Context
“How could they think their answer is even close to being correct? What were they thinking? Did they seriously just add those two numbers together? I didn’t teach it that way! Do they even know what a ratio is? Why are they cross-multiplying everything? Did they read the problem? Why are they not take the time to set up the proportion correctly?” Thoughts and questions like these ran through my mind when analyzing student work from my ratio and proportion unit last year. I have found that it is easy as a teacher to fall into this frustrating line of thinking, questioning whether or not I taught a certain skill correctly, if students are ever paying attention, or if some are even capable of applying sound proportional reasoning. Upon reflection, I concluded that the way I perceived my student’s deficits was at the very least flawed, and counterproductive to my practice. In writing this unit I aim to teach ratios and proportions in a way that promotes the development of proportional reasoning and avoids the dependence on rules and procedures that lead to shallow understandings. In order to drive my unit in a productive manner, I kept the following guiding questions at the forefront. What has obstructed the development of my students’ proportional reasoning? Why have students consistently made the same mistakes, employing similarly flawed reasoning in problem solving, and how are curriculum and instructional strategies contributing to these problems?
I teach at an elementary school on the southwest side of Chicago. We are a neighborhood school that is 95% low income and serves roughly 1,200 students in pre-kindergarten through eighth grade. This next year I will be teaching four sections of sixth grade math in a general education setting. According to district and school assessments, this upcoming class, by a significant margin, presents the most remedial needs in mathematics when compared to other grades at my school. They will be entering middle school with large deficits in the fundamental areas of fractions, operations and algebraic thinking. I chose to write my unit on the subject of ratios, proportions and proportional reasoning because the concepts overlap in almost all other areas in the middle grades math standards and is determined by the Common Core to be a major work the sixth grade (CCSS Initiative 2015). Developing a robust and conceptual understanding of ratios and proportions will be important in the effort of setting a solid foundation for the entire school year. Ideally, through this unit, students will become accustomed to learning conceptually before procedurally, setting the standard for attaining a deeper understanding of subsequent concepts and rational problem solving that utilizes sound reasoning. Besides its foundational nature, the subject of ratios and proportions offer venues to remediate gaps in my students’ prerequisite skills such as fractions, operations and measurement. Throughout the unit’s lessons, I will draw out these basic skills to demonstrate how these concepts extend to more advanced ratio and proportion problems.
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