There are a slew of math textbooks out now that build in a constructivist approach to teaching math, yet temper it with direct instruction. It is as if the publishers have had their ear to the ground view Twitter, edu-blogs and other gathering places in which teachers vent about what they prefer in teaching. The publishers have gathered that there is some rebellion against student-centered, inquiry-based learning, and an equal amount against direct, explicit and whole-class instruction.
The result are textbooks that bridge this gap by proclaiming as “Big Ideas Math” series does on the front cover, as part of the title, the words “A Balanced Approach”. In the case of Big Ideas Math, their idea of balance is to start with an activity that is usually ill-defined as to what the goal of the activity is or what is to be discovered, followed by an explicit direct-instruction lesson. Some of the ideas from the activity are then incorporated into the direct-instruction lesson.
The idea of an activity in which the goal is not stated is like teaching someone how to get from point A to point B, by not telling them where Point B is, nor how it figures in the general layout and giving them some paths to follow. Based upon the paths, the person being led is supposed to then know when Point B has been reached. Or not. In any event, at some point they will be told.
Teachers who despair of such techniques (or hold to Anna Stokke’s rule of thumb which she wrote about in a CD Howe report, for “balance” being 80% direct and 20% student centered, activity/inquiry-based) will probably do the following: Incorporate the crux of the activity into a ten minute intro for the direct- and whole-class instruction lesson. Or, after mastery of material, have students do an activity, now having the prior knowledge to appreciate it and actually learn from it.
Because some schools monitor teachers closely and may not allow such latitude, I offer as a public service, this advice from the late Grant Wiggins and his co-author Jay McTighe who unwittingly provide a way out of this mess. These two masters are generally respected by those who subscribe to the edu-group-think that passes for “best practices”. Teachers can go outside the textbooks while claiming that they are still adhering to student-centered principles per Wiggins and McTighe. In the Japanese art of jiu jitsu, it’s a way of turning the opponent’s force away from you and towards them. It’s a strategy worth a try at any rate. Here it is.
More generally, weak educational design involves two kinds of purposelessness, visible throughout the educational world from kindergarten through graduate school. We call these the “twin sins” of traditional design. The error of activity-oriented design might be called “hands-on without being minds-on”—engaging experiences that lead only accidentally, if at all, to insight or achievement. The activities, though fun and interesting, do not lead anywhere intellectually. Such activity-oriented curricula lack an explicit focus on important ideas and appropriate evidence of learning, especially in the minds of the learners.
A second form of aimlessness goes by the name of “coverage,” an approach in which students march through a textbook, page by page (or teachers through lecture notes) in a valiant attempt to traverse all the factual material within a prescribed time. Coverage is thus like a whirlwind tour of Europe, perfectly summarized by the old movie title If It’s Tuesday, This Must Be Belgium, which properly suggests that no overarching goals inform the tour.
As a broad generalization, the activity focus is more typical at the elementary and lower middle school levels, whereas coverage is a prevalent secondary school and college problem. No guiding intellectual purpose or clear priorities frame the learning experience. In neither case can students see and answer such questions as these: What’s the point? What’s the big idea here? What does this help us understand or be able to do? To what does this relate? Why should we learn this? Hence, the students try to engage and follow as best they can, hoping that meaning will emerge.