Introduction

importance to effective instruction in any area of the curriculum – namely, the need torecognize diversity in the classroom and to ensure equity for all students.Foster Positive Mathematical AttitudesOf paramount importance for successful mathematics instruction is promoting positiveattitudes in students. Sustaining such attitudes has its challenges. Many students,as they become socialized in the school environment, begin to view mathematics veryrigidly; they see it as dependent on memory and speed rather than on conceptual understanding.They view mathematics as a subject that only some students can succeed in,and their positive attitudes towards mathematics decline. The eager engagement thatmay have been observed in earlier mathematical environments diminishes as studentsare rushed to use symbols and algorithms before they have developed a sense of number.“Their view of mathematics shifts gradually from enthusiasm to apprehension, fromconfidence to fear” (National Research Council, 1989, p. 44).Educators and parents can prevent this erosion of students’ enthusiasm for mathematics.They can foster in students the positive attitudes about mathematics that help to buildconfidence by:• encouraging the belief that everyone can “do” mathematics – emphasizing effort,not innate ability;• modelling enthusiasm for teaching and learning mathematics;• addressing the learning styles of students by providing a variety of ways forstudents to gain an understanding of difficult concepts (e.g., pictures, concreterepresentations, drama, art, music, movement);• engaging all students, including English language learners, in mathematicalactivities that involve investigation, problem solving, and mathematicalcommunication;• helping students to appreciate the value of mathematics in their lives;• choosing activities carefully (not too easy, not too hard), so that students can beboth challenged and successful;• capitalizing on the “math moments” that occur naturally at home and in theclassroom.There is evidencefrom brain-basedlearning theories(Jensen, 1998) thata solid conceptualunderstanding ofnumeracy by the ageof seven is a strongindicator of futuresuccess in mathematicsand thata lack of strengthin this area is verydifficult to overcomelater on.The learning curvesof those who understandmath at anearly age and thosewho do not divergesignificantly by thetime students reachthe higher grades.Research by Steen(1990) has shownthat by Grade 8there is a seven-yearachievement-ratedifference in mathbetween studentswith the highestachievement andthose with the lowestachievement,and that this gap isnever closed.Focus on Conceptual UnderstandingInstruction in mathematics must emphasize conceptual understanding and not justprocedural knowledge. Conceptual understanding occurs when students recognizemeaningful relationships in numbers and make connections between mathematicalChildren learn bestwhen they understandwhat theyare learning.24 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One