Introduction

Acknowledge and Utilize Students’ Prior KnowledgeFor learning to be effective, it must utilize and build upon theprior knowledge of the student. Children’s natural inclination toplay almost from birth ensures that all students bring some priorproblem-solving knowledge to the primary classroom. The levelof such prior learning varies greatly across cultures and socioeconomicgroups, but the extent of prior knowledge in students isoften greater than has traditionally been assumed.“Young children possess aninformal knowledge of mathematicsthat is surprisingly broad,complex and sophisticated.”(Baroody, 2004, p. 10)Teachers in the primary grades connect this “home-grown” intuitionand understanding with new knowledge by developinglearning experiences that help foster mathematical understanding.Similarly, in the junior years, students acquire experiences related totheir interests in sports, the arts, and various hobbies. Teachers canuse these experiences to connect mathematics to the ”outside world”.Some examples of the connections teachers can make are as follows:• Students often come to school able to count to 5 or 10. Teacherscan build on this skill to help students begin to see patterns inour number system and relationships between one number andanother (6 is 1 more than 5 and 2 more than 4).• Many students have had experiences with earning money.Teachers can use this knowledge to help students build theirunderstanding of place value and make decimal calculations(e.g., four quarters equal $1.00, so 0.25 x 4 =1.00).“Children can differ in their priorknowledge for a variety ofreasons (e.g., a child may be anew Canadian or come from adifferent cultural background).What is important to keep inmind is that general knowledgeimportant for new learning mayneed to be restated and reinforcedfor some children and actuallytaught to others.”(Expert Panel on Literacy and NumeracyInstruction for Students With SpecialEducation Needs, 2005, p. 40)• Students have natural problem-solving strategies that they useas they figure out the fair distribution of pencils among friends. Teachers can helpstudents make connections between these strategies and the strategies used in“school” mathematics.Provide Developmentally AppropriateLearning TasksStudents go through stages of mathematical development,with considerable individual variation from student to student.Recognition of this variation is key to establishing the mosteffective learning environment. For the teaching and learningprocesses to be successful, it is important that the student’sexisting conceptual understanding of mathematics be recognized.Students need to encounter concepts in an appropriate manner, atan appropriate time, and with a developmentally appropriateapproach.“Developmentally appropriatemeans challenging but attainablefor most children of a given agerange, and flexible enough torespond to inevitable individualvariation. That is, expectationsmay have to be adjusted forchildren with differentexperiential backgrounds.”(Clements, Sarama, & DiBiase,2004, p. 13)28 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One