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Assessment

Assessment. Mathematics TEKS Refinement Project. Assessment. Assessment. Lower level - reproduction, procedures, concepts, definitions. Assessment. Middle level - connections and integration for problem solving. Assessment.

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Assessment

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  1. Assessment Mathematics TEKS Refinement Project

  2. Assessment

  3. Assessment Lower level - reproduction, procedures, concepts, definitions

  4. Assessment Middle level - connections and integration for problem solving

  5. Assessment Higher level - mathematization, mathematical thinking, generalization, insight

  6. 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?

  7. Assessment Items - Where?

  8. 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?

  9. Your Assessment Items - Where? • Teacher questioning? • Homework? • Quizzes? • Tests?

  10. 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?

  11. 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

  12. The Assessment Principle Assessment should become a routine part of the ongoing classroom activity rather than an interruption. NCTM’s Principles and Standards for School Mathematics (2000)

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

  14. Our focus • Think about current classroom assessments • How can they improve?

  15. Take one typical assessment • What is the purpose of the assessment? • Where are the items in the pyramid? • Are you satisfied with the balance?

  16. 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

  17. 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]

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

  19. 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.

  20. 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.

  21. So, let’s look at some ways to improve …

  22. 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.

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