Introduction

materials. Learning activities that involve dramatization,the construction of concrete mathematicalmodels, and the use of manipulatives helpkinaesthetic learners understand mathematicalconcepts.learning log. See journal.learning styles. Different ways of learning andprocessing information. For instance, visual learnersneed to see visual representations of concepts.Auditory learners learn best through verbalinstructions and discussions, by talking thingsthrough and listening to what others have to say.Tactile/kinaesthetic learners learn best through ahands-on approach, actively exploring the physicalworld around them.level of achievement. See achievement level.magnitude. The size of a number or a quantity.Movement forward or backwards, for example,on a number line, a clock, or a scale results inan increase or decrease in number magnitude.making tens. A strategy by which numbers arecombined to make groups of 10. Students canshow that 24 is the same as two groups of 10 plus4 by placing 24 counters on ten frames. Makingtens is a helpful strategy in learning addition facts.For example, if a student knows that 7+3=10,then the student can surmise that 7+5 equals 2more than 10, or 12. As well, making tens is auseful strategy for adding a series of numbers(e.g., in adding 4+7+6+2+3, find combinationsof 10 first [4+6, 7+3] and then add anyremaining numbers).manipulatives. (Also called “concrete materials”.)Objects that students handle and use in constructingtheir own understanding of mathematical conceptsand skills and in illustrating that understanding.Some examples are base ten blocks, interlockingor connecting cubes, construction kits, numbercubes (dice), games, geoboards, hundreds charts,measuring tapes, Miras (red plastic transparenttools), number lines, pattern blocks, spinners, andcolour tiles.mathematical concepts. A connection of mathematicalideas that provides a deep understandingof mathematics. Students develop their understandingof mathematical concepts through richproblem-solving experiences.mathematical model. (Also called “model” or“representation”.) Representation of a mathematicalconcept using manipulatives, a diagram or picture,symbols, or real-world contexts or situations.Mathematical models can make math conceptseasier to understand.mathematical pedagogical knowledge. Anunderstanding of how students learn mathematics,and a foundation of effective strategies for teachingmathematics.mathematical procedures. (Also called“procedures”.) The operations, mechanics, algorithms,and calculations used to solve problems.mathematical sense. The ability to makemeaningful connections between mathematicalideas, and between mathematical ideas and thereal world.mathematical skills. Procedures for doingmathematics. Examples of mathematical skillsinclude performing paper-and-pencil calculations,using a ruler to measure length, and constructinga bar graph.mathematizing. Reflecting on and interpretingmathematical ideas to make sense of them. Also,recognizing and interpreting mathematics in reallifesituations.math forum. An instructional strategy by whichstudents share work and ideas with other students.Students gather at a designated location inthe classroom to explain solutions to problems,tell problems they have created, or explain anddemonstrate what they have learned.Glossary 95