Brief Constructed Responses

1
(No Transcript)
2
WHAT IS BCR and EC R

• BCR basic constructed response
• ECR extended constructed response

3
How is a Math BCR scored?

• Score 2 - The response demonstrates a complete
  understanding and analysis of a problem.
• - Application of a reasonable strategy in the
  context of the problem is indicated.
• - Explanation of and/or justification for the
  mathematical process(es) used to solve a problem
  is
• clear, developed, and logical.
• - Connections and/or extensions made within
  mathematics or outside of mathematics are clear.
• - Supportive information and/or numbers are
  provided as appropriate.
• Score 1 The response demonstrates a minimal
  understanding and analysis of a problem.
• - Partial application of a strategy in the
  context of the problem is indicated.
• - Explanation of and/or justification for the
  mathematical process(es) used to solve a problem
  is
• partially developed, logically flawed,
  or missing.
• - Connections and/or extensions made within
  mathematics or outside of mathematics are partial
  or
• overly general, or flawed.
• - Supportive information and/or numbers may or
  may not be provided as appropriate.
• Score 0 - The response is completely incorrect,
  irrelevant to the problem, or missing.
• Note 1 Explanation refers to students' ability
  to communicate how they arrived at the solution
  for an item using the language of mathematics.
• Note 2 Justification refers to students' ability
  to support the reasoning used to solve a problem,
  or to demonstrate why the solution is correct
  using mathematical concepts and principles.

4
Kid-Friendly Checklist
5
How is a Math ECR scored?

• Score 3 - The response demonstrates a
  comprehensive understanding and analysis of a
  problem.
• - Application of a reasonable strategy in the
  context of the problem is indicated.
• - Explanation of and/or justification for the
  mathematical process(es) used to solve a problem
  is
• clear, fully developed, and logical.
• - Connections and/or extensions made within
  mathematics or outside of mathematics are clear
  and
• stated explicitly.
• - Supportive information and/or numbers are
  provided as appropriate. 3
• Score 2 - The response demonstrates a general
  understanding and analysis of a problem.
• - Application of a reasonable strategy in the
  context of the problem is indicated.
• - Explanation of and/or justification for the
  mathematical process(es) used to solve a problem
  is
• feasible, but may be only partially
  developed.
• - Connections and/or extensions made within
  mathematics or outside of mathematics are partial
  or
• overly general, or may be implied.
• - Supportive information and/or numbers are
  provided as appropriate.
• Score 1 - The response demonstrates a minimal
  understanding and analysis of a problem.
• - Partial application of a strategy in the
  context of the problem is indicated.
• - Explanation of and/or justification for the
  mathematical process(es) used to solve a problem
  is
• logically flawed or missing.
• - Connections and/or extensions made within
  mathematics or outside of mathematics are flawed
  or

6
ECR Sample
7
Sample Response
Sample Student Response 1
                                                                                                                                                                                                                                                                                                                            
Sample Student Response 1
                                                                                                                                                                                                                                                                                                                            
8

• Score for Sample Student Response 1
• Step A - Content (Knowledge of Algebra, Patterns,
  and Functions) 0
• Step B - Processes of Mathematics 1
• Annotation for Step B, Using the Rubric In this
  response, the student explains the first step in
  solving the problem, and by indicating a relevant
  starting point on the number line ("I went over
  to two"), this response demonstrates a minimal
  understanding and analysis of number lines.

9
Sample Response
Sample Student Response 2
                                                                                                                                                                                                                                                                                                                            
10

• Score for Sample Student Response 2
• Step A - Content (Knowledge of Algebra, Patterns,
  and Functions) 1
• Step B - Processes of Mathematics 1
• Annotation for Step B, Using the Rubric The
  student repeats the answer in the space for Step
  B, so no credit in Step B is derived from the
  second page of this response. However, the
  correctly plotted point on the number line in
  Step A is a partial explanation of the
  mathematical process used to solve the problem.
  Admittedly, the explanation uses no words, only
  symbols, but the symbol (the point) drawn on the
  number line is correct and relevant to the
  problem. Therefore, Step B is considered to
  demonstrate a minimal understanding and analysis
  of the problem.

