Critical Thinking in the Quantitative Reasoning Pathway

Understanding a quantity as a measurable attribute of an object is foundational for understanding how to work with numbers and making sense of what numbers represent. It also provides the basis for variational, proportional, and covariational reasoning. Students should be able to quantify a given situation, reason with variables that represent quantities, represent changes in quantities, and make estimates. Students should also understand what it means to measure a quantity, which involves envisioning a measurement process that results in a multiplicative comparison between a targeted magnitude and the unit of measure.

Faculty at the MIP Quantitative Reasoning Initiation Workshop in May, 2021 recommended that instructional resources developed by CoRDs and ARCs addressing Critical Thinking for success in the Oklahoma Quantitative Reasoning Pathway should:

1. Base problems in contexts that afford students an opportunity to address the social context of the data (e.g. including multiple values/perspectives/needs, attending to implicit biases). Critical thinking goes hand-in-hand with social contexts in Quantitative Reasoning, as one of the goals is to help students become more knowledgeable citizens.

2. Identify the cognitive habits and characteristics of critical thinkers and how these habits and characteristics might be elicited in instruction.

3. Develop students’ critical thinking in real-world contexts.

Addressing Components of Inquiry

Participants of the MIP Workshop on Quantitative Reasoning suggested the following ways resources about Critical Thinking could address the three MIP components of mathematical inquiry:

Active Learning: Students can rely on critical thinking as they work with problematic situations. In fact, active learning provides a way to operationalize what is meant by “critical thinking”: critical thinking is the act in which one devises, selects, performs, and evaluates actions related to a given problematic situation. These “stages” (devise, select, perform, and evaluate) could provide a useful framework for CoRDs as they design tasks that elicit critical thinking.

Meaningful Applications: Critical thinking supports students in transferring mathematical ideas across contexts because it is inherently not specific to one context or topic. Designing experiences for students in which a few key principles of critical thinking (such as intentionally engaging in iterative cycles of devising, selecting, performing, and evaluating) emerge as essential across very different contexts could be a productive way to support students.

Academic Success Skills: Critical thinking is a key habit of mind that supports students in mathematical success, and as such, can build students’ growth mindsets and make them feel capable of doing and learning mathematics. Because critical thinking often requires critiquing others’ reasoning, it is an ideal tool in building a classroom community. (Of course, critiquing others’ reasoning must be done respectfully; it is therefore suggested that CoRDs proposing such activities carefully consider how they might be framed and implemented in a way that contributes, and is not detrimental to, the classroom community.)

References

Carlson, M. P., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational studies in Mathematics, 58(1), 45-75.