Blog Post #6: Discussion of my Content Area Standard

As I discussed in my earlier post, I've chosen the following content standard as my focus in this class:

Algebra and Functions
Content Standard 9: Students will use algebraic skills and concepts, including functions, to describe real-world phenomena symbolically and graphically, and to model quantitative change.
	a.     model and solve problems that involve varying quantities with variables, expressions, equations, inequalities, absolute values, vectors and matrices
	b.     model real-world phenomena using polynomial, rational, trigonometric, logarithmic and exponential functions, noting restricted domains
	c.     analyze the effect of parametric changes on the graphs of functions
	d.     translate among and use tabular, symbolic and graphical representations of equations, inequalities and functions
	e.     develop, explain, use and analyze procedures for operating on algebraic expressions and matrices
	f.     solve equations and inequalities using graphing calculators and computers as well as appropriate paper-and-pencil techniques

 This standard applies to both my upper and middle school classes, since both deal with various algebraic concepts and strive to relate them practical applications. Even better, the focus on modeling, relation to real-world examples, graphing, and technology (see f above) all lend themselves nicely to the content of our course.

Visual learning is key to understanding these concepts. Although I aim to instill the notion that graphical representations are just a TOOL for understanding algebra (ideal for visual learners, but not for others), many students struggle to grasp the notion of derivative without visual aids. Integration (typically defined as area under a curve) is even more challenging without a graph or picture. And these graphs are often painstaking to create, and impractical to generate accurately. But tools like TI calculators or CAS emulators allow for easy interface and effective visualization.

These graphical tools satisfy many of the requirements of this standard. But I think that there is room for technology in the simple, everyday organization of my classroom. As I noted in an earlier post, inspiration could serve as a means of relating ratios, rates, and percents--a topic that confuses some students. Even the complex notions of limit, derivative, and integral (with their respective applications) get confused. A simple outline relating these topics and noting their differences might help the students maintain their grasp on the proverbial forest, despite the trees.

Inspiration would not really lend itself well to analyzing algebraic transformations or parametric changes, but this organization could prove useful. And were I to ever teach a combinatorics or probability course, the tree-building functionality could prove quite appropriate for problem-solving.

In short, the more technology I can utilize to convey concept visually, the better. Whether these concepts are basic notions of arithmetic or advanced topics in Calculus, the new graphical and imagining tools I've encountered offer additional options for shaping my curricula.