Active Learning and the Teaching of Math

Presented by Ida Umphers

During the October 8th, 2007 ATLE luncheon, Ida Umphers used learning as an acronym to discuss ways all teachers can help students master difficult and intimidating concepts.

Using Learning to Teach Math

Listen to your students. You may be the content expert, but they are the experts in HOW they learn.

Explain, with examples, how to organize information. Students can be overwhelmed with the vocabulary in a new discipline, impeding them from focusing on the important part(s) of a problem. As students begin to maintain a grasp of new concepts, have them work in groups to create and explain their organizational schemes.

Assess and concentrate on what you really want students to know.

Revise your in-class approach based on students’ feedback. If students find their suggestions are ignored, they will stop giving useful feedback.

Notice the “little” things, which are really the “big” things. For example, to find the probability of one event that follows another, we write P(A|B) the probability that A occurs given that B has already occurred. One of my students said, “You know, that is really confusing for me,” and when I looked at the class, they were all nodding in agreement. I said, “O.K. From now on, let’s write it as P(B|A), the probability that B occurs given that A has already occurred.” The class was much less confused, and I have used this notation since.

Increase your font size and white space on handouts.

Never give up. Repeat often.

Gradually shift the focus of the class from you to the students. Train students to actually put pencils on the paper and work rather than trying to keep everything in their head. Tell them making mistakes is OK if they just try something. My goal is to make them independent so subtly that they never notice it has happened.


Ida Umphers (College of Science & Mathematics) has taught full time as an instructor at UALR since 1986. She has taught elementary, intermediate, and college algebra; college mathematics; business and applied calculus; statistical methods and applied statistics; early childhood and middle childhood mathematics education courses; and elementary physics I and II. She prefers to teach freshman courses and work with students who have had poor experiences with math in the past in an effort to improve their self-confidence in mathematical problem-solving.

Ida Umphers on Teaching Demonstrations

“I enjoyed my presentation to the Teaching Academy very much. I found it valuable to get feedback and questions from faculty in other disciplines, particularly our discussion of how to structure course demands of students to ensure that they get the early success necessary for them to feel confident enough to risk becoming more and more independent in their learning as the semester progresses.”


Here are the handouts provided at the seminar:


Ida Umphers‘ Webpage

Email address

Ida Umphers

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