Chapter 4: Why is it so hard for students to understand abstract ideas?

Why Don't Students Like School? by Daniel T. Willingham (John Wiley & Sons, 2009).

Blogging Note - it's somewhat frowned upon in the blogosphere to erase your mistakes once an item has been posted - frequently the mistake will be caught by readers and commented upon. If you erase the mistake, the comments become confusing or meaningless. Hence the common practice of using strike through text and adding the correction afterward. I do make minor edits for grammar, spelling, or clarity without notification.

I'm going to give chapters 4,5, & 6 relatively short summaries. The information is, I think, pretty well known and reasonably uncontroversial. In chapter 7, on the other hand, the author explodes some myths about "multiple intelligences" and "learning styles" that will surely raise some eyebrows. Chapter 8 addresses differentiated instruction head on, and chapter 9 deals with teacher self-reflection and professional development (from a personal standpoint as opposed to an outside mandate).

Willingham sums up chapter 4 as follows:

We understand new things in the context of things we already know, and most of what we know is concrete.

In science education this idea has been the cornerstone of virtually every program and class that I've been involved with. The whole constructivist approach is in part built upon (and perhaps takes a little t0o far sometimes) the idea that our traditional way of teaching science is wrong precisely because we typically start out teaching abstract ideas first and then use concrete experiences only later and sporadically to illustrate those abstract ideas.

For example, to take the concept that Willingham uses, Newton's laws of motion are sometimes taught first as a series of abstract statements (an object at rest tends to stay at rest, an object in motion tends to stay in motion, etc.) or even a more abstract mathematical expression of the ideas (F=ma). Maybe later if the students are lucky they will be given a lab activity to illustrate the idea, and maybe the lab will have the intended effect or not, depending on how well it is set up and how good the equipment is and how seriously the students actually think about the consequences of the lab.

The constructivist approach, and the part of it that is more or less supported by Willingham's research, suggests a better way might be to turn this model on its head and begin a unit of study on Newton's laws with a series of concrete experiences that students can then think about and relate to the abstract concepts of motion described by Newton. Where Willingham might part ways with the strict constructivist approach (not that he discusses it, I'm just inferring here) is in allowing that we can simply use previous concrete experiences, tap into the prior knowledge that students have stored in memory, rather than having to come up with a novel hands-on, concrete experience for every new idea we present. F = ma is an abstract concept that doesn't make intuitive sense until you use a couple of examples; compare hitting a baseball with a bat and hitting a car with a bat - obviously the car will not move much (the a or acceleration in the formula) compared to the baseball because of the different masses of the two objects. Stated that way it is "intuitive" because we all have the concrete experience of trying to move objects of different masses.

The point is that in order for students to be able to understand the abstract laws, they must relate them in some way to concrete experiences. And this is itself a universalized law - ALL abstraction is built upon a foundation of the concrete world and physical experience.

Chapter 4 also deals with the related difficulty of knowledge transfer. Having described a situation above (the baseball and the car example) and hearing the familiar chorus of "ohhhh, I get it," you might think it would be a simple matter to then have the students apply the law to a similar problem, let's say throwing a baseball versus throwing a softball. It is entirely possible, however, that a student with limited experience would not recognize that the key element of the first scenario is the mass of the objects. Instead the student might get hung up on the fact that a ball is a small spherical object whereas the car is a vehicle with wheels, or the use of a bat in the first scenario might make them think that the use of a throwing arm in the second scenario requires a completely different set of rules. In other words, a student with shallow knowledge might not know which elements of the scenario to generalize or transfer.

Implications for teaching

Recognize that for many students a single concrete example will not suffice to allow them to generalize a rule or concept. Provide as many different examples as possible so the student begins to see the pattern and can identify key elements.

Make sure that "understanding" (deep knowledge) is incorporated into every aspect of your teaching, from homework to class activities to assessments. Especially assessments. If your assessments are testing shallow knowledge, that's what students will focus on.

