A Story of African American Students as Mathematics Learners
Educational systems throughout the world serve students from diverse populations. Often students from minority populations (i.e. racial, ethnic, linguistic, cultural, economic) face unique challenges when learning in contexts based on the cultural traditions and learning theories of the majority population. These challenges often leave minority populations labeled as incompetent, unmotivated, and cognitively deficit. In the United States, African American female students are among minority populations who are often positioned as deficit when compared to the majority White population. This study investigates middle school African American female perceptions of themselves as learners and students’ knowledge of the meaning of ratio, proportionality, and how to apply and explain their application of proportionality concepts by examining written problem solving strategies over a three-year period. Students’ responses are analyzed according to the strategies they used to reach their final solution. The categories of strategies include no-response, guess and check, additive build up with and without a pictorial representation, and multiplicative. The majority of students in this study 86.5%, 69.2%, and 68.6% did not attempt or demonstrated no understanding in year one, two, and three respectively. Additionally, participants reported positive dispositions about themselves as mathematics learners.
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Conceptual Understanding Scoring Rubric A class has 28 students. The ratio of girls to boys is 4 to 3. How many girls are in the class? Concepts Assessed Understand and apply proportional reasoning used in scaling. Understand that a fraction always represents a part-to-whole relationship. Understand that a ratio can represent part-to-part or part-to-whole relationships. Scoring Rubric Level Identifiers Examples of student responses Understanding No work or states they do not understand with no answer given. “I don’t understand.” No attempt 1 No evidence of understanding concepts related to fractions or proportionality. 2 Written or symbolic explanation shows an understanding the meaning of a ratio, but does not apply the ratio to solve the problem. Correct written or drawing work but provides no explanation of how the answer was found. 3 Explanation is accurate does not thoroughly explain the rationale used in solving the problem. The explanation is procedural rather than conceptual. 4 Evidence of full understanding of proportionality either verbally or visually (scaling 4:3 or using and explaining the proportion 4/7 = 16/28).
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