Algebra in Early Mathematics: What is Critical?

The panel will present an overview of research-grounded evidence about what is critical for students to learn about algebra in grades 1–5.

Date/Time
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Panel

In this panel discussion, panelists will identify some ideas that are becoming well-established by researchers even though they were by no means evident just 15–20 years ago and are yet to be assimilated into curricula and teacher education programs. They will identify what they consider to be critical issues for children to make progress in algebra in grades 1–5.

Susan Jo Russell (TERC) and Deborah Schifter (EDC) will describe their work on students, generalizing about arithmetical operations in elementary and middle grades and how such a focus both supports computational fluency and connects to algebra. They will also show what their findings mean for a range of students, including those students who have and have not been successful with grade-level computation.

Paul Goldenberg (EDC) will give several examples of how, from a very young age, learners are attentive to causal, quantitative, sequential, and probabilistic relationships. They show how such proclivities can be constructively built upon in the early grades in activities that highlight mathematical structures. They also argue that success in such activities often requires “abstracting the rhythm from repeated actions” or noting structural invariants common to a class of computations.

Maria Blanton (UMass-Dartmouth) will discuss what she and her colleagues have learned (and have yet to learn) about how students' understanding of functions develops across grades 1–5. She will relate this to her work with Eric Knuth about the development of a learning progression for algebra in the early grades.

Joan Moss (University of Ontario at Toronto) will talk about young children's’ (grades 1–4) mathematical reasoning and generalizing about patterns and function rules. She will argue that, although students will very naturally extend geometric patterns, their understanding is transformed in fundamental ways when they learn to capture the regularity of such patterns in natural language and written notation. One of the critical conditions for this to occur is that students become aware of the existence of an independent variable (the step number) that needs to be related to the structure or cardinality of the pattern at any given step.

Analúcia Schliemann (Tufts) will report on her work undertaken with David Carraher (TERC) and Barbara Brizuela on how students in grades 3–5 develop an understanding of functions. She will emphasize the critical importance of students’ treating the arithmetic operations as functions and becoming adept at moving across representations of functions in natural language, tables, number lines and Cartesian graphs, and algebraic notation. Compared with control groups, the students in the intervention group outperformed their control peers and profited more.