reversing this traditional sequence so that exploratory problem-solving precedes instruction could be more beneficial.
To test this hypothesis, researchers conducted an experimental classroom study on 213 ninth Graders, randomly allocating them to 5 different conditons.
The objective of the class was to teach the mathematical formula for how to compute the slope of a linear function.
In the first control condition, students were directly taught the formula, then asked to apply it to 8 cases (graphical representations).
In the other conditions, students were not taught the formula at first, but only after going through a booklet with the same eight cases and being asked to find out by themselves how to calculate the slopes of the represented functions.
These experimental conditions differed in that some students were given the coordinates of two points as well as labeled axes (grounded condition), while others were not given that information (idealized condition).
Likewise, some students were given the value of the slope, and asked how to derive it through 4 guided questions (explain condition), while others were not given that information (invention condition)
Results showed that problem-solving was more effective than the traditional tell-and-practice sequence (based on assessments immediately after the class, and 4 weeks later), but only in the idealized-invention condition, i.e., when students were asked to find the formula in an abstract context, without any of the information given to the other groups.
This approach with rudimentary scaffolding was about 17% more efficient than the traditional one in terms of students’ grades. What is more, this superiority increased over time.
Interestingly, this approach proved superior regardless of the fact that students in this condition succeeded or not in finding the formula.
Thus, researchers theorized that this approach proved more successful precisely because of its challenging nature, which required more effort and cognitive engagement than the other methods.
More precisely, it was the right kind of difficult. Indeed, the authors hypothesized that the additional information given to the other groups increased the “extraneous load” associated with the exercise, thus diminishing the students’ “germane load.”
“Extraneous load” refers to the presentation of the problem to the students and its degree of complexity, while “germane load” refers to the processes generated by the students to understand and memorize information.
Source: Schalk et alia (2018)