TEKS

I intend to teach High School Mathematics.  Since this is a relatively broad category, I selected Algebra I for this blog post.

§111.32. Algebra I (One Credit).
(a)  Basic understandings.

1. Foundation concepts for high school mathematics. As presented in Grades K-8, the basic understandings of number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics are essential foundations for all work in high school mathematics. Students will continue to build on this foundation as they expand their understanding through other mathematical experiences.
2. Algebraic thinking and symbolic reasoning. Symbolic reasoning plays a critical role in algebra; symbols provide powerful ways to represent mathematical situations and to express generalizations. Students use symbols in a variety of ways to study relationships among quantities.
3. Function concepts. A function is a fundamental mathematical concept; it expresses a special kind of relationship between two quantities. Students use functions to determine one quantity from another, to represent and model problem situations, and to analyze and interpret relationships.
4. Relationship between equations and functions. Equations and inequalities arise as a way of asking and answering questions involving functional relationships. Students work in many situations to set up equations and inequalities and use a variety of methods to solve them.
5. Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model mathematical situations to solve meaningful problems.
6. Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, language and communication, and reasoning (justification and proof) to make connections within and outside mathematics. Students also use multiple representations, technology, applications and modeling, and numerical fluency in problem-solving contexts.

 (Source: Texas Education Agency at http://www.tea.state.tx.us/)

            The TEKS above will serve to guide me when I create new lesson plans for my students.  Though, time permitting, I will not limit myself to only the above general topics.  This TEKS will provide me with a goal so that I can ensure my students meet a minimum standard of knowledge.  The general expectations listed in the TEKS describe not only what will be tested over, but, in a perfect world, they also describe what students will need to know to be successful in their lives and future math classes.  Since the TEKS above is for Algebra I, it is even more important that my lesson plans are well rounded and complete as this class will be the foundation for all future math classes.


            Though I believe every point listed above is important, I’d select “Algebraic thinking and symbolic reasoning” as the most important.  Algebraic thinking is far more than simply being able to add common variables together or solving for x.  Algebraic thinking is a process of reasoning that can be applied every facet of life.  A large portion of discrete mathematics deals with logic and reasoning that can be used to describe anything and everything.  The foundation for discrete mathematics begins with algebraic thinking in junior high and high school.  It also teaches students to analyze problems logically, to dissect them, and then sometimes rebuild them into a useful answer.