**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.

**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.

**Supporting Research: **

*Fuchs, L.S., Fuchs D., et al (2006) The cognitive correlates of third grade skill in arithmetic, algorithmic computation and arithmetic word problems, Journal of Educational Psychology, 98, 29-43**Geary, D.C., Mathematical difficulties: cognitive, neuropsychological and genetic components, Psychological Bulletin, 1993, Vol.114, No.2, 345-362**Heirdsfield, A. M., & Cooper, T. J. (2004). Factors affecting the process of proficient mental addition and subtraction: Case studies of flexible and inflexible computers. The Journal of Mathematical Behavior, 23, 443-463.**K. S. McGrew, R. W. Woodcock, Woodcock-Johnson III Technical Manual (Riverside Publishing, Itasca, IL, 2001). The technical manual for the Woodcock-Johnson III Test of Achievement Battery - a widely used and recognized battery of achievement tests - shows that performance on math fluency and calculation subscales is significantly, positively correlated with performance on the applied problems subscale, suggesting that fluency may be critical for freeing up resources to attend to conceptual processing and to making mathematical discoveries (e.g. the correlations are .46 and .57 for math fluency and calculation, respectively for children aged 9-13, see page 170). This reference is provided as an example - these findings are not unique to the WJ-III.*

**Solution: **Make mental math exercises, like the ones in the JUMP Teachers Guide, part of the lesson. Let students develop their own strategies for computation, but don't neglect to teach the basic operations rigorously so students master them and understand how they work.

**Supporting Research: **

*Foundations for numeracy: An Evidence-based Toolkit for the effective mathematics teacher. Ottawa: CCCF. Child 92. Psychology and Psychiatry, 35, 283-2Canadian Child Care Federation (CCCF), 2010.**Murata, A., & Fuson, K. (2006). Teaching as assisting individual constructive paths within an interdependent class learning zone: Japanese first graders learning to add using 10. Journal for Research in Mathematics Education, 37(5), 421-456.*

**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.

**Related Information**