**ERIC Number:**EJ1074839

**Record Type:**Journal

**Publication Date:**2015-Sep

**Pages:**7

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

**EISSN:**N/A

Learning about Functions through Learner-Generated Examples

Dinkelman, Martha O.; Cavey, Laurie O.

Mathematics Teacher, v109 n2 p104-110 Sep 2015

In many mathematics classrooms, the teacher provides "worked examples" to demonstrate how students should perform certain algorithms or processes. Some students find it difficult to generalize from the examples that teachers provide and cannot apply what they have learned in new situations (Watson and Mason 2002). Instead, teachers might consider asking students to generate their own examples. Examples created by students are often called learner-generated examples (LGEs) and have proven to be a powerful teaching tool (Dinkelman 2013; Bills et al. 2006; Meehan 2007; Watson and Mason 2002; Watson and Shipman 2008). When students generate their own examples, they behave more like mathematicians, drawing on connections and taking ownership of the concepts. As a result, generating examples can be motivating for students at all levels (Watson and Mason 2002); Watson and Shipman 2008). Students benefit by becoming better problem solvers (Watson and Mason 2002) and developing a rich array of example types (Dinkelman 2013). Further, when students generate their own examples, they reveal information about their thinking that is not readily available otherwise (Sinclair et al. 2011). Thus, LGEs are informative tools for assessing student thinking. In this article, the authors share some of the LGE tasks they developed for an instructional unit on functions for students in an introductory Algebra 2 course--a slower-paced course that introduces most but not all concepts in the regular Algebra 2 course. The student examples shared come from two sections of the course in which a total of fifty students were enrolled. About 58 percent of the students were seniors; the rest were juniors, about 50 percent of whom were male. A bibliography is included.

Descriptors: Mathematics Instruction, Teaching Methods, Algebra, Generalization, Student Role, Mathematical Concepts, Concept Formation, Mathematics Skills, High School Students, Formative Evaluation, Comprehension, Responses

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: orders@nctm.org; Web site: http://www.nctm.org/publications/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**High Schools; Secondary Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Grant or Contract Numbers:**N/A