ERIC Number: EJ1458642
Record Type: Journal
Publication Date: 2024
Pages: 34
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-1062-9017
EISSN: N/A
Intellectual Need, Covariational Reasoning, and Function: Freeing the Horse from the Cart
Teo Paoletti; Kevin C. Moore; Madhavi Vishnubhotla
The Mathematics Educator, v32 n1 p39-72 2024
Supporting young students in developing meanings for the set-theoretic function definition is emphasized in 6th-12th grade curricula around the world. In prior work, we have highlighted how covariational reasoning supports college students in constructing relationships that afford considering mathematical properties important for a set-theoretic definition. In this paper, we show how such reasoning can provide similar affordances for younger students by presenting one sixth grade student's, Ariana's, sense-making. To characterize Ariana's sense-making related to her quantitative reasoning in contextual situations, we build on Harel's work to articulate the constructs of situational intellectual need and situational epistemological justification. We highlight how Ariana's covariational reasoning supported her development of a situational epistemological justification, which included a structure entailing numerous quantitative relationships. We also highlight how this epistemological justification supported her work representing conceived relationships graphically and making determinations regarding properties of a set theoretic function definition. However, we characterize that Ariana constructed functional and non-functional relationships alike; determinations regarding properties of function were spurned by teacher-researcher prompts rather than an intellectual need experienced as she conceived such relationships. Through this analysis, we build an anti-deficit story of Ariana's sense-making that leads us to call into question the value of focusing on the set-theoretic definition of function early in students' experiences.
Descriptors: Secondary School Curriculum, Grade 6, Middle School Students, Thinking Skills, Affordances, Comprehension, Mathematics Education, Student Attitudes, Student Needs, Problem Solving, Cognitive Development, Situational Tests, Situated Learning, Mathematical Concepts, Graphs, Experimental Teaching, Constructivism (Learning), Hispanic American Students, Females
Mathematics Education Student Association, University of Georgia. 105 Aderhold Hall, Athens, GA 30602. Tel: 706-542-4194; Fax: 706-542-4551; e-mail: mesaprez@gmail.com; Web site: http://tme.journals.libs.uga.edu/index.php/tme/index
Publication Type: Journal Articles; Reports - Research
Education Level: Secondary Education; Elementary Education; Grade 6; Intermediate Grades; Middle Schools; Junior High Schools
Audience: N/A
Language: English
Sponsor: National Science Foundation (NSF), Division of Research on Learning in Formal and Informal Settings (DRL)
Authoring Institution: N/A
Grant or Contract Numbers: 2142000