This research and development project provides resources for ninth-grade mathematics students and teachers by developing, piloting, and field-testing intervention modules designed as supplementary materials for Algebra 1 classes (e.g., double-period algebra). Rather than developing isolated skills and reviewing particular topics, these materials aim to foster the development of mathematical habits of mind—in particular, the algebraic habit of abstracting from calculations, a key unifying idea in the transition from arithmetic to algebra.
Transition to Algebra, A Habits of Mind Approach, is aimed at very quickly giving students the mathematical knowledge, skill, and confidence to succeed in algebra, and showing them that they can be good at things they believed they couldn't do. The students were all smart and intrepid when they were six. Even now, they are better and more persevering than we are about figuring out their smartphones and video games. Transition to Algebra aims to tap that smart, intrepid, persevering spirit of puzzling things out and making sense of them by presenting mathematics based in common sense, not arbitrary rules.
This project is developing a collection of modules introducing key ideas of algebra in ways that complement the core curriculum when a school is offering double period algebra. The key habit of mind being developed is abstracting from calculation. Modules deal with the transition from arithmetic to algebra, rational numbers, expressions/equations/word problems, graphs and equations, geometry of algebra, and proportional reasoning. The target population is students in urban high poverty schools with a significant ELL sector.
Our hypothesis is that instructional materials focused on developing conceptual understanding and mathematical habits of mind can complement traditional skill-focused algebra instruction in ways that are engaging to students. Furthermore, they argue that using materials with such meta-cognitive aims will actually strengthen the learning of core algebraic concepts and skills.
The supplementary algebra modules are being developed by a form of design research. Concurrent with development and field test of the student and teacher materials, the investigators are addressing four research questions. The first two questions are focused on the effects of the intervention in developing student habits of mind and in improving their competence and confidence in algebra. The other two address the feasibility of implementing the new approach to double-period algebra in a variety of school settings. A small-scale quasi-experimental field test is being used to give preliminary estimates of the effectiveness of the instructional materials and the implementation guidelines. The core purpose of these research activities is to inform development and refinement of the student and teacher instructional materials.
Products of this development effort will be a valuable resource to schools as they devise strategies for helping all students master the essentials of elementary algebra.