Be realistic. At any particular level of education, there will be limits to how deeply a student will be able to achieve understanding. Sometimes we have to accept that we are simply planting the seed of an idea that students will be able to build upon in the future will grow as students gain more experience and exposure to the concepts (edited, I hate accidental mixed metaphors).

Next: Chapter 5, Is drilling worth it? picks up and expands on the question of how to help students achive deep understanding.

Chapter 3: Why do students remember everything that's on television and forget everything I say? (Part 4)

Why Don't Students Like School? by Daniel T. Willingham (John Wiley & Sons, 2009).

Rote memorization

The proximal goal of teaching is to get students to think about content, because students will remember what they think about. One way to get students to think about content is to present problems, puzzles, issues, etc. that require solutions. Another is to structure content around stories. Of course the two approaches are not mutually exclusive and both of these strategies activate or take advantage of natural brain processes.

But what to do when you want students to learn things that they cannot think meaningfully about right now but that they need to know anyway in order to progress in a discipline? For example, we might ask students to memorize the multiplication table before they are really able to understand the concept of multiplication. In chemistry students might need to memorize a certain number of chemical elements on the periodic table, or in humanities the names of the 50 states and their capitols, etc. Willingham accepts the notion that these things may be necessary , although they should be needed sparingly and not make up the bulk of your teaching strategies. Nonetheless, in a world where some background factual knowledge is a prerequisite for critical thinking, we need strategies to help commit certain facts to memory. This is traditionally referred to as rote memorization.

The answer, not surprisingly, is to us mnemonic devices that we are all familiar with. Willingham outlines a few of these techniqies, all of which I already know about except three, which are so ridiculous I won't even bother to summarize them.

The older ones that we all know about are 1) acronyms (ROY G BIV, for the colors of a rainbow), 2) the first letter method (My Very Elegant Mother Just Served Us Nine Peanuts, for the planets), and 3) songs (think of the ABCD song or "Conjunction Junction" from schoolhouse rock)



On to the implications for the classroom, which in this chapter seem merely to summarize ideas that have already been presented.

First, be careful in planning lessons so that students think about what you want them to think about. Beware of the potential for students to become distracted by material that was meant as an aside or as a motivational activity that students then have a difficult time turning away from to think about the real objective of the lesson. Make sure your attention grabbers really require students to think about the core concepts.

Secondly, make assignments so that students can't avoid thinking about meaning. In the example given earlier of having the students actually make biscuits and get distracted by the logistics of measuring and baking, Willingham instead proposes asking students to ponder questions of how runaway slaves could have obtained food, how they would have cooked it, etc.

Overall, these little day-to-day details should be organized in some way around a conflict. A conflict is central to a story, central to the idea of looking for solutions, therefore central to getting students to think about meaning.

Next
Chapter 4: Why is it hard for students to understand abstract ideas?

Intermission

Here's an interesting puzzler - this is not from Willingham's book but it illustrates something he writes about.

Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

A) Yes.

B) No.

C) Cannot be determined.

Click here for the answer.

Chapter 3: Why do students remember everything that's on television and forget everything I say? (Part 3)

Why Don't Students Like School? by Daniel T. Willingham (John Wiley & Sons, 2009).

Storytelling

In the previous section Willingham describes 4 teachers who have their own unique teacher personalities, but all are consistently rated as good teachers and they all have one other thing in common - they organize their lessons around stories.

Willingham is quick to caution he is NOT suggesting that storytelling is the only way to teach content. And if you've been around a while and seen district education specialists prescribing one "true" pedagogical method after another, it's easy to understand why Willingham issues this caveat. Whether it helps or not remains to be seen. He also defines storytelling broadly enough that it may not resemble at all what you think of when you first hear the term "storytelling."

We are surely all aware by now that humans are particularly drawn to stories. Long before written language was developed, verbal stories were one of the primary vehicles for transmitting cultural knowledge over generations. The word "history" in English conveys the sense of a "story," the German word for story and history are one & the same (Geschichte). It is perhaps a testament (no pun intended) to the power of stories that they frequently take on the form of (sometimes harmful) myths and legends that are persistent over generations and impervious to reason and evidence.

