The Importance of Flexibility

Flexibility in reasoning is essential. Oberlin’s 1982 study found that when students are told that there is only one correct problem solving approach, this information furthers the apprehensive thinking of already math anxious students. Math anxious students who adopt the belief that there exists a singular path toward a problem’s solution may become rigid in their mathematical reasoning, which could, in turn, discourage critical thinking when processing mathematical content. De-emphasizing rote memorization is especially relevant given the current emphasis on standardized tests, which rely heavily on problems with convoluted phrasings and multiple steps to their solution, rendering rote memorization an insufficient means of study. 

Entity Vs. Incremental Theory

Research on implicit theories about the origins intelligence has delineated two primary perspectives; while some believe intelligence is relatively fixed (therein adopting an entity theory perspective), others view intellect as malleable, changing as a result of educational exposure and effort expenditure (therein adopting an incremental theory perspective). Research supports the assertion that if students believe their ability is fixed and they feel they are less naturally mathematically inclined, they are more likely to give up at the first sign of difficulty. While tutoring, I stress the importance of celebrating effort as a necessary component in achievement, helping students shift towards a mindset that encourages their academic growth.  For additional information on the impact implicit theories can have, please read Carol Dweck's 2007 book titled "Mindset." 

Seeking Structure in Mathematics

When inundated with facts and formulas, students can feel easily overwhelmed. Research Psychologists Neuberg and Newsom (1993) identify two primary strategies we often enlist for reducing cognitive load: Avoidance strategies and imposing a structure on complex stimuli. When complexity levels rise, reliance on heuristic processing similarly increases; however, crucial information may be lost when the categories formed as part of this process are 
inaccurate or incomplete (Bodenhausen & Wyer, 1985). Possible implications for individual differences in the need for structure serves as just one more area in which sensitivity to each student’s cognitive needs is key. Some may require additional drills when learning new concepts, or when disassociating concepts that have been inappropriately grouped. However, once the true structure behind each concept is understood, these students have shown a tremendous capacity and aptitude for discerning appropriate applications and excelling in mathematics!