Ken Heller School of Physics and Astronomy University of Minnesota Assessing quantitative skills Supported in part by Department of Education (FIPSE), NSF, and the University of Minnesota Details at

First step - Setting Goals Skills Mathematical Logical Organizational Integration of Quantitative reasoning and concepts a broader knowledge base Second step - Determining the Initial State of the Learner Pre-tests Third step - Determining the Final State of the Learner Post-tests Assessment Types of Assessment Skill Characterization Quality Assurance (QA) Task Progress Pattern Recognition Rubrics

Characterization of Initial Sample Easy to administer and analyze Skills used in the class Math Diagnostic 30 question multiple choice test on math skills

Math Diagnostic Test Powers of ten (a) 4 x [10-20%](b) (d) 40 [51-63%](e) 4 x 10 7 = ? (c) 4 [20-28%] Triangles For this right triangle, cos  = ? a 3c 2b    (a) 2b/3c (b) a/3c (c) 2b/a [7-16%] (d) 3c/a [69-89%](e) a/2b Graphs The slope of the curve pictured is equal to: (a)0 m/s(b) 1/3 m/s [85-96%](c) 2 m/s(d) (d)3 m/s [4-12%](e) 6 m/s

Quality Assurance Easy to administer and analyze Correlates with desired learning Force Concept Inventory (FCI) for Mechanics 30 question multiple choice test on concepts

FCI Question 17 An elevator is being lifted up an elevator shaft at a constant speed by a steel cable, as shown in the figure. All frictional effects are negligible. In this situation, forces on the elevator are such that: (A)the upward force by the cable is greater than the downward force of gravity. (B)the upward force by the cable is equal to the downward force of gravity. (C)the upward force by the cable is smaller than the down ward force of gravity. (D)the upward force by the cable is greater than the sum of the downward force of gravity and a downward force due to the air. (E)None of the above. (The elevator goes up because the cable is shortened, not because an upward force is exerted on the elevator by the cable). Pre Post

Change to semesters FCI changes

Final State Pattern Recognition - Student Problem Solutions Initial State

Physics Approach – deciding on an appropriate way to use physics knowledge in the problem. Symbolic Translation of Physics Approach - deciding how to translate the physics approach into symbols that can be used in mathematics. Appropriate Mathematics – use of mathematical rules to reach an answer Logical Progression – an organized progress from the problem statement to an answer Rubric for evaluating problem solving

Logical Progression (entire problem solution) 0 Nothing written can be interpreted as logical progression. 1 Haphazard solution with obvious logical breaks. 2 Part of the solution contradicts stated principles, the constraints shown in the explicit statement of the problem situation, or the assumptions made in another part of solution. 3 Solution is logical but does not achieve the target quantity or haphazard but converges to the target. 4 Solution is organized but contains some logical breaks. 5 Progress from problem statement to an answer includes extraneous steps. 6 Consistent progress from problem statement to answer.

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