Politicians, movie-makers, television producers, journalists, motivational speakers, all take advantage of our innate vulnerability to stories. I dislike television but if I make the mistake of tuning in for a couple of minutes to whatever my wife is watching I can easily be drawn in by the drama and wind up watching entire episodes of Top Chef. In a classic episode of Seinfeld we were let in on the joke that could equally apply to virtually all TV sitcoms, namely that it was all along a show about nothing at all (yes, my bias is showing).

Obviously there's something going on here that we might take advantage of in the classroom. Although Seinfeld may have been a show about nothing, it was also a show that took full advantage of the structure of stories, which Willingham breaks into the 4 Cs - causality, conflict, complications, character. The first term, causality, may need some clarification but I trust that the other three are pretty self-explanatory and you will no doubt be able to identify those components in any traditional story you can recall. Causality is equally simple to explain but not necessarily something you may have thought about in the context of a story's structure. It simply means that the events that take place in a story all have a cause. Things don't happen randomly or for no reason.

The causality component of stories seems to fit particularly well with Willingham's major pedagogical goal, getting students to think about content. That's because a good story doesn't tell you all the causal links, instead it requires the listener (or viewer, reader) to infer causal connections. We do this all the time and automatically. Who doesn't feel a little rush of pride that comes from making predictions throughout a movie or book and finding out that our predictions are correct (unless it's too obvious). Even being wrong can be satisfying if the story is well told and we can think how clever the writer was to have outwitted the audience.

So how do we apply this power of stories to engage an audience to classroom teaching? Do we all have to turn every content objective now into a story? The answer is no, although if you could pull it off it wouldn't necessarily be a bad thing. However, you can take those key elements of a story, the 4 Cs, and structure just about any content objective around them. It's pretty easy to understand how that would work in history or literature classes, and in science the historical development of many ideas can certainly be used extensively as the backbone of our lessons. But even absent a compelling historical narrative, there are many concepts in science that can be arranged around the 4 Cs.

Take photosynthesis, for example. Causality is easy, it's embedded in the "story" of science itself. It's what science is looking for. "What caused living things to evolve the ability to produce glucose" could be answered in a number of different ways. Evolution provides its own story structure that students can apply to any similar question in biology. Conflict? Easy, there's competition, survival of the fittest, limited resources, etc. Long ago in a heterotroph world ("dog-eat-dog" more or less), resources would have become limited and organisms that could get some or all of their nutrition "automatically" (autotrophs) would have prospered. Complications? You have to live near a light source, you have to get rid of this new, toxic, waste product called oxygen, etc. (Wait, oxygen is toxic???) What about characters? The organism itself, or the population of organisms if you want to get technical, can be seen as the characters in the story. I know some scientists/teachers are uncomfortable withanthropomorphizing, but I'm not one of them. Having students imaginethemselves as a plant, or even a carbon atom can make it easier tobring out the "character" in a story-structured lesson. In developing this story of photosynthesis I would want to ask questions and lead a discussion that has students making many of the causal connections for themselves.

Willingham actually uses an example from a math lesson, and while I can see that what he presents is reasonable and contains some of the elements of a story, it seems a bit of a stretch to use it as an model for the 4 Cs he has just presented - I fail to see how the "character" component fits in, personally. Maybe a math teacher can read it over and set me straight. Nonetheless, maybe that's a good thing anyway. Willingham has already explicitly stated that he is not proposing some rigid formula for organizing a lesson, and getting caught up in making sure that your lesson fits to a T some artificial structure misses the real goal, getting students to think about what you are teaching. Sometimes the conflict is between competing ideas, or how to decide whether something is true or not, and doesn't involve "characters" in the traditional sense. And that's OK.

Next Section:
What if there is no meaning? (On rote memorization)