数学教学中学生创新意识的培养

为培养学生的创新意识和创新思维能力，数学教师在教学中应引导学生勤于思考、质疑，以孕育创新；大胆猜测、联想，勇于创新：一题多法，以培育创新；引进开放题型，拓展创新。     

Teaching multiplication to low math performers: Guided versus structured instruction

The results of an intervention program forstudents with difficulties learning mathematicsare reported. Two kinds of math intervention,guided versus structured instruction, werecompared to regular math instruction. A totalof 75 students from regular and specialeducation, aged seven to thirteen,participated. Ability and automaticitymultiplication tests were administered beforeand after the four-month training period. Theresults show that the students in both of theexperimental conditions improved more than thestudents in the control condition. Someadditional differences were found between thetwo experimental interventions. Guidedinstruction appeared to be more effective forlow performing students than structuredinstruction and especially for those studentsin regular education. Special educationstudents appear to benefit most from structuredinstruction for the automaticity ofmultiplication problems. A three monthfollow-up test showed the acquired knowledge tobe well-established in both groups.     

Students’ formative assessment perceptions,feedback use and mathematics performance in secondary schools in Tanzania

This study investigates the impact of secondary school students’ perceptions of mathematics teachers’ formative assessment practices and feedback delivery on their feedback use, and mathematics performance. The sample consisted of 2767 Form 3 (Grade 11) students from 48 secondary schools in Tanzania. Surveys and focus group discussions were used to measure students’ perceptions of formative assessment, feedback delivery, and feedback use. Structural Equation Modelling (SEM) of survey data showed that students’ perceptions of the quality of teacher feedback delivery and perceived scaffolding positively predicted students’ feedback use whereas perceived monitoring negatively predicted feedback use. In turn, students’ feedback use positively predicted their mathematics performance to a small extent. Content analysis of focus group discussions illustrated that most students valued their mathematics teacher’s assessment practices. The findings imply that in Sub-Saharan African educational systems the quality of teacher feedback delivery and promotion of student feedback use can improve students’ mathematics performance.     

奥苏贝尔的学习动机理论对数学教学的启示

学生的学习动机集中反映在成就动机上。奥苏贝尔对其提出了与众不同的看法 ,他认为成就动机是由认知内驱力、自我提高内驱力和附属内驱力三个方面组成。通过对奥苏贝尔学习动机理论的分析和理解 ,最后提出关于数学教学的若干建议     

Moving towards transdisciplinarity: an ecological sustainable focus for science and mathematics pre‐service education in the primary/middle years

One reason we have difficulty finding sustainable solutions is in part because we are unable to see the bigger picture. Capra (2000 Capra, F. 2000. The challenge of our time.. Resurgence, 203: 18–20.  [Google Scholar]) argues, “To become ecologically literate we must learn to think systemically – in terms of connectedness, context and processes” (p. 270). We have attempted to structure connected learning experiences through our transdisciplinary approach to teaching for learning science, mathematics and ecological aspects of society and environment. We support Jucker's (2002 Jucker, R. 2002. Our common illiteracy: Education as if the Earth and people mattered, Frankfurt: Peter Lang.  [Google Scholar]) view that we must have lateral rigor across disciplines and vertical rigor within disciplines in order to best prepare students for teaching. This paper explores the theoretical underpinning of this complex approach to undergraduate teaching and reports on how our teaching team has worked collaboratively to structure a sequence of three, one semester integrated, core courses that explicitly uses an educating for ecological sustainability theme as the basis for each course and associated assessment.     

数学的对称美及其作用

对称美是数学美的重要组成部分，它普遍存在于初等数学与高等数学的各个分支。对称美在数学研究中有重要作用，它是数学创造与发现的美学方法之一。对称美在数学解题中也有广泛的应用，在解题过程中，考虑对称美的因素有时可起到事半功倍的效果。     

Should we embed careers education in STEM lessons?

Schools have a particular responsibility to introduce young people to the range of possible options for them after they leave education as few families can provide this. However, in the United Kingdom, careers education is currently not strong in most schools for a number of reasons but principally due to its low status and shifts in government policy and funding. As a result, too many young people make subject choices for post-16 study that they subsequently regret. In particular, fewer young people in the United Kingdom choose post-16 STEM subjects than might do. Yet, STEM (science, technology, engineering and mathematics) graduates are especially valued by employers. We draw on the findings of two research projects, ASPIRES and UPMAP, and argue that one way forward may be to embed careers education in STEM lessons. This can be done in ways that are respectful of and helpful to students. We recommend that an England- or UK-based project to investigate the consequences of embedding careers education in STEM lessons be undertaken.     

数学教师专业化与高师数学教育专业课改

数学教师专业化是世界数学教师教育的发展潮流,其内涵包括:数学教师数学专业化、数学教师教育专业化和数学教师专业情意.当前高师数学教育在课程设置上不适应数学教师专业化要求,改革重点是构建合理的课程体系.     

Learning to observe: using video to improve preservice mathematics teachers’ ability to notice

Video has assumed an increasingly prominent role in teacher education, particularly in the form of the viewing of videotaped class lessons by preservice teachers. Yet there is little research that confirms whether preservice teachers attend to the aspects of the video(s) that teacher educators anticipate or desire. This article explores this issue and reports on the impact of video viewing as a means to improve teachers’ ability to be observers of classroom practice. We utilized a pre- and post-test design to measure the quantity and type of classroom events that preservice mathematics teachers noticed before and after a teaching methods course where improving observation skills was an explicit goal. The results of the pre-assessment suggest that preservice teachers generally do not enter teaching methods courses with well-developed observation skills. The post-assessment indicates that the course led to significant increases in preservice teachers’ observation skills, particularly in teachers’ ability to notice features of the classroom environment, mathematical content of a lesson, and teacher and student communication during a lesson.

反馈对儿童早期数学学习效果的影响元分析

反馈被认为是促进学生学习的最有力方式,信息技术的发展为反馈设计提供了支持.采用元分析方法考察反馈对儿童早期数学学习的影响,研究发现:反馈对儿童早期数学学习有较小的积极效果.通过调节分析发现,任务类型和反馈类型对反馈效果具有调节作用,反馈媒介、反馈时机和反馈效果测量时间对反馈效果无调节作用.未来关于反馈对儿童早期数学学习效果影响的研究,应在教育信息化背景下从任务特征、学习者特点和反馈特征3个方面综合考虑,提高反馈的针对性和个性化.