Many people believe that only a minority of children are born with mathematical talent, while the rest simply do not have the ability to succeed at a high level. Recent discoveries in cognitive science are challenging this myth of ability. The brain is not hard wired; it continues to change and develop throughout life. Steady incremental learning can result in the emergence of new abilities.

JUMP Math is a Canadian charity that was founded on the belief that all children can learn math, all teachers can teach it and both can and should enjoy it. For us, a root cause of many children's troubles in math is the belief in natural academic hierarchies. As early as kindergarten, children start to compare themselves with their peers and to identify some as talented or "smart" in math. A child who decides that she is not talented will often stop paying attention or making an effort to do well. The more the child struggles (because she is unengaged or inattentive), the more her negative view of abilities is reinforced and the less efficiently she learns.

In the past 15 years most schools in North America have adopted some kind of discovery based math program in which students are supposed to figure out concepts by themselves rather than being taught them explicitly. Discovery based lessons tend to focus less on problems that can be solved by following a general rule, procedure or formula and more on complex problems based on real-world examples that can be solved in more than one way and that have more than one solution. In discovery lessons, students spend less time learning basic facts and standard methods of calculation and more time exploring their own approaches to problem solving and computation.

Although we agree with many of the aims and methods of the discovery approach, a growing body of research suggests that some of its elements have significant drawbacks. Discovery based lessons can sometimes overwhelm students with too much extraneous material or information. And such lessons don't always give students enough time to practise and consolidate skills and concepts or provide enough help or guidance for students who struggle. In a 2011 meta-analysis (quantitative review) of 164 studies of discovery based learning, psychologist Louis Alfieri and his colleagues concluded: "Unassisted discovery does not benefit learners, whereas feedback, worked examples, scaffolding and elicited explanations do."

JUMP lessons are based on a method called "guided discovery": students explore and discover concepts independently in manageable steps, but the teacher provides enough guidance, examples, feedback and scaffolding for all students to meet their full potential. In a well scaffolded lesson, the teacher breaks learning into chunks and provides relevant examples and practice to help students tackle each chunk. Concepts are introduced in a logical progression with one idea leading naturally to the next. In a randomized controlled study presented at the Society for Research in Child Development in 2011, cognitive scientists from OISE and the Hospital for Sick Children found that students from 18 classrooms using JUMP showed twice the rate of progress on a number of standardized math tests as those receiving standard instruction in 11 other classrooms. Other studies suggest that students in JUMP classes are engaged, confident and co-operative.

The JUMP Math **Teachers Guides** (available at jumpmath.org) show teachers how to deliver exciting, interactive lessons based on the method of guided discovery. Each lesson starts with sufficient review and practice and proceeds through a series of incrementally harder questions, challenges and activities that help students develop confidence and deep conceptual understanding in math. At the end of the lesson students work from the JUMP Math **Assessment and Practice** (AP) books: The exercises in these books match the material taught in the lesson, so students can consolidate skills and concepts from the lesson and teachers can pinpoint exactly where students need help. JUMP also provides training for teachers and is working with Canadian universities to provide instruction on JUMP for teacher candidates.

New research in cognitive science has shown that achievement in math is a better predictor of long term academic success for children than achievement in any other subject, including reading. JUMP's mission is to provide teachers and parents with the resources and support they need to ensure that children reach their full potential in the subject.

*John Mighton is an author, playwright and the founder of JUMP Math. This is the first in a series on teaching math.*