Introduction

GlossaryNote: Words and phrases printed in boldface italics in the following definitions are also defined in this glossary.abstraction. In counting, the idea that a quantitycan be represented by different things. For example,5 can be represented by 5 like objects, by 5 differentobjects, by 5 invisible things (5 ideas), or by 5 pointson a line.abstract level of understanding. Understandingof mathematics at a symbolic level. See alsoconcrete level of understanding.accommodation. A support given to a student toassist him or her in completing a task (e.g., providingmore time for task completion, reading printedinstructions orally to the student, scribing forthe student).achievement level. The level at which a studentis achieving the Ontario curriculum expectations forhis or her grade level. The Ministry of Educationdocument The Ontario Curriculum, Grades 1–8:Mathematics, 2005 provides an achievement chartthat describes student performance at four levelsof achievement in four categories of knowledgeand skills: Knowledge and Understanding, Thinking,Communication, and Application. Teachersare expected to base their assessment and evaluationof students’ work on these four levels ofachievement. Level 3 is defined as the provincialstandard.to the student’s cognitive involvement in learningactivities, rather than to physical participation orthe use of concrete materials.algorithm. A systematic procedure for carryingout a computation.anchors (of 5 and 10). Significant numbers,inasmuch as 10 is the basis of our number system,and two 5’s make up 10. Relating other numbersto 5 and 10 (e.g., 7 as 2 more than 5 and 3 lessthan 10) helps students to develop an understandingof number magnitude, to learn basic additionand subtraction facts, and to acquire number senseand operational sense. See also five frame andten frame.anecdotal record. (Also called “anecdotalcomment”.) A brief written description made bythe teacher of observed student demonstrationsof knowledge and skills. Anecdotal records canprovide valuable information for assessing andevaluating student achievement.array. A rectangular arrangement of objects intorows and columns, used to represent multiplication(e.g., 3 x 5 can be represented by 15 objects arrangedinto 3 rows, with 5 objects in each row).active learning. Instruction that involves thestudent in developing personally meaningfulconcepts through engaging problem-solvingactivities and investigations. Active learning refers87