Monday, August 5, 2013

How Can Less Studying Produce More Learning?

Frederick Alfred Slocombe Wandering thoughts 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?


  1. I can relate to Susan’s frustration; I too only memorized formulas. I think the only reason I passed high school chemistry is because, for our final, we were tasked to design, demonstrate, and explain chemical reactions for any experiment of our choosing. I chose baking a chocolate cake; it was valid and tasted good…

    There as so many important concepts is this post. I have rewritten my response at least four times trying to narrow the focus. I have numerous examples of my own epiphany moments where learning subject matter without true understanding occurred. This happens in any domain of learning, not just formal education.

    I believe that thousands of teachers teach to understanding; what is rare (or a better word might be inefficient) however, is hearing about these classrooms---which speaks to the question of “readily accessible by teachers in regular classrooms.”

    There is no shortage of workshops, books, conferences, research studies, or blogs…There are plenty of people who “get” this. The problem, I think, comes back to (at least) two major points:
    1) Implementing what we know needs to happen; having the support necessary to do this; and then sharing these practices with others.

    2) Teachers (presenters, facilitators, subject experts…) do not comprehend that memorizing a formula and solving a problem correctly does not necessarily mean understanding exists. Our standardized testing only adds to this problem. (I am not bashing standardized testing, but the way we interpret results and then implement change needs a great deal of work!)

    So, we have come full circle…back to sharing. Do we assume that educators attending workshops, or reading relevant professional development material, have understanding? Do we see more diffused impact from the types of educators who do seek professional development relating to this topic? Do we assume our instructional methods are good enough and that we have thoroughly presented the subject matter? If the answer to any of these questions is yes, and I think it is, how can we change or improve? The answer, I think, is complex and involves variables like time, interest, acknowledging this happens… just to name just a few. I also believe that the best models for teaching for understanding come from educators and therapists working in the field of special education.

  2. Thanks, Rene.

    I wish more teachers would share their experience and insights like this. Anyone can have an opinion about what "should" work in education. At the end of the day, though, shouldn't we be asking teachers to tell us what actually _does_ and _doesn't_ work in the classroom - and why or why not?

  3. Embedded in both Mike's powerful story and Rene's personal experience is an important insight for educators: Our brains are pattern detectors. Our brains have evolved to detect patterns, like recognizing that in Spanish and English "-dad" and "-ty" are the only differences in cognates like “city” and “ciudad” … well almost, my pattern recognition machine just picked out the “u” in “ciudad.” The literature is very deep in pointing out this important function of the brain. Of course the brain does more than this, but this level of insight is sufficient to suggest a solution to Susan’s problem (which is her instructor’s as well). I might design a lesson that begins like this: “Look at the six formulas you think are different (and you feel you need to memorize), and pick out what is similar and different in each. The brain loves problems like this (excuse the anthropomorphism). What the teacher does next is build on Susan’s observations and scaffold her ability to find richer more complex patterns regarding these six formulas. Together they may find she needs skills in algebra to complete the translation of the formula, a complex sentence represented initially as PV=nRT. They may need to talk about why “P” is capitalized and not “n.” They may find themselves talking about what is pressure, why is temperature important in this complex relationship, etc. It’s hard to tell where the conversation goes next, but the structure that will lead both to deeper understanding (through richer patterns) and teaching skills (by seeing more clearly the patterns in student learning) is by capitalizing on what the brain does naturally.

    The stories here are like windows into how the brain functions. They highlight contexts where the brain either struggles to make sense of meaningless and decontextualized symbols or is supported in unpacking and deciphering what at first looks like some form of hieroglyphics.

    Perhaps one outcome of this blog is a parallel activity where we list the insights or guiding rules that teachers should observe based upon the stories we share. This forum could be a place where we debate the usefulness or power of a learning or teaching rule, which might necessarily lead us to the literature or experiments of our own. Here is a story from the literature that bears on what we are talking about:

    Potgieter, M., Harding, A., & Engelbrecht, J. (2008). Transfer of algebraic and graphical thinking between mathematics and chemistry. Journal of Research in Science Teaching, 45(2), 197-218.

  4. Wonderful - thanks, Marc.

    I like your idea of capturing insights that emerge from the conversation for teachers. Let me think a bit about how best to do that. Stay tuned...

  5. Hello Everyone,
    I am a member of the 2nd cohort with thoughts concerning surface learning vs deep understanding. In our last class with Dr. Palko, he summarized with a three column chart outlining the main concepts of the course. He explained the relationships between these concepts as a function of mind, brain, and education. This organizer will benefit me as I look back to construct my understanding of dynamic systems (completely new content to me). Now I have some surface knowledge of nonlinear dynamic systems, coherence, and emergence, etc., but I need to make sense of my notes and Dr. Palko's chart so that I can create my own narrative that will allow me to share my understanding with others. At the end of the course, Dr. Palko's final comment to our class was to say his intent had been to teach the information well enough that we could teach it back to him.
    Until our students can construct their narrative and teach the concepts to each other as well as the instructor, we will continue to have students who are unable to transfer concepts and skills from one context to another.

    1. Hi, Vicki. Thanks for sharing this example from your own experience. (For context: you are a member of the 2nd cohort in the Mind, Brain, and Education program at the University of Texas at Arlington, yes?).

      Your example illustrates several important points, including:
      * We use one term - "learning" - even though the knowledge we are talking about actually takes many different forms; "Surface learning" vs. "deep understanding" is one distinction that people often make
      * The fact that we commonly use just one word ("learning") to describe a variety of processes and forms of knowledge can mislead people into thinking that there is only one type of assessment (that measures "learning"), when in fact we need different kinds of measures to assess these different forms of knowledge; for example, being able to *explain* the concepts effectively to someone unfamiliar with them sets a much, much, much higher bar on understanding than answering some multiple choice questions about the material covered in a lecture
      * Learning does not start and stop on the same schedule as the classroom teaching that is meant to facilitate it - as you note in your example, after the initial exposure to concepts in your class, you still have work to do to makes sense of the course materials handed out (including Dr. Palko's chart) and your own notes, so that you can "create your own narrative" that will enable you to explain the concepts to someone else - the teaching has stopped, but learning is an ongoing, iterative process - at least if the desired outcome is deeper levels of understanding

    2. Yes, you are right-I am part of the 2nd cohort of MBE at UT Arlington. I agree with you on the many facets of learning and the element of time that deep understanding requires. When I try to explain the concept of deep learning, I use a layer cake as a metaphor. The cake batter is the procedural and surface information such as the introductory MBE courses I took last fall, necessary for a foundation, but not enough to explain the way the brain works and how we might use research to impact teaching practices. After taking two more classes, I am adding layers of information that connect to the initial foundation. These layers are adding the connections and richness to the narrative that I am developing. The cake is more appealing and interesting as new layers appear. You are right, Dr. Connell, my deep understanding takes time and effort on my part to go beyond the semesters I attend class. Eventually, the important question will be, "What will I do with the cake? Am I confident of the quality, and am I able and willing to share it?"