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CRITERIA FOR QUANTITATIVE PROFICIENCY (QP) CERTIFICATION FOR COURSES

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Application for Course Certification in QP

In order to qualify for QP certification-half, a course should have a sizable component (one third of the course or more) that addresses four out of the following seven components:

1. Requires students to demonstrate proficiency in formal reasoning, including the ability to use deductive logic, and to understand abstract models, abstract reasoning and mathematical derivations.
This component is particularly important in a purely mathematical context perhaps, but also in that it is important for students to apply the other quantitative proficiencies flexibly, i.e. transfer them to other contexts.

2. Requires students to demonstrate proficiency in basic algebra.
Considering the notion of proficiency in basic algebra, courses taught for Quantitative Proficiency - Half should require students to demonstrate proficiency at manipulating equations or inequalities. We expect that the typical QP-Half course will require students to isolate variables, work with powers and roots, perform operations on both sides of an equation, etc., and to work with linear and non-linear functions of one variable, functions of more than one variable, and inequalities. Courses will, of course, introduce equations and inequalities within the context of the course material, but we expect that there will be some discussion of the general significance of the concepts. Students should learn the difference between independent versus dependent variables in mathematical relationships.

3. Requires students to demonstrate proficiency at representing mathematical relations graphically.
Considering next the notion of graphical proficiency, students should demonstrate proficiency at relating particular classes of equations (linear vs non-linear equations of a single variable, linear vs non-linear and equations of two or more variables) with different types of curves (i.e. straight vs curved lines or planar vs irregular surfaces). Students should demonstrate proficiency in the use of graphical representations of information and the ability to draw conclusions from these representations. Also of importance is understanding rate of change of one variable as a function of the rate of change of another variable corresponds to the appropriate slope or tangent of a relevant curve. Further, students should be able to relate different curves to the areas beneath or enclosed by the curve.

4. Requires students to formulate equations or inequalities from word problems, represent them graphically, and derive formulate equations or inequalities and word statements from graphical representations.
This general area requires students to formulate equations or inequalities from word problems and then to represent these relationships graphically. Students should be able to derive formulate equations or inequalities and word statements from graphs.

5. Requires students to formulate hypotheses, translate them into observations, etc.
This concerns testing those formulations against observations and/or data. The importance of understanding the relationships between graphs, equations, and word problems is critically important given the proliferation of graphical images and the ease of drawing graphs using readily available software packages.

6. Requires student to understand probability and statistical inference, including statistical significance.
This general area concerns probability and statistical inference. As part of this, students could fit curves to data, but this task is not, in our view, necessary. In fact, some committee members prefer to see curve-fitting done conceptually and by hand rather than relying upon software packages to fit curves.

7. Exposes students to the differences between correlation and causation, extrapolation and interpolation, and accuracy and precision.
The seventh general area, for example, might address dimensional reasoning: understanding and identifying the correct order of magnitude.

For QP Full certification, these concepts are to be woven into essentially all of the course material, so that students could not understand and master any of the fundamental concepts in the course without a high degree of proficiency with each of these concepts. In light of the fact that we do not require the calculus for QP certification, we cannot require notions of differentiation or integration for Full certification. Still, these ideas are addressed at some rudimentary level in statements #3 and #4 above.