Quantitative Reasoning 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 Quantitative Reasoning for success in the Oklahoma Quantitative Reasoning Pathway should support students’:
1. Reasoning about quantities in contextual problems, affording students an opportunity to address the social context of the data (e.g. including multiple values/perspectives/needs, attending to implicit biases).
2. Understanding that a quantity is a measurable attribute of an object.
3. Understanding how/why/when to use numerical values rather than qualitative descriptions and why this is important.
4. Understanding how numerical values can be visually represented and interpreted (for example, by length, position, area, etc) and how various representations relate to each other.
5. Understanding the use of variables for unknown or varying quantities.
6. Developing number sense to estimate, predict, and evaluate the “reasonableness” of numerical answers to context problems.
Addressing Components of Inquiry
Participants of the MIP Workshop on Quantitative Reasoning suggested the following ways resources about Quantitative Reasoning could address the three MIP components of mathematical inquiry:
Active Learning: Quantities are constructed in the mind (Thompson, 2011). As such, good quantification tasks necessarily engage students in the mental activity of selecting, performing, and evaluating actions related to quantities and their relationships. Good tasks will expose students to a variety of different quantities and quantitative relationships, and help students see quantitative relationships as common mathematical structures.
Meaningful Applications: Quantities are present in all Quantitative Reasoning problems, and as such, helping students understand quantification allows them to identify and interpret meaningful relationships among quantities and to see quantitative relationships as a common and useful mathematical structure.
Academic Success Skills: An understanding of quantities supports student success in many mathematical topics. Building successful experiences for students can help them see themselves as capable doers of mathematics. In the process of those experiences, students can gain perseverance in problem solving, further increasing their mathematics self-efficacy.
References
Confrey, J., & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative unit. Educational Studies in Mathematics, 26(2), 135-164.
Ellis, A. B. (2007). The influence of reasoning with emergent quantities on students’ generalizations. Cognition & Instruction, 25(4), 439-478.
Lobato, J. & Siebert, D. (2002). Quantitative reasoning in a reconceived view of transfer, Journal of Mathematical Behavior, 21, 87–116.
Thompson, P. W. (2011). Quantitative reasoning and mathematical modeling. In L. L. Hatfield, S. Chamberlain & S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education. WISDOMe Monographs (Vol. 1, p. 33-57). Laramie, WY: University of Wyoming Press.