Introduction

graphic organizer. A visual framework that helpsthe learner organize ideas and make connectionsbetween them. Graphic organizers can be preparedby the teacher or by students. Graphic organizersinclude, for example, mind maps, T-charts, flowcharts, and Venn diagrams.guided mathematics. An instructionalapproach in which the teacher guides studentsthrough or models a mathematical skill or concept.Instruction is planned, yet flexible enoughto capitalize on alternative ideas and strategiesprovided by students. See also independentmathematics and shared mathematics.holistic evaluation. Judgement about theoverall quality of a piece of work, rather thanan analysis and scoring of individual parts ofthe work. A rubric is often used to evaluate apiece of work holistically.homework. Out-of-class tasks assigned to studentsto prepare them for classroom work or to havethem practise or extend classroom work. Effectivehomework engages students in interesting andmeaningful activities.horizontal format. A left-to-right arrangement(e.g., of addends), often used in presentingcomputation questions. See also vertical format.23+48Horizontal formathundreds chart. A 10 x 10 table or chart witheach cell containing a natural number from 1 to100 arranged in order. The hundreds chart allowsstudents to explore number patterns and relationships.identity rule. In addition, the notion thatthe sum of 0 and any number is that number(e.g., 0+4=4). In multiplication, the notion thata number multiplied by 1 equals that number(e.g., 4 x 1=4).independent mathematics. An instructionalapproach in which students work alone to focuson and consolidate their own understanding,and learn to communicate this understandingindependently. Students who are workingindependently should know that they canrequest assistance when they need it.interview. An assessment strategy usuallyinvolving a planned sequence of questions posedto an individual student. It provides informationabout a student’s thinking processes.inverse operations. The opposite effects ofaddition and subtraction, and of multiplication anddivision. Addition involves joining sets; subtractioninvolves separating a quantity into sets. Multiplicationrefers to joining sets of equal amounts; divisionis the separation of an amount into equal sets.investigation. An instructional activity in whichstudents pursue a problem or an exploration.Investigations help students develop problemsolvingskills, learn new concepts, and apply anddeepen their understanding of previously learnedconcepts and skills.join problem. A problem that involves the actionof increasing an amount by adding another amountto it. A join problem involves a start amount, achange amount, and a result amount. Any ofthese amounts can be unknown in a join problem.journal. (Also called “learning log”.) A collectionof written reflections by students about learningexperiences. In journals, students can describelearning activities, explain solutions to problems,respond to open-ended questions, report oninvestigations, and express their own ideasand feelings.kinaesthetic learner. (Also called “tactilelearner”.) One who learns best through physicalmovement and the manipulation of concrete94 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One