**External Research that Supports JUMP Math's Approach**

The JUMP Math program delivers the mathematical curriculum through the method of "guided discovery." In JUMP lessons, students explore and discover mathematical concepts independently in manageable steps, while the teacher provides sufficient guidance, examples, feedback and scaffolding for all students to meet their full potential.

JUMP Math is recommended by the Canadian Language and Literacy Research Network as a program that "offers educators... complete and balanced materials as well as training to help teachers reach all students".

*J. Bisanz et al. (2010) Foundations for Numeracy: An Evidence-based Toolkit for the Effective Mathematics Teacher. Canadian Child Care Federation and Canadian Language and Literacy Research Network, p. 44.*

In 2011, L. Alfieri et al. conducted a meta analysis of 164 studies of discovery-based learning and concluded that "Unassisted discovery does not benefit learners, whereas feedback, worked examples, scaffolding and explicit instruction do." The authors recommend "enhanced discovery" (discovery with the instructional supports mentioned above) as the most effective approach to instruction in mathematics.

*Alfieri, L., et al. (2011) Does Discovery Based Instruction Enhance Learning? Journal of Educational Psychology, Vol. 103, Issue 1, p 1-18.**See also the references below for evidence that discovery needs to be balanced with rigorous guidance: Anderson (2000), Gobet (2005), Van Merrienboer (2005), Ross (2006), Kirshner (2006).*

JUMP Math's extensive Teacher Materials are the core of the JUMP program. The lesson plans in the guides cover the full curriculum and include ideas for contextualizing mathematical concepts, mini-assessments and questions for formative assessment, problems and challenges that allow students to investigate and develop concepts, mental math exercises to help students develop computational fluency and automatic recall of facts, extension questions for students who finish their work early, and a variety of games and activities with concrete materials. The JUMP workbooks, which are used at the end of a lesson, help teachers assess whether students understood the lesson and give students sufficient practice to consolidate skill and concepts.

JUMP Math lesson plans and materials allow teachers to differentiate instruction by providing extra practice, scaffolding and continuous assessment for students who need it, and more advanced work for students who finish their work early. But while instruction is differentiated, the significant majority of students are expected to meet the same standards.

A growing body of evidence in education and cognitive science suggests that, with proper instruction, children can develop abilities in subjects for which they previously showed no real aptitude or gift. (see for instance, Ross, P. E. (2006) "The Expert Mind." Scientific American, July.) But research also shows that new abilities are more likely to emerge when a child's brain is attentive and engaged.

**Supporting Research: **

*Posner, M., Rothbart, M. (2005) Influencing brain networks: implications for education, TRENDS in Cognitive Science, v.9, no. 3**Gathercole, S. E., Alloway, T. P., Kirkwood, H. J., Elliott, J. G., Holmes, J., & Hilton, K. A. (2008). Attentional and executive function behaviours in children with poor working memory. Learning and Individual Differences, 18(2), 214-223.*-
*Schwartz, J., Bregley, S. (2002) The Mind and the Brain. NY, Regan Books.*

In designing the JUMP Math program we asked:

# What barriers prevent students from paying attention and being engaged in math lessons?

*Click on the posters below to read research that supports common barriers and our strategies for teachers.*

**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.

**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**