Teaching large Math classes

Teaching Mathematics courses in large classes
(applicable also for Physics, Chemistry, Engineering, Computer science, etc.)

The critical task in teaching large mathematics class is to maintain student attention with a logical presentation of the concepts, and actively involving their thinking process. There are several good strategies to be used in mathematics large classes to encourage active engagement:

1. Active practice: “Math is not a spectator sport” – give students notes sheets with space to practice the problems you teach at the blackboard. Include essential terms and formulas and ask students to fill in definitions and problems that are worked in class.

2. Time to practice: when working on a problem in class give time to your students to work on the problem individually, then ask them to compare their work with the person sitting next to them. Display your own solution or ask a student to come to the blackboard and present their results. Discuss the process and any errors and ask questions on other modalities of solving the problem and discuss the errors. One way to do this is to distribute transparencies around the room and ask students to work in groups to solve the problem then post several transparencies on the projector calling attention to correct solving methods and eventual errors. Always discuss the errors: why was that error made, what was the thinking process in the error as compared to the correct thinking process. Discuss what are the common mistakes students make in that type of problem.

3. Warm-ups: as students enter in class have a problem on the board/overhead to be solved. This will keep the attention focused, the class silent and bring the attention to the topic of study for the day. Ask for volunteers to put their responses on the board. A good way to keep everyone involved in by not asking for volunteers but randomly calling on students, this will make sure that everyone is working on the warm-up.

4. Group work: Put a multiple choice question on the board/overhead. The question should test understanding of a particular concept. Ask students to vote on the correct choice. This helps you determine whether or not more discussion is needed on that particular concept.

5. Practice and review: Assign carefully chosen practice problems for homework, or for quiz. To keep students from simply doing the exercise for a correct answer ask questions that test their understanding “Explain what type of problem is this?” “Explain what type of concepts (or definitions or theorems or formulas) you need to use in order to solve this problem. Explain why is that the correct choice.” “Define variables that will help you to solve this problem. Describe what your first step will be.”

6. Interaction: Always use an interactive lecture style. When you ask a question (and that should be often!) pause long enough for students to think about the question and suggest an answer. Ask first the question and then call on random students. Do not jump to the next student if one does not know the correct answer. Give prompts, and help, ask the class to suggest a prompt NOT the correct response. Put only the conditions of a theorem on the board then turn to class and ask “What do you think we can conclude?”

Strategies to develop problem solving skills

Let students see: instead of posting on the overhead a ready solved problem solve it in front of your students. Talk thru the steps, and ask yourself questions so your students see how you think about solving that particular problem.
Ask questions: when solving problems ask questions. Pose a question and leave enough time for students to think about it. Some questions that fit any problem solving are:
- How do I start?
- What do I know?
- What formulas do I need to know here?
- Am I making sense?
- What are the possible approaches?
- What am I forgetting?
- Does this answer make sense?

Model strategies: model your process of thinking about how to solve a problem by talking it thru out loud. Another strategy is to present several problems of the same type then ask students to look for patterns.
Give credit for analysis: teach your students to explain their thinking process when they stumble in exam and give partial credit for explanation even if the result is not the correct one, if the student at least solves half way the problem and shows you the correct strategy of thinking give credit to your student for thinking about the problem.

Encourage thinking process evidence: if a student asks a question in class or via e-mail ask your student to explain his/her thinking process up to the point where they get stuck. It is not uncommon that students do not choose the appropriate approach and that is the reason why they do not find the solution, or might be they misunderstood up front the entire problem.
Provide focus: ask focused questions, give many problems of the same type so they have enough time to familiarize with one type of problem and practice solving skills.

Use small group work: post a problem on the board and ask students to turn to their neighbors or work in pairs and take turns thinking out loud while they solve a problem the other will monitor the process.

To increase student confidence and motivation use the following strategies:

Eliminate negativity: encourage your students to think about what they know and accept that everyone experiences at times lack of knowledge or strategies to solve problems. Do not allow generalized statements such as: “I am not good at this!” “I will never be good at this” “I will never be able to learn it”.
Be direct: especially when working with first year students warn them that if they were successful in high school that does not mean they do not work to work much harder in college. Explain them that college course level is different than high school and how that might be in your particular domain. Explain what exactly you expect. It is always good to have Student Learning Outcomes in your syllabus and explain them in detail at the first day of classes. Remind them again as semester goes on and as you introduce new topics. Student must be aware what do you expect from them, what kind of skills they must demonstrate by the time the course completes that particular topic.

Be personable: make an effort to know your students. Might be you will not learn all the names, but use all opportunity to know information related to the students in your class. A good idea is to use a short questionnaire in the first day of class by asking demographic questions. Tell them about your availability in office hours and encourage them to use the opportunity, a good idea is to come early to class so you can ask questions and chat about their interests. It makes you look more like a person and more approachable than the professor at the blackboard or behind a desk in the office. Share your out of class interests and ask them what are they interested in.

Communicate and encourage: Write notes on exams and quizzes, encourage them to come to your office if the performance is poor. Offer praise where you see success. They need your encouragement as well. If possible offer the chance to improve or retest. If too many fail a certain type of problem on an exam it is a sign most likely students did not understand the topic; give a quiz with the commonly missed problems – it is not fair to have so many fail because they did not understand the theory. Anytime the number of those who fail approaches 1/4th of class it is good to think about re-teaching the failed topic.