Introduction

assessment. The ongoing, systematic gathering,recording, and analysis of information about astudent’s achievement, using a variety of strategiesand tools. Its purpose is to provide the teacherwith information that he or she can use to improveprogramming. Peer assessment, the giving andreceiving of feedback among students, can alsoplay an important role in the learning process.associative property. A property of additionand multiplication that allows the numbers beingadded or multiplied to be regrouped without changingthe outcome of the operations. For example,(7+9)+1=7+(9+1) and (7 x 4) x 5=7 x(4 x 5).Using the associative property can simplifycomputation. This property does not generallyhold for subtraction or division.attitude. The emotional response of studentstowards mathematics. Positive attitudes towardsmathematics develop as students make sense oftheir learning and enjoy the challenges of richmathematical tasks.attitudinal survey. (Also called “questionnaire”.)An investigation of students’ feelings aboutmathematics, learning activities, and the classroomenvironment. Younger students can respond orallyto a teacher’s survey questions.attribute. A quantitative or qualitative characteristicof an object or a shape (e.g., colour, size,thickness).automaticity. The ability to use skills or performmathematical procedures with little or no mentaleffort. In mathematics, recall of basic facts andperformance of computational procedures oftenbecome automatic with practice. See also fluency.backwards design. (Also called “design down”.)An approach to program planning in whichteachers determine, foremost, how studentswill demonstrate their learning of curriculumexpectations, and then develop learning activitiesthat support students in achieving learning goals.balanced mathematics program. A mathematicsprogram that includes a variety ofteaching/learning strategies, student groupings,and assessment strategies. In a balanced program,teachers provide opportunities for students todevelop conceptual understanding and proceduralknowledge. A balance of guided mathematics,shared mathematics, and independent mathematicssupports students in learning mathematics.barrier games. An instructional activity usedto develop or assess students’ oral mathematicalcommunication skills. Students work in pairs,giving instructions to and receiving instructionsfrom each other while unable to see what the otheris doing behind a screen – such as a propped-upbook – between the two students. The goal ofthe activity is to develop students’ ability to usemathematical language clearly and precisely.base ten blocks. Three-dimensional modelsdesigned to represent whole numbers and decimalnumbers. Ten ones units are combined tomake 1 tens rod, 10 rods are combined to make1 hundreds flat, and 10 flats are combined tomake 1 thousands cube. The blocks help studentsunderstand a wide variety of concepts in numbersense, including place value; the operations(addition, subtraction, multiplication, and division);and fractions, decimals, and percents.basic facts. (Also called “basic number combinations”.)The single-digit addition and multiplicationcomputations (i.e., up to 9+9 and 9 x 9) and theirrelated subtraction and division facts. Studentswho know the basic facts and know how they arederived are more likely to have computationalfluency than students who have learned the basicfacts by rote.benchmark. A number or measurement that isinternalized and used as a reference to help judgeother numbers or measurements. For example,knowing that a cup holds 20 small marbles88 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One