and complete
  the problem?

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Why Questions

• Why questions ask children to explain their
  reason for answering Step A as they did. This
  requires a justification or defense of their
  answer.
• To respond to a Why question, students need to
  make sure that they tell definition of terms and
  verify their answer with specific numbers.
• Students should focus on Can the reader of my
  answer know that I understand the problem and
  explain the math vocabulary?

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• Change to BCR Format
• THIS WILL ONLY OCCUR ON SOME ITEMS OF THE 2005
  TEST FORMS
• Grade 3 and 4 Current form-
• Use what you know about (fractions) to explain
  how you found your answer. Use words and/or
  numbers in your explanation. 
• Or
•  Use what you know about (fractions) to explain
  why your answer is correct. Use words and/or
  numbers in your explanation.

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• New form-
• Explain how you found your answer.
• Use what you know about (fractions) in your
  explanation.
• Use words and/or numbers in your explanation.
•  
• Or
•  
• Explain why your answer is correct.
• Use what you know about (fractions) in your
  explanation.
• Use words and/or numbers in your explanation.
•  

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•  Grade 5 and 6
• Current form- Same as above
•  
• New form-
• Explain how you found your answer. (or Explain
  why your answer is correct.) Use what you know
  about (fractions) in your explanation. Use words
  and/or numbers in your explanation.
• Grades 7 and 8 Remain the same

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Constructed Response Instructional Purposes

• Assess mastery
• Monitor growth (diagnosis)
• skill/concept
• communication
• Encourage improvement

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Constructed Response Scoring Steps

• Review the task independently respond to the
  task in writing
• Review the rubric (BCR or ECR)
• Determine the components of a 2 response
• Group student responses into high/medium/low
  categories
• Score papers according to the components of a 2
  response (adjusting as needed)

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Writing a 2 Response

• Each grade pick one BCR question to work on
  together
• Individually write a response that you think
  would be given a score of 2
• Share your responses and decide on the best
  response of a 2
• Make a good copy of that response
• If time, do another question

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Constructed Response

• Implications for instruction?
• Changes to this particular item?
• Key points you would make about constructed
  responses?
• Questions you would like to continue to
  investigate?

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Classroom Strategies
Use what you know about
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Other Reminders

• This is not MSPAP!- Dont rewrite the prompt
• Teach the vocabulary-
• Avoid only teaching gimmicks or tricks- This
  could lead to partial scores
• Pictures can be used in Part B to support an
  answer- it will never say use pictures but they
  may be used
• Put all work in the box- Even checked
  work-Scorers read all of Part A and B for the
  answer to Part B.

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Bridging to Practice

• Pick an idea that came up today that you found
  particularly interesting. What is your current
  thinking about this idea?
• What are one or two things that you will go back
  and pursue to move yourself along with this idea?