Conceptions of Expressions and Equations in Early Algebra: A Learning Trajectory

Centre for Innovation in Mathematics Teaching. 5th Floor Rolle Building, Faculty of Education University of Plymouth, Drake Circus, Plymouth, PL4 8AA, UK. Tel: +44-1752-585346; Fax: +44-1752-585344; e-mail: feedback@cimt.org.uk; Web site: http://www.cimt.org.uk/ijmtl/index.php/IJMTL/about

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23

Algebra; Equations (Mathematics); Mathematical Formulas; Grade 6; Middle School Students; Early Adolescents; Common Core State Standards; Mathematics Education; Cognitive Style; Educational Experiments; Learning Processes; Sequential Approach; Urban Schools; Hispanic American Students

1473-0111

This article describes a learning trajectory on expressions and equations based on the sixth-grade Common Core State Standards for Mathematics (NGA/CCSSO, 2010). A classroom teaching experiment using design research (Lamberg & Middleton, 2009) was conducted. The data was analysed using Corbin and Strauss' (2014) Constant Comparative method and Creswell's (2007) data analysis spiral. The realized trajectory that emerged and the design decisions that were made were documented. The findings reveal that student understanding of the changing meaning of letters and variables within a problem context played a central role in student development of conceptual understanding of expressions and equations. Specifically, solving the different problem types involved the following types of thinking: "Label Thinker," "Formulaic Thinker," "Substituter," "Solver," and "Functional Thinker." The letter was interpreted as a label representing a category, a known value, a variable as an unknown value, and a variable as a changing quantity depending on the problem context. Implications for classroom instruction and curriculum development are discussed.

As Provided

2019

EJ1237193