Humanizing Intervention: Opening Problem Solving and Ending Timed Activities
At the Math Learning Center, we believe that all students can make sense of mathematics. Some students just need more time, more opportunities, and more support than others. Our approach emphasizes problem solving, the use of faithful visual models, and a focus on developing fluency.
In March 2021, the Institute of Education Sciences (IES) and the What Works Clearinghouse released a new version of their guidance on assisting students who struggle with mathematics. Our original Bridges Intervention materials were aligned to the 2009 IES recommendations, but we found a mismatch between some of their new recommendations and our understanding based on a broader review of the research about teaching, learning, and intervention. For example, rather than teachers providing students time to explore and drawing out their prior knowledge and capabilities, the new IES recommendations imply that teachers should “show and tell,” potentially leaving students to perceive mathematics as disconnected facts and procedures to memorize. Two specific areas of concern are the approach to word problem instruction and the use of timed activities.
We value developing students as persistent problem solvers and recognize the need for opportunities to productively deal with and work through struggle, whether or not a student has been identified as needing additional support. Research has shown students who are neurodiverse can and do benefit from inquiry-oriented instruction (Hunt & Empson, 2015; Lambert & Tan, 2017); it is therefore inequitable to offer only skills-focused instruction, which leaves students hesitant about their abilities to problem solve. In the recently released revised edition of Bridges Intervention, we continue to provide opportunities for problem solving throughout the materials. We also modified the problem contexts to be more equitable and inclusive, particularly in terms of gender and socioeconomic class. This means more students will be able to relate to and access the problem situations.
In contrast to the more direct instruction approaches recommended by IES, we support students using faithful visual models alongside building, drawing, and acting out what is happening in the problem, as scaffolds. As recommended by Lambert (2018, 2021), we offer a multimodal approach that supports students with representing their thinking by concurrently modeling quick sketches, providing graphic organizers, and using equations as ways to communicate and make connections (NCTM, 2014a).
The problem situations in the Bridges Intervention modules include a range of problem types with unknowns in varied locations. Instead of teaching particular strategies for solving these problems, as recommended in the IES guidelines, we encourage students to unpack and solve problems, share their own thinking and listen to others, and ultimately recognize that there are multiple correct solution strategies and representations. We see problem solving as a vehicle for learning mathematics rather than viewing it only as an application of previously learned content. We believe students’ strategies must make sense to them. This is what empowers them to confidently take on new problems and ultimately develop strong mathematical identities (Nasir, 2002; NCTM, 2020).
Just as we took issue with the IES recommendation about direct instruction, our review of the research also caused us to question the IES recommendation about timed activities. Timed activities are anxiety producing for many students, particularly those who may struggle with mathematics or have challenges with memory (Ashcraft, 2002; Ramirez, et al., 2013; Young, Wu & Menon, 2012). While we agree there is benefit to students knowing some facts from memory, we removed timed activities and references to speed through our intervention revisions. Our approach to considering multiple correct approaches, with some being more efficient than others, will support students in seeing the benefits of various strategies and developing a positive relationship with mathematics.
Our focus on fluency aligns with NCTM’s definition (2014b). That is, we see accuracy, flexibility, and efficiency as equally important characteristics of what it means to be fluent. We want students to confidently know how to use facts they already know to derive other facts. Our materials develop procedural fluency that is based on strong conceptual understanding, supported with models that help students justify their approaches. We also want students to be strategic about the computational approaches they use, selecting based on the numbers in the problem they are solving. The result of these experiences is a deep, flexible, and connected understanding that serves students well as they continue their mathematics journey (NRC, 2001).
In support of students’ development of fact fluency, language, strategy names, and activity sequences in Bridges Intervention have been updated to reflect current research. In particular, Volumes 2 and 5 have been organized around the development of foundational facts, followed by a focus on derived fact strategies. By focusing on fluency instead of memorization and providing time and opportunity for sensemaking and strategy development, the materials support students’ development of positive mathematics identities.
We believe each and every student is better served by mathematics learning experiences that simultaneously develop deep, well-connected understandings, a positive mathematics identity, and a strong sense of agency. Students do this best when engaged with tasks that promote reasoning, problem solving, and sensemaking.
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