In conversations about differentiation, strategies to scaffold learning for students who need more support, and strategies to extend the learning for students who are ready for more challenge often come up. One topic that is rarely considered however, is the importance of finding ways to offer students who typically need more support, opportunities to think about a task in ways that will extend their thinking about the mathematics.
In the following conversation, excerpted from the Supporting Math Learning online course, four participants discuss the importance of providing students who may need more support in math with opportunities to extend their thinking, and how doing so can challenge a teacher’s assumptions about who can and can’t engage in rigorous, meaningful mathematics tasks.
…The idea of making sure that students who typically need support also have the benefit of activities and tasks that extend their thinking is very powerful, and it directly relates to my student, Sam.
Sam is a slower learner than his peers, but he is eager and enthusiastic. It is in differentiating that a teacher can keep Sam “hooked” while also meeting his needs and helping him progress.
In general, differentiation that will be most beneficial to Sam will provide intervention and clarity in a challenging task. Sam is very visual and kinesthetic, and anywhere a visual or concrete manipulative can be brought in gives Sam a strong starting point. Sam also does well in a small group where he feels safe and supported and more willing to take risks.
In terms of giving Sam an opportunity to extend his thinking, varying the problem comes to mind. This would allow Sam to work in different ways while still using differentiations that assist his understanding. For example, Sam could be asked to create a problem of his own…but can do so using visuals in addition to numerals to maintain the strength that he gets from pictorial representations.
Cynthia: I love when you said: “making sure that students who typically need support also have the benefit of activities and tasks that extend their thinking.” This is so true. So often we view a student as needing more support and sometimes forget that they may be capable of more. However, we will never know what they are capable of or what levels of conceptual understanding they can achieve if we never allow them.
Jordan: I agree! There have been many times when students have surprised me with the things they know that I would have never thought they were capable of. This is such an important thing to remember!
Nadia: Well said…struggling students need opportunities to extend their thinking just as much as strong students need opportunities to explain their thinking to those who do not understand…yet. I have been surprised by both groups of students during intervention when struggling learners come up with an amazing insight into the problem, while those who breeze through it are unable to explain how they got their answer. We assume that kids on math support won’t understand certain concepts because we think they are not yet ready. We also assume that extension kids are all set because they know the answers. It’s time to review these assumptions and explore the potential of all students to be math thinkers.
A couple of takeaways from this conversation:
- Jane described specific strategies she could use to support Sam during a challenging task. These strategies built on Sam’s enthusiasm for learning, his preferred learning style (visual and kinesthetic) and his preference for working in a small group. By leveraging Sam’s strengths, and using what she knew about how Sam learned best, Jane was able to set Sam up for success.
- Cynthia, Jordan and Nadia each point out that assumptions about students who typically need more support and students who “know the answers” are often incorrect. Providing all students with opportunities to extend their thinking is one way to examine these assumptions.
- These teachers’ comments reflect their openness to hearing mathematical ideas from their students that they may not have anticipated, as well as their eagerness to be surprised by their students’ thinking.
In discussing this topic together, Jane, Cynthia, Jordan and Nadia were able to support one another in their practice and make their thinking explicit. Their comments illustrate how honoring students’ strengths while keeping the mathematical focus strong, allows all students to access the problem or task. This not only provides teachers with an important opportunity to learn more about students’ mathematical understandings, but also has a powerful impact on how students view themselves as mathematicians.
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