# Helping Students Gain Control in Developmental and First-Year College Mathematics Courses

By A. Gwinn Royal, Ivy Tech Community College of Indiana

Currently, I am focusing on mitigating “learned helplessness” with respect to the study of mathematics. According to an article on the APA website (https://www.apa.org/monitor/2009/10/helplessness.aspx), newer research on learned helplessness suggests that the real issue is (lack of) control. This leads me to believe that by affording my students greater control over their own learning (within the bounds of mandated curriculum and instruction), I can deliver them from helplessness to a place where they acquire a keen sense of agency in their academic endeavors. Many of the students I teach are in my courses because somewhere along the way, their study of mathematics has primarily concerned learning to fail. I teach them how to fall.

Teaching Students How to Fall

On an ice-skating outing, a parent of a toddler wants the child to enjoy the experience. There are several approaches to this scenario: the parent can just let the toddler have free reign on the ice, the parent can hold hands with the child, or the child can use a skate trainer. Suppose the toddler is free to explore. This could be dangerous, as there may be no safe place for the toddler to learn to skate by trial and error. Now, suppose the parent and child hold hands to skate. Put yourself in the position of the toddler for a moment—you’re doing your best to keep up with someone whose strides are far longer, smoother, and faster than yours, you’ve got to keep one arm up at an uncomfortably steep angle with the other one frantically waving around, and losing your balance means you’ll just get dragged along. This is less than ideal. Enter the skate trainer: this solves a lot of problems for the toddler because it now becomes a situation within which our inexperienced skater has some measure of control (slower speed, ability to take breaks when frustrated or fatigued, the separation of balancing skills from skating skills). The use of the skate trainer reminds me of Amanda Serenevy’s description for the Traditional Math approach, which includes heavy scaffolding. The kind of helplessness that often results is one of dependency; math students who are almost completely reliant on the instructor to provide hints, cues, and prodding aren’t going to make much headway toward increasingly bigger ideas if they are not given the opportunity to become more metacognitive and confident in their ability to teach themselves how to learn. Moreover, the skate trainer has limited usefulness; the skill of skating is still yet to be fully exploited—the more fun and interesting maneuvers, such as jumping and spinning, would be hampered by the use of extra equipment. If the skate trainer is used moderately, tapered off, and given up during childhood, the child will learn to be resilient (i.e. comfortable with falling and getting back up) as the skills of skating emerge. However, if the child grows into an adult who is still dependent on the skate trainer, it’s much more difficult to separate the two. Adults have an affective filter that tends to inhibit the necessary risk-taking behavior that paves the way for learning. I mitigate this kind of lack of control by incorporating a different approach.

With the Conceptual Math approach, the learner is required to exert a measure of control over certain aspects of their experiences so that deeper understanding can be cultivated. For example, students may be expected to start with a lot more of their own thinking and they are encouraged to explore their own ideas and approaches as they stumble along the path of learning. This is also where I, the instructor, can practice the art of “be[ing] less helpful,” as proposed by Dan Meyer (https://www.ted.com/talks/dan_meyer_math_curriculum_makeover#t-613428).