“At all ages, there are several ways to improve the functional capacity of working memory. The most central of these is the achievement of automaticity, that is, the fast, implicit, and automatic retrieval of a fact or a procedure from long-term memory.”
— Final Report of the National Mathematics Advisory Panel (2008).
The goal of learning is to be able to solve problems. As instructors, the most important questions we face are:
- How does the student brain solve problems in chemistry?
- What actions should we advise students to take to learn to solve problems?
Over the past decade, research in cognitive science has reached agreement on how students between about age 12 and graduate school solve “well-structured problems” (those with clear “right answers”) in math and science. A brief summary of that model follows. Citations and opportunity for discussion are provided at the end of this post.
How the Brain Solves Problems
To solve problems, the brain uses two types of memory: working memory (WM) and long-term memory (LTM). WM is where the brain manipulates knowledge: where you think and reason. WM can accept input from your senses (such as seeing an object or reading a problem) and from your LTM.
We will define LTM very roughly for now (more in later postings) as where the brain holds knowledge that you can recall, but your have not seen or heard in the past 2 minutes. An example is: 6 x 7 = 42 As knowledge in LTM is encountered in a variety of contexts, it is tagged with meaning, via links to other knowledge, to form a conceptual framework (also termed a schema).
Since 2001, the characteristics of WM have been scientifically measured and verified. The key finding is this:
During problem solving, working memory can manipulate
Virtually all related elements of knowledge that can be recalled quickly and accurately from LTM based on “element cues” in the problem, plus
Up to 3-5 elements of knowledge, each for up to 30 seconds, that cannot be fluently recalled from LTM based on element cues.
To help with understanding, let’s restate this law and its implications in different ways.
- Working memory is very limited when dealing with information that has not previously been well memorized.
- In the working memory where you think, space for non-memorized information is minimal, but space for well-memorized relationships is enormous.
- When trying to solve a problem, if just a few elements of knowledge needed to solve the problem cannot be recalled from LTM, limits on the capacity of WM are exceeded. This will likely lead to confusion that prevents the problem from being solved.
- Your ability to solve problems depends primarily on how much knowledge you have “automated” — how much you can “recall with automaticity” (fluently) from LTM.
- To get around the quantified bottleneck in the ability of the mind to reason, students must begin by memorization: They must work to move elements relationships into a long-term memory that is resistant to change. Then, as they work to gain procedural fluency and conceptual understanding in the use of new knowledge, automaticity in recall from LTM is gradually achieved.
- The strength of LTM is that it is long term. Once information is well memorized and well organized, the ability of WM is able to recall and apply that knowledge fluently (automatically and effortlessly) often lasts for decades.
In a nutshell, that’s the foundation for learning math and science. The unexpected finding that the brain is very limited when reasoning with what has not been well memorized is now verified, accepted science, and it will force a re-examination of many recent theories on teaching and learning.
Some educators will be dismayed with a finding that memorization is required for problem-solving, but the value of science is that it measures what is true, whether we like that truth or not. Thanks to recent research, instructors now have a much better understanding of how to advise our students to learn efficiently and effectively. That’s the best possible scientific progress.
At this point, we’d like to ask our readers to answer some questions in the Comments that will “set the agenda” for this blog. (Click on Comment below the title of this post.)
- After reading one or two of the brief references below, do you see any discrepancies between the statements above and what cognitive science is saying?
- What questions would you like to see addressed to further explore these data?
In upcoming posts, we will explore these issues in additional detail. We will also try to suggest answers to your questions based on our reading of cognitive research.
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For short summaries in non-technical terms of recent research in cognition, see the brief Clark and NMAP readings in the “Read Recs” tab above.
Make It Stick, a new book describing the importance of memorization in learning, was recently reviewed in the Chronicle of Higher Education at this link: MakeItStick .
For a recent review on the NIH website of the “3-5 chunk limit” research, see http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2864034/
Any first-year textbook in cognitive psychology with a copyright date in the past 5 years will detail the interaction between WM and LTM in its chapter titled “Problem Solving” or “Cognitive Architecture.”
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