Is direct instruction a better approach to teaching math?

I received the following in my email today:

An intriguing question that I often wonder about myself. Cambourne's research found that learning requires engagement, which means it depends on how engaging the lecture is to the learner. I clicked on the link hoping for some clarity. I was disappointed.

Here is a sampling from Paul E. Peterson’s article, Eighth-Grade Students Learn More Through Direct Instruction, reviewing the research:

As an instructor myself, I’ve had trouble making up my mind. I can cover a lot of ground in classes where lectures consume about two-thirds of the time. But those classes get less enthusiastic student evaluations than some smaller classes where students are encouraged to solve problems through discussion. I, too, like those problem-solving classes. They require less preparation and are easier to teach.

Before we more on, here are my reactions to this portion of the article. The first is nit-picky, but when Peterson says, “I can cover a lot of ground” it is a red flag for me. I, too, cover more material through lecture, but research shows that many students fail to cover the same ground or retain any memory of the landscape. Second, there is the statement, “I, too, like those problem-solving classes. They require less preparation and are easier to teach.” All I can say is that if planning a problem-solving lesson requires less preparation, then it is not really a problem-solving lesson.

Peterson continues:

So when Guido Schwerdt and Amelie Wuppermann of the University of Munich figured out a way to test empirically the relative value of the two teaching styles (see “Sage on the Stage,” research), it is worth trumpeting the findings. These analysts took advantage of the fact that the 2003 Trends in International Mathematics and Science Survey (TIMMS) not only tested a nationally representative sample of U.S. 8th graders in math and science, but also asked their teachers what percentage of class time was taken up by students “listening to lecture-style presentations” rather than either “working on problems with the teacher’s guidance” or “working on problems without guidance.” Teachers reported that they spent twice as much time on problem-solving activities as on direct instruction. In other words, U.S. middle-school teachers have drunk deep from the progressive pedagogical well.

It is important to note that the results are based on teachers' reporting instructional approaches and not direct observation. This is important because Stigler and Hiebert (1999) found that: “Although most U.S. teachers report trying to improve their teaching with current reform recommendations in mind, the videos show little evidence that change is occurring. Furthermore, when teachers do change their practice, it is often in only superficial ways.” (The Teaching Gap p. 12) This also comes from TIMSS data. However, there is no corroborating evidence in Schwerdt and Wuppermann’s study that supports teachers’ claims that they are using problem-solving approaches.

Furthermore, as the Learning Pyramid shows, not all direct-instruction methods are equal in their effectiveness. A demonstration (think aloud) would be a superior method to simply “covering content” through a traditional lecture. Again, Cambourne has shown that demonstrations are a necessary condition for learning but not sufficient. Learners must be given the opportunity to take responsibility for their learning and “give it a go.”

None of this seems to matter to Peterson who ends his review with, “Sadly, U.S. middle-school pedagogy is weighted heavily toward problem-solving.” In my opinion, what’s sad is that he would try to pass this research off as settling what is clearly a complex issue.

My reading of the Schwerdt and Wuppermann study suggests that it tries to answer the question, “Is traditional teaching really all that bad?” without considering how their methodology might misinterpret the data. I already discussed the problem with associating teacher reporting with using observable data. I am also concerned that they combined, “working on problems with the teacher’s guidance and working on problems without guidance” into the single problem-solving category.

Watch this lesson of a U.S. classroom where students are "working on problems with the teacher’s guidance" (from the original 1995 TIMSS research) and decide for yourself whether this teacher “drunk deep from the progressive pedagogical well.” (You will need to sign up for a password but it is free.) My answer is, “No,” but this would be categorized as problem-solving time in the Schwerdt and Wuppermann study.

“Is traditional teaching really all that bad?” – based on this research, the jury is still out.