Reading Proficiency and Comparability of Mathematics and Science Scores for Students From English and Non-English Backgrounds: An International Perspective

The purpose of this research is to examine the comparability of mathematics and science scores for students from English language backgrounds (ELB) and non-English language backgrounds (NELB). We examine the relationship between English reading proficiency and performance on mathematics and science assessments in Australia, Canada, the United Kingdom, and the United States. The findings indicate a strong relationship with reading proficiency accounting for up to 43% of the variance in mathematics and up to 79% in science. In all comparisons, ELB students either outperformed NELB students or performed at the same level. However, when statistical adjustments were made for reading proficiency, in both mathematics and science, the score gap between the groups became statistically non-significant in three out of the four countries. These findings point to differences in score meaning in mathematics and science assessments and limitations in comparing performances of ELB and NELB.     

Does calling it “Morgan's way” reduce student learning? Evaluating the effect of person-presentation during comparison and discussion of worked examples in mathematics classrooms

Mathematics textbooks sometimes present worked examples as being generated by particular fictitious students (i.e., person-presentation). However, there are indicators that person-presentation of worked examples may harm generalization of the presented strategies to new problems. In the context of comparing and discussing worked examples during extended classroom instruction, the current study compared the impact of person-presentation to strategy labels on students' posttest accuracy and ratings of strategy generalizability. Five algebra teachers and their 168 students used worked examples either presented using fictitious students or with a strategy label during a multiweek unit on equation solving, with teachers randomly assigned to condition. All students compared and discussed the worked examples. In this context, we found no effect of condition on student accuracy at posttest, nor on their ratings of the generalizability of the presented strategies. We discuss why previously found negative effects of person-presentation may not have extended to this context.     

Do examples of failure effectively prepare students for learning from subsequent instruction?

Studies on the productive failure (PF) approach have demonstrated that attempting to solve a problem prepares students more effectively for later instruction compared to observing failed problem-solving attempts prior to instruction. However, the examples of failure used in these studies did not display the problem-solving-and-failing process, which may have limited the preparatory effects. In this quasi-experiment, we investigated whether observing someone else engaging in problem solving can prepare students for instruction, and whether examples that show the problem-solving-and -failing process are more effective than those that only show the outcome of this process. We also explored whether the perceived model–observer similarity had an impact on the effectiveness of observing examples of failure. The results showed that observing examples effectively prepares students for learning from instruction. However, observing the model's problem-solving-and-failing process did not prepare students more effectively than merely looking at the outcome. Studying examples were more effective if model–observer similarity was high.     

SIMONE WEIL'S SPIRITUAL CRITIQUE OF MODERN SCIENCE: AN HISTORICAL‐CRITICAL ASSESSMENT

Simone Weil is widely recognized today as one of the profound religious thinkers of the twentieth century. Yet while her interpretation of natural science is critical to Weil's overall understanding of religious faith, her writings on science have received little attention compared with her more overtly theological writings. The present essay, which builds on Vance Morgan's Weaving the World: Simone Weil on Science, Necessity, and Love (2005), critically examines Weil's interpretation of the history of science. Weil believed that mathematical science, for the ancient Pythagoreans a mystical expression of the love of God, had in the modern period degenerated into a kind of reification of method that confuses the means of representing nature with nature itself. Beginning with classical (Newtonian) science's representation of nature as a machine, and even more so with the subsequent assimilation of symbolic algebra as the principal language of mathematical physics, modern science according to Weil trades genuine insight into the order of the world for symbolic manipulation yielding mere predictive success and technological domination of nature. I show that Weil's expressed desire to revive a Pythagorean scientific approach, inspired by the “mysterious complicity” in nature between brute necessity and love, must be recast in view of the intrinsically symbolic character of modern mathematical science. I argue further that a genuinely mystical attitude toward nature is nascent within symbolic mathematical science itself.     

Parental perceptions of mathematical talent

Parents often become frustrated when their perception of their child’s talent in mathematics differs from that held by the school. Yet for the young child, research suggests parents have a much deeper insight into the interests and talents of their child. Failure to recognize talent can result in lost opportunities for the child as well as a loss to society. This article evaluates the development of an instrument designed to assess parent perceptions of mathematical talent. Parental perceptions and family demographics were collected for third grade students participating in Project M³: Mentoring Mathematical Minds, a research program conducted collaboratively by the University of Connecticut, Northern Kentucky University and Boston University, and for second grade students under consideration for the program. The data were correlated with other identification tools used for the identification of talented second graders for Project M³ to explore a research-based means of parent identification of mathematical talent.

刻板印象的自动激活实验研究

本研究应用模糊主次评判方法配合语义启动技术进行实验。结果表明;在年龄刻板印象上存在自动激活,而且没有性别差异;用不同性质的启动词来激活与年龄有关的刻板印象,激活后的刻板印象对年龄的判断有不同的影响,而且被试没有一个人意识到这点,表明内隐刻板印象的存在;人的判断具有模糊性,模糊主次评判方法有助于社会认知领域的量化研究,这是一个全新的尝试。     

Math Talk and Student Strategy Trajectories: The Case of Two First Grade Classrooms

This study investigated different math-talk facilitations, and conceptualized the teachers' talk moves for productive student mathematics discussions. Our findings suggest that students' strategy development is supported by talk moves coordinating a wide range of student strategies, representations and discussions that are at a process-level and maintain student ownership of ideas, and transitional strategies that connect students' beginning ideas with target strategies.     

Academic Cheating in Mathematics Classes: A Motivational Perspective

We investigated the frequency of secondary school students’ self-reported cheating in mathematics and relationships between cheating and motivational beliefs, as well as neutralizing attitudes. Two types of cheating were examined: active cheating, which is aimed to increase a person’s own success, and second-party cheating, aimed to help other students achieve success. Students use second-party cheating very often and more than active cheating. Motivational beliefs are significantly related to active cheating but uncorrelated with second-party cheating. Thus, although active and second-party cheating are both classified as dishonest acts, they do not have the same motivational mechanisms in their background.     

近似数量系统敏锐度与数学能力的关系

近年来,来自认知发展、比较认知、跨文化认知和神经生物学的研究证据都表明近似数量系统的存在,并且相较于一般认知能力,它更可能是决定个体数学能力差异最为重要的因素。本文综述了有关近似数量系统敏锐度与数学能力相互关系的横断研究、纵向研究、训练研究及认知神经科学的研究成果,分析了影响二者关系的因素,包括个体年龄、数学能力高低、抑制控制等,并总结了多种理论对二者间显著正相关关系的解释。未来研究需要在确定更具信效度的测量范式的基础上探讨近似数量系统与数学能力各维度的关系,以及这种相互关系背后的原因,并将研究结论运用于数学教学及计算障碍个体的干预。     

初中生数学家庭作业质量、控制感与作业情绪对作业努力的影响

采用问卷调查法,以 463 名初中生为被试,探讨了初中生感知到的数学家庭作业质量、控制感和家庭作业情绪影响家庭作业努力的内在作用机制。结果发现：(1)积极数学家庭作业情绪和消极数学家庭作业情绪均在数学家庭作业质量和数学家庭作业努力之间起完全中介作用;(2)数学家庭作业质量可以通过数学控制感分别经积极和消极数学家庭作业情绪的多重中介来预测数学家庭作业努力。研究表明,初中生感知到的数学家庭作业质量、控制感和家庭作业情绪均是其家庭作业努力的重要影响因素。