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.
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.
- Nesher, P., Hershkovits, S., & Novotna, J. (2003). Situation model, text base and what else? Factors affecting problem solving. Educational Studies in Mathematics, 52, 151 - 176.
- Adler, J. (1998). A language of teaching dilemmas: Unlocking the complex multilingual secondary mathematics classroom. For the Learning of Mathematics, 18(1), 24-33.
- Kotsopoulos, D. (2007). Mathematics discourse: "It sounds like hearing a foreign language." Mathematics Teacher, 101(4), 310-305.
- Hayfa, N. (2006). Impact of language on conceptualization of the vector. For the Learning of Mathematics, 26(2), 36-40.
- Jordan, N., Hanich, L., & Kaplan, D. (2000). A longitudinal study of mathematical competence in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development, 7, 834-850.
- Rasanen, P. & Ahonen, T. (1995). Arithmetic disabilities with and without reading difficulties: a comparison of arithmetic errors. Developmental Neuropsychology, 11, 275-295.
- Jordan, N. C., Huttenlocher, J. E., & Levine, S. C. (1992). Differential calculation abilities in young children from middle and low income families. Developmental Psychology, 28, 644-653.
- Jordan, N. C., Huttenlocher, J. E., & Levine, S. C. (1994). Assessing early arithmetic abilities: effects of verbal and non-verbal response types on the calculation performance of middle- and low- income children.
- Jordan, N. C., Levine, S. C., & Huttenlocher, J. E. (1994). Development of calculation abilities of middle- and low- income children after formal instruction in school. Journal of Applied Developmental Psychology, 15, 223-240.
- Fuchs, L., Fuchs, D. & Prentice, K. (2004). Responsiveness to mathematical problem-solving instruction: comparing students at risk of mathematics disability with and without risk of reading disability. Journal of Learning Disabilities, 37, 293-306.
Solution: Minimize the use of text in student materials, and introduce language gradually and rigorously. Place activities or exercises that require lengthy descriptions in the Teachers Guides. Ask students to communicate their understanding, but allow pictures, numbers or oral answers when writing is a challenge.
- Jordan (1992, 1994, 1994). The three papers referenced immediately above, show particularly well that allowing alternative (non-verbal) response modalities can reveal knowledge that would not be revealed if responses relied heavily on language.
- Uttal, D. H., Liu, L. L., & DeLoache, J. S. (2006). Concreteness and symbolic development. In L. Balter and C. S. Tamis-LeMonda (Eds.), Child Psychology: A Handbook of Contemporary Issues (2nd Ed.) (pp.167-184). Philadelphia, PA: Psychology Press.
- Chamot, A., & O'Malley, J. M. (1994). The CALLA handbook: Implementing the cognitive academic language learning approach. Mass: Addison-Wesley Publishing Co.
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.