This study focuses on the history of school mathematics through the discourse surrounding the function concept. The function concept has remained the central theme of school mathematics from the emergence of both obligatory schooling and the science of mathematics education. By understanding the scientific discourse of mathematics education as directly connected to larger issues of governance, technology, and industry, particular visions for students are described to highlight these connections. Descriptions from school mathematics focusing on expert curricular documents, developmental psychology, and district reform strategies, are meant to explain these different visions. Despite continued historical inquiry in mathematics education, few studies have offered connections between the specific style of mathematics idealized in schools, the learning theories that accompanied these, and larger societal and cultural shifts. In exploring new theoretical tools from the history of science and technology this study seeks to connect shifting logic from efforts towards rational organization of capitalist society with the logic of school mathematics across the discursive space. This study seeks to understand this relationship by examining the ideals evinced in the protocols of educational science. In order to explore these architectures, the science of mathematics education and psychology are examined alongside the practices in the New York City public schools--the largest school system in the nation. To do so, the discourse of the function concept was viewed as a set of connections between mathematical content, psychology, and larger district reform projects. Four architectures--the mechanical, thermodynamic, cybernetic, and network models--are examined.

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The study reported here examined the move towards online assessments and addressed the question of whether or not different assessment tools affect student scores and student learning. The research activities covered a three-week period, from June 5, 2006 to June 23, 2006. During this time, seventeen third grade students served as their own control group by taking several math tests online and several math tests with paper and pencil. Results were compared to see if performance on computer-based tests would be more successful than pencil-and-paper tests. A follow-up survey to evaluate and interpret the quantitative results was also used. Findings revealed that 59% of the students did better on the paper tests. Further analysis revealed that the overall average of the computer tests was 71.9%, while paper tests revealed an average of 69.9%. In summary, these findings report that there is no significant difference in scores when taking a test on the computer or a test on paper. Suggestions for further research and recommendations are included.

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