Analyzing Early Algebra Learning Progressions for Grades 3-8

This session will critically examine conjectured Early Algebra Learning Progressions for grades 3–8 for coherence, alignment, and completeness.

Product Feedback Session

This session will critically examine conjectured Early Algebra Learning Progressions for grades 3–8 for coherence, alignment, and completeness.

Teaching and learning algebra has undergone a critical transformation over the past two decades. The primary reason for this transformation stemmed from historically poor student performance in an algebra education that was based on an “arithmetic-then-algebra” approach, in which arithmetic in the elementary grades was followed by a largely superficial treatment of algebra in secondary grades (see e.g., Hiebert, et al, 2005). As a result, it is now argued that students need sustained algebra experiences beginning in the elementary grades that build students’ informal intuitions about patterns and relationships into formalized ways of mathematical thinking (e.g., Kilpatrick et al., 2001; NCTM, 2000). 

An implicit assumption of this longitudinal approach is that algebra education in the elementary grades (early algebra) will have a positive impact on students’ successful performance in algebra in the middle grades and beyond. However, for a variety of reasons, this remains a largely unexplored question. The presenters see an initial step in examining this impact to be the design of an instructional intervention to help establish the impact of early algebra education. Such an intervention entails first identifying early algebra learning progressions (EALP) across upper elementary and middle grades (grades 3–8) that will coordinate research,  curriculum, and mathematical perspectives to identify core algebra concepts and their progression in children’s thinking. The EALP would then provide a critical basis for designing assessments that would help measure the potential impact of early algebra.

Currently, the presenters have developed EALP for grades 3–8 as part of their ongoing DR K–12 project. The EALP are organized around five core ideas, which include (1) Equality, Expressions, Equations, and Inequalities, (2) Functional Thinking, (3) Generalizing Arithmetic, (4) Variables, and (5) Proportional Reasoning. The purpose of this proposed session is to critically examine these EALP for completeness, alignment, and cohesiveness. The session is designed to draw significantly on audience participation. In particular, after an introduction to frame the objectives of the session, a brief description of the proposed EALP, and the process for developing them, small groups will then be established to examine the following specific questions: 


  1. Do the EALP identify essential algebra ideas connected to the study of arithmetic, functions, equivalence (including equations and inequalities), variable, and proportional reasoning in a way that is complete and cohesive, and aligned with research,  curriculum, and mathematical perspectives? Are there other mathematical domains that should be considered in the elementary grades as a route into algebra?
  2. What algebraic aspects of proportional reasoning can be included in the elementary grades as a way to strengthen important algebra ideas in middle grades (e.g., slope)?
  3. What should the role of symbolic manipulation be across grades 3–8 and how can this be addressed conceptually in elementary grades? 


The small groups will be structured to connect to participants’ expertise as it relates to the content domains of the EALP (e.g., functions, arithmetic). Feedback provided during this session will be essential for revising the existing EALP and developing associated assessments in Year 3 of the project.