Introduction
The National Assessment of Educational Progress revealed some alarming deficits in students’ ability to compute and reason with numbers. The performance on one particular test item highlights this deficit.
“Students were asked to estimate the answer to 12/13 + 7/8. The choices were 1, 2, 19, 21, and, "I don't know." Only 24 percent of the thirteen-year-olds responding chose the correct answer, 2. Fifty-five percent of the thirteen-year-olds selected 19 or 21-they added either the numerators or the denominators.” (Bezuk, Cramer 1989)
This example resonates with my experience teaching middle school mathematics. The most significant obstacle I face as a teacher is that my students lack a complete understanding of number and basic operations. As a means of coping with these deficits students have learned and become dependent on tricks and algorithms. This unit simply but boldly aims to once and for all give students a unifying way of conceptualizing numbers and operations.
Context
This next year I will be teaching one section of seventh grade math and two sections of eighth grade math at Brentano Math and Science Academy in Chicago’s Logan Square neighborhood. The school qualifies for title 1 funding and has an enrollment that is predominately Hispanic. According to a district assessment that tests student performance on grade-level Common Core standards in each area, my incoming students consistently perform significantly lowest in the area of number systems. It is in this area where students are required to reason and operate with fractions, decimals, and negative numbers. My students’ deficit in this area is apparent not only on tests, but is a persistent obstacle that impacts their day-to-day performance in my classroom.
When students are asked to operate with unfamiliar rational numbers they cling to previously learned algorithms without a conceptual understanding of what is actually happening with the numbers. Their shaky grasp of foundational number and operation concepts are major contributors to an overall intolerance and avoidance of working on any task involving these unfamiliar numbers. This creates recurrent problems, both for them individually and for the class as a whole, since our middle school curriculum assumes and requires a fundamental and flexible understanding of numbers. I have never been able to successfully implement a thorough intervention to remediate these needed foundational concepts. This unit will aim to formally and methodically address the fundamental issue of my students’ patchy and deficient number and operation sense via the use and study of the number line.
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