September 29, 2010

Assessment with CAS

The article on using a Computer Algebra System for teaching mathematics had several major points. The introduction was about how CAS changes teaching and learning of math. In a classroom where students are using CAS, the topics, focus within topics, and goals of lessons will change. Lessons are no longer algorithmic but focus on using operations to understand meaning. The article also mentioned two goals for teaching: to develop theory of mathematical concepts, and to use mathematical concepts in real-world models and applications. Teachers should try to construct exam questions to meet these goals. There were two schemes for analyzing exam questions.

  1. The first scheme was based on testing skills and abilities of students, and took a more educational approach. It measured the educational value of problems as questions on an exam. The educational scheme had five categories.
    1. The CAS-Insensitive Questions did not make very much use of the CAS, and computation plays a minor role.
    2. The Questions Changing with Technology made a big difference once the CAS was introduced because time needed to solve the problem was greatly reduced.
    3. The Questions Devalued with CAS involved rare tricks and hard-to-remember equations to solve, so the CAS appeared insignificant.
    4. The Questions Testing Basics became trivial when using CAS because the answer would be produced immediately; however, the student needed knowledge about syntactical structure.
    5. The last category, Rediscovered Questions, are geared to support creativity, fluency, and flexibility, but are rare because of the difficulties in evaluating and grading.
  2. The second scheme was based on the usefulness of CAS and took a rather technical approach. It measured the role of technology for answering a question. The technical scheme also had five categories, grouped into how significant CAS was in solving the problem, and how well the student should be familiar with CAS.
    1. In terms of significance, Primary Use needed CAS as a major activity,
    2. while Secondary Use did not facilitate CAS as strongly.
    3. Regarding familiarization, Advanced Use required in-depth knowledge of CAS,
    4. while superficial knowledge of CAS suffices for Routine Use.
    5. CAS is of very little help for questions in the last category, No CAS Use.

After discussing different types of problems in different categories, the article compared the two and made some observations about CAS. It facilitates the two teaching goals discussed above, it reveals educational value of exam questions, forces teacher to be conscious about exam questions, and revives the “forgotten” questions. When choosing exam questions, teachers need to keep the aforementioned goals in mind, but also question how they test the student. Exam questions should test general abilities rather than computational skills. In any testing environment the act of understanding and the act of overcoming an obstacle are equally important in the learning process. In addition, intellectual concentration and emotional tension are present and culminating, which creates a learning situation per se.


  • Kokol-Voljc, V. (year unknown). Exam questions when using CAS for school mathematics teaching. publication unknown.

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