We designed a fully online assessment measuring students’ covariational reasoning.

Here’s a preview of our Three Design Principles:

Assess for a Spectrum, rather than a switch

In our assessment, we are working not only to assess the presence of covariational reasoning (a switch), we are working to assess gradations in students’ covariational reasoning (a spectrum). We applied Tzur’s method of fine grain assessment. With fine grain assessment, designers begin with items that include no supports, then move to subsequent items including increasing amounts of supports. Such a method for design may seem counterintuitive. For example, why include “harder” questions first and “easier” questions later?  Because including items with no supports before items with supports opens the possibility to investigate different levels, or gradations of students’ reasoning.

Leverage Tech to Promote Access + Opportunity

In our title, we use the term networking theories. By “networking theories,” we mean interweaving and applying theories. For our purposes, we interweave and apply Thompson’s theory of quantitative reasoning and Marton’s variation theory.

With Thompson’s theory of quantitative reasoning, we designed assessment items in which students have opportunities to notice changing attributes AND to conceive of those attributes as possible to measure and capable of varying. Hence, we interrogated the types of attributes and variation (change) that we included in the assessment.

With Marton’s variation theory, we designed for variation (difference) within and across the assessment items. Within assessment items, we incorporated different types of graphs (linear/nonlinear). Across assessment items, we incorporated different backgrounds (e.g., a turning Ferris wheel, a toy car, etc.) and different types of variation (change) in attributes (e.g., variation in direction of change and variation in unidirectional change).

Leverage Tech to Promote Access + Opportunity

We created an online assessment to ensure that students could easily complete it whether using a computer, a tablet, or a mobile phone. We were especially interested in designing an assessment that could viably work on a mobile phone, as so many students have access to a mobile phone. Furthermore, we found no statistically significant differences in students’ performance across items when completing the assessment with a different electronic device (tablet, computer, or phone).

Want to know more? Read our Conference paper

ITSCoRe at the 2018 PME-NA Conference [Psychology of Mathematics Education-North American Chapter]

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