Active Learning Methods in Developmental Mathematics

We’ve all had this … students who attempt to complete a math course based on memorization; such students often report frustration when asked to apply knowledge in any way that differs from what they ‘learned’.  As mathematicians, we see the process of that frustration as a key part of what mathematics is all about.

As teachers, we sometimes behave in the same memorizing way.  For example, we attend a workshop session on a particular active learning method or methods.  After some planning, we begin to use those methods in our classes and usually feel good about the experience.

Any teaching method will be more effective if the teacher understands the whole story — how the method works and WHY it works, with connections to other knowledge about the learning process.

If you look for data and research on active learning methods, the results look very good.  However, most of that data collection is done by experts using the methods.  An observational study was done using a random sample of college biology teachers, with an eye towards seeing this positive impact of active learning methods.  Some faculty used little ‘active learning’, some used a lot, and some were in-between.  The results?  Well, not so good for ‘active learning’.  See http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3228657/?report=classic for the Andrews article “Active Learning Not Associated with Student Learning in a Random Sample of College Biology Courses”

It turns out that many faculty using active learning methods have memorized the ‘steps’ for the method but did not understand the method well enough to adjust it for their students … and also could not accurately monitor the process.  Putting students in pairs with a problem for ‘think-pair-share’ will not automatically produce better learning.  Understanding is important for us, as well.  The authors of the study listed above believed that was the critical factor for not seeing positive results.

I’ve been saying something for 20 years, and believe it is still true today:

Developmental mathematics … we are a desperate people!

Partially because we’ve been teaching the wrong courses, our work has not been successful over a long period of time and over a large range of locations.  That process results in us looking for something … almost anything … that might help in our classrooms.  In many ways, this is the same attitude that our students bring to our developmental math courses.  We see something — it might help, so we quickly try it out in our classes.  Learning a new teaching method is like any other learning: there is a process, and ‘knowing steps’ does not equal ‘learning’.

Here are some pointers on how to use new teaching methods effectively … ‘active learning’ or otherwise.

  1. Experience the method yourself repeatedly:  for example, use the think-pair-share process to learn something new.  Look for the how & why of the method, and develop an intuition for what it looks like when it works.
  2. Read and use multiple sources of information.  You are most likely hearing about a method from somebody who heard about it from somebody who heard about it … each of those stages involves filtering and distortion (just because it’s human communication).  Multiple sources will provide a more accurate picture of the method.
  3. Use the engineering principle: estimate the time it will take, then double the number and use the next larger size.  “10 minutes” becomes “20 hours”.  That’s a little extreme, but valuable as a guideline … nothing breaks a teaching method quicker than rushing it.  This applies to both your planning time, and to the operational time in the classroom for the method.
  4. Don’t be deceived by appearances and initial student reactions, which are often skewed (more positive) by ‘something new’.  Assess the results using multiple measures — direct observation, one-minute paper, survey, quiz, etc.
  5. Assume that your first use is a crude approximation requiring a number of adjustments based on analysis of results.  Proficiency is the result of lots of practice … and learning from that practice.
  6. Allow yourself to reject one method and switch to something else.  We all need to become effective teachers, but we don’t need to become the SAME teacher.  Use methods you can be enthusiastic about, since that helps students almost as much as the details of the method.
  7. Talk about your experiences with colleagues you trust.  You are learning something new, and it’s complicated … verbalizing helps your brain clarify the process and the results.  Ideally, you would form a ‘lesson study’ type group working on the teaching method.

I wrote those pointers with active learning methods in mind, but they apply to any method — including lecture (aka “direct instruction”).  Lecture, sometimes defined as continuous elaboration by the ‘teacher’, is a valuable tool for us; it’s just not adequate in general, and needs to be used intentionally.  My own classes tend to be several lectures of 5 to 10 minutes separated by some active learning method.  You might experience ‘experts’ who claim that we don’t remember what we hear; the irony is that the message the expert is delivering is one which they HEARD.   The critical thing is to have the learner’s brain engaged with the material using multiple teaching methods appropriate to the content; listening is an effective method for some things.

We each need to develop high levels of skills with a variety of teaching methods, because that is what experts do.  Limiting our methods, or using methods poorly, impedes our student’s learning … or even causes damage to their learning.  Just like our students, we need to have a growth mind set.

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