Effects of playing mathematics computer games on primary school students’ multiplicative reasoning ability

This study used a large-scale cluster randomized longitudinal experiment (N = 719; 35 schools) to investigate the effects of online mathematics mini-games on primary school students’ multiplicative reasoning ability. The experiment included four conditions: playing at school, integrated in a lesson (E_school), playing at home without attention at school (E_home), playing at home with debriefing at school (E_home-school) and, in the control group, playing at school mini-games on other mathematics topics (C). The mini-games were played in Grade 2 and Grade 3 (32 mini-games in total). Using tests at the end of each grade, effects on three aspects of multiplicative reasoning ability were measured: knowledge of multiplicative number facts, skills in multiplicative operations, and insight in multiplicative number relations and properties of multiplicative operations. Through path analyses it was found that the mini-games were most effective in the E_home-school condition, where both students’ skills and their insight were positively affected as compared to the control group (significant ds ranging from 0.22 to 0.29). In the E_school condition, an effect was only found for insight in Grade 2 (d = 0.35), while in the E_home condition no significant effects were found. Students’ gameplay behavior (time and effort put in the games) was in some cases, but not always, related to their learning outcomes.     

First-graders’ knowledge of multiplicative reasoning before formal instruction in this domain

Our study investigated children’s knowledge of multiplicative reasoning (multiplication and division) at the end of Grade 1, just before the start of formal instruction on multiplicative reasoning in Grade 2. A large sample of children (N = 1176) was assessed in a relatively formal test setting, using an online test with 28 multiplicative problems of different types. On average, the children correctly answered more than half (58%) of the problems, including several bare number problems. This indicates that before formal instruction on multiplicative reasoning, children already have a considerable amount of knowledge in this domain, which teachers can build on when teaching them formal multiplication and division. Using analysis of variance and cross-classified multilevel regression analysis, we identified several predictors of children’s pre-instructional multiplicative knowledge. With respect to the characteristics of the multiplicative problems, we found that the problems were easiest to solve when they included a picture involving countable objects, and when the multiplicative situation was of the equal groups semantic structure (e.g., 3 boxes of 4 cookies). Regarding student characteristics, pre-instructional multiplicative knowledge was higher for children with higher-educated parents. Finally, the mathematics textbook used in school appeared to have influenced children’s pre-instructional multiplicative knowledge.     

Literature review – Parent involvement and mathematic outcome

The impact of parent involvement with their children's educational outcomes can have a profound effect on learning, achievement, motivation, engagement, values, and goals. This literature review is the first to focus on parental involvement and educational outcomes in the subject of mathematics. Search engines identified 1397 articles from 2010 to 2019. In the wake of the inclusion and exclusion process, 169 articles (n-group) related to children aged from 6 to 16 years were selected for review. As a result, an extensive range of indicators associated with parent involvement was identified and linked to 37 different outcomes for children studying mathematics. Framed by a structured coding analysis, the parent involvement indicators were classified into 12 new categories and discussed in the context of established theories. Finally, the outcome indicators were coded in the following categories: Learning, Belief, Motivation, Emotion, and Behaviour. The analysis uncovered 403 indicator connections linking children's mathematic outcomes to parental involvement. A predominance of the research focused on parents' different beliefs, motivations, communication, and support. Many of the parent involvement indicators were related to the children's mathematical achievement, performance, and skills. An effects matrix revealed that a majority of indicators showed positive effects. Nevertheless, a positive generalisation about parental involvement has the potential to erroneously hide negative aspects. Further research is needed to ensure consistency and unambiguous operationalisation of parental involvement, while also covering blind spots in the research field documented in the review. Finally, this review contributes to a further discussion outside the mathematics context with respect to the parent involvement concept and the need for increased research quality and scientific rigour.     

一些高等数学知识在中小学数学中的体现

高等代数和数学分析是高校数学专业学生的基础课程之一。同学们普遍感到这些课程抽象,不易理解,且应用性不强．似乎对中小学数学教育没有实质性帮助。本文主要介绍坐标变换公式,哥西一施瓦兹不等式（Cauchy—Schwarz）中小数学中的体现,以期对广大数学专业学生有所帮助,从而改变他们对高等数学的认识。     

The purpose, design and use of examples in the teaching of elementary mathematics

This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching, and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the analysis of these lessons was to discover, and to construct theories around, the ways that these novice teachers could be seen to draw upon their mathematics teaching knowledge-base in their lesson preparation and in their observed classroom instruction. A highly-pervasive dimension of the findings was these teachers’ choice and use of examples. Four categories of uses of examples are identified and exemplified: these are related to different kinds of teacher awareness.

