Discounting the Difficult: How High Math-Identified Women Respond to Stereotype Threat

In this study, we examined how math identity moderates women's response to gender-related stereotypes in the domain of mathematics. Male and female college students with varying degrees of math identification took a challenging math test with a gender-related stereotype either activated (i.e., stereotype threat) or nullified. Consistent with previous research, women performed worse than men in the stereotype threat condition, but equal to men in the stereotype nullification condition when performance was adjusted for math SAT scores. Moreover, when faced with stereotype threat, high math-identified women discounted the validity of the test more than did less math-identified women or men in general. We discuss potential benefits and drawbacks of a discounting strategy for women who are highly identified with math.     

Behavioral fluency and mathematics intervention research: A review of the last 20 years

Behavioral fluency refers to the relationship between the achievement of performance standards, or frequency ranges of behavior, and critical learning outcomes. Over the past 20 years, Precision Teaching and related research have contributed a number of studies examining behavioral fluency. The subsequent review investigates the empirical evidence from mathematics intervention research. Several studies suggest numerical markers that best support behavioral fluency. Results indicate that fluency interventions set to performance standards increased behavioral fluency and associated critical learning outcomes; however, more research is warranted to operationalize and standardize each outcome to the principles of behavior and numerical markers that constitute behavioral fluency.     

Who uses more strategies? Linking mathematics anxiety to adults’ strategy variability and performance on fraction magnitude tasks

Adults use a variety of strategies to reason about fraction magnitudes, and this variability is adaptive. In two studies, we examined the relationships between mathematics anxiety, working memory, strategy variability and performance on two fraction tasks: fraction magnitude comparison and estimation. Adults with higher mathematics anxiety had lower accuracy on the comparison task and greater percentage absolute error (PAE) on the estimation task. Unexpectedly, mathematics anxiety was not related to variable strategy use. However, variable strategy use was linked to more accurate magnitude comparisons, especially among adults with lower working memory performance or those who use mathematics less frequently, as well as lower PAE on the estimation task. These findings shed light on the role of strategy variability in fraction problem solving and demonstrate a link between mathematics anxiety and fraction magnitude reasoning, a key predictor of general mathematics achievement.     

Programming for Maintenance: An Investigation of Delayed Intermittent Reinforcement and Common Stimuli to Create Indiscriminable Contingencies

Generalization across time or maintenance of behavior change is a fundamental concern for behavior analysts and educators that remains insufficiently understood. This study examined the maintenance of mathematics responding during and following delayed intermittent reinforcement when common stimuli were programmed across the treatment and maintenance phases. Two third-grade girls who were referred by their classroom teacher due to concerns in the area of mathematics participated. Students were exposed to baseline, contingent reinforcement, delayed intermittent reinforcement, and a maintenance condition. The maintenance condition followed exposure to delayed intermittent reinforcement and included common stimuli from the reinforcement condition, but did not include a contingency for correct responding. Both students exhibited substantial prolonged maintenance during this condition. Implications of these results for future research examining maintenance and applied programming for maintenance are discussed.     

Does Treatment Integrity Matter? A Preliminary Investigation of Instructional Implementation and Mathematics Performance

This study examined the impact of three levels of treatment integrity on students' responding on mathematics tasks. Instruction was provided separately for addition and subtraction to six second-grade students who were referred due to poor performance with these operations. The treatment consisted of a computer delivered delayed prompt to use a counting strategy to solve problems, accuracy feedback, and intermittent presentation of animated praise sequences. Instruction was presented via computerized instruction to assure precise delivery of the varying levels of treatment integrity. The study examined the delivery of prompts for all, two-thirds, and one-third of instructional trials. Continuous delivery of instructional prompts was the most effective treatment or one of the most effective treatments for all participants. Lesser levels of prompt implementation were associated with poorer outcomes for the majority of the students. The implications of these findings for continuing research regarding the impact of reduced treatment integrity on student outcomes are discussed.     

小学3-6年级学生解决比较问题的研究

本研究对465名小学3—6年级学生解决不同类型的比较问题进行了研究。结果表明：(1)小学生解决比较问题的成绩受问题类型及年级的交互影响。儿童在一致算术问题上的成绩都很好,且显著优于不一致算术问题。在不一致算术问题、一致代数问题及不一致代数问题上,存在年级差异。5、6年级学生优于4年级学生。(2)小学生在算术问题上的通过率高于代数问题,5、6年级学生的通过率高于3、4年级。除一致算术问题外,其它类型比较问题的通过率较低。(3)小学生解决比较问题的成绩无性别差异。     

小学生数学学习观调查研究

采用开放题、多选题与单选题相结合的问卷调查方法．调查190名二、四、六年级学生的数学学习态度和数学学习观,结果表明：1)小学生普遍喜欢数学．并对自身的数学能力有信心．但这种积极态度随年级升高而逐渐下降,尤其是在四、六年级之间达到了显著性;2)小学生的数学知识性质观是倾向于建构性的,并随年级升高而显著提高．但总体上还是比较素朴、直观和肤浅的;3)小学生的数学学习过程观总体上并不十分明确．同时注重表层上的接受学习和深层上的主观参与。     

The influence of sharing on children's initial concept of division.

We report three studies that investigate young children's ability to solve partitive division problems when presented with a concrete model of a problem. In the studies, 5- to 8-year-olds were given problems about sharing "sweets" between dolls, and the sweets were grouped in one of two different ways. When the sweets were grouped by the divisor, the number of groups coincided with the number of dolls (divisor) and the number in each group was the answer (quotient). When the sweets were grouped by the quotient, the reverse was true. In all three experiments, children found it much easier to solve the problems in the Grouping-by-Divisor condition than in the Grouping-by-Quotient condition (although there was some evidence of a developmental improvement in the tasks). It is suggested that the Grouping-by-Divisor condition is easier because it coincides with the end point of sharing. The findings are discussed with reference to schemas of action in children's mathematical understanding.     

Mathematics and Spiritual Interpretation: A Bridge to Genuine Interdisciplinarity

This article is a spiritual interpretation of Leonhard Euler's famous equation linking the most important entities in mathematics: e (the base of natural logarithms), π (the ratio of the diameter to the circumference of a circle), i (√‐1),1 , and . The equation itself (e^πi+1 = 0> ) can be understood in terms of a traditional mathematical proof, but that does not give one a sense of what it might mean. While one might intuit, given the significance of the elements of the equation, that there is a deeper meaning, one is not in a position to get at that meaning within the discipline of mathematics itself. It is only by going outside of mathematics and adopting the perspective of theology that any kind of understanding of the equation might be gained, the significant implication here being that the whole mathematical field might be a vast treasure house of insights into the mind of God. In this regard, the article is a response to the monograph by George Lakoff and Rafael Núñez, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (2000), which attempts to approach mathematics in general and the Euler equation in particular in terms of some basic principles of cognitive psychology. It is my position that while there may be an external basis for understanding mathematics, the results are somewhat disappointing and fail to reveal the full measure of meaning buried within that equation.