Investigating Proportional Relationships from Two Perspectives (InPReP2)

Principal Investigator: 
Project Overview
Background & Purpose: 

The InPReP2 project is investigating how preservice middle and secondary school mathematics teachers use their quantitative understanding of multiplication, division, and fractions to build quantitative understanding of ratios and proportional relationships, and applications of such relationships to linear relationships and statistical samples. The study focuses on two perspectives on ratios and proportional relationships, one of which has been largely overlooked in past mathematics education research. The two perspectives are developed in mathematics content courses the preservice teachers take as part of their programs. We are studying the preservice teachers' reasoning as they participate in these courses and comparing their facilty with proportional relationships to that of preservice teachers in a “business as usual” content course at a second university.


The InPReP2 project is taking place in teacher education programs at two universities in the southeast U.S.

Research Design: 

The project uses a comparative research design and will generate evidence that is descriptive [case study] and causal [AI1] [psychometric modeling, test about fractions designed for Diagnostic Classification Models is used to select interview participants]. Whole class video and written artifacts (homeworks and tests) are being collected on entire cohorts of preservice middle and sceondary teachers and intensive interview data are being collected on a subset of those teachers selected for mathematical diversity using assessments of fractions. The performance of preservice teachers in the mathematics content courses developing the two perspectives on ratios and proportional relationships is being compared to the performance of preservice teachers in a “business as usual” content course at a second university on common measures of proportional reasoning.

We are using the Diagnosing Teachers’ Multiplicative Reasoning (DTMR) project’s Fraction survey to select a mathematically diverse sample for the intensive interviews. The survey, whose development was supported by NSF (DRL-0903411), is one of the first tests built from the ground up for use with Diagnostic Classification Models. The survey measures four components of reasoning necessary for using drawn models (e.g., number lines and area models) to develop methods for multiplying and dividing fractions. For more information, see Bradshaw, L., Izsák, A., Templin, J., & Jacobson, E. (2014). Diagnosing teachers’ understandings of rational number: Building a multidimensional test within the diagnostic classification framework. Educational Measurement: Issues and Practice, 33(1), pp. 2–14. DOI: 10.1111/emip.12020.

We are analyzing the item response data from the DTMR Fractions survey using the log-linear cognitive diagnostic model. Theses analyses result in multidimensional profiles of attribute mastery that describe patterns of strengths and weaknesses in reasoning about fraction arithmetic in terms of quantities. . We are analyzing the interview data using micro-genetic methods that involve inferring participants' reasoning using line-by-line data on talk, gesture, and inscriptions (things written on the page).


Findings will be posted as they become available.

Publications & Presentations: 



Beckmann, S., & Izsák, A. (2015). Two perspectives on proportional relationships: Extending complementary origins of multiplication in terms of quantities. Journal for Research in Mathematics Education, 46(1), pp. 17–38.

Research Design: 


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