When creating assessments it is important to make sure that they are valid and that they accurately support and reflect upon the learning outcome being assessed. Kubiszyn and Borich (2010) provide a wealth of material when it comes to creating effective assessments.
The assessment activities recommended for my first two learning outcomes meet one of the authors' key criteria: applying "previously learned principles or procedures to novel situations" (p. 147). Having the students reproduce the math from the work of others provides the opportunity for students to "use the principle or procedure with new information" (p. 147).
Fortunately, when it comes to testing for Learning Outcome 3, creating written tests for math lessons is far less demanding than those for other subjects. As math problems generate concrete answers, it is relatively easy to avoid many of the pitfalls of written tests, including "too many correct responses" and "ambiguous lists" (p. 136).
The suggested essay question also meets the requirements as set forth by the authors, who state, "the well-constructed essay item…" calls for "the student to organize, integrate and synthesize knowledge… and to be original and innovative in problem solving" (p. 158). Applying the skills learned with the objects used in the matrices to scenarios involving different quantities and objects provides the opportunity for just the kind of synthesis the authors call for.
Reference
Kubiszyn, T. & Borich, G.. (2010). Educational testing & measurement: Classroom application and practice (9th ed.). John Wiley & Sons, Inc: Hoboken, NJ.
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