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ERIC Number: EJ1122999
Record Type: Journal
Publication Date: 2016-Dec
Pages: 9
Abstractor: ERIC
ISSN: ISSN-1072-0839
Generalizing and Skepticism: Bringing Research to Practice
Yopp, David A.; Ellsworth, Jacob L.
Mathematics Teaching in the Middle School, v22 n5 p284-292 Dec 2016
Empirical arguments rely on examples without necessarily addressing all cases. Students should be skeptical of empirical evidence and should seek more secure arguments for generalizations, such as those that explain why a generalization is true for all cases. Generalizing on the basis of patterns in data is an important mathematical practice; however, overgeneralizing can occur when students focus solely on patterns in their data results. Students should also determine whether patterns are expressed in the processes used to construct data (Harel 2001). In this way, students can link patterns in their processes to patterns in their results and perhaps explain why patterns hold for all cases. We should not discourage students from making such conjectures. However, we should encourage skepticism. In this article, we offer activities that encourage skepticism and a way to contrast empirical arguments that are not viable with empirical arguments that are viable, even when students lack sufficient deductive-reasoning skills. The data presented in this article are from a teaching experiment with a class in which more than 60 percent of students scored below proficient on their 2015 Grade 7 Smarter Balanced Assessment Consortium end-of-year assessments (SBAC 2012). A bibliography is included.
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Grade 8; Junior High Schools; Middle Schools; Elementary Education; Secondary Education
Audience: Teachers
Language: English
Sponsor: National Science Foundation (NSF)
Authoring Institution: N/A
Grant or Contract Numbers: DRL0918326