Assessment

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Assessment

• Mathematics TEKS Refinement Project

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Assessment
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Assessment
Lower level - reproduction, procedures, concepts,
definitions
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Assessment
Middle level - connections and integration for
problem solving
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Assessment
Higher level - mathematization, mathematical
thinking, generalization, insight
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Consider the following

• A rectangular prism is 2cm x 4cm by 6cm. One
  dimension is enlarged by a scale factor of 3.
  What is the volume of the enlarged figure?
• A rectangular prism is 2.7cm x 0.45cm by
  609.01cm. One dimension is enlarged by a scale
  factor of 3.5. What is the volume of the
  enlarged figure?
• When a figure is dilated by a scale factor k to
  form a similar figure, the ratio of the areas of
  the two figures is ___ ___ .
• A certain rectangular prism can be painted with n
  liters of paint. The factory enlarged it by a
  scale factor of 3 to make a similar prism. How
  much paint do they need to paint the larger box?

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Assessment Items - Where?
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Assessment Items - Where?

• A rectangular prism is 2cm x 4cm by 6cm. One
  dimension is enlarged by a scale factor of 3.
  What is the volume of the enlarged figure?
• A rectangular prism is 2.7cm x 0.45cm by
  609.01cm. One dimension is enlarged by a scale
  factor of 3.5. What is the volume of the
  enlarged figure?
• When a figure is dilated by a scale factor k to
  form a similar figure, the ratio of the areas of
  the two figures is ___ ___ .
• A certain rectangular prism can be painted with n
  liters of paint. The factory enlarged it by a
  scale factor of 3 to make a similar prism. How
  much paint do they need to paint the larger box?

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Your Assessment Items - Where?

• Teacher questioning?
• Homework?
• Quizzes?
• Tests?

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Guiding Questions

• How can I formulate balanced assessments?
• How can I ask questions for which students can
  not just memorize their way through? How can I
  ask questions that demand that students actually
  understand what is going on?
• How can I ask questions that students can learn
  from while answering?
• How can I make sure that I have higher level
  reasoning questions and not just more
  computationally difficult questions?

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Passive Assessment Expertise

• Understanding the role of the problem context
• Judging whether the task format fits the goal of
  the assessment
• Judging the appropriate level of formality (ie.,
  informal, preformal, or formal)
• Judging the level of mathematical thinking
  involved in the solution of an assessment problem
• Feijs, de Lange, Standards-Based Mathematics
  Assessment in Middle School

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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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TAKS Item 9th grade 2004
Tony and Edwin each built a rectangular garden.
Tonys garden is twice as long and twice as wide
as Edwins garden. If the area of Edwins garden
is 600 square feet, what is the area of Tonys
garden?
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Our focus

• Think about current classroom assessments
• How can they improve?

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Take one typical assessment

• What is the purpose of the assessment?
• Where are the items in the pyramid?
• Are you satisfied with the balance?

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Changing existing questions

• to higher leveling reasoning
• to concept questions
• maintain balance between concept and skill
  questions
• shift focus from what students do not know to
  what they do know

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Targeted Content

• (A.2) Foundations for functions. The student uses
  the properties and attributes of functions. The
  student is expected to (D) collect and organize
  data, make and interpret scatterplots (including
  recognizing positive, negative, or no correlation
  for data approximating linear situations), and
  model predict, and make decisions and critical
  judgments in problem situations. vocabulary of
  zeros of functions, intercepts, roots

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Targeted Content

• (A.4)(C) connect equation notation with function
  notation, such as y x 1 and f(x) x 1.

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Targeted Content

• (G.11) Similarity and the geometry of shape. The
  student applies the concepts of similarity and
  justifies properties of figures and solves
  problems. The student is expected to (D)
  describe the effect on perimeter, area, and
  volume when one or more dimensions of a figure
  are changed and apply this idea in solving
  problems.

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Targeted Content

• (G.6) Dimensionality and the geometry of
  location. The student analyzes the relationship
  between three-dimensional geometric figures and
  related two-dimensional representations and uses
  these representations to solve problems. The
  student is expected to C) use orthographic and
  isometric views of three-dimensional geometric
  figures to represent and construct
  three-dimensional geometric figures and solve
  problems.

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So, lets look at some ways to improve
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Consider the following

• Factor x2 - 5x - 6
• Factor 36x2 45x - 25
• A soccer goalie kicks the ball from the ground.
  It lands after 2 seconds, reaching a maximum
  height of 4.9 meters. Write the function that
  models the relationship (time, height).
• Define root of an equation.