Introduction
In this post, the fourth in our second series and seventh overall, we delve into the crucial area of problem-solving teaching and its strong alignment with Maths Australia’s I-CRAVE pedagogy, drawing insights from John Hattie’s Visible Learning research.
Understanding Problem-Solving Teaching
Problem-solving teaching, with an overall effect size of 0.61 in Visible Learning, is a vital component of effective mathematics education. Hattie defines problem-solving as a multifaceted process involving defining the problem, identifying solutions, using multiple perspectives, designing an intervention plan, and evaluating the outcome. These are not necessarily formal methods but can be integrated into any teaching method.
Visible Learning highlights several strategies that contribute to successful problem-solving, including problem-posing, generation, writing, and the use of strategies. Interventions for students with maths disabilities show high effects (0.78) when employing strategies like strategy cues, sequencing, task reduction, advance organisers, questioning, elaboration, and skill modelling, particularly when not combined with teaching computational skills in isolation. Developing cognitive flexibility is also linked to high effects in problem-solving. A key conclusion is that problem-solving teaching is most valuable when taught within the context of the subject knowledge.
Problem-Solving within I-CRAVE
Maths Australia’s I-CRAVE pedagogy aligns significantly with the principles and successful strategies of problem-solving teaching outlined in Visible Learning. I-CRAVE’s focus on conceptual understanding, systematic instruction, and application within context directly supports effective problem-solving.
A core principle of I-CRAVE is building deep understanding through the Concrete, Representational, and Abstract stages with “Mastery before progression”. This ensures students have a solid conceptual foundation, which directly supports “schema construction” and understanding the “cause of the problem,” as mentioned in Hattie’s definition.
I-CRAVE’s emphasis on conceptual understanding before focusing solely on abstract procedures aligns with Hattie’s finding that interventions are more effective when not combined with teaching computational skills in isolation. The multi-sensory approach, particularly the Concrete and Representational stages, helps students build robust mental models (schemas) of mathematical concepts. This foundational understanding is critical for the first phase of problem-solving: “understanding the problem”.
The use of manipulatives “to build rectangles and create understanding for application in real life” exemplifies teaching problem-solving within the context of subject knowledge and links understanding to practical application.
The systematic and explicit nature of I-CRAVE aligns with successful intervention strategies like “sequencing” and “skill modelling” mentioned in Hattie. I-CRAVE provides a clear sequence and models for approaching mathematical tasks, which can be extended to problem-solving strategies. The link to specialist training in heuristic methods (effect size 0.71), such as Pólya’s four phases, also highlights the importance of teaching explicit strategies for problem-solving, which aligns with I-CRAVE’s explicit teaching.
I-CRAVE’s progression through different modalities helps students develop a more flexible understanding of concepts, allowing them to approach problems from multiple perspectives. This aligns with the development of cognitive flexibility in problem-solving mentioned by Hattie.
The alignment is justified by the explicit evidence in both the I-CRAVE training and pedagogy and the “Problem-solving teaching” section from Visible Learning. I-CRAVE’s methodology, with its emphasis on building deep conceptual understanding through a systematic, multi-sensory, and applied approach, directly addresses key components and successful strategies for problem-solving teaching identified by Hattie. This collectively demonstrates a positive impact on student achievement (overall effect size 0.61). I-CRAVE supports the development of necessary schema, promotes application within context, and provides a systematic structure that aligns with effective problem-solving interventions highlighted in Visible Learning.
.Conclusion
Problem-solving teaching is a powerful approach that can significantly impact student achievement. Maths Australia’s I-CRAVE pedagogy provides a robust framework that effectively integrates key principles and strategies of problem-solving teaching identified in Visible Learning. By focusing on deep conceptual understanding, providing systematic instruction, and situating learning within relevant contexts, I-CRAVE equips students with the necessary skills and flexibility to become successful problem solvers in mathematics. Equip your students to think critically and solve problems—learn how to apply I-CRAVE in your maths teaching today. To learn more about our training, visit mathsaustralia.com.au/training