Quantitative Reasoning in Mathematics Education: Directions in Research & Practice Heather Lynn Johnson Waterbury Summit Session 3: Quantitative Reasoning August 8, 2013

A Filling Triangle How is the area of ABCD changing as the length of AD is increasing?

Aspects of Quantitative Reasoning (QR) An individual’s conception of a measurable attribute of an object (Thompson, 1993) Decision making process related to measuring a quantity (Mayes et al., 2013; Thompson, 2011) Comprehending a situation in terms of quantities involved (nonnumerical) – result is a relationship between quantities (Thompson, 1994) Mental process composed of operations on objects (quantities), involving the process of quantification.

Aspects of Quantitative Literacy (QL) Process involving drawing on one’s mathematical knowledge to interpret or explain results of quantification (Mayes et al, 2013) Being able to make meaning from numerical situations (e.g., AACU, 2010) Follows the process of quantification (Thompson, 2011) Making sense of situations involving different contexts (e.g., Steen, 2001)

QR vs. QL

Relationships between Quantitative, Multiplicative, Algebraic & Covariational Reasoning Multiplicative Reasoning –How might students operate on composite units (“things” made up of things)? Algebraic Reasoning –How might algebraic symbols represent relationships between quantities? Covariational Reasoning –What kinds of relationships can be formed between quantities that are changing together? 2*7 + 4*7 = 7(2+4) 2x + 4x = x (2+4)

Discussion: Quantification & Measurement How might quantification and/or measurement undergird LTs related to students’ development of QR? What role might quantification and measurement play in the development and implementation of tasks designed to elicit students’ QR? How might emphasis on quantification and measurement be useful for making distinctions between QR and QL?