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ERIC Number: EJ1044045
Record Type: Journal
Publication Date: 2014-Nov
Pages: 9
Abstractor: ERIC
ISSN: ISSN-1072-0839
Revisiting Mr. Tall and Mr. Short
Riehl, Suzanne M.; Steinthorsdottir, Olof Bjorg
Mathematics Teaching in the Middle School, v20 n4 p220-228 Nov 2014
Ratio, rate, and proportion are central ideas in the Common Core State Standards (CCSS) for middle-grades mathematics (CCSSI 2010). These ideas closely connect to themes in earlier grades (pattern building, multiplicative reasoning, rational number concepts) and are the foundation for understanding linear functions as well as many high school mathematics and science topics. As students journey toward mature proportional reasoning, teachers can gain insight into their thinking by carefully analyzing their solution strategies on a single problem. Robert Karplus and his colleagues began using the Mr. Tall and Mr. Short problem (described herein) in this way in the late 1960s. Karplus, Karplus, and Wollman (1974), influenced by Piaget, aimed to chart the development of abstract reasoning in young students. Beyond its use in formal research, this problem is a "classroom challenge" explored in the 2002 NCTM Yearbook, "Making Sense of Fractions, Ratios, and Proportions" (Khoury 2002). Teachers using this challenge are encouraged to assess their students at one of four broad levels of proportional thinking. In this spirit, and as part of a larger project to examine proportional reasoning, the authors gave the Mr. Tall and Mr. Short problem to over 400 middle school students in a small Midwestern town. Their aim in this article is to share the categories of solution strategies they found and to discuss what these strategies reveal about student thinking.
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Middle Schools; Secondary Education; Junior High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A