In the study presented, as we report in this paper, we describe our theoretical and practical consideration to engage first-year pre-service teachers in proving activities in the context of a transition-to-proof course. We investigated how students argued to verify a claim of elementary number theory on entering university and compared the results…

This work is part of a larger project that seeks to understand how students blend (integrate) chemistry and mathematics as they work through chemical kinetics problems. Here we focus on four students from our larger sample: two students that demonstrated more instances of blending chemistry and mathematics in their interviews ("high-frequency…

Students in upper secondary education encounter difficulties in applying mathematics in physics. To improve our understanding of these difficulties, we examined symbol sense behavior of six grade 10 physics students solving algebraic physic problems. Our data confirmed that students did indeed struggle to apply algebra to physics, mainly because…

This study is to reveal the construction process of student representation in solving of ill-structured geometry problems. The three phases involved in the construction process are interpreting the problem, giving opinions, and concluding. A total of four high school students participated in Surabaya and Sidoarjo in this qualitative study. They…

The concept of equivalence can be elusive to students and can be confounded with unproductive understandings of the equals sign. Using the game-based digital algebraic notation system, From Here to There! (FH2T), students explore ideas of equivalence by dynamically transforming expressions or equations among mathematically equivalent states. In…

Rate of change concepts from calculus are presented and applied rather differently in college mathematics, physics, biology, and chemistry classes. This is not simply a matter of pedagogical style but reflects real cultural differences between these disciplines. We describe the efforts of our interdisciplinary collaboration to understand and…

Undergraduate mathematics instructors often report that students make careless errors or have not previously learned key mathematical ideas and strategies. The purpose of this study is to explore evidence of an alternative explanation that at least some of these "errors" may result from students' application of conceptions developed in…

This study, firstly, aimed at investigating the various types of the multiple math representations and transitions among them in the 8th grade math textbook, and secondly, teachers' use of these representations in teaching. The current study employed the content analysis approach to investigate the multiple mathematical representations and…

The purpose of the reported study was to investigate the social science students' concept images and concept definitions of anti-derivatives. Data were collected through asking students to answer 10 questions related to anti-derivatives and also by interviewing them. The theory of concept image and concept definition was used for data analysis.…

The purposes of this study were (a) to test the efficacy of whole-class equal-sign instruction, (b) to contrast the effects of symbolic and nonsymbolic instructional representation, (c) to determine whether visual representation compensated for language deficits, and (d) to evaluate maintenance of intervention. We randomly assigned 195 children…

The aim of this paper is to analyse the reasoning and symbolisations used by sixth grade Moroccan students in solving a task based on figurative patterns. Our analysis aims at identifying the systems of actions elaborated by the students to give the general expression of the sequence, according to their perceptions of the sequence of its patterns.…

The usage of symbol, unit and formula of some fundamental physical quantities are quite important for science and engineering students regardless of their majors. The purpose of the present research was to examine the students' knowledge regarding the usage of symbol, unit, and formula of the fundamental physical quantities. The opinions of…

The present study was conducted to compare the performances of high-achieving sixth grade students on written computation, symbolic representation, and pictorial representation tests. The study enrolled 107 sixth-grade students in three schools. Data were analyzed by using the Kruskal Wallis and Mann Whitney-U Tests and interviews were conducted…

Structure sense can be interpreted as an intuitive ability towards symbolic expressions, including skills to perceive, to interpret, and to manipulate symbols in different roles. This ability shows student algebraic proficiency in dealing with various symbolic expressions and is considered important to be mastered by secondary school students for…

Parents are frequently advised to use number books to help their children learn the meaning of number words and symbols. How should these resources be designed to best support learning? Previous research has shown that number books typically include multiple concrete representations of number. However, a large body of mathematics education…