Being a sheep in a "cattle's kraal" does not make you a cow: Black students' thought processes in measurement activity
Piyose, Nosisi N.
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This dissertation describes Black students' internalization of measurement concepts. Black students continue to perform very low in mathematics from both countries where this study was conducted, the United States and South Africa. This lower performance is related to their history of alienation and discrimination that continue to exist in different forms. Ethno-mathematics pedagogy offers promise to facilitate these students' mathematics learning by bringing in cultural artifacts in their classroom, which allows them to learn mathematics in culturally relevant contexts. However, very few studies examine students' mathematical thinking using this theoretical framework. While results using ethno-mathematics pedagogy are promising, they are also complicated by the fact that the traditional artifacts bring historical stereotypes with them. For example, Mozambique and South African traditional games tend to favor girls over boys. So whereas the games are culturally relevant and facilitate the learning of mathematical concepts, they have the potential to perpetuate negative gender stereotypes, a potentially harmful byproduct. The over-arching gap in the research is regarding the instructional needs as well as the cultural capital that Black students bring to the mathematics classroom. Given the reality that most Black students in the United States will learn math from a white, middle-class, monolingual teacher, these students' native languages are not understood, nor is the role played by language in their cultures, which could actually become an asset to facilitate deeper conceptual learning, if it were possible for teachers to tap into this resource. In South Africa, code switching and use of native languages in previously disadvantaged schools have been researched and support this study's results. However, how Black students deal with language issues in ex-Model C schools is left unattended. The collective case studies of 10 fifth grade Black students and 3 mathematics teachers illustrate that using oral dialogue to facilitate Black students' introduction to mathematical conceptual thinking, as well as diagrams, native language prompts when possible, and manipulatives allowed Black students to achieve the higher levels of abstraction in their thinking. By contrast, teacher-centered, text-based instruction caused a disconnection in communication that prevented students' ability to grasp or retain critical, foundational concepts. This dissertation supports Vygotsky's theory of connecting external tools (new concepts) to internal tools (learned concepts) in constructing meaning. This study reveals that Black students bring frequently untapped unique experiences and cultural capital into their mathematics classrooms. These experiences and tools they bring have the potential to lay a strong foundation for learning. By ignoring their experiences and the tools they bring, either through ignorance or disinterest, educators create disconnected structures of knowledge that cannot be used by these students. The school culture influences instruction and positions students in the classroom in a way that results in inequality regarding access to education and lacks equity. More research is needed on the cultural role played by language in Black students' learning of mathematics in both countries. Especial in South Africa, it needs to define the meaning of equity and to monitor teaching practices in previously advantaged schools, which have experienced declines due to sociopolitical issues.