Gender and Mathematical Problem Solving

The relationship between gender and mathematical problem-solving among high ability students depends on the attributes of the problem solving questions. This was evident in the present study of 12-year-olds. The children were from predominately White families. Eighty-three males and 76 females were tested in both the fall and the spring on the Fennema-Sherman Mathematics Attitudes Scales and on the Canadian Test of Basic Skills (CTBS). In the Spring, students were also tested on the GAUSS. Both the CTBS and the GAUSS measure mathematical problem solving. Among high ability students, there were gender differences on the problem-solving scale of the CTBS but not on the GAUSS, even though the GAUSS was independently rated as the more abstract and difficult of the two tests. The present study describes the implications of this for the question of the origin of gender differences in mathematics, and also looked at the relationship between attitudes toward mathematics and mathematical problem-solving performance.     

Intuition and Visualization in Mathematical Problem Solving

In this article, I will discuss the relationship between mathematical intuition and mathematical visualization. I will argue that in order to investigate this relationship, it is necessary to consider mathematical activity as a complex phenomenon, which involves many different cognitive resources. I will focus on two kinds of danger in recurring to visualization and I will show that they are not a good reason to conclude that visualization is not reliable, if we consider its use in mathematical practice. Then, I will give an example of mathematical reasoning with a figure, and show that both visualization and intuition are involved. I claim that mathematical intuition depends on background knowledge and expertise, and that it allows to see the generality of the conclusions obtained by means of visualization.     

Emergent Leadership in Children's Cooperative Problem Solving Groups

Social skills involved in leadership were examined in a problem-solving activity in which 252 Chinese 5th-graders worked in small groups on a spatial-reasoning puzzle. Results showed that students who engaged in peer-managed small-group discussions of stories prior to problem solving produced significantly better solutions and initiated significantly more effective leadership than control students. A mediation analysis suggested that it was because of effective leadership that groups who had experienced discussions achieved better problem solutions.     

论数学问题解决的生态模式

随着教育学和心理学生态化研究的兴起,以及数学教育改革的理论发展与实践诉求,从生态观的角度来审视数学问题解决具有重要的理论意义和实践价值。文章以数学问题解决的生态观为基础,从理论上构建了一个关于数学问题解决的生态模式,并论述了该生态模式的5个内部系统(即,数学文化、数学问题、数学知识、问题解决者和问题解决程序)的相互关系及其作用机制。     

Designing Knowledge Scaffolds to Support Mathematical Problem Solving

We present a methodology for designing better learning environments. In Phase 1, 6th-grade students' (n = 223) prior knowledge was assessed using a difficulty factors assessment (DFA). The assessment revealed that scaffolds designed to elicit contextual, conceptual, or procedural knowledge each improved students' ability to add and subtract fractions. Analyses of errors and strategies along with cognitive modeling suggested potential mechanisms underlying these effects. In Phase 2, we designed an intervention based on scaffolding this prior knowledge and implemented the computer-based lessons in mathematics classes. In Phase 3, we used the DFA and supporting analyses to assess student learning from the intervention. The posttest results suggest that scaffolding conceptual, contextual, and procedural knowledge are promising tools for improving student learning.     

复杂问题解决中计算机模拟情境的逻辑框架

计算机模拟情境摆脱了实验室研究和现场研究的不足,满足了复杂问题解决的复杂性、动态性和模糊性等特征,受到研究者们的青睐.近年来,各种模拟情境在复杂问题解决研究中得到运用,其内部逻辑结构主要有线性结构方程和有限状态自动化,线性结构方程适用于等距数据,而有限状态自动化适用于称名数据.当前,对复杂问题解决的测量注重结果,而相对忽视过程.未来的模拟情境可以从问题特征、任务逻辑和测量方式来提高信度和效度.     

问题表征、工作记忆对小学生数学问题解决的影响

以104名小学六年级学生为被试, 采用4个相对独立的研究探讨了工作记忆广度、问题表征方式与小学生数学应用题解决的关系。结果表明：(1)言语工作记忆广度只影响高难度应用题的解决, 在低难度、中等难度的应用题解决上, 高、低言语工作记忆广度者不存在显著差异; (2)视觉-空间工作记忆广度对低难度、中等难度、高难度应用题的解决都存在影响; (3)问题表征方式影响数学应用题的解决, 应用题的解题成绩与问题表征方式的使用有关; (4)言语工作记忆广度对应用题的表征方式没有影响, 高、低言语工作记忆广度者在三种难度水平应用题的表征方式上不存在显著差异; (5)视觉-空间工作记忆广度对应用题的表征方式存在影响, 高、低视觉-空间工作记忆广度者在三种难度水平应用题的表征方式上均存在组间差异。     

Decision Development in Small Groups V Test of a Contingency Model

This study tested a model of the factors that influence groups to follow various paths as they make decisions. Three panels of contingency variables, which indexed the nature of the group's task and group structure, were used to predict properties of the group's developmental path. The decision path properties included type of decision path, the complexity of the path, the amount of disorganized behavior the group engaged in, and the relative emphasis on various types of decision activity, such as orientation, problem analysis, and solution development. The contingency variables were quite effective in predicting decision paths and their properties. Group structure variables were stronger predictors than were task variables. Results suggested that significant revisions in the original contingency model were necessary. Most notably, the groups appeared to be much more rational in adapting their paths to the contingencies than we had originally supposed they would be.     

