# Pedagogical Case Studies

I became interested creating and applying methodologies for mathematics education because the entry-level mathematics students often encounter difficulties in understanding magnitudes of large numbers. I shall begin my case study from some experiments that how accurately the children could estimate the numbers magnitudes by various aspects of a stimulus.

Thus far, my research has followed two lines of inquiry. The first line of study is to identify children’s different understanding levels for number magnitudes and to accurately estimate numbers7. Specifically I am interested in incremental changes in children’s early-stage estimation strategies that have far-reaching influence on later mathematics development.

. The second

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I am investigating the link between children’s tangible representations and abstract algebra to determine how they influence one another. One of the most actively developing and technically difficult areas of, for instance conceptualization and computation, the number-naming systems of East Asian languages such as Chinese follow the rules of the base-ten system (e.g., “two-tens eight” for 28) (Miura & Okamoto, 1988). My project examined whether patterns in actual research practice correspond to the following problem solving and conceptualization. I will explore the ramifications of cross-cultural contacts between the descendants of different pedagogical schools. But by incorporating Santa Barbara community with the diverse populations as well as their cultural knowledge, my background researching has sparked my interest in providing similar types of experiences for the children. With a partnership of select schools or classrooms in the local area, I look to expand my investigation to more community-based experiences that contribute to students’ mathematics learning

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In light of this, I plan to incorporate Korean, Malaysia and Japan mathematics curriculum to compare the representation of multi-digit number magnitudes, which will have the effect of expanding the understanding levels. Ultimately, my investigations into the cognitive science of numerical representation lead to two major theories. First, I argue for building up accurate estimation skills and corresponding representation models to help low-performed students. My future research will continue in this pursuit to determine additional factors can influence change in children’s numerical