Introduction

composition of numbers. The putting togetherof numbers (e.g., 2 tens and 6 ones can be composedto make 26). See also decomposition ofnumbers and recomposition of numbers.computation. The act or process of determiningan amount or a quantity by calculation.concept map. A strategy for helping studentsconstruct meaning by linking new concepts withwhat they already know. A hierarchical frameworkis used, with the main concept at the topand the linking ideas arranged under this concept,beginning with general ideas or categories andmoving down towards more specific ideas orcategories. An example is shown below.needed byengineersartistscartographerse.g., the artist M.C. EscherGeometryconsists of2-D shapesmovementlocationspace3-D figurese.g., pyramidconceptual approaches. Strategies that requireunderstanding on the part of the student and notjust rote memorization.conceptual understanding. The ability touse knowledge flexibly and to make connectionsbetween mathematical ideas. These connectionsare constructed internally by the learner and canbe applied appropriately, and with understanding,in various contexts. See also procedural knowledge.concrete level of understanding. The levelof understanding that students achieve throughthe manipulation of concrete materials. See alsoabstract level of understanding.concrete materials. See manipulatives.conference. An informal conversation betweenteacher and student for the purpose of assessment.A conference provides opportunities for studentsto “talk math” and for teachers to probe students’understanding.conjecture. A conclusion or judgement thatseems to be correct but is not completely proved.Through investigations, students make conjecturesabout mathematical ideas. Given ongoing experiencesin exploring mathematical ideas, studentsdevelop an increasingly complete and accurateunderstanding of concepts.conservation. The property by which somethingremains the same, despite changes such as physicalarrangement. For example, with conservationof number, whether three objects are closetogether or far apart, the quantity remains thesame.consolidation. The development of strongunderstanding of a concept or skill. Consolidationis more likely to occur when students see howmathematical ideas are related to one another andto the real world. Practice and periodic reviewhelp to consolidate concepts and skills.context. The environment, situation, or settingin which an event or activity takes place. Real-lifesettings often help students make sense ofmathematics.continuous quantities. Quantities that do nothave distinct parts. For example, a length of ribbonthat is 55 cm long is not made up of 55 separatepieces. See also discrete quantities.cooperative group norms. Behaviours within agroup of students working collaboratively. Studentsshould understand what behaviours make a groupfunction effectively. For example, it is importantthat all group members have opportunities toshare ideas, that the group stays on task, andthat group members attempt to answer questionsasked by anyone in the group.90 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One