Journal of Mathematical Behavior最新文献

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Shared drawings in a mathematical modelling activity: An exploratory study 数学建模活动中的共享图：一项探索性研究

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematical Behavior

Pub Date : 2025-01-08 DOI: 10.1016/j.jmathb.2024.101234

Caterina Bassi, Domenico Brunetto

Recently, scholars highlighted the crucial role played by drawings in students’ modelling performance. Nevertheless, the correlation between the use of drawings and modelling performance cannot be extended when complex modelling activities are considered. In this work, we focus on the students’ drawing activities when dealing with a complex geometry problem. In particular, the paper reports an exploratory case from 11-grade students exposed to a realistic scenario from the sport context, on which they have worked for 4 hours. The analysed data, which focus on one of the class discussions, show that an important aspect for drawings to help students in the mathematical modelling process is that drawings must be shared among students. In this way, students can put into play different strategies for connecting both solution-relevant and non solution-relevant drawing elements, such as understanding, coordinating, contrasting and integrating, that help them in proceeding throughout the mathematical modelling process.

最近，学者们强调了绘画在学生建模表现中的重要作用。然而，当考虑到复杂的建模活动时，图纸的使用与建模性能之间的相关性不能被扩展。在这项工作中，我们重点关注学生在处理复杂几何问题时的绘画活动。特别地，本文报告了一个探索性的案例，从11年级的学生接触到一个现实的场景，从体育背景下，他们已经工作了4 小时。分析的数据集中在一次课堂讨论上，表明绘图在数学建模过程中帮助学生的一个重要方面是绘图必须在学生之间共享。这样，学生就可以运用理解、协调、对比、整合等不同的策略来连接与解相关和与非解相关的绘图元素，从而帮助他们在整个数学建模过程中进行。

引用次数: 0

Mathematics Education for Young Women and Girls from the Birth of the Kingdom of Italy (1861) to Fascism 从意大利王国诞生（1861年）到法西斯主义时期年轻妇女和女孩的数学教育

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematical Behavior

Pub Date : 2025-01-03 DOI: 10.1016/j.jmathb.2024.101210

Fulvia Furinghetti

In 1861, when the Kingdom of Italy was proclaimed, the school system of the new state was organized in a highly centralized manner based on an 1859 law inherited from the Kingdom of Sardinia. This law, which with some changes regulated education in Italy until 1923, included the principle that the first two years of primary school should be compulsory for both boys and girls. A later law in 1877 reinforced this principle and led to more regular school attendance by girls, although, as the documents cited in this article show, the prejudice that literacy was unnecessary or even dangerous for women remained for many years. In elementary school curricula there were differences between math content aimed at females and that aimed at males. In secondary schools, math programs were not differentiated by gender, but for a long time access to these schools was difficult for girls. After elementary school, however, there was the teacher-training school called scuola normale (normal school), where girls could enroll. The math syllabuses were the same for boys and girls. In this article I focus on this type of school with the aim of understanding what math the girls encountered and how they reacted to it. As sources for my study I use answers to questions published in Italian mathematics journals addressed to students.

1861年，当意大利王国宣布成立时，这个新国家的学校系统以高度集中的方式组织起来，其基础是继承自撒丁岛王国的1859年法律。这项法律在1923年之前对意大利的教育进行了一些修改，其中包括男童和女童都必须接受小学前两年教育的原则。后来在1877年颁布的一项法律强化了这一原则，使更多的女孩有规律地上学，尽管，正如本文所引用的文件所显示的那样，多年来，认为识字对女性来说是不必要的，甚至是危险的偏见仍然存在。在小学课程中，针对女性和针对男性的数学内容存在差异。在中学，数学课程不按性别区分，但很长一段时间里，女孩很难进入这些学校。然而，小学毕业后，有一所叫做scuola normale（师范学校）的教师培训学校，女孩可以在那里入学。男孩和女孩的数学教学大纲是一样的。在这篇文章中，我把重点放在这种类型的学校，目的是了解女孩们遇到的数学以及她们对数学的反应。作为我研究的来源，我使用了意大利数学期刊上发表的针对学生的问题答案。

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引用次数: 0

Understanding mathematical conditionals: An educational perspective informed by philosophy, linguistics and psychology 理解数学条件：以哲学、语言学和心理学为基础的教育视角

