SIMIODE

Way back in March 2016 there appeared a very interesting article, “Can Math Education Research Improve the Teaching of Abstract Algebra,” in the  Notices of the American Mathematics Society. Here is complete citation:

Fukawa-Connelly, Tim, Estralla Johnson, and Rachel Keller. 2016. Can Math Education Research Improve the Teaching of Abstract Algebra. Notices of the AMS. 64(3): 276-281.  .

The research is an attempt to find out if undergraduate teachers of abstract algebra are implementing results from the research into improving teaching of abstract algebra, often through moving away from the lecture-centered teaching approach. The simple answer is, “No.” This is unfortunate and the authors attempt to show the reasons for this situation, but can only request that, “If you are dissatisfied with your current practice or results, if you are frustrated in lecture-dominated classes, if you are looking for inspiration – we might have the answer. All you have to do is ask!”  BTW we believe that in SIMIODE we are here as a change agent, an enabler, and a community to help colleagues move to modeling based differential equation instruction in an active learning setting and all you have to do is visit SIMIODE. 

Among the best influencers on teaching practice is personal experience as student and teacher, but then talking to colleagues ranked a solid third, while reading about new techniques, workshops/conferences,  and MAA Notes/PRIMUS, fell to dismal lows. The inference by the authors was that “it appears that the majority of math departments might be closed to outside influences on teaching.”

The research questions were, “(1) What pedagogical practices do abstract algebra professors report using in their classrooms and why? (2) What encouragement and constraints on their use of nonlecture practices do they perceive?”

We quote from the conclusions,  “There are four major findings that we highlight. First, lecture is the predominant mode of instruction(97/126), and even those who have tried other pedagogies appear to switch back to lecturing at surprisingly high rates (10/29). Moreover, given the significant amount of time, money, and en­ergy spent developing, testing, promoting, and training mathematicians to use new curricula and pedagogies, there is almost no uptake. Those using nontraditional materials are far more likely to have developed their own materials than to have adopted NSF-supported curricula.

"The second major finding relates to the factors that influence pedagogical decisions. In decreas­ing order of significance, the participants reported that their experiences as a teacher and student were far and away the most significant influence, followed by talking to colleagues about how to teach specific content; the least significant source of influence was grant-supported distribution methods such as publications and workshops. If mathematicians essentially give no weight to the traditional means of dissemination of new peda­gogical ideas and techniques (and evidence of their effectiveness), reformers have few means of pro­moting change other than individual conversation. This alone suggests why reforming undergraduate, mathematics, and abstract algebra in particular, is difficult.

“Third, while faculty claim they have the ability to change their courses, the reported satisfaction levels indicate they do not have the desire to do so. Furthermore, the majority of dissatisfaction stems from perceived problems with the students and not the course materials. Given the strong content focus and high belief in the efficacy of (and preference for) lecture, it appears that as a collective, the abstract algebra teaching faculty has little interest in adopting new pedagogical ap­proaches at this time.

“We propose two concurrent research direc­tions. First, we need to better explore the reasons that mathematicians appear to strongly believe in their current practice, the types of evidence that they hold as dispositive, and what means of dis­semination of new approaches achieve meaningful penetration. Second, we need to further explore the types of changes to the practice of lecture that mathematicians would adopt. There appears to be a conflict between the stated goals of policy boards and national organizations and the way that fac­ulty, on the ground, think about their courses. Math educators are responding to the claims of the stated goals of changing undergraduate courses to include more student-active work, but if math­ematicians have different perceived needs, as our work shows, these new ideas won't gain traction. Thus, we want to have a conversation about what is understood as practical and feasible in the eyes of those charged with delivering the instruction.

“Finally, for us and mathematics education researchers generally, we wonder how best to propose new strategies about teaching and how to receive feedback from the mathematical commu­nity as to their interest and feasibility. Basically, if the only people that mathematics instructors ever talk to are their colleagues, it is a closed circle with no obvious entry point for new ideas.”

One issue that came up repeatedly was the high price of textbooks and “complaints about pricing and frequency of new editions were rampant.”

This is a thoughtful study and evokes questions in readers minds as to how to effect change and what are the obstacle in the way of change.  We commend it to you.

1. abstract algebra
2. lecture
3. mathematics education
4. teach