Mathematics teachers’ ability to identify situations appropriate for proportional reasoning

ABSTRACT

In this study, we investigated teachers’ abilities correctly to identify situations that are appropriate for proportional reasoning and factors that might influence their ability using data on 148 teachers from the U.S. Learning Mathematics for Teaching assessment and other, similar items (with a smaller sample). Through a quantitative exploratory data analysis, we found middle school mathematics teachers are relatively proficient at correctly identifying situations that are proportional. However, we also found these same teachers were challenged by identifying situations as appropriate for proportional reasoning when in fact they were not, particularly in linear cases with a non-trivial constant term or inversely proportional situations. We also examined teachers’ backgrounds and perceived expertise to determine whether there were correlations between their abilities to discern proportional situations and these attributes. We found that teachers are relatively proficient at self-assessing their expertise. Our findings imply that the middle school mathematics teachers in our study seemed to over-identify situations as proportional even when the situations were not proportional.

KEYWORDS:

• Appropriateness
• proportional reasoning
• teacher knowledge

Acknowledgements

The views expressed here reflect those of the authors and may not necessarily be the views of the NSF. The authors wish to thank James Burke for his work on earlier versions of this paper. They also wish to thank Heather Hill for allowing them access to the national dataset from the Learning Mathematics for Teaching Proportional Reasoning form.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Travis Weiland http://orcid.org/0000-0002-5901-5683

Chandra Hawley Orrill http://orcid.org/0000-0002-3907-554X

Rachael Eriksen Brown http://orcid.org/0000-0002-1709-3130

Gili Gal Nagar http://orcid.org/0000-0002-0294-9530

Additional information

Funding

The work reported here was support by grant number DRL-1054170 from the National Science Foundation's Division of Research on Learning in Formal and Informal Settings.