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematical Behavior

Pub Date : 2024-12-24 DOI: 10.1016/j.jmathb.2024.101233

Lara Alcock

Conditionals – sentences of the form ‘if A then B’ – are ubiquitous in mathematics, where they are treated as true unless A is true and B is false. Conditionals are ubiquitous in everyday life, too, but there interpretations vary. This creates a challenge for students, who must learn an interpretation that might feel unnatural. How can we help them toward mathematically valid reasoning? In this theoretical paper, I argue that a sensible answer should build on work in philosophy, linguistics and psychology. I apply work from these fields to mathematical learning, especially at the transition to proof. I argue that day-to-day use of mathematical conditionals reflects the common inferential reading of everyday conditionals, so that an effective explanation of mathematical conditionals might: discuss the peculiarities of the material conditional, with reference to truth-functionality; observe that universal mathematical conditionals are sensibly subject to an inferential reading; and entrench habitual counterexample search.

条件句——“如果A则B”形式的句子——在数学中无处不在，除非A为真，B为假，否则它们被视为真。条件句在日常生活中也无处不在，但有不同的解释。这给学生们带来了挑战，他们必须学习一种可能感觉不自然的解释。我们如何帮助他们进行数学上有效的推理？在这篇理论论文中，我认为一个合理的答案应该建立在哲学、语言学和心理学的基础上。我将这些领域的工作应用到数学学习中，特别是过渡到证明的部分。我认为，数学条件的日常使用反映了对日常条件的共同推理阅读，因此对数学条件的有效解释可能：根据真值功能讨论物质条件的特性；请注意，普遍的数学条件是合理地服从于推理的阅读；巩固习惯性的反例搜索。

引用次数: 0

Examples from English female mathematics exercise books of the 19th century 19世纪英国女性数学练习册中的例子

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematical Behavior

Pub Date : 2024-12-20 DOI: 10.1016/j.jmathb.2024.101231

Peter Howard Ransom

This study compares the mathematical examples tackled by females and males in 19th century UK schools. It is based on a private collection of 101 mathematical manuscripts and compared with a collection of 231 similar exercise books at the University of Leicester. A summary of female mathematical education in England at the time will provide a background for the research. Illustrations will be given covering some of the associated textbooks on which these manuscript books are based. A comparison will be made between the problems given to each gender and some mathematical textbooks written specifically for females will be examined to identify any specific differences between them and the more widely used textbooks of the time. The purpose of such manuscript books will be considered. Based on the evidence examined, the ratio of such books in existence is 1:4, females to males.

这项研究比较了19世纪英国学校中女性和男性处理的数学问题。这本书是基于私人收藏的101本数学手稿，并与莱斯特大学收藏的231本类似的练习本进行了比较。对当时英国女性数学教育的概述将为研究提供背景。插图将涵盖一些相关的教科书，这些手稿书是基于。将对每个性别的问题进行比较，并检查专门为女性编写的一些数学教科书，以确定它们与当时更广泛使用的教科书之间的任何具体差异。这些手稿的目的将被考虑。根据调查的证据，现存这类书的男女比例是1:4。

引用次数: 0

“They do not have the same needs”: Mathematics education for girls and young women in France (19th-early 20th century) “她们没有相同的需求”：法国女孩和年轻女性的数学教育（19世纪至20世纪初）

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematical Behavior

Pub Date : 2024-12-18 DOI: 10.1016/j.jmathb.2024.101232

Renaud d’Enfert

This article examines the main places and characteristics of mathematics education for girls and young women in primary and secondary schools during the 19th and early 20th century. It looks at, in particular, the mathematical content that pupils learned in these schools and the aims of the teaching they received. It shows how female mathematics teaching differed from its male counterpart by responding to various gender stereotypes referring to the ‘nature’ and social role of women. The article also presents to what extent the girls’ mathematics programs were progressively aligned with those of boys, until they became almost identical from the 1920s onwards.

