"The ultimate goal of differentiation is to meet the needs of the varied students in a classroom during instruction. This becomes manageable if the teacher can create a single question or task that is inclusive not only in allowing for different students to approach it by using different processes or strategies but also in allowing for different students at different stages of mathematical development to benefit and grow from attention to the task. In other words, the task is in the appropriate zone of proximal development for the entire class. In this way, each student becomes part of the larger learning conversation, an important and valued member of the learning community. Struggling students are less likely to be the passive learners they so often are.”
Lovin, A., Kyger, M., & Allsopp D. (2004) Differentiation for special needs learners. Teaching Childen Mathematics, 11, 158-167
Since the range of abilities in any one classroom is so varied and complex, it is difficult to come up with "a single question or task that is inclusive …” In Great Questions: Great Ways to Differentiate Mathematics Instruction, (2009) NCTM, Marion Small proposes big ideas for each strand of mathematics and then presents the strategy of using Open and Parallel tasks related to the same big mathematical ideas as a way to better meet the needs of all students in a classroom. Each strand of mathematics starts out with the list of big ideas, which are followed up with samples of tasks organized into the grade bands K-2, 3-5 and 6-8.
Teacher to Teacher’s Making Sense of Problem Solving program is built around the big ideas presented in the National Council of Teachers of Mathematics Curriculum Focal Points and progress in difficulty from Kindergarten to Grade 8. Teacher to Teacher has an underlying belief in the importance of differentiation at the heart of each of the classroom resource books. In each unit, we start with Warm Ups that introduce or reinforce concepts the students will need in order to fully engage in the problem solving task. Then students move forward to solve the main task. Finally, we offer at least one Extension to challenge
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the thinking of students who are ready to go beyond the basic math concepts embedded in the basic problem solving task.
As a gift to our community of learners, we have applied the ideas from Ms. Small’s book to expand some tasks presented in each classroom resource book for this newsletter by sharing related Open and Parallel Tasks. Marilyn Small defines open tasks in this way: "A task is open when it is framed in such a way that a variety of responses or approaches are possible." She explains parallel tasks as "Sets of tasks, usually two or three, that are designed to meet the needs of students at different developmental levels, but that get at the same big idea and are close enough in context that they can be discussed simultaneously."
This newsletter links to Open and Parallel Tasks that are based on problems published in the “Developing a Problem Solving Environment” Chapter of Making Sense of Problem Solving for Levels A/Kdg through C/Grade 2. Watch for future newsletters with links to Open and Parallel Tasks for Grades 3 to 8:
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