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Algebraic symbolism as a conceptual barrier in learning mathematics
Get PDFThe use of symbolism in mathematics is probably the mostly quoted reason people use for explaining their lack of understanding and difficulties in learning mathematics. We will consider symbolism as a conceptual barrier drawing on some recent findings in historical epistemology and cognitive psychology. Instead of relying on the narrow psychological interpretation of epistemic obstacles we use the barrier for situating symbolism in the ‘ontogeny recapitulates phylogeny’-debate. Drawing on a recent study within historical epistemology we show how early symbolism functioned in a way similar to concrete operational schemes. Furthermore we will discuss several studies from cognitive psychology which come to the conclusion that symbolism is not as abstract and arbitrary as one considers but often relies on perceptually organized grouping and concrete spatial relations. We will use operations on fractions to show that the reliance on concrete spatial operations also provides opportunities for teaching. We will conclude arguing that a better conceptual understanding of symbolism by teachers will prepare them for possible difficulties that students will be confronted with in the classroom
Using Sign Language videos to help deaf students understand and solve word problems in mathematics: results of a school intervention
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International Cooperation in Education in Thailand
No full text今日まで，国際協力分野と教育分野にはあまり接点がなかった．しかし，グローバリゼーションの影響下で，国際関係と教育の両分野は次第に近づき，更に“協力”という概念を持ち込むことによって，新しい研究分野である「国際教育協力」が成立している．本稿では，国際教育協力がいかなる過程を経て新たな研究分野となりえたかを指摘すると同時に，同分野におけるタイ国の現状について述べる
International Cooperation in Education in Thailand
Get PDF今日まで，国際協力分野と教育分野にはあまり接点がなかった．しかし，グローバリゼーションの影響下で，国際関係と教育の両分野は次第に近づき，更に“協力”という概念を持ち込むことによって，新しい研究分野である「国際教育協力」が成立している．本稿では，国際教育協力がいかなる過程を経て新たな研究分野となりえたかを指摘すると同時に，同分野におけるタイ国の現状について述べる．departmental bulletin pape
From discreteness to infinity: Stages in students' understanding of the rational number density
No full textThis research investigated students’ intermediate stages in understanding the dense structure of rational numbers. A cross-sectional study with 953 students from 5th to 10th grade was performed. After an inductive analysis coding the open answers to a question about how many numbers there are between two given rational numbers, a TwoStep Cluster Analysis was carried out revealing
different student reasoning profiles. Results showed that the most naïve natural number bias did not disappear at the end of secondary school. Moreover, different intermediate stages in the understanding of density were found along grades. A characteristic of these stages is that the understanding of infinity was reached in decimal numbers earlier than in fractions.status: Published onlin
The predictive role of domain-specific vocabulary in early proportional reasoning
No full textProportional reasoning is a pivotal concept in elementary mathematics. More insight into early predictors of later proportional reasoning might be useful to guide early interventions. Research indicates that language is of major importance for mathematical thinking and learning. The present study investigated the longitudinal association between vocabulary that is specific to proportional situations and children’s ability to reason about proportional situations. Results showed that each of the five concepts measured was indeed significantly correlated with proportional reasoning ability, and this relation persisted after controlling for children’s SES.status: Published onlin
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