kitchen table math, the sequel: Facts, Facts, Facts!

Wednesday, July 8, 2009

Facts, Facts, Facts!

I've just written review of Dan Willingham's book "Why Children Don't Like School." Here it is:

Every once in a while, an empirical study comes along that provides solid evidence against one of those Constructivist practices that some of us whose thoughts on education come more from actual practice than from education theory have often been skeptical about. There is, for example, Jennifer Kaminski’s Ohio State study, which suggests that too much of a focus on “real-world” math obscures the underlying mathematics, such that students are unable to transfer concepts to new problems.

Dan Willingham's book Why Don't Students Like School presents a whole bunch of these experimental results. Together, they challenge the notions that:

1. Students need to learn inquiry, argumentation, and higher-level thinking rather than tons of facts.

2. Integrating art into other subjects enhances learning; so does integrating computer technology.

3. Children learn best through self-guided discovery.

4. Drill is kill. Multiple strategies in a given lesson are better than a single strategy practiced multiple times.

5. Students learn best when constructing their own knowledge.

6. The best way to prepare students to become scientists and mathematicians is to teach them to solve problems the way scientists and mathematicians do.

The empirical data that Willingham cites show that, in fact:

1. Factual knowledge, lots of it, is a prerequisite to higher-level thinking.

2. Students are most likely to remember those aspects of a lesson that they end up thinking about the most. Corollary: Incorporating art or computer technology into another subject may sometimes cause students to think about the art or the technology more than the lesson content, such that they don’t retain the latter.

3. Discovery learning should be reserved for environments where feedback about faulty strategies is immediate: "If students are left to explore ideas on their own,” Willingham writes, they may “remember incorrect 'discoveries' as much as they will remember the correct ones."

4. In Willingham’s words, "it is virtually impossible to become proficient at a mental task,” or transfer ones learning to new environments, “without extended practice."

5. Unlike experts in a field, "students are ready to comprehend but not create knowledge."

6. Novices don’t become experts by behaving like experts do. "Cognition early in training,” Willingham writes, “is fundamentally different from cognition late in training."

Of course, Willingham could be making all this up. But consider just one of his empirical claims:

"Data from the last thirty years lead to a conclusion that is not scientifically challengeable: thinking well requires knowing facts... The very processes that teachers care about the most--critical thinking processes such as reasoning and problem solving--are intimately intertwined with factual knowledge that is stored in long term memory..."

This is a strong statement that could easily be debunked by anyone who knows the empirical literature. There are plenty of highly articulate, outspoken people out there who don’t like what Willingham has to say, but I haven’t seen a single critical review that contradicts his empirical claims.

Of course, if all that matter in life are inquiry, argumentation, and “higher-level” thinking rather than lots and lots of facts, one can say whatever one wants to about Why Children Don’t Like School.


ChemProf said...

"thinking well requires knowing facts"


"Novices don’t become experts by behaving like experts do."

This is also a pet peeve, as it applies to math and science education. When I start a new project, the first thing I have to do is read the existing literature. This requires a HUGE base of knowledge. Our junior and senior chemistry majors are just about able to do this, with support. High school kids aren't, typically. Anecdotal evidence of students engaging with the literature almost always involves highly motivated and very bright students being given a selected problem in a field that has a relatively low barrier to entry. The case I'm thinking of is a Princeton freshman seminar, where students who chose to be in that particular seminar dealt with articles in developmental biology, carefully chosen to contain as little biochemistry as possible. I'm sure that worked great, but it hardly means that all high school kids should be doing that, rather than developing a framework in biology, chemistry, or whatever!

Redkudu said...

If I had any control over teacher training (ha ha), this would be the first book incoming teachers would read. I'm on my second reading of it.

Catherine Johnson said...


Tour de force

Catherine Johnson said...

When I start a new project, the first thing I have to do is read the existing literature. This requires a HUGE base of knowledge.


When I start a new project, I not only have to read as much of the existing literature as I have time for -- AND CAN UNDERSTAND -- I also have to re-read and study it until I've committed a significant amount of it to long term memory.

Working on the second book with Temple, I **really** strained, trying to get the intricacies of stereotypies 'down' -- meaning memorized.

It took me a while to realize I had to do this, btw. I would read an article, understand it pretty well, and then have no ability to write about it at all. I was assuming, as constructivists assume, that I could just look things up.

I finally discovered (!) that I absolutely could not 'look things up.'

I had to have a certain level of factual material memorized. THEN - and only then - I could look things up.

I think this corresponds to what Hirsch calls "exemplary facts." I had to memorize (memorize in a conceptual schema, not in random order) the exemplary facts.

I suspect that one of the reasons Primary Mathematics is such a successful curriculum is that the people who wrote it figured out what the exemplary facts are.