Rationale for Unit
This unit will be the first of the eighth grade algebra year for students I taught last year in seventh grade pre-algebra. Their understanding of linear algebra will be a solid foundation from which to build their knowledge of functions, statistics, and how data is communicated along with why being critical consumers of data is a vital life skill. To address my students' dissatisfaction with the relevance of math to their lives, I will focus heavily on the problem-solving process and how it can be applied across disciplines to solve problems, and then how math can be used to strengthen those solutions by quantifying impact and communicating clearly with numerical evidence. This unit plays directly into the curiosity of my students about the world we live in, the problems they will inherit, and the challenges they must learn to address. While we will all focus on the large topic of food and the environment, students will break off into more focused interest groups to pinpoint problems that relate directly to their diets and quantify solutions that will be meaningful in their own lives and the lives of their families.
Beginning the school year with this unit will enable me to set the foundation for the problem-solving environment of inquiry that I want my classroom to be for students. Following Polya's "How to Solve It" framework, students will learn how mathematicians and scientists approach problems to formulate solutions. They will see more of the mathematical thinking required to implement change and make interdisciplinary connections to see how it can be applied to solve any problem. Polya's four-step process includes: understanding the problem, devising a plan, carrying out the plan, and looking back. By explicitly teaching each of these steps using data students gather from their food logs, we will establish common language and strategies for following the process in a repeatable way to attack problems throughout the year.
In addition to strategic thinking, students will focus on questioning problems as well as information they encounter during research. While students are excellent at knowing to question data, they often struggle with knowing what to ask. I do not think there is a quick fix for this, as it is something even the most seasoned problem solvers must constantly struggle to do. However, the more experiences students have that require critical analysis and deep thinking to solve, especially around problems they choose, the better they will get at it. Along the way, we will establish shared beliefs and behaviors to foster an environment of questioning, which I am basing largely on work by Francis Hunkins and the book Quality Questioning (Walsh, 2005).
As Francis Hunkins noted, "We are shifting from viewing questions as devices by which one evaluates the specifics of learning to conceptualizing questions as a means of actively processing, thinking about, and using information productively. Many educators are weaning students from believing that questions are phrased to attain certain answers and are helping them to accept questions as key vehicles that elicit awareness of the diversity, complexity, and richness of knowledge. More educators are assisting students in comprehending that questions are linguistic goals that enable thinking and production of knowledge" (1995). The kinds of questions Hunkins is talking about are vastly different from the typical classroom questions that assess whether students are prepared, or if they understand what we have taught them; these new questions will lead students to better understandings of the information and its relevance to their lives.
"Creating a Culture of Inquiry is about establishing and nurturing norms that promote powerful and productive conversations. Leaders attend to this element when they talk with members of their school communities about the value of inquiry, model inquiry, and build a climate of trust and mutual respect" (Walsh, 2005).
This is no small task. The barriers that exist to students' comfort with questioning are especially deep in math, as the subject is often presented in black and white; you either understand or you don't. These barriers are also particularly pervasive during the formative and often frightening middle school years when students are extremely self-aware and try their best to avoid scrutiny, especially in academics. However, I believe that middle school is also an amazingly opportune time to have students investigate topics they care about, as their passion against injustice is strong and they are always willing to argue. By focusing on a problem they choose that stemmed from their own diets, asking questions will be more important and personal to them, which I think will make it a more natural process.
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