Differentiating Instruction through Mathematical Tasks

by Tara Russo

The use of mathematical tasks is an effective strategy to differentiate the process by which students develop an understanding of mathematical concepts. Tasks have multiple entry and exit points and, at times, are not limited to one answer. Well-written tasks allow students to make sense of mathematical concepts they have learned and use them in meaningful ways. They demand a high level of cognitive engagement and promote productive struggle through problem solving.

When solving a mathematical task, students must first make sense of the task and the essential information provided. The goal of a mathematical task is not limited to finding a correct answer. A major goal is for students to be able to explain the connections they made when deriving their answer.

Depending on the learner’s mathematical understanding, students may choose to create representations or equations as they make sense of the task. To change the degree of difficulty within a task, mathematical vocabulary, wording, pictures, symbols, and/or numbers can be modified.

Two types of tasks commonly used tasks to differentiate mathematics instruction are parallel tasks and open-ended questions.

Parallel tasks are two or three tasks that focus on the same learning objective, however, require different levels of cognitive demand. Ultimately, the students are solving the same task, but the information is modified to accommodate each student’s mathematical understanding. As shown within the examples below, both tasks require a different level of cognitive demand and aim to assess students’ understanding of patterning. Task 2 includes additional parameters, which will limit the range of possible answers.

  • Task 1: Create a repeating pattern with hexagons and pentagons.
  • Task 2: Create a repeating pattern with hexagons and pentagons. The pattern should contain more hexagons than pentagons.

Open-ended questions are mathematical tasks created with the intent that students at different levels can be successful even though they may arrive at their answers in a variety of ways. There is not one correct answer, process, nor strategy students must use. Students may answer the task through various pathways. Consider the following examples:

  • Example 1: How are the numbers 675 and 576 similar? Explain your answer.
  • Example 2: Create a word problem that has 1,632 as the answer.

A student may state 675 and 576 are similar because they both have values greater than 500. Another student may say that both numbers can be subtracted from a four-digit number and still hold a positive value greater than one hundred. A student with a lower level of mathematical understanding may simply state that both numbers contain the digits 5, 6 and 7.

Mathematical tasks allow students of all ability levels to be successful when engaging in solving them. Tasks are tailored toward the individual needs of students, yet maintain consistent expectations that are aligned to the lesson’s objective. They engage students in scenarios that promote a high level of cognitive engagement that will allow them to apply their understanding of mathematical concepts.

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  • Dennis Cullen
    Mathematics, Paraprofessionals, Multi-Tiered Systems of Support (MTSS/RtII)
  • Tara Russo
    Mathematics, Paraprofessionals, Multi-Tiered Systems of Support (MTSS/RtII)
  • Jonathan Regino
    Mathematics, Multi-Tiered Systems of Support (MTSS/RtII)
  • Jared Campbell
    Autism, Mathematics, Multi-Tiered Systems of Support (MTSS/RtII)
  • Elaine Neugebauer
    Mathematics, Family Engagement, Multi-Tiered Systems of Support (MTSS/RtII)
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