Whats Your Problem

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Whats Your Problem?
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Ways to Modify Questions

• Given limited time
• Focus on three categories
• Not the only ones
• Prompt other methods

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Three Ways to Modify Questions

• Un-Doing
• Error Analysis
• Snap Shot

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Examples of the Three Types
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A Typical Textbook Item

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What might it look like .
as an Un-Doing problem?
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Un-Doing Example
Write and graph 2 quadratic functions that have
zeros x -12, x 3
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Un-Doing Example

• Write and graph a quadratic function that has
• one x-intercept.
• two x-intercepts.
• no x-intercepts

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What might it look like .
as a snap shot problem?
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Snap Shot Example
Yesterday in class we solved some equations
graphically. What was the equation we were
solving below? What was the solution?
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Snap Shot Example
Chelsea dropped her homework in a puddle. Help
her reconstruct the blurry areas. What question
was she answering?
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What might it look like .
as an error analysis problem?
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Error Analysis Example
Ralph Factor
Eleanor Solve
Sanna Solve
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Error Analysis Example
Diane Graph
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TAKS Item (9th grade 2004)
a. b. c. d.
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TAKS Item (10th grade 2004)
a. (-1, -9) and (0, -8) b. (0, -4) and (2, 0) c.
(-4, 0) and (2, 0) d. (0, 2) and (0, -4)
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TAKS Item (10th grade 2004)
a. (-5/2, 0) b. (-4, 0) c. (-5, 0) d. (-20, 0)
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Earlier with Roger
Earlier we looked at a series of graphs and
tables that modeled Roger throwing a baseball
upward from a downward moving elevator. Based on
that work, answer the following. The graphs and
tables below represent Roger starting from a
different height, throwing at a different initial
velocity.
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Earlier with Roger

• Match the graph with the appropriate table.
• What are the roots, solutions shown?

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Earlier with Roger

• When will Roger and the baseball be at the same
  height?
• Equations have ____ or ____, whereas functions
  have
• ______ or _______.

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Earlier with Roger
5. What is Rogers new starting height?
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Earlier with Roger
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Earlier with Roger
Bo was absent yesterday. When you started
telling him about the Roger-throwing-the-ball-elev
ator activity, he said, Whats the big deal?
Roots, zeros, solutions, x-intercepts they are
all the same thing. How do you respond to Bo? A
complete answer includes graphs, tables,
equations and discussion.
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Part 2 As A Class

• Everyone should have one problem from the set
• Discuss the problems in your group.
• Decide where the items would best fit.
• Post your problem
• Gallery walk - do you agree?
• Choose one to discuss as a group

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Discussion

• Un-Doing
• Error Analysis
• Snap Shot

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Advantages and Disadvantages

• Grading
• Conceptual understanding
• Memorization

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Write your own

• Choose a TEKS statement
• Write a typical question to assess it.
• Write it as an Un-Doing question
• Write it as an Error Analysis question
• Write it as a Snap Shot question

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Snap Shot Problems

• What are two ideas, processes, or representations
  that students mix up? Juxtapose them and ask
  which is which.
• What part of a large activity can you grab to
  assess if students got the gist of the large
  activity?

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Un-Doing Problems

• Can you start with the answer?
• Can you start in the middle?
• Can you change one constraint?
• Can you start with a different representation?
• Ask students to create or invent the beginning of
  a problem.

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Error Analysis

• What are the typical errors that students make?
• Pose an incorrect solution
• Ask students to explain what went wrong.
• Sometimes show the incorrect process, sometimes
  just show the incorrect answer

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The Assessment Principle

• Assessment should become a routine part of the
  ongoing classroom activity rather than an
  interruption.
• NCTMs Principles and Standards for School
  Mathematics (2000)

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Another Example

• The following slides begin with a different stem
  problem based on geometry and scale factors.

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A Typical Textbook Item

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What might it look like .
as an Un-Doing problem?
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Un-Doing Example
If the volume is increased by a factor of 8, what
is the change in the length of the side of a cube?
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Un-Doing Example
Below is Craigs work. What might have been the
question?
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What might it look like .
as a snap shot problem?
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Snap Shot Example
Yesterday in class we explored figures formed by
dilations. Abby dropped her paper in a puddle.
Help her fill in the missing titles and values.
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What might it look like .
as an error analysis problem?
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Error Analysis Example
The length of rectangle OLDR was enlarged by a
scale factor of 3 to create rectangle NEWS. If
OLDR has a width of 3 cm and perimeter of 16 cm,
what is the area of NEWS? Sandi wrote the
following. What do you say to her?
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TAKS Item (9th grade 2004)

• What scale factor was used to transform ?MNP to
  ?RST?

a. 1/3 b. 1/2 c. 2/7 d. 5
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TAKS Item (11th grade 2004)

• If the surface area of a cube is increased by a
  factor of 4, what is the change in the length of
  the sides of the cube?

a. The length is 2 times the original length. b.
The length is 4 times the original length. c. The
length is 6 times the original length. d. The
length is 8 times the original length.
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TAKS Item (11th grade 2004)
a. 36 ft. b. 42 ft. c. 108 ft. d. 126 ft.