本文考察了19世纪和20世纪初中小学女生和年轻女性数学教育的主要场所和特点。它特别关注学生在这些学校学习的数学内容和他们所接受的教学目的。它显示了女性数学教学如何通过回应涉及女性“性质”和社会角色的各种性别刻板印象而与男性数学教学不同。这篇文章还介绍了女孩的数学课程在多大程度上逐渐与男孩的数学课程保持一致，直到20世纪20年代以后他们几乎完全相同。

引用次数: 0

It’s just a state of mind: The effect of deliberate and implemental mindset states on word-problem solving 这只是一种思维状态：深思熟虑和执行的思维状态对解决单词问题的影响

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematical Behavior

Pub Date : 2024-12-16 DOI: 10.1016/j.jmathb.2024.101230

Benjamin Rott , Timo Leuders

In this paper, we draw on the distinction of states and traits to investigate the influence of humor and awareness prompts on solving word problems with a reflective component. Two studies with n = 144 and n = 401 mathematics pre-service teachers were conducted, using the three-item Cognitive Reflection test and a ten-item test on mathematical critical thinking, respectively. In both studies, students seeing jokes or awareness prompts showed significantly better results than students solving routine tasks before working on the test items. Drawing on the mindset theory by Gollwitzer, we explain these results with deliberate and implemental mindsets being induced by humoristic and awareness prompts prompts or routine tasks, respectively.

在本文中，我们利用状态和特征的区别来研究幽默和意识提示对解决带有反思性成分的单词问题的影响。对n名 = 144名和n = 401名数学职前教师进行了两项研究，分别采用三项认知反思测试和十项数学批判性思维测试。在这两项研究中，看到笑话或意识提示的学生比在做测试项目之前解决常规任务的学生表现出明显更好的结果。根据Gollwitzer的心态理论，我们用幽默提示和意识提示或日常任务分别诱导的深思熟虑和执行心态来解释这些结果。

引用次数: 0

Philosophy of mathematical practice and mathematics education: Cross-fertilization, dialogue and prospects 数学实践哲学与数学教育：相互借鉴、对话与展望

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematical Behavior

Pub Date : 2024-12-09 DOI: 10.1016/j.jmathb.2024.101208

Yacin Hamami

Mathematics education and the philosophy of mathematical practice are two fields of research whose domains of investigation overlap in a striking way. And yet, interactions between the two fields have been very limited so far, research being mostly conducted in parallel, sometimes on the very same issues. As a consequence, the potential for interaction and cross-fertilization between the two fields remains largely under-explored and under-exploited. The aim of this article is to encourage these interactions by indicating a number of concrete research opportunities where existing contributions in one field may lead to original developments in the other.

数学教育和数学实践哲学是两个研究领域，它们的研究领域有着惊人的重叠。然而，到目前为止，这两个领域之间的互动非常有限，研究大多是并行进行的，有时是在相同的问题上。因此，这两个领域之间相互作用和交叉施肥的潜力在很大程度上仍未得到充分探索和开发。本文的目的是通过指出一些具体的研究机会来鼓励这些相互作用，其中一个领域的现有贡献可能导致另一个领域的原始发展。

引用次数: 0

Advances in research on mathematical problem posing: Focus on task variables 数学问题的研究进展：关注任务变量

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematical Behavior

Pub Date : 2024-12-01 DOI: 10.1016/j.jmathb.2024.101186

Jinfa Cai , Boris Koichu , Benjamin Rott , Chunlian Jiang

In this paper, we aim to present an overarching picture of Mathematical Problem Posing (MPP) with a focus on the impact of task variables on MPP products and processes. Admittedly, there are many different settings with which to approach research related to task variables and their associated products and processes in MPP among mathematics students and teachers. In this paper, we approached related research in three kinds of settings: (1) the individual setting, (2) the group setting, and (3) the classroom setting. We then provide some theoretical considerations and literature review in examining task variables in MPP based on four questions: (1) What variables are considered in research on MPP? (2) What methods do researchers use to examine variables in MPP? (3) What do we learn from research on variables about MPP? (4) What might be future directions of research on MPP involving variables?

