Description of The Multiple Unit Approach and Progression of Learning
By now, I hope, I have convinced you that there must be a better way of sequencing instruction about expressions and equations. The series of student outcomes are split between four units including my own. Each unit will address a particular aspect of the complex process of translating, simplifying, and solving algebraic expressions and equations.
This order will lead to better student fluency and discourse. The four units will begin with Rachelle Soroten’s unit titled “Formulating Algebraic Expressions From Word Problems.” Rachelle will use problems that are relatively simple in nature, to help students learn how to translate words problems into algebra. She will give a variety of examples of translating word problems in to equations involving ‘simple’ expression. Rachelle will teach her students how to appropriately use Singapore bar models and algebra side by side. This gives students an entry point into the curriculum.
Next, my unit will allow students to work on a series of increasingly difficult phrases that are directions to make symbolic expressions. I will rely on Rachelle’s unit for motivation. Since Rachelle is focusing her efforts on conveying foundational understanding of problem structure, my unit presents varied phrases that represent mathematical statements. Since my students are much less familiar with variables, students are not sure how to contextualize or apply variables. During the problem set discussions, students will see that the use of parentheses helps to show the structure of mathematical expressions, and that expressions can be transformed according to the rules of mathematical operations. My students need a reason why they need to be exposed to wide-ranging problems with varying difficulty levels. Multiple representations of verbal expressions will allow students to understand the identification needed for equivalent expressions in a discussion-based classroom.
Immediately following my unit, Xiomara Pacheco’s unit entitled “Simplifying The Issues With Expressions.” She will explain how to manipulate expressions and especially how to reduce first order expressions into standard form. Her problem sets will focus on deepening student knowledge of the distributive property and combining like terms.
Finally, Sally Yoo’s unit “Making Sense of Solving Equations Through Word Problems – The Cornerstone of Algebra” will show how to use all of the above to solve pretty complicated systems of linear equations motivated by word problems. Once Xiomara has reduce the complicated to the more simple, students will be able to focus their efforts primarily on solving two-step equations, or equations that have variables on both sides.
The four units will be taught by all mentioned above in the hopes of creating flexible problem solvers who have built up both their computational fluency and reading capacity. Traditionally, curriculums that I have come across, or even taught for years, have never gone in such detail as the four units that make up this series. This will be new to me as well because I am not satisfied by the end product of my equation/expression units. Starting with word problems as the main motivation for using symbolic algebra makes more sense. Bar models are great tools to use in simple problems, however students need a more sophisticated language to work with. The intent of the series of curriculum units is to replace traditional models with broader investigations into expressions and equations that can take most of the semester to implement.
Figure 2. Progression of Combined Unites
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