How Can Less Studying Produce More Learning?

In a previous post, I introduced two notable examples of applied learning science: SHERLOCK and RightStart. They demonstrate that the difference between an average instructional design and an optimal design can be huge - much bigger than most people realize. In this post, I use those examples as a jumping off point to explore two questions:

1) What could cause such large differences in learning outcomes if the basic "subject matter" being taught doesn't change?

2) How unusual are the SHERLOCK and RightStart results? In particular, should we only expect those kinds of results from formal, long-term, well-funded research studies?

But first, I need to introduce the following key insight.

Key Insight: Don't Mistake Subject Matter for Knowledge

When I was in high school, I ran a tutoring business. I loved helping my peers learn about subjects like math, science, and writing. As a bonus, not only did I deepen my own understanding of these subjects, but I also learned a ton about how other people come to understand them.

One of the more interesting insights I gleaned was this:
Subject matter taught is not the same as subject matter learned.  

Let me illustrate with an example based on actual events. 

One of my tutoring clients was a good friend named Susan. She was a diligent student in all subjects and a strong writer, but she struggled with math and science. One day we were studying math at her house. As I was packing up to leave at the end of the hour, Susan groaned, "Now I have to study for tomorrow's chemistry test. I hate chemistry."

"Why?" I asked.

"There's too much to remember!" she complained.

"Show me," I said.

She pulled out a stack of homemade flashcards and flipped the first one onto the table. Written on it was the formula for the "Ideal gas law" in chemistry:

PV = nRT

"There are all these formulas," Susan said, "and I can't keep them straight in my head because they all look alike." Then she dealt out a bunch more cards to illustrate her point:

P = nRT / V

V = nRT / P

n = PV / (RT)

R = PV / (nT)

T = PV / (nR)

I stared at the cards. "Susan, that's algebra." 

"No, this is for my chemistry test," she insisted.

"No, I mean those aren't six different formulas," I explained, "It's the same formula written six different ways. If you start with any one of them you can get to all five of the others using simple algebra. In fact, you just used the same algebra in some of your math homework during the last hour."

Her eyes widened with dawning recognition. "Oooohhhhhh - I never realized you could use algebra in another subject like that!"

No wonder chemistry was so hard for her! She had to memorize about five times as much subject matter as the student sitting next to her who realized he could use algebra there. Note that both students would have been exposed to the same subject matter - algebra and chemistry. It would have been their knowledge (or understanding) of the two subjects that was organized slightly differently. But the implications for future learning were not slight at all - they were quite huge.  Huge on the scale of SHERLOCK and RightStart, in fact. The picture below illustrates this scenario.

This example also suggests a way to think about how SHERLOCK and RightStart could produce such large gains compared to other curricula covering similar subject matter. In particular, if we imagine two students taking the exact same classes at the exact same time, we can see how one student could easily spend twice as much time as the other student to learn half as much material with less understanding. It stands to reason that a curriculum designed to ensure that every student has mastered key concepts and skills before moving on could produce dramatically better learning outcomes than a curriculum that leaves it up to each student to find their own way - even if the subject matter is ostensibly the same in both designs.

And we should note that even though Susan eventually made the connection between algebra and chemistry, she had already suffered (unnecessarily) through years of tedious studying just to make a passing grade in science while watching some of her peers seem to breeze through with top marks. How often does a single, critical misstep like this prevent a student from pursuing - or even exploring - entire categories of career? The stakes are very high in education - people's life outcomes hang in the balance.

Example: Arithmetic

The chemistry example is not unique - far from it. Consider a similar example from arithmetic - memorizing the times tables from 1x1 up to 12x12.

Memorizing all of these multiplication facts would involve 144 flashcards: 1x1, 1x2, 2x1, 2x2, and so on, all the way up to 12x12 (as shown in the left panel of the next figure).

But if the student knows the commutative property of multiplication (which means, for example, that 1x2 = 2x1) then suddenly there are only 78 facts to remember (plus one rule), as shown in the right panel in the figure below. The student who doesn't understand the commutative property has to memorize nearly twice as much information as the student who does. The same observation applies to learning the addition tables.

Example: Foreign languages

The problem is not limited to math and science, either. Consider foreign language studies. Linguists use the term "cognate" to describe words in different languages that derive from the same origin. For example, "university" in English and "universidad" in Spanish are cognates, as are "city" / "ciudad" and "accident" / "accidente." The Spanish student who recognizes the general patterns by which cognates are related (for instance: "-ty" in English becomes "-dad" in Spanish and vice versa) will have quite a bit less to learn than the student who doesn't pick up on those patterns.

Just the tip of the iceberg...

As these examples from familiar school subjects illustrate, knowing what (or how much) subject matter is being taught doesn't tell us what (or how much) subject matter is being learned. The differences are not on the order of 1% or 10% either - even in these simple cases the swings are closer to 200% to 500%. 

But these simple cases represent just the tip of the iceberg. As the example  from Susan illustrates, the differences accumulate and compound as multiple subject areas interact (or not), and as new knowledge is layered on top of old. 

At still deeper levels of analysis where we apply insights from Cognitive Science, we find that issues arise when knowledge is stored in one type of memory system in the brain that should really be stored in a completely different type of memory system.  For example, a child could memorize the steps involved in tying one's shoes as declarative facts (Step 1: hold the shoelaces apart near the tips, Step 2: cross the right lace over the left and exchange the tips between hands, ...), but to actually tie their shoes effortlessly they will need to transfer that information to procedural memory. That should be obvious in the case of tying shoes, but it applies equally well to the difference between being able to recite the "six key features of a persuasive essay" (declarative facts) and the procedural knowledge required to actually compose an essay that influences people.

What do you think?

In this post we have explored the question of whether the dramatic learning gains documented in projects like SHERLOCK and RightStart are likely to be rare - perhaps only discoverable and accessible through systematic, long-term, and expensive formal research projects - or whether they are more commonplace and readily accessible by teachers in regular classrooms. I think the examples above provide pretty compelling evidence for the latter. 

What do you think? What experiences or examples can you share to push the conversation forward?