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.
Barrier 3: Students who believe that success depends on innate ability do poorly compared to those who believe that success depends on effort.
- Usher, E. L. (2009). Sources of middle school students' self-efficacy in mathematics: A qualitative investigation. American Educational Research Journal, 46(1), 275-314.
- Kamins, M. L. & Dweck, C. S. (1999). Person versus praise and criticism: implications for contingent self-worth and coping. Developmental Psychology, 35, 835-847.
- Mueller, C. M. & Dweck, C. S. (1998). Praise for intelligence can undermine children's motivation and performance. Journal of Personality and Social Psychology, 75, 33-52.
- Licht, B. G. & Dweck, S. C. (1984). Determinants of academic achievement: the interaction of children's achievement orientations with skill area. Developmental Psychology, 20, 628-636. Canadian Child Care Federation (CCCF).
Solution: Give students problems that get incrementally harder to show them they can surmount any challenge through their work. Students learn best when they are allowed to take moderate risks with positive feedback.
- 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.
- Clifford, M. (2009). Students need challenge not easy success, Educational Leadership, September.
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.