在本文中，我们的目标是呈现数学问题提出（MPP）的总体图景，重点是任务变量对MPP产品和过程的影响。诚然，在数学学生和教师的MPP中，有许多不同的设置来处理与任务变量及其相关产品和过程相关的研究。本文主要在三种情境下进行相关研究：(1)个体情境、(2)群体情境、(3)课堂情境。然后，我们基于以下四个问题，对MPP中任务变量的研究提出了一些理论思考和文献综述：(1)MPP研究中考虑了哪些变量？(2)研究人员用什么方法来检验MPP的变量？(3)从MPP的变量研究中我们了解到什么？(4)涉及变量的MPP的未来研究方向是什么？

引用次数: 0

Overcoming impasses in proving processes: Novice provers’ productive actions when encountering stuck points 克服证明过程中的僵局：新手证明者在遇到瓶颈时的富有成效的行动

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematical Behavior

Pub Date : 2024-11-28 DOI: 10.1016/j.jmathb.2024.101211

Yaomingxin Lu

Research has shown that many undergraduate students struggle to learn to prove, including those who major in mathematics (Moore, 1994; Selden, 2012). While studies have explored how expert mathematicians construct proofs to inform teaching practices, expert strategies might not be equally beneficial to novice provers with limited abilities in proving. Novice provers often face difficulties and impasses when engaged in problem-solving or proving tasks. Looking through the lenses of impasses, this study provides a more fine-grained account by characterizing novice provers’ navigating actions when they encounter impasses to better support them in their proving processes. This research draws on task-based interviews conducted with undergraduates enrolled in a transition-to-proof course. A framework was developed to identify productive actions students took when navigating stuck points in the proving process. The result of this study shows that productive actions around stuck points can develop important proof skills in students, even if the student did not ultimately complete the proof successfully. Therefore, instructors are encouraged to recognize and support these productive actions, prioritizing them over mere proof completion when guiding students in their proving processes.

研究表明，许多本科生都在努力学习证明，包括那些主修数学的学生(Moore, 1994；塞尔登,2012)。虽然研究已经探索了专家数学家如何构建证明来指导教学实践，但专家策略可能对证明能力有限的新手证明者并不同样有益。新手证明者在从事解决问题或证明任务时经常面临困难和僵局。通过僵局的镜头，本研究通过描述新手证明者在遇到僵局时的导航行为来更好地支持他们的证明过程，提供了一个更细致的描述。这项研究利用了对参加过渡证明课程的本科生进行的基于任务的访谈。开发了一个框架，以确定学生在验证过程中遇到瓶颈时采取的富有成效的行动。这项研究的结果表明，围绕卡住点的富有成效的行动可以培养学生重要的证明技能，即使学生最终没有成功地完成证明。因此，鼓励教师认识并支持这些富有成效的行动，在指导学生进行证明过程时，优先考虑他们而不是仅仅完成证明。

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引用次数: 0

Decentering to support responsive teaching for middle school students 去中心化支持中学生响应式教学

IF 1 Q3 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematical Behavior

Pub Date : 2024-11-28 DOI: 10.1016/j.jmathb.2024.101205

Amy J. Hackenberg , Fetiye Aydeniz Temizer , Rebecca S. Borowski

A classroom study was conducted to understand how to engage in responsive teaching with 18 seventh grade students at three stages of units coordination during a unit on proportional reasoning co-taught by the first author and classroom teacher. In the unit, students worked on making two cars travel the same speed. Students at all three stages of units coordination learned to do so, as reported elsewhere (Hackenberg et al., 2023). This paper focuses on the practice of inquiring responsively in small groups. We found that teacher-researcher decentering was a mechanism underlying this practice. Decentering involves adopting the perspective of another person by setting one’s own perspective to the side and using the other’s perspective as a basis for interaction. We found that two patterns of decentering actions and a type of question, leveraging questions, supported students across stages of units coordination to sustain challenges and learn.

以18名七年级学生为研究对象，在第一作者与班主任共同授课的比例推理单元中，进行了单元协调三个阶段的课堂研究，以了解如何进行响应式教学。在本单元中，学生们努力使两辆汽车以相同的速度行驶。根据其他地方的报道，在单元协调的所有三个阶段的学生都学会了这样做（Hackenberg et al., 2023）。本文的研究重点是在小组教学中进行响应式探究的实践。我们发现，教师-研究人员的去中心化是这种做法背后的一种机制。去中心化包括采用另一个人的观点，把自己的观点放在一边，把别人的观点作为互动的基础。我们发现，两种分散行动模式和一种问题类型，即利用问题，支持学生跨单元协调的各个阶段，以维持挑战和学习。

引用次数: 0

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