Creative Problem Solving in Small Groups: The Effects of Creativity Training on Idea Generation,Solution Creativity,and Leadership Effectiveness

This investigation evaluated the degree to which creativity training, idea generation instruction, and creative process impacted idea production, creativeness of solutions, and leadership effectiveness. Three sets of hypotheses were tested with a 114 groups of adults. First, groups whose members had some (i.e., one CPS course) or advanced training (i.e., graduate-level study in creativity or creativity professionals) were significantly more effective at idea generation than groups without training. Furthermore, leaders with some and advanced training were perceived to be significantly more effective than those with no creativity training. With respect to creativeness of solutions, the advanced training groups outperformed all others. The second set of hypotheses focused on the effectiveness of idea generation instruction (i.e., instructions without brainstorming, brainstorming, and brainstorming with criticism). Analysis revealed no significant difference for idea generation instruction relative to idea production or creativeness of solutions. The final set of hypotheses examined the use of a simple process structure for groups without prior creativity training (i.e., distinct phases for idea generation and solution development). Analysis revealed that those meetings that followed a simple process structure out performed groups that did not follow a process for both idea generation and creativeness of solutions. Further results are presented and implications discussed.     

Facilitative Style,Individual Innovation,and Emergent Leadership in Problem Solving Groups

ABSTRACT This study responded to an issue raised in a recent review of leadership research regarding the lack of available data concerning leader characteristics and management of creative work groups. Specifically, the effects of facilitative leadership style and individual creative contributions on emergent leadership were assessed in an initially leaderless creative problem solving situation. Participants were 34 university security officers who were divided into four groups to play Island Commission. At the end of the session, participants rated each other on facilitative style, innovative contribution, and leadership behavior. Both independent variables made a significant contribution to perceptions of leadership (R = .82, p < .0001). Results are discussed in terms of leadership theory, and implications for personnel selection, training, and development of creative problem solving teams.     

Influence of Item Content and Stereotype Situation on Gender Differences in Mathematical Problem Solving

On standardized tests of mathematical problemsolving, the typical finding has been that women scorelower than men. Experiment 1 manipulated gender labeling(female character, male character, or gender neutral) within the problem question to seewhether this accounted for gender differences inmathematical problem solving. Sixty-four seventh andeighth graders were tested on modified versions of theCanadian Test of Basic Skills (CTBS) with the resultsshowing that although gender labeling affected studentsperformance, it did not account for gender differences.Experiment 2 manipulated both gender labeling and gender stereotype threat for 174 universitystudents writing modified versions of a modelStandardized Achievement Test (SAT). Again, genderlabeling within problem questions did not account forgender differences. However, women scored lower thanmen when they believed that the test had previouslyshown gender differences. There was no gender differencein the performance of the same women and men when they believed that the test was merelycomparing Canadian students with American students. Thissuggests that gender stereotype threat could be a keyfactor in explaining gender differences in mathematical problem solving.     

课程嵌入型表现性评定对数学问题解决影响的实验研究

课程嵌入型表现性评定是当前基础教育新课程改革倡导的重要的学生学业评价方式。以335名初中一年级学生为被试,采用为期一学年的追踪实验研究方式,探索课程嵌入型表现性评定对数学问题解决的影响效果。研究结果表明,此方式对学生的数学问题解决能力发展具有显著促进作用,且促进作用随实验进程不断增加并受到学生原有学业水平的影响。对口语报告资料的分析进一步表明,此评定方式对数学问题解决的促进作用主要体现在理解问题、元认知与问题解决策略等方面。     

小学生数学问题解决中视觉空间表征的研究

本研究区分了两类数学应用题:非视觉化题目与视觉化题目,采用数学测验与个别访谈相结合的方法,考察了54名小学四、五、六年级不同学业水平学生的视觉空间表征。结果表明:图式表征在非视觉化题目与视觉化题目上都极大地促进了问题解决,图像表征妨碍非视觉化题目的解决但与视觉化题目的解决无关,并提出图式表征和图像表征在两类题目上有不同的含义。六年级学生的解题成绩及图式表征有显著的提高,但图像表征与年级因素无关。差生的图式表征能力很差,而在视觉化题目上使用图像表征显著地多于优生及中等生。在非视觉化题目的非视觉空间表征与图式表征之间的转换灵活性上,优生表现了明显的优势。