Assessing kindergarteners’ mathematics problem solving: The development of a cognitive diagnostic test

This study aimed to develop an instrument for assessing kindergarteners’ mathematics problem solving (MPS) by using cognitive diagnostic assessment (CDA). A total of 747 children were recruited to examine the psychometric properties of the cognitive diagnostic test. The results showed that the classification accuracy of 11 cognitive attributes ranged from .68 to .99, with the average being .84. Both the cognitive diagnostic test score and the average mastery probabilities of the 11 cognitive attributes had moderate correlations with the Applied Problem subtest and the Calculation subtest of the Woodcock–Johnson IV Tests of Achievement. Moreover, the correlation between the cognitive diagnostic test and the Applied Problems subtest was higher than that between the cognitive diagnostic test and the Calculation subtest. The results indicated that the formal cognitive diagnostic test was a reliable instrument for assessing kindergarteners’ MPS in the domain of number and operations.     

Distinguishing adaptive from routine expertise with rational number arithmetic

Adaptive expertise is a valued, but under-examined, feature of students' mathematical development (e.g. Hatano & Oura, 2012). The present study investigates the nature of adaptive expertise with rational number arithmetic. We therefore examined 394 7th and 8th graders’ rational number knowledge using both variable-centered and person-centered approaches. Performance on a measure of adaptive expertise with rational number arithmetic, the arithmetic sentence production task, appeared to be distinct from more routine features of performance. Even among the top 45% of students, all of whom had strong routine procedural and conceptual knowledge, students varied greatly in their performance the arithmetic sentence production task. Strong performance on this measure also predicted later algebra knowledge. The findings suggest that it is possible to distinguish adaptive expertise from routine expertise with rational numbers and that this distinction is important to consider in research on mathematical development.     

高职高专《同步数学实验基础》课程的研究与建设——以柳州铁道职业技术学院弱电类专业为例

提高高职高等数学课的教学质量、学生的应用能力和综合素质,有必要开设《同步数学实验基础》课程。课程的实施要求教学内容分层次并针对不同专业进行选取,强调辅助软件工具的使用,基于问题的开展来组织教学,有利于促进高职数学和高职专业课程教学的效率,提高高职生的全面素质,同时要加强师资队伍、实验设备和实验教材建设。     

技术优先级数学模型的若干补充与发展

本文对作者曾提出的一种技术优先级确定的数学模型作出一些补充，从而可以进一步提高该数学方法应用的可行性与适用性。     

学前儿童“三阶梯”数学教学法及应用

学前儿童＂三阶梯＂数学教学法,指在数学教学过程中,教师根据学前儿童认知发展的三个阶段和思维发展的三级水平,有目的、有计划地引导其认知能力由低级向高级、由外部向内部、由感知运动阶段向形象表象阶段达至词语概念阶段的递进式发展的教学方法。此方法符合学前儿童认知发展的由易到难、循序渐进和螺旋式上升的规律,是发展学前儿童思维结构、促进其数学思维能力发展的有效策略。其理论依据主要是认知发展理论和信息加工理论。     

Mathematica平台上极限与连续的数学实验研究

数学软件在高等数学教学中的应用,将对教师的教学和学生的学习都产生巨大影响。在极限和连续的教学中引入Mathematica,通过实例进行绘制图形、动画演示、数值计算的介绍,使学生对极限和连续思想的理解都得到了很好的改善,增强学习兴趣,使课堂教学也更具活力。     

超级画板在高中数学概念教学中的应用

概念是数学中的基本内容。介绍超级画板的特点,结合教学设计案例从概念的形成与概念的同化两个方面探究了超级画板在数学概念教学方面的应用。     

数学素质意识与高职数学教育教学

本文围绕高职数学教育教学中有关学生素质培养、教学环境完善以及教育作用发挥等,阐述了数学素质意识的作用和意义,认为将增强数学素质意识纳入高职数学教育教学的必然要求和突出内容是很必要的。     

Subtraction by addition in children with mathematical learning disabilities

In the last decades, strategy variability and flexibility have become major aims in mathematics education. For children with mathematical learning disabilities (MLD) it is unclear whether the same goals can and should be set. Some researchers and policy makers advise to teach MLD children only one solution strategy, others advocate stimulating the flexible use of various strategies, as for typically developing children. To contribute to this debate, we compared the use of the subtraction by addition strategy to mentally solve two-digit subtractions in children with and without MLD. We used non-verbal research methods to infer strategy use patterns, and found that both groups of children switch between the traditionally taught direct subtraction strategy and subtraction by addition, based on the relative size of the subtrahend. These findings challenge typical special education classroom practices, which only focus on the routine mastery of the direct subtraction strategy.