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Quantitative Reasoning ReactionRose Mary Zbiek - Penn StateAugust 2013Capturing a Tension Between Structure and VariabilitySTEMMMEHTAMIENCESATIC

CS

LASTEM RelationshipsMathematics and StatisticsDeductive reasoning & Probabilistic reasoningStructure & Variability (Peck, Gould, & Miller, 2013) Variance as inevitableInvariance as theorem (Sinclair, Pimm, & Skelin, 2012)Role of Context (Peters, 2010) Interpretive stance (van Oers, 1998; Johnson, 2013)

STEM RelationshipsSTE M (dis)connectMath as tool for STEapply mathematical routine to quantitiespreform mathematical calculation(s) (Waterbury Summit) STE as setting for MathBacterial growth exponential functionsF=ma rational functions Curricular math in contrast to modeling (especially in U.S.A.)(Zbiek & Conner, 2008)

Freudenthal:Children should be granted the same opportunities as the grown-up mathematician claims for himself [or herself]. (1971, p. 424) Practices & ProcessesSTEM integration happens at the level of borrowed concepts (which might be quantities as numbers or measures)and appropriated procedures(which might be the tools applied).

Practices & ProcessesSTEM integration happens at the level of borrowed concepts (which might be quantities as numbers or measures)and appropriated procedures(which might be the tools applied).Integrate based on practices or processes.CCSSM [Use mathematics to model]Guidelines for Assessment and Instruction in Statistics Education [GAISE](Franklin et al., 2007)

What would be a learningprogression (or landscape) if we strive for P-16 S,T,E,M co-develop with a focus on processesandpractices?Elaboration of model

Math /JohnsonStat/Lehrer & PetrosinoQuantificationMeasurementPromise of Quantitative ReasoningLearning trajectories & learning progressions for STEM

Johnson:Connections to other forms of reasoning Learning trajectoriesEssential Understanding (big ideas for teachers)Lehrer & Petrosino:Summary of Learning Trajectory for Data Modeling

Promise of Quantitative ReasoningJohnson (Reasoning/Essential Understanding series)Lehrer & Petrosino (Learning trajectory for data modeling)Number & numeration (EU)Multiplicative reasoning (R, EU)Proportional reasoning (R, EU)

Algebraic reasoning (R)Function (EU)

Difference among measures

Shapes of same dataSample-to-sample variability

Promise of Quantitative ReasoningJohnson (Reasoning/Essential Understanding series)Lehrer & Petrosino (Learning trajectory for data modeling)Number & numeration (EU)Multiplicative reasoning (R, EU)Proportional reasoning (R, EU)[Statistics (EU)]

Algebraic reasoning (R)Function (EU)

Difference among measures[Mean as fair share?][Proportionality?]Shapes of same dataSample-to-sample variability[Symbol sense, Representational fluency]Teacher Development/SupportTrain to know/to be able to do Prepare to engageExample: Focus on process/practice, Acknowledge systemsMid-Atlantic Center for Mathematics Teaching and Learning [MAC-MTL] (NSF funded 2001-present)

MAC-MTL: Micro & Macro Levels Process-and-action approach (Zbiek, Heid, & Blume, 2012)Mathematical processes (generative acts such as defining and generalizing)Products (e.g., definition, generalization)Actions (performed on products; manipulating, linking, )Teaching Triad(Jaworski, 1994; Potari & Jaworski, 2002)Mathematical challengeCognitive and affective sensitivity to studentsManagement of learning

Thank you for the insightsandinspiration