Learning to Teach High School Mathematics in Philadelphia
- 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
- The conflicting notions of conducting classes that emphasize skill versus critical thinking.
- Varying levels of ability within the classroom.
- 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. Developing critical thinking skills helps students to analyze situations and make thoughtful decisions. Developing competence in this area is more long-term 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 accommodating these varying levels of ability will create a classroom environment in which students are bored, frustrated, and more apt to behaving inappropriately.
- Many students who are easily frustrated and "afraid" of mathematics may not attempt problems that seem to be out of their league. Unfortunately, such students may avoid learning mathematics because of low self-esteem.
What can be done? Ideas for working towards a mathematics classroom that promotes critical thinking, cooperative learning, and is comfortable for all students
Students tend to have different mathematical learning styles. Some may need to work step by step, others may learn best through conversation and visuals, and others may learn best when they see the big picture. Knowing this, a teacher must attempt to accommodate different learning styles so as to give each student an opportunity to succeed.
Ideas for Activities
- 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 students create their own timeline for due dates along with consequences for not following through. When finished, let the students 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.
In cooperative learning, students work together and are responsible not only for their own learning, but also for the learning of their teammates.
Ideas for Activities
- 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 thoughts concerning the problem. At this stage, students should discuss possible solution routes and work towards execution.
In guided discovery, students develop an understanding of a mathematical topic on their own through a step-by-step discovery of new information.
Ideas for Activities
Building a working relationship is essential in helping students who have low self-esteem in their skills as mathematicians. Demonstrate that you care about your students and that you are only there to help them learn.
Tips for relationship building
- Provide positive feedback whenever a student shows improvement.
- 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 him or her to the right answer.
- Ask students about their lives outside the realm of mathematics.
Questions or concerns that can be answered by future editors
- How can we provide students with support without teaching them "learned helplessness"?