Quantitative Reasoning in Mathematics Education: Directions in Research & Practice Heather Lynn...
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Quantitative Reasoning in Mathematics Education: Directions in Research & Practice Heather Lynn Johnson Waterbury Summit Session 3: Quantitative Reasoning August 8, 2013
Quantitative Reasoning in Mathematics Education: Directions in Research & Practice Heather Lynn Johnson Waterbury Summit Session 3: Quantitative Reasoning
Quantitative Reasoning in Mathematics Education: Directions in
Research & Practice Heather Lynn Johnson Waterbury Summit
Session 3: Quantitative Reasoning August 8, 2013
Slide 2
A Filling Triangle How is the area of ABCD changing as the
length of AD is increasing?
Slide 3
Aspects of Quantitative Reasoning (QR) An individuals
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.
Slide 4
Aspects of Quantitative Literacy (QL) Process involving drawing
on ones 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)
Slide 5
QR vs. QL
Slide 6
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)
Slide 7
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?