This article describes a learning trajectory on expressions and equations based on the sixth-grade Common Core State Standards for Mathematics (NGA/CCSSO, 2010). A classroom teaching experiment using design research (Lamberg & Middleton, 2009) was conducted. The data was analysed using Corbin and Strauss' (2014) Constant Comparative method and…

This paper analyzes the impact of a Course Transformation process based on a Flipped Classroom strategy on Chilean Engineering students' attitudes toward university-level mathematics. The Attitudes Toward Mathematics Inventory (ATMI) questionnaire was applied as both pre- and post-test to 76 students in three mathematic courses (Calculus I,…

This paper examines the implementation of an instructional module on preservice elementary teachers' professional noticing of children's mathematical thinking. The module focuses on professional noticing skills through the content focus of early algebraic reasoning and uses complex video vignettes from whole class instruction in authentic…

This study explores the relationships among students' perceived learning opportunities in school mathematics, their perceptions of self in mathematics, and their desire to learn more mathematics in the future. Data included student survey responses from eighth and tenth grade students from a state in the Southeast region of the United States.…

A growing body of research suggests that interventions promoting students' utility value for a subject can improve their academic outcomes. However, numerous questions remain regarding how much to adapt prior intervention materials to promote utility value in new educational contexts and how implementation constraints of an educational context may…

Mathematics, along with the need for logic and thinking, is becoming more important in many fields. Therefore, many universities in Korea have opened and operated a college basic math course to improve basic math skills for freshmen in science and engineering. The new generation of digital generation is creative, familiar with cooperation and…

In this article we describe secondary school practising teachers' professional noticing expertise, which includes (a) attending to the details of students' written or verbal responses, (b) interpreting students' mathematical understandings, and (c) deciding how to respond to students based on their understandings, with a focus on algebraic-pattern…

The purpose of this case study was to examine prospective mathematics teachers' lessons in the context of choice and use of representations while teaching limit. The participants were four senior prospective mathematics teachers. The data were obtained from the participants' lessons plans, the video recordings of their lessons, and the…

A growing body of research suggests that interventions promoting students' utility value for a subject can improve their academic outcomes. However, numerous questions remain regarding how much to adapt prior intervention materials to promote utility value in new educational contexts and how implementation constraints of an educational context may…

This study examines how students' opportunities to engage in argumentative activity are shaped by the teacher, the class, and the mathematical topic. It compares the argumentative activity between two classes taught by the same teacher using the same textbook and across two beginning algebra topics--investigating algebraic expressions and…

Multiplicative thinking is accepted as a "big idea" of mathematics that underpins important mathematical concepts such as fraction understanding, proportional reasoning, and algebraic thinking. It is characterised by understandings such as the multiplicative relationship between places in the number system, basic and extended number…

The purpose of this paper is to present an analysis of the difficulties faced by students when working with different representations of vectors, planes and their intersections in R[superscript 3]. Duval's theoretical framework on semiotic representations is used to design a set of evaluating activities, and later to analyze student work. The…

The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…

In line with the latest positions of Gottlob Frege, this article puts forward the hypothesis that the cognitive bases of mathematics are geometric in nature. Starting from the geometry axioms of the "Elements" of Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in…

The purpose of this study was to examine eighth grade students' algebra achievement scores across various states, over years, and by students' demographics (including ethnicity/race, language spoken at home, SES factors, and academic resources). The questions guiding the study were, (a) What are the differences in eighth grade students' algebra…