Teaching High School Mathematics

Introduction

 * This page should be used as a reference for those learning to teach high school mathematics. The information should primarily focus on overcoming difficulties that can arise in the classroom.  Please feel free to edit and contribute any ideas that you might have.  Ideas for activities and lesson plans are greatly appreciated.

Difficulties in teaching high school mathematics

 * 1) The conflicting notions of conducting classes that emphasize skill versus critical thinking.
 * 2) Varying levels of ability within the classroom.
 * 3) Mathematics as a source of anxiety for students who attribute their success in mathematics to their ability to get the right answer.

Why we need to overcome these difficulties

 * The difficulties mentioned above inhibit students from learning at their greatest potential. Memorizing formulas and procedures may be useful in easing the process of problem solving, but if not continually reinforced, most of what was memorized may be lost.  On the other hand, developing critical thinking skills helps students to analyze situations and make thoughtful decisions.  Developing competence in this area is more longterm and useful as students grow to be adults because these are skills that can be used in all aspects of life.


 * In a classroom of about thirty students, you will have quick learners, moderate learners, and slow learners. Not accomodating these varying levels of ability will create a classroom environment in which students are bored, frustrated, and more apt to behaving inappropriately.


 * Many students are easily frustrated and "afraid" of mathematics may not attempt problems that seem to be out of their league. Unfortunately, students like these will avoid learning mathematics because of low self-esteem.

Ideas for Activities

 * 1) Independent Study
 * For students who are catching on quickly, give them the opportunity to do an independent study. Have them take a post chapter test to see how competent they are in the material.  If they pass, give them a set of guidelines that indicate required components of the project and then let them design the rest.  Have them create their own timeline for due dates along with consequences for not following through.  When students are finished, let them present their project to the class.  After the class completes a chapter, all students should be required to take the test.
 * Offer guidelines that vary in structure so that students who are slower learners have the opportunity to participate in an independent study as well. Provide them with more structure so that the project is easier to accomplish.

Ideas for Activities

 * 1) Pair Sharing
 * When presented with a problem requiring some critical thinking, give students a few minutes to work on it on their own. They should focus on understanding what the problem is asking for, the given information, and any possible solution routes.  Afterwards, ask students to get into pairs to compare what they think about the problem.  At this stage, students should discuss possible solution routes and work towards executing one of them.

Relationship Building

 * To help students who have low self-esteem in their own skills as mathematicians, building a working relationship is essential. Demonstrate that you care about your students and that you are only there to help them learn.

Tips for relationship building

 * 1) Provide positive feedback whenever a student shows improvement.
 * 2) Avoid embarrassing a student. When working out a problem on the board and a student has offered an incorrect answer, ask leading questions to guide students to the right answer.
 * 3) Ask students about their lives outside the realm of mathematics.

Questions or concerns that can be answered by future editors

 * 1) How can we provide students with support without teaching them "learned helplessness"?