Introduction

math word wall. See word wall.mental calculation. See mental computation.mental computation. (Also called “mentalcalculation”.) The ability to solve computationsin one’s head. Mental computation strategies areoften different from those used for paper-and-pencilcomputations. For example, to calculate 53 – 27mentally, one could subtract 20 from 53, andthen subtract 7 from 33.metacognition. Reflection on one’s own thinkingprocesses. Metacognitive strategies, which canbe used to monitor, control, and improve one’sthinking and learning processes, include the followingin the context of mathematics: applyingproblem-solving strategies consciously, understandingwhy a particular strategy would be appropriate,making a conscious decision to switch strategies,and rethinking the problem.mind map. A graphic representation of informationthat is intended to help clarify meaning.In making a mind map, students brainstorminformation about a concept and organize it bylisting, sorting, or sequencing the key words, orby linking information and/or ideas. Mind mapscan be used to help students understand theinterrelationships of mathematical ideas.minuend. In a subtraction question, the numberfrom which another number is subtracted. In theexample 15 – 5=10, 15 is the minuend.misconception. An inaccurate or incompleteunderstanding of a concept. Misconceptionsoccur when a student has not fully connecteda new concept with other concepts that areestablished or emerging. Instructional experiencesthat allow the student to understand how a newconcept relates to other ideas help to alleviatemisconceptions.model. See mathematical model.modelling. The process of representing a mathematicalconcept or a problem-solving strategyby using manipulatives, a diagram or picture,symbols, or real-world contexts or situations.Mathematical modelling can make math conceptseasier to understand.movement is magnitude. The idea that, as onemoves up the counting sequence, the quantityincreases by 1 (or by whatever number is beingcounted by), and as one moves down or backwardsin the sequence, the quantity decreases by 1(or by whatever number is being counted by)(e.g., in skip counting by 10’s, the amount goesup by 10 each time).multiplicative comparison problem.A problem that involves a comparison of twoquantities where one quantity is the multiple ofthe other. The relationship between the quantitiesis expressed in terms of how many times largerone is than the other. For example: Lynn has 3pennies. Miguel has 4 times as many pennies asLynn. How many pennies does Miguel have?multiplicative relations. Situations in whicha quantity is repeated a given number of times.Multiplicative relations can be representedsymbolically as repeated addition (e.g., 5+5=5)and as multiplication (e.g., 3 x 5).next steps. The processes that a teacher initiatesto assist a student’s learning following assessment.“nice” numbers. See under estimationstrategies.non-standard units. Measurement units used inthe early development of measurement concepts –for example, paper clips, cubes, hand spans, andso on. See also standard units of measure.number line. A line that matches a set of numbersand a set of points one to one.–3 –2 –1 0 1 2 396 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One