Brain-Based Math Learning

I have been amazed (and appalled) by the phrase ‘brain-based learning’. The suggestion is that there is learning NOT based on how the human brain functions; like mathematics, the brain uses ‘existence proofs’ — if learning happened, the brain must have worked.

The point of this post is to talk about what we commonly report as facts about the human brain. For example:

Learning occurs through modification of the brains’ neural connections.

This is just about the most basic statement we can make, and it is actually correct. Of course, it does not lead to an easy-to-implement teaching method.

Take a look at the following statements with an eye towards truthfulness:

Individuals learn better when they receive information in their preferred learning style (e.g.,
auditory,visual, kinesthetic).
We only use 10% of our brain.
Differences in hemispheric dominance (left brain, right brain) can help explain individual
differences amongst learners.

Each of these statements is false; these statements are examples of ‘neuromyths’, a phrase used by the Organization for Economic Co-operation and Development (in “Understanding the Brain:
Towards a New Learning Science”, 2002). In other words, experts in neuroscience have determined that these statements are false.

The first myth listed is dangerous, because it leads to easy-to-implement teaching methods which will not help learning (and can reduce learning). Even if “learning style” was a valid construct with a solid research basis, matching a trait to a treatment has shown to be a very difficult design strategy for learning (based on decades of research on attempts). However, the recent summaries I’ve seen on “learning styles” are still showing concerns about the construct itself. The phrase ‘learning styles’ is most often used by educators trying to influence others; learning theorists and cognitive psychologists will seldom use the phrase (and often react very negatively to the phrase).

So, what would “brain based math learning” look like? This is equivalent to asking what math learning would look like. To me, the key is to keep focused on the basic statements about the human brain — like the one above about modifying neural connections. Each learning task in a college math classroom is an interaction between new information and existing connections in the brain.

The default response by the brain is “what I have now is correct” and is reinforced by the new information
The need for modifying existing neural connections is based on some level of conflict
“Learning” occurs during the resolution of the conflict
The strength of this learning is based on multiple factors, including the use of verbal conclusions and practice (amount and variety)
The learning may create a new set of neural connections that store information in conflict with pre-existing information; which set is accessed in the future depends upon the processing of inputs
Resolving conflicting neural information takes the most effort but results in the most stable set of knowledge

As an example, we used about 6 class days last semester in my intermediate algebra course on a better understanding of rational expressions. Most students responded based on their existing (incorrect) ideas about fractions. The classes created enough conflict (mentally) that most students developed some new information about fractions. Later (on the chapter test, or the final exam) some students retrieved the new (correct) information while other students retrieved the old (incorrect information). In a perfect world, students would have further learning experiences based on these assessments.

We seldom have sufficient time for students to learn math in college when they have existing incorrect information. At the developmental level, the New Life project courses (Mathematical Literacy; Algebraic Literacy) focus on reasoning and communication with a more defined content — allowing some additional learning time.

As a profession, we need to move beyond pseudo-science so that our pedagogy is based on a body of knowledge accepted by scientists specializing on the human brain. For a single-source, you might try Applications and Misapplications of Cognitive Psychology to Mathematics Education at http://act-r.psy.cmu.edu/papers/misapplied.html

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