Barrier 1: Students who are anxious or who lack a sense of self efficacy have trouble focusing and staying on task.
Barrier 2: Students who feel inferior are less likely to be engaged in their lessons. In early primary school, children start to believe some children are superior or "smarter" in math.
- Henderlong Corpus, J., et. al. (2006). The effects of social-comparison versus mastery praise in children's intrinsic motivation. Motivation and Emotion, 30, 335-345
- Hong, E., Peng, Y., & Rowell, L. L. (2009). Homework self-regulation: Grade, gender, and achievement-level differences. Learning & Individual Differences, 19(2), 269-276.
- Dweck, C.S. (1975). The role of expectations and attributions in the alleviation of learned helplessness, Journal of Personality and Social Psychology, 31, 674-684.
- Dweck, C. S. (1999). Self-Theories: Their role in motivation, personality, and development. Philadelphia, PA: Psychology Press.
- Dweck, C. S. (2006) Mindset: The New Psychology of Success, Random House, NY, 2006
- Ma, X. & Xu, J. (2004). Determining the causal ordering between attitude toward mathematics and achievement in mathematics. American Journal of Education, 110, 256-280.
Solution: Review basic skills and concepts thoroughly before introducing new topics, so all students can start on an equal footing, and target less confident students with special "bonus" questions that allow them to experience success. When students feel equally capable, their brains work efficiently, and they tend to become equally capable.
- Pashler, H., Bain, P., Bottge, B., Graesser, A., Koedinger, K., McDaniel, M., and Metcalfe, J. (NCER 2004-2007). Organizing Instruction and Study to Improve Student Learning. Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education
- Geary, D. C. (2006). Development of mathematical understanding. In W. Damon (Ed.), Handbook of child psychology (6th ed., Vol. 2, D. Kuhl & R. S. Siegler (Eds.). Cognition, perception, and language, pp. 777-810). New York: John Wiley & Sons.
- Hutton, L. A., and Levitt, E. (1987). An academic approach to the remediation of mathematics anxiety. In R. Schwarer, H. M. van der Ploeg and C. D. Spielberger (Eds.), Advances in test anxiety research, Vol. 5, 207-211.
- Humbre, R., (1990). The nature, relief and effects of mathematics anxiety. Journal for Research in Mathematics Education, 12(1), 33-46.
Barrier 3: Students who believe that success depends on innate ability do poorly compared to those who believe that success depends on effort.
Barrier 4: Research has shown that students need extensive practice to master new concepts and skills, but they aren't always motivated to practice.
Barrier 5: The brain is easily overwhelmed by too much new information; math problems that are too complex or overly contextualized or texts that have too many new ideas on a page can discourage and confuse students.
Barrier 6: Weak readers and ESL students can be overwhelmed by too much text, making their language challenges a barrier to achievement in math.
Barrier 7: It is important to teach mathematics using models, but sometimes concrete materials can be distracting or confusing: students don't necessarily learn efficiently from using manipulatives in unstructured lessons.
Barrier 8: Students who haven't mastered basic number facts and operations and committed them to long term memory must use short term memory to do so, leaving inadequate short term memory capacity for problem solving. Students who haven't mastered basic number facts also have trouble seeing patterns and making estimates and predictions.
Barrier 9: Students often memorize rules or procedures without understanding. This may enable them to answer narrowly put questions, but without promoting true understanding: math doesn't always make sense to them.
Barrier 10: To succeed in later grades, students must master the concepts and skills taught in the elementary curriculum. But many students never master these skills and concepts, even though the vast majority are capable of doing so.