Introduction

ich mathematical learning environments.Learning environments that support the needs ofall students, value the prior knowledge of learners,help students link the mathematics in their realworld with the mathematics learned at school,and build positive attitudes towards mathematics.These rich environments require insightfulplanning by a thoughtful teacher who understandswhat students know, what they need to learn,how they can best learn it, what evidence willattest to their having learned what they needed to,and where they need to go next.rod. In base ten blocks, the representation for 10.rounding. See under estimation strategies.rubric. A scoring scale in chart form, oftendeveloped in connection with a performancetask, that provides a set of criteria related toexpectations addressed in the task and describesstudent performance at each of the four levelsof achievement. Rubrics are used to assess andevaluate students’ work and to help studentsunderstand what is expected of them.scaffolding. An instructional technique in whichthe teacher breaks a strategy, skill, or task intosmall steps; provides support as students learnthe strategy, skill, or task; and then graduallyshifts responsibility for applying the strategy orskill or undertaking the task independently to thestudents. Scaffolding allows students to build ontheir prior knowledge and modify their currentunderstandings.scribing. Recording the words said by a student.Teachers can scribe for students who have notdeveloped the skills necessary for recording theirown ideas.self-assessment. A student’s assessment of hisor her own progress in developing the knowledgeand skills set out in the curriculum expectations.separate problem. A problem that involvesdecreasing an amount by removing another amount.shape. See two-dimensional shape.shared characteristics. Attributes that arecommon to more than one object.shared mathematics. An instructionalapproach in which students, in pairs or in smallgroups, participate collaboratively in learningactivities. In this approach, students learn fromone another, with guidance from the teacher.spatial patterns. Orderly visual representations.The recognition of a quantity by the arrangementof the objects (e.g., the dot arrangements onstandard number cubes).stable order. The idea that the countingsequence stays consistent. It is always 1, 2, 3, 4,5, 6, 7, 8, . . ., not 1, 2, 3, 5, 6, 8.standard units of measure. Measurement unitsthat are normally used by common agreement(e.g., centimetres, square centimetres, cubiccentimetres, grams, litres, degrees, degreesCelsius, hours). See also non-standard units.strands. The broad areas of knowledge and skillsinto which curriculum expectations are organized.In the Ontario mathematics curriculum forGrades 1–8, there are five strands: Number Senseand Numeration, Measurement, Geometry andSpatial Sense, Patterning and Algebra, and DataManagement and Probability.strategy wall. A classroom display of postersthat provide brief explanations and diagrams ofmathematical procedures or strategies (e.g., measuringperimeter, recording a fraction, making alist). Teachers and students refer to the strategywall to review how procedures are performedor to consider various approaches to problems.subitizing. Being able to recognize the numberof objects at a glance without having to count allthe objects.100 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One