Fostering the use of pedagogical practices among teachers to support elementary students’ motivation to write

Based on self-determination theory, this research aimed at evaluating the effectiveness of the CASIS professional development (PD) program for fostering (1) teachers’ use of five recommended pedagogical practices during a writing lesson and (2) students’ motivational resources (intrinsic, identified, and controlled regulations) toward writing. Two quasi-experimental studies with two-time points were conducted among preservice (Study 1, n = 32) and inservice (Study 2, n = 111) elementary teachers and their students (Study 1, n = 559; Study 2, sample 1, n = 1779; sample 2, n = 1471). In both studies, the CASIS PD program appeared to foster the use of two of the five recommended pedagogical practices. For the other three, some effects were observed in one study but were not always reproduced in the other. Although the CASIS PD program fostered greater use of the pedagogical practices, this effect did not always translate directly to the students’ motivational resources. However, some significant differences were observed between students of the CASIS and the control groups on identified and controlled regulations, as a function of the socioeconomic background of the schools in which teachers and students were sampled. The results are discussed in light of past research and relevant theories.     

小学数学教学中思维导图的应用

数学本身是一门抽象性与逻辑性都较强的学科,要想学好数学,需要具备数学思维,具有充分的想象力与理解能力。而且数学知识之间的联系性也较强,有很多知识是前后连贯的,这就需要学生数学思维清晰才能更好地利用已有知识结构更好地学习新的数学知识。思维导图作为一种辅助工具,能够将教学知识点的脉络结构清晰化,应用在小学数学教学中能够弥补小学生的思维能力上的不足,帮助学生更好地学习数学知识。     

Do they really need to raise their hands? Challenging a traditional social norm in a second grade mathematics classroom

In an attempt to examine dialogue within a second grade classroom, students were encouraged to participate in whole-class mathematics discussions without raising their hands before speaking. Beneficial social and sociomathematical norms developed in place of this traditional social norm. Effects of this change on the dialogue and written mathematical explanations of a class of second grade students are described. Focus was placed on student participation in whole-class discussions. The study helped to determine the effects of student-centered dialogue on students' mathematical explanations and justifications as demonstrated in the students' discussions, participation, and written expression related to their mathematics learning.     

初等数学直觉审美思维方式探讨

数学是研究客观世界数量关系和空间形式的科学,在它特有的抽象概念、公式符号、命题模型等范畴中蕴含有简单性、统一性、相似性和奇异性等美的形式。运用数学直觉审美思维、调动已有的知识经验去求解初等数学问题能够简约思维过程,寻求到问题解答的最佳途径。     

小学中高年级儿童造型能力培养的思考与探究

对儿童绘画进行辅导时,教师要尊重儿童的生理、心理特征,对于不同时期的儿童,应当选择相应的教学内容、教学方法,以满足他们的心理需求。在小学中高年级开展造型训练,能有效结束学生随意绘画的习惯,帮助他们提高造型表现能力,促进儿童绘画兴趣进一步发展。     

小学数学教学中趣味元素的渗透

小学生在攀登数学高峰的时候,容易因为眼前对数学的片面了解,而认为数学这座山峰太难爬,丧失了前进的勇气。小学数学教师要及时帮助学生改变这一学习念头,为学生增添数学学习的乐趣,让学生能够在攀登的过程中享受数学的风光,找到攀登的动力。教师可以围绕生活、情境、问题、实践,展开趣味元素的渗透。在课堂中,学生对数学有了更多的了解,发展了自己的数学能力。由此可见,教师的实践是成功的,是值得探索的。     

小学数学教学中有效应用思维导图路径分析

教学方式的创新是教育工作者面临的共同难题。而思维导图方法有助于学生打下坚实的知识基础,增强学生对于知识点内容的理解,加深学生的记忆能力。本文以小学数学教学为例,通过对思维导图教学方法的深度剖析,帮助教师解决教学中所遇到难题,推进我国教育事业的发展创新。     

Does prior mathematics knowledge really lead to variation in elementary statistics performance? Evidence from a developing country

A model incorporating prerequisite mathematics performance and other variables deemed to be associated with learning elementary statistics (ES) is developed. The relationship between ES performance and the explanatory variables is well represented by the logistics form. Aptitude, effort and motivation are the only significant explanatory variables of ES performance. Since prerequisite mathematics is not significant, statistical thinking at the tertiary level may be mostly intuitive and non-mathematical. Students with low aptitude experience increasing returns to effort over the first half of the feasible effort interval, while high-aptitude students experience diminishing returns at all levels of effort. The levels of effort required to achieve a minimum pass are interpreted.     

小学数学教学生活化的有效策略

数学是一门与生活紧密相连的学科,俗语有云:“学会数理化,走遍全天下。”其中数学位于首位,足以见得数学知识能够很好地解决实际问题。利用生活化教学策略进行数学教学,能够让小学生对数学内容产生一定的学习兴趣与好奇心,并且能够有效提升学生对数学知识的重视程度,学生愿意主动学习数学,其综合能力才能够有效提升起来。为了实现上述教学效果,本文主要研究小学数学教学生活化的有效策略。     

调动学习数学的“发动机”,促进学生自我学习

数学的逻辑性很强,如果不认真去学习,就会无效学习。所以必须调动学生身上的发动机,促进学生自我学习。为此,可以采取以下策略教学:创设数学生活情境,使枯燥的数学有趣化;借助现代教育技术,让数学动起来;分层次教学,挖掘学生自我学习的潜力;采取激励措施,长效调动学生的积极性;激发学生主体意识,调动其学习积极性;授之以渔,教给学生自我学习的方法。