As a tutor working with my students, I have encountered a recent trend in education that I call "spiraling." The idea behind this tactic is that, instead of breaking subjects and levels of work into distinct categories, the curriculum introduces students to concepts and skills early on and then circles back to them through the years, adding more in-depth knowledge each time. For instance, instead of learning everything about quadratic equations in Algebra 2, a math student might first encounter them in a limited basis in Pre-algebra, a little more in Algebra I, and then even more in Algebra 2. This method has obvious benefits.
First, classes can move quickly through the material because the focus is on exposure and familiarity instead of mastery. Second, studies on learning have shown that people retain information better when it is learned in spaced sessions. Third, it encourages students to think critically and creatively about the concepts at hand. Because the students do not have to concentrate on perfecting one skill by performing it over and over, they should, in theory, be less bored and more engaged. Indeed, the spiraling technique reflects a more general trend away from memorization and mastery towards creative thinking. I am forever an advocate of creative and critical thinking where the student develops a “deep” knowledge of the curriculum and a capacity to infer new ideas and connections. However, I would argue that some students do not mesh well with the spiraling system. Many students have no problem flying from one skill or concept to the next as long as they get relatively decent grades, but students with low confidence feel lost with this technique. While they may learn from the technique in the way intended, the lack of a sense of mastery is unsettling to them. The negative feelings they experience while tackling the work sometimes has more impact on their confidence than their test grades do. I have seen these feelings build into a state of panic, which, in turn, starts to bleed over into homework and tests further destroying the student’s confidence. In tutoring, I have found that students with extremely low confidence and high levels of math anxiety respond well to practicing a skill more than the text or teacher requires, even more than needed to improve grades. They also do well when focused on one skill at a time and feel uncomfortable with the variety that keeps other students interested. This kind of repetition would hinder students with higher confidence levels by causing them to tune out and disengage. But, for a student with low confidence, whipping out the answer to a specific type of problem ten times in a row brings a smile and a sense of accomplishment. I try to remember that for them, the most important thing is not whether or not they are learning things but whether or not they feel like they are learning. Hence, while educators look down on memorization and repetition in terms of their cognitive effectiveness, it is important not to forget their emotional impact.