数学教学评价的内容和方法

数学教学评价的问题是关系到数学教学改革的成败问题，因此，必须正确认识数学改革中的数学教学评价，深刻理解它的意义和功能，建立科学有效的评价手段和方法。     

模糊数学对哈尔滨市新老工业区土壤重金属污染对比研究

以哈尔滨市新老工业区土壤重金属污染为研究对象,对新老工业区土壤中的Cu、Pb、Zn、Cd、Cr和Ni等6种重金属元素进行了分析测定,采用模糊数学模型对新老工业区土壤重金属污染进行对比研究。研究结果表明,对照松嫩平原土壤背景值,研究区域重金属污染较严重,老工业区土壤环境质量为III级,新兴工业区为II级。该研究力图反映经济社会的发展对土壤环境不同的影响,为哈尔滨市工业区合理布局及土壤重金属防控提供科学依据。     

康托实数集合不可数证明中的四种错误探析

从逻辑、无穷观、极限论和证明的思路及具体的操作过程,分析了新发现的康托在实数集合不可数证明中所存在的四种错误,得到＂由于与现有经典无穷理论体系、经典极限论和经典数量体系密切相关的数学基础理论中所存在的缺陷,康托在这类证明中无法回避这四种很严重但却很隐蔽的错误＂的明确结论.特别是其中的逻辑错误使这样的证明无意中成了一种典型的数学魔术.     

Teaching primary mathematics with challenging tasks: How should lessons be structured?

Engaging students in a challenging (cognitively demanding) task and launching a mathematics lesson with a task before instruction are two characteristics of a reform-oriented approach to mathematics instruction often considered together. The authors systematically contrasted teaching with challenging tasks using a task-first lesson structure with that of a discussion-first lesson structure to three composite classes of first- and second-grade students (n = 73). Subsequent assessments of mathematical performance revealed that the discussion-first lesson structure was somewhat more efficacious in improving fluency performance but both structures similarly improved problem-solving performance. The findings suggest there is more than one way of incorporating challenging tasks into mathematics lessons to produce sizeable learning gains.     

Gender differences in mathematics and science competitions: A systematic review

Gendered patterns in mathematics and science interest emerge in early childhood, develop over time, and ultimately reflect advanced course selection in secondary education. During the crucial time adolescents become aware of their strengths and interests and specialize accordingly, they get the opportunity to participate in out-of-school learning programs such as mathematics and science competitions. This raises the question whether mathematics and science competitions contribute to gender equity by equally promoting female and male interests. In this article, we present a systematic review on gender differences and the mechanisms explaining success and failure in mathematics and science competitions. On an international level, we found large gender differences regarding participation in all Olympiads with the exception of the biology Olympiad. In fairs and national Olympiads, overall participation rates were not gendered as such, but females preferred biology topics whereas males preferred physics related topics. Male and female achievement in fairs was comparable, but males clearly outperformed female participants at the Olympiads, with the smallest differences in the biology Olympiad. Variables and theoretical frameworks explaining participation and achievement and the role of gender in mathematics and science competitions are discussed. We suggest that gender stereotypes, through their influence on self-concept and interest, play an important role in the mechanisms resulting in low female participation rates in and beyond mathematics and science competitions (especially in physics and chemistry). The mechanisms we found explaining female representation during a national selection competition might be considered as reflecting those in female mathematics or science careers and could thus serve as food for thought on countering the gender gap in mathematics and science.     

Transitioning from practicing teacher to teacher leader: a case study

Given US students’ lack of international competitiveness in mathematics and science, many states have adopted the Common Core State Standards for Mathematics (CCSSM). To help ensure that the Standards for Mathematical Practice within the CCSSM and effective teaching practices are implemented appropriately, many teachers are emerging as teacher leaders with the intent of supporting teachers with this implementation. Unfortunately, not all of these teachers are necessarily prepared in the field of teacher leadership. Recognizing the importance of having well-prepared teacher leaders, this article describes the case of Ms. Hodges, as she transitioned from mathematics teacher to teacher leader. Data revealed that several factors affected Ms. Hodges’ transition, some positively and others negatively. These results as well as implications for teacher leader development are provided.     

元认知训练对高等数学教学效果影响的实验研究

采用对比实验的方法考察元认知训练对高等数学教学效果的影响,研究结果表明,结合元认知训练的教学效果高于普通教学,元认知训练促进了学生高等数学学业成绩的提高,同时有助于培养学生数学学习的自我意识,使他们掌握矫正与控制数学学习活动的技能,从而深刻领悟数学的真谛.     

数学建模在高等数学教学中的应用实例

数学建模的思想已经渗入理科各个学科,而数学建模真正走进课堂还需要认真探讨与实践。分析了高等数学教学中结合数学建模思想的重要性与可行性,联系高等数学教学中的一个内容即微分方程问题,探讨了高等数学教学与数学建模的有机结合.     

高等职业院校高等数学课学习动机激发策略

高等数学是高等职业教育的一门重要的基础课。我国大部分高职院校高等数学的教学效果并不理想,未能达成预定的教学目标,其中一个很重要的原因就是学生对该学科认知不足,学习动机缺乏。奥苏贝尔学习动机理论认为学习者的学习动机将直接影响着学习效果,因此,有必要提出高等职业院校高等数学课学习动机激发的几点策略。     

对大学数学与高中数学课程内容的衔接问题的思考

首先分析当前大学数学与高中数学缺乏衔接所造成的问题,然后回顾我国在基础教育领域开始了由应试教育向素质教育转变的新一轮的课程改革,对《高中数学新课程标准》要求的教学内容和大学数学的教学内容两者作了比较分析,最后提出了大学数学教学改革的几方面的建议。