A case study of teachers' mathematics content knowledge and attitudes toward mathematics and teaching

This study intended to measure teacher mathematical content knowledge both before and after the first year of teaching and taking graduate teacher education courses in the Teach for America (TFA) program, as well as measure attitudes toward mathematics and teaching both before and after TFA teachers’ first year. There was a significant increase in both mathematical content knowledge and attitudes toward mathematics over the TFA teachers’ first year teaching. Additionally, several significant correlations were found between attitudes toward mathematics and content knowledge. Finally, after a year of teaching, TFA teachers had significantly better attitudes toward mathematics and teaching than neutral.

Motivation and Learning in Mathematics Pre-service Teachers

Based on a review of literature of conceptual and procedural knowledge in relation to intrinsic and extrinsic motivation, the purpose of this study was to test the relationship between conceptual and procedural knowledge and intrinsic and extrinsic motivation. Thirty-eight education students with a mathematics focus (elementary or secondary) in their junior, senior, or fifth year completed a survey with a Likert scale measuring their preference to learning (conceptual or procedural) and their motivation type (intrinsic or extrinsic). Findings showed that secondary mathematics focused students were more likely to prefer learning mathematics conceptually than elementary mathematics focused students. However, secondary and elementary mathematics focused students showed an equal preference for learning mathematics procedurally and sequentially. Elementary and secondary students reported similar intrinsic and extrinsic motivation. Extrinsically motivated students preferred procedural learning more than conceptual learning. While there was no statistically significant preference with intrinsically motivated students, there was a trend favoring preference of conceptual learning over procedural learning. These results tend to support the hypothesis that mathematics focused students who prefer conceptual learning are more intrinsically motivated, and mathematics focused students who prefer procedural learning are more extrinsically motivated.

The Congressional Budget Process and the Aggregate Level of Spending

This paper analyzes whether the Congressional budget process (instituted in 1974) leads to lower aggregate spending than does the piece-meal appropriations process that preceded it. Previous theoretical analysis, using spatial models of legislator preferences, is inconclusive. This paper uses a model of interest group lobbying, where a legislature determines spending on a national public good and on subsidies to subsets of the population that belong to nationwide sector-specific interest groups. In the appropriations process, the Appropriations Committee proposes a budget, maximizing the joint welfare of voters and the interest groups, that leads to overspending on subsidies. In the budget process, a Budget Committee proposes an aggregate level of spending (the budget resolution); the Appropriations Committee then proposes a budget. If the lobby groups are not subject to a binding resource constraint, the two institutional structures lead to identical outcomes. With such a constraint, however, there is a free rider problem among the groups in lobbying the Budget Committee, as each group only obtains a small fraction of the benefits from increasing the aggregate budget. If the number of groups is sufficiently large, each takes the budget resolution as given, and lobbies only the Appropriations Committee. The main results are that aggregate spending is lower, and social welfare higher, under the budget process; however, provision of the public good is suboptimal. The paper also presents two extensions: the first endogenizes the enforcement of the budget resolution by incorporating the relevant procedural rules into the model. The second analyzes statutory budget rules that limit spending levels, but can be revised by a simple majority vote. In each case,the free rider problem prevents the groups from securing the required changes to procedural and budget rules.