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Wednesday, October 8, 2008

The "Laws" of Learning

A central tenet of reform mathematics and constructivist teaching is that children should work cooperatively in groups to “explore” and “discover” math and figure out concepts on their own. Reformers say this method makes math interesting and fun and leads to “deeper understanding.”

Jayne Sherman, a teacher in Prince Williams County, Va., and parent of four children, said the reform program "Investigations in Number, Data, and Space" was getting her students to “think mathematically” (Sherman, 2008).

“Using the inquiry method of learning, children explore, discover and articulate their thinking,” she said. Her students supposedly discover “many strategies to solve problems.” They communicate and collaborate with each other, sharing their thinking and becoming “math literate, all while having fun.” They “make their own representations to solve problems.”

Sherman summed up her feelings by taking a poke at traditionalists: “The traditional approach to teaching no longer serves our students.”

I’m not sure how much fun this process actually is for the students, who tend to be concrete thinkers and who generally appreciate straightforward, logical approaches to learning. Experimentation in groups can be fun for them, but I suspect they’d rather it come in small doses. Otherwise, they can become stressed out trying to teach themselves 5,000 years of math in the small snippets of time they have available to them.

I was thinking about this while reading an Air Force training manual from 1974 called “Principles and Techniques of Instruction.” The manual is old, its cover is lost, and the pages are yellowed. It’s been around the block – well, around the world, actually. It contains much valuable information about teaching, learning, leadership, ethics, guidance, counseling and critiquing effectively – all presented in an incredibly concise, straightforward, readable and accessible format.

As I read through this manual, I caught myself nodding my head in agreement, saying at one point to the cat, “Now, that’s what I’m talking about!” According to this manual, there are six basic "Laws" of Learning. If I were a proponent of reform mathematics, I could see myself using three of them to support my approach:

The Law of Effect – “learning is strengthened when it is accompanied by a pleasant or satisfying feeling”
The Law of Intensity – “a vivid, dramatic, or exciting learning experience teaches more (information) than a routine or boring experience (does)”
The Law of Readiness – “a person learns best when he or she is ready to learn”

Proponents of reform mathematics could argue that those three laws support their approach: Keep it pleasant, keep it exciting, and for heaven’s sake, keep it simple. But I think those three laws actually support the other three:

The Law of Primacy - People tend to draw on the skills they learned first:

“Primacy, the state of being first, often creates a strong, almost unshakeable, impression. For the instructor, this means that what he teaches must be correct the first time. For the student, it means that his learning must be correct. Unteaching is more difficult than teaching … The student’s first experience should be positive and functional in preparation for what follows” (“Principles,” 1974).

Therefore, teachers of mathematics should want students to learn math processes properly the first time – in the most efficient, most effective and most precise way possible. Teaching them mathematics as reformers do – by asking them to muddle around in herds – is inefficient, ineffective, unpleasant and ultimately counterproductive.

The Law of Exercise – Practicing a concept is critical to learning it.

“Things most often repeated are best remembered. It is the basis of practice and drill… The mind can rarely retain, evaluate, and apply new concepts or practices after a single exposure. A student … learns by applying what he has been told, and, every time he practices, his learning continues … Repetition consists of many types of activities, including recall, review, restatement, manual drill, and physical application.”

Proponents of reform, however, have called this practice “drill and kill” and tossed it under a bus. To reformers, practicing is “rote” and “boring.” It’s an odd attitude to have about something we all do when we want to learn anything of value.

The Law of Recency – The longer we go without practicing a new concept, the easier it is for us to forget it.

“Other things being equal, the things most recently learned are best remembered, while the things learned some time ago are remembered with more difficulty.”

This law conflicts entirely with the “spiral” technique – so common in reform mathematics – where teachers briefly touch on a new concept, don't give their students the opportunity to practice it, and then present the concept again some time later (often with a new twist).

The Air Force training manual is old, and it’s probably been revised since 1974, but I like it. As a tutor, this is what I take away from these six "Laws" of Learning:

  1. Make sure students are ready for the lesson.
  2. Prepare an experience that they’ll enjoy.
  3. Teach students the most efficient, most effective methods first.
  4. Make the lesson exciting.
  5. Have students practice the lesson.
  6. Build on recently learned concepts.

This approach makes sense to me. Apparently, there is much to be learned from the things we used to know.

Please note: The information in this post is copyrighted. The proper citation is: Rogers, L. (October, 2008). "The "Laws" of Learning." Retrieved (date) from the Betrayed Web site:

This article was also published October 9, 2008, in at


Anonymous said...

Isn't it interesting that so much new that our children are now being taught is NOT based on so much of the old that we know as adults? Seems like a waste of precious learning time, energy, and money not to build on solid, old foundations, rather than tearing everything down and trying to start from scratch.

Interestingly, this being an Air Force training manual sets up my reminding people that John Saxon, of Saxon Publishers, was retired Air Force. The two laws of “Recency” and “Exercise” are the basis of Saxon Mathematics.

This has been substantiated in a report called, "The Effects of Overlearning and Distributed Practise on the Retention of Mathematics Knowledge," by Doug Rohrer and Kelli Taylor, published in Applied Cognitive Psychology online 6 July 2006 (

Anonymous said...

I have a child who was sick last year with low vitamin D and mono and was behind. I asked a language teacher for a meeting and she refused said "he wasn't trying". He now has epstein Barr this year and being put on 504 disability altough taking forever. This past teacher gave my A/B studnet a D
and I even offered school 20 per hour AND ASKED THEM TO HELP find tutot etc all failed and they had no tutors, no after school homework center etc..

What can I do to get my now a/b disability students grade raised from last year when all his tachers let him down by not realizing how sick he was? The school just looked the other way even though I sent emails to counselors with the teacher remarks and counselor requested teacher meet with is but she met with tight lips and attitude- no help then punished him with a bad grade??

Bruce Deitrick Price said...

Don Potter quoted you in an email to me; and i quoted you on a hub on

I'd like to suggest your making a lighter version of Laws of Learning for hubpages. To steer young parents in the right direction. (Or if you don't want to, tell me and maybe I will.)

We are strategic allies.

Bruce Price

Laurie H. Rogers said...

Thank you for your comment. I can do that for you.