This paper deals with the use of original sources in mathematics education, with emphasis on preservice teachers' education and the exploration of historical texts. In this context, there is a real challenge, for both teachers and learners, to conduct both 'synchronic' and 'diachronic' reading. As reported extensively in research, learners seem to…

Computer-based testing of humanities students has some inconveniences and difficulties, where the whole learning process is practically based on communicative methods. In this regard, one needs such a testing system, which would allow one to ask open-ended questions, and students would be able to enter detailed answers. Despite the popularity of…

The goal of this paper is to describe the teaching of initial multiplication concepts and skills, up to the multiplication table, in the Croatian educational system. As Stiegler and Hiebert (1999) concluded, teaching is a complex system rooted in a cultural script of a given society. To describe it without ignoring certain features of it that…

Many challenges are identified when students solve mathematic problems especially in solving probability word problems. This study was conducted to identify the major challenges faced by matriculation college students while solving the probability of an event word problem. Seven matriculation college students were the sample for this case study.…

While mathematics and reading instruction share an emphasis on vocabulary, strategies may seem in conflict. Use the strategies presented here for connecting new learning to previous knowledge and experiences and providing meaningful paths for students' vocabulary development in the mathematics classroom.

Every application of integration by parts can be done with a tabular method. The trick is to identify and consider each new integral in the table before deciding how to proceed. This paper supplements a classic introduction to integration by parts with a particular tabular method called Row Integration by Parts (RIP). Approaches to tabular methods…

This paper presents ideas for constructing mathematics homework assignments based on lessons from the cognitive science of learning and memory. In particular, we focus on two popular techniques from the field: spaced practice and mixed practice. The paper describes the techniques and supporting research, and then discusses various straightforward…

Considerable amount of research in educational data mining has focused on developing efficient algorithms for Knowledge Tracing (KT). However, in practice, many real-world learning systems used at scale struggle to implement KT capabilities, especially if they weren't originally designed for it. One key challenge is to accurately label existing…

Multiplicative thinking underpins much of the mathematics learned beyond the middle primary years. As such, it needs to be understood conceptually to highlight the connections between its many aspects. This paper focuses on one such connection; that is how the array, place value partitioning and the distributive property of multiplication are…

Undergraduate students majoring in mathematics often face difficulties in comprehending mathematical proofs. Inspired by a number of studies related to students' proof comprehension, and Mejia-Ramos et al.'s study in particular, a test was designed in relation to the proof comprehension of the Cauchy Generalized Mean Value Theorem (CGMVT). The…

In this paper, a number of STEM educational proposals are systematically analyzed from the lens of mathematics education. An extensive innovation project was implemented during the 2019/2020 academic year in a pilot study carried out in Schools and Teacher Training Programs in Navarre (Spain), comprising a bibliographical and source analysis as a…

In this paper, we introduce and discuss a construct called "graphical forms," an extension of Sherin's symbolic forms. In its original conceptualization, symbolic forms characterize the ideas students associate with patterns in a mathematical expression. To expand symbolic forms beyond only characterizing mathematical equations, we use…

Duncan Symons and Derek Holton discuss the different types of mathematical reasoning and what each of these might look like in the classroom. By suggesting language that can be used to describe the different methods of reasoning, they hope to provide teachers with the tools they need to better recognise and assess student reasoning.

This paper discusses the place of precision in mathematics education by exploring its role in curricular guidelines and in classroom life. By means of a joke on precision delivered by a school student in South Sweden, our study focuses on student participation in mathematical tasks that require precision in processes of measuring and reasoning.…

We describe the effects of a change in the mathematics placement policy at a large 4-year public university. The change resulted in a sharp reduction of the number of students placed in remedial courses, while the levels of academic preparedness of the students, the course content, and the instruction methods remained the same. This allows us to…