DEV Description:

Teaching developmental algebra from a function approach means using function, function representation, and function behaviors to teach algebraic concepts and skills. Formal f(x) function notation is delayed because it is not integral to the teaching/learning process during the initial stages. Function notation is introduced at an appropriate time after other representations are utilized.

The above mentioned definition of a function approach implies that function is an underlying theme throughout a course in developmental algebra – not just studied as a chapter. It also suggests that a “function implementation module” is needed before any traditional algebra is taught. The module provides content that begins with real-world numeric representations of functions and leads to students learning to move freely through representations with a graphing calculator. This is followed by an analysis of the geometric behaviors of functions integrated with studying parameter-behavior connections. The implementation module facilitates teaching of a slightly revised and re-ordered traditional curriculum that allows us to capitalize on the cognitive learning concepts of associations, pattern recognition, attention, visualizations, priming, meaning, and an enriched teaching environment. These ideas play an extremely important role in teaching and learning of developmental algebra, and are naturally and seamlessly integrated into the mathematics and pedagogy through using a function approach implemented with a graphing calculator. A graphing calculator is required for all students at all times – both in the implementation module and throughout the algebra course.

Richard P. Feynman was a Nobel Laureate in physics, and in his 1985 book “Surely You’re Joking Mr. Feynman!” he makes the following observation: “I don’t know what’s the matter with people: they don’t learn by understanding; they learn by some other way – by rote, or something. Their knowledge is so fragile! … this kind of fragility is, in fact, fairly common, even with more learned people.” So, learning through memorizing is, in effect, not learning. Referencing education in Brazil, 40 or so years ago, Feynman made the following observations, “After a lot of investigation, I finally figured out that the students had memorized everything, but they didn’t know what anything meant.” … “Everything was entirely memorized, yet nothing had been translated into meaningful words.” … It was pitiful! All the work they did, intelligent people, but they got themselves into this funny state of mind, this strange kind of self-propagating “education” which is meaningless, utterly meaningless!”

These thoughts provide a philosophical foundation for your teaching – students must be taught in a way that promotes understanding of the mathematics taught. We are interested in our students understanding developmental algebra, as opposed to just memorizing algorithms. We can accomplish this goal by teaching algebra through using a function approach.

The course also includes the use of TI-Connect software, apps, testing and pedagogical issues, and Internet information. Many of the AMATYC Crossroads in Mathematics - Standards for Introductory College Mathematics Before Calculus standards have been implemented in the course.

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