From Arithmetic to Algebra: Variables, Word Problems, Fractions and the Rules

Overview and Rationale

The students whom I have been teaching have an incomplete understanding of algebraic expressions involving variables. This hinders their effectiveness in creating and manipulating expressions and puts them at a disadvantage when the expressions become more complicated. This can become overwhelming for my students, who have limited English fluency, and come from a variety of backgrounds and varying levels of content knowledge. By 7^th grade, students in Chicago are expected to be able to create, combine, and translate expressions into mathematical statements in various forms. (See the list of relevant mathematics standards in the Appendix.) It is very apparent that not enough time is spent on this critical skill. I will also discuss the need to reorder present curriculum to generate further content knowledge. When content is rushed, students are left with partial knowledge whose academic gaps widen as the year progresses. With limited knowledge of operations, my students struggle greatly with interpreting symbolic expressions and do not grasp the rules for transforming them.

In this unit, students will be exposed to a variety of problem sets that require them to translate verbal phrases into symbolic notation. These problems will increase my students’ ability to function and participate in a discussion-based classroom, once they practice and become attuned to the ways these phrases differ. The method that I favor in my classroom is the Math Talk. This protocol will be structured by guiding questions that I will keep in mind while teaching this unit. Students can then profit from the powerful idea of taking authority and ownership of their own learning and can then build on this very detailed approach. This will be especially valuable when the expressions and operations get more difficult later on in the school year.

Towards the end of the 2016-2017 school year I had been looking to transition into a new role within Chicago Public Schools. I will be moving schools from Lowell Elementary to another elementary school called Helen C. Peirce School of International Studies. My new school is located in the northern part of the city in the neighborhood of Andersonville. Peirce’s mission statement is as follows: “Our mission is to guide students to take ownership of their learning through experiential engagement and reflective thinking. We provide a balanced curriculum designed to meet the academic, cultural, and social-emotional needs of our diverse student body. All members of the Peirce community are committed to grow as productive, globally-minded citizens.”¹

Peirce is a neighborhood school composed of a wide demographic with the majority of students having Hispanic descent. Peirce has a low-income population of about two-thirds with students having limited English proficiency hovering around one in five. This is relevant to my unit, because it will primarily focus on how expressions are translated to English. As in every neighborhood school with diverse populations, there is a link between increasing English fluency and overall math achievement. From my experiences, I see students struggle with making expressions from mathematical statements and transforming them into English. Developing a keen eye as to what problems are saying is very challenging for all students in the middle school classroom, and the more so with students not fluent in English. This unit will be a series of discussion-based and exploratory lessons accompanied with Polya’s Problem Solving Method that will help students appreciate the multiple aspects of problem solving. The majority of the Standards for Mathematical Practice of the Common Core Mathematics Standards will be relevant at some point in this unit. However, I will focus on students being able to persevere and attend to precision (Practices 1 and 6).

The majority of my students rely on the latest ‘trick’ or shortcut to finish a problem without any real understanding of the major problem solving techniques. I want to wean them off of these tricks and give my students the foundation that can be applied in other areas. In order for them to engage and reflect critically in a mathematics setting, they need to further their own understanding by building on their own specific understanding of algebraic notation. I want to emphasize to my students that they need to take genuine care when reading word problems. They need to pay special attention to the issue of translating statements, and to analyzing what the problem is asking them to do. I will specifically ask my students to translate expressions into symbolic statements and then back into verbal statements.