Context
The students whom I’ve been teaching have always seen the various ways of writing numbers symbolically – fractions, decimals, and integers - as siloed representations of quantities with no relation between them. For instance, they learn counting principles at early ages. This continues to more sophisticated counting principles like money combinations. But later on in their math careers, students learn about decimals and fractions, without making the connections to their previous learning at the primary levels. Many curriculums that I’ve seen use the area model to represent fractions. This is a fine concept and is important to help students visualize rational numbers however; my students view this representation as independent from their previous learning. Most of my students are left with an incomplete idea of what fractions represent when using the area model. Difficult as it may be, changing from the area-model approach to a number line approach will allow my students to have a fuller idea of basic number sense topics. The number line is the perfect vehicle to give these different representations of numbers a common home.
I work at Lowell Elementary, which is a neighborhood school in a K-8 building located next to Humboldt Park in Chicago. With a 19% African American and 79% Hispanic population, the overwhelming majority of students are low income (95%). We have a large diverse learner population with a similar percentage of students having limited English proficiency. With all of the daily struggles my students face, Lowell is still in good standing and is a Level 1 school. This means that Lowell is exceeding the district’s expectations in student tests scores and closing the achievement gap. Lowell also has good attendance and is creating a successful school climate that puts learning first. Students are below average in math attainment in 2015. However, they have made above average growth overall according to the NWEA results.
I found that my students need concrete representations of abstract concepts to solidify their understanding of number sense topics. A tool that is readily available to them, but often forgotten, is the number line. By the 7th grade students are expected to, according to the CCSS, apply previous knowledge of fractions and solve real-world examples using all four operations. Without a stronger foundation on fractions and what they really represent, students will fall sort of being fully able to understand why certain truths are evident and how the rules and formulas are developed. My class is all about the why to a problem, not just getting the answer without making any connections to previous learning, connections that they so desperately need. Classroom routines are usually a shock to the students who have me for the first time. Not only are they unable to explain the mathematics, my students are not used the rigor of thinking and application to connect the dots. The challenge I face is weaning students off of answer driven and very surface-level understanding. My students have a difficult time using rote memorization, let alone being able to apply formulas in slight variations.
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