11
Sample Response
Sample Student Response 3
                                                                                                                                                                                                                                                                                                                            
Sample Student Response 3
                                                                                                                                                                                                                                                                                                                            
12

• Score for Sample Student Response 3
• Step A - Content (Knowledge of Algebra, Patterns,
  and Functions) 1
• Step B - Processes of Mathematics 2
• Annotation for Step B, Using the Rubric The
  response demonstrates a general understanding and
  analysis of the problem. In the first part of the
  response, the explanation for the mathematical
  process used to solve the problem ("put lines
  inbetween all of the smaller lines, each
  represents marked the first one") is partially
  developed, as the student never justifies why
  each line represents . The student simply lists
  the steps taken to solve the problem, without
  specifying why those steps were correct. In the
  second part of the response, the student fully
  justifies the underlying mathematics ("Because
  number lines never change the location of a
  number").

13
Sample Response
Sample Student Response 4
                                                                                                                                                                                                                                                                                                                            
Sample Student Response 4
                                                                                                                                                                                                                                                                                                                            
14

• Score for Sample Student Response 4
• Step A - Content (Knowledge of Algebra, Patterns,
  and Functions) 1
• Step B - Processes of Mathematics 2
• Annotation for Step B, Using the Rubric This
  response demonstrates a general understanding and
  analysis of the problem. The student describes
  the mathematical process of plotting the point
  ("2 wholes so go past 2 on the number line put
  the point half way between 2 and 2 ") and
  logically justifies why that process is correct
  ("number line is split in 's is half of ").
  However, the second part of the response is
  incorrect, ("point would need to be at 2½ or a
  equivalent fraction point's location will
  change").

15
Sample Response
Sample Student Response 5
                                                                                                                                                                                                                                                                                                                            
16

• Score for Sample Student Response 5
• Step A - Content (Knowledge of Algebra, Patterns,
  and Functions) 1
• Step B - Processes of Mathematics 3
• Annotation for Step B, Using the Rubric This
  response demonstrates a comprehensive
  understanding and analysis of the problem. The
  mathematical process used to solve the problem
  ("I put after the 2 but before the mark")
  comes with a justification that is fully
  developed and logical ("because it is less than
  first line shows "). In addition, the
  justification for the mathematical process used
  to solve the second part of the question is fully
  developed, logical, and clear, given the words
  ("the halfway point is still the same") and
  symbols (comparison of the two number lines drawn
  in Step B), which show that 2 is equivalent to 2
  and that 2 is equivalent to 2 .

17
Sample Response
Sample Student Response 6
                                                                                                                                                                                                                                                                                                                            
Sample Student Response 6
                                                                                                                                                                                                                                                                                                                            
18

• Score for Sample Student Response 6
• Step A - Content (Knowledge of Algebra, Patterns,
  and Functions) 1
• Annotation for Step A, Using the Rubric The
  point is plotted correctly.
• Step B - Processes of Mathematics 3
• Annotation for Step B, Using the Rubric This
  response demonstrates a comprehensive
  understanding and analysis of the problem. The
  mathematical process used to plot the point is
  explained ("2 is halfway between 2 and 2 ") and
  justified clearly and logically ("if 2 fractions
  have the same numerator and one's denominator is
  double the other fraction the one with the
  smaller denominator is 2 the other fraction").
  In the second part, the explanation for why the
  location of the point will not change is fully
  developed, logical, and clear ("even if the
  number line is changed the value of 2 stays the
  same point represents the value of 2 also
  constant."

19
How to Help

• The best way to prepare for a BCR or ECR is to
  ask your child to explain everything that they
  are doing to solve the problem. Pretend like the
  person they are talking to knows absolutely
  nothing about how to solve a math problem.
• Its not enough to just say what they did they
  must also say WHY they did it.

20
Time to Discuss

• Using the rubric, sample responses, and your
  childs response, talk with your child
• What are things he/she is doing well?
• What are things he/she needs to work on?
• What was he/she missing?
• What should he/she continue to do?
• If time, work with your child to fix his/her
  response.

21

• Questions?
• Comments?
• Please complete the feedback form so that we may
  improve this event for the future.
• Thank you for supporting your childs education.
  We truly appreciate all of your support!