# Differentiating Math Instruction Article

January 5, 2015
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By Jeannette Johnson
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2 More Good Questions: Great Ways to Dif erentiate Secondary Mathematics Instruction mathematical talent/interest/con dence, to ensure that each student can learn important mathematics. “Equity does not mean that every student should receive identical instruction; instead, it demands that reasonable and appropriate accom- modations be made as needed to promote access and attainment for all students” (NCTM, 2000, p. 12). THE PARTICULAR CHALLENGE IN GRADES 6–12 The challenge for teachers of grades 6–12 is even greater than in the earlier grades, particularly in situations where students are not streamed. Although there is much evidence of the value, particularly for the struggling student, of being in hetero- geneous classrooms, the teacher in those rooms must deal with signi cant student differences in mathematical level. While some students are still struggling with their multiplication facts or addition and subtraction with decimals, others are comfortable with complex reasoning and problem solving involving fractions, decimals, and percents. The differences between students’ mathematical levels, beginning as far back as kindergarten or grade 1, continue to be an issue teachers must face all through the grades. Where some see the answer as streaming, many believe that the answer is a differentiated instruction environment in a destreamed classroom. WHAT IT MEANS TO MEET STUDENT NEEDS One approach to meeting each student’s needs is to provide tasks within each stu- dent’s zone of proximal development and to ensure that each student in the class has the opportunity to make a meaningful contribution to the class community of learners. Zone of proximal development is a term used to describe the “distance between the actual development level as determined by independent problem solving and the level of potential development as determined through problem solv- ing under adult guidance or in collaboration with more capable peers” (Vygotsky, 1978, p. 86). Instruction within the zone of proximal development allows students, whether with guidance from the teacher or by working with other students, to access new ideas that are beyond what the students know but within their reach. Teachers are not using educational time wisely if they either are teaching beyond the student’s zone of proximal development or are providing instruction on material the student already can handle independently. Although other students in the classroom may be progressing, the student operating outside his or her zone of proximal develop- ment is often not bene ting from the instruction. For example, a teacher might be planning a lesson on calculating the whole when a percent that is greater than 100% of the whole is known, using a problem such as asking students to determine what number 30 is 210% of. Although the skill that the teacher might emphasize is solving a proportion such as 210 100 = 30 x

### More from Jeannette Johnson

2 More Good Questions: Great Ways to Dif erentiate Secondary Mathematics Instruction mathematical talent/interest/con dence, to ensure that each student can learn important mathematics. “Equity does not mean that every student should receive identical instruction; instead, it demands that reasonable and appropriate accom- modations be made as needed to promote access and attainment for all students” (NCTM, 2000, p. 12). THE PARTICULAR CHALLENGE IN GRADES 6–12 The challenge for teachers of grades 6–12 is even greater than in the earlier grades, particularly in situations where students are not streamed. Although there is much evidence of the value, particularly for the struggling student, of being in hetero- geneous classrooms, the teacher in those rooms must deal with signi cant student differences in mathematical level. While some students are still struggling with their multiplication facts or addition and subtraction with decimals, others are comfortable with complex reasoning and problem solving involving fractions, decimals, and percents. The differences between students’ mathematical levels, beginning as far back as kindergarten or grade 1, continue to be an issue teachers must face all through the grades. Where some see the answer as streaming, many believe that the answer is a differentiated instruction environment in a destreamed classroom. WHAT IT MEANS TO MEET STUDENT NEEDS One approach to meeting each student’s needs is to provide tasks within each stu- dent’s zone of proximal development and to ensure that each student in the class has the opportunity to make a meaningful contribution to the class community of learners. Zone of proximal development is a term used to describe the “distance between the actual development level as determined by independent problem solving and the level of potential development as determined through problem solv- ing under adult guidance or in collaboration with more capable peers” (Vygotsky, 1978, p. 86). Instruction within the zone of proximal development allows students, whether with guidance from the teacher or by working with other students, to access new ideas that are beyond what the students know but within their reach. Teachers are not using educational time wisely if they either are teaching beyond the student’s zone of proximal development or are providing instruction on material the student already can handle independently. Although other students in the classroom may be progressing, the student operating outside his or her zone of proximal develop- ment is often not bene ting from the instruction. For example, a teacher might be planning a lesson on calculating the whole when a percent that is greater than 100% of the whole is known, using a problem such as asking students to determine what number 30 is 210% of. Although the skill that the teacher might emphasize is solving a proportion such as 210 100 = 30 x

**Published:**Jan 5, 2015