OPEN-ENDED MATH PROBLEMS

Does your current math instruction involve only situations where there is one answer? Are students expected to solve problems following rigid procedures that do not require critical or creative thinking? Perhaps open-ended math problems is what your learners need to become true mathematicians who use diverse problem solving strategies to explore mathematical situations where there isn't necessarily one "right" answer.



This blog post will...

  • explain what an open-ended math problem is
  • identify the pros and cons of open-ended math problems
  • offer 3 ways to implement open-ended math problems in your classroom


WHAT IS AN OPEN-ENDED MATH PROBLEM?

An open-ended math problem is a real world math situation presented to students in a word problem format where there is more than one solution, approach, and representation. This instructional strategy is more than reciting a fact or repeating a procedure. It requires students to apply what they have learned while using their problem solving, reasoning, critical thinking, and communication skills to solve a given problem. This strategy naturally allows for differentiation because of it’s open-ended nature. In addition, it is a valuable formative assessment tool that allows teachers to assess accuracy in computation and abilities to think of and flexibly apply more than one strategy. In addition to the teacher being able to learn about their students from this tool, the students can thoughtfully extend their learning and reflect on their own thinking through whole group discussions or partner talks.

WHAT ARE THE PROS AND CONS OF OPEN-ENDED MATH PROBLEMS?

Pros:
  • Provides valuable and specific information to the teacher about student understanding and application of learning.
  • Allows the teacher to assess accuracy in computation and abilities to think of and flexibly apply more than one strategy.
  • Permits the teacher to see flexibility in student thinking.
  • Gives students the opportunity to practice and fine tune their problems solving, reasoning, critical thinking, and communication skills.
  • Creates opportunities for real-world application.
  • Empowers students to extend their learning and reflect on their thinking.
  • Fosters creativity, collaboration, and engagement in students.
  • Facilitates a differentiated learning experience where all students can access the task.

Cons:
  • Increases time in collecting data.
  • Provides a higher complexity of data.
  • Requires the implementation and practice of routines.
3 WAYS TO IMPLEMENT OPEN-ENDED MATH PROBLEMS
  1. Start a lesson with an open-ended math problem for students to solve independently. Invite them to share their work and reasoning with a partner. Ask a few students to share their ideas with the whole class.
  2. Use the open-ended math problems for fast finishers. If a student or a group of students tend to finish independent work before the rest of the class, invite them to work on an open-ended math problem.
  3. Utilize open-ended math problems as a center during math workshop. You will not have to worry about students finishing that math center before it is time to switch to the next center.

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