This study examined "backward transfer," which we define as how students' ways of reasoning about previously encountered concepts are modified when learning about new concepts. We examined the backward transfer produced when students learned about quadratic functions. We were specifically interested in how backward transfer may vary for…

Incorporating open-ended real-world tasks enhances students' access to mathematical and real-life knowledge and maximizes learning experiences. This article examines how a secondary mathematics teacher used an open-ended problem on distributing pay raises to teach mathematical concepts and fairness to students. The teacher's actions exemplify…

This study investigates the interplay between student reasoning and instructional strategies in trigonometry education. A qualitative case study was conducted to examine how Grade 10 students employ various reasoning approaches -- deductive, inductive, abductive, analogical, and algorithmic -- when solving trigonometry problems. Each approach…

Mathematically gifted students have a high potential for understanding and thinking through mathematical relations and connections between mathematical concepts. Currently, it is thought that generalizing patterns algebraically can serve to provide challenges and opportunities that match their potential. This article focuses on a mathematically…

In this study, we examined students' mathematical understanding and retention in a problem-based learning (PBL) classroom. The participants were 48 Grade 10 students, and the data were collected in December of 2016. After the end of the PBL lessons, the Mathematical Understanding of Function Test (MUFT) and the Retention Test (RT) were…

In this brief article, the author illustrates the flaws of FOIL (multiply the First, Outer, Inner, and Last terms of two binomials) and introduces the box method. Much like FOIL, the box method can become easy to use. Unlike FOIL, however, the box method is a more direct and visible link to using the distributive property to determine area, a…

Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

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 examines how joint exploration is established and maintained among students and the teacher in secondary mathematics classrooms. We use the theoretical perspective of positioning to conceptualize joint exploration as involving the negotiation and coordination among participants to position students with epistemic agency and authority.…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

The coronavirus disease 2019 (COVID-19) pandemic supported an investigation of ongoing challenges as to whether and how to make mathematics relevant to learners' lifeworlds. Given that COVID-19 created major disruptions in all learners' lives, we developed and taught tasks that attempted to make links between their experiences of the pandemic and…

Textbook content has the ability to influence mathematical learning. This study compares how linear functions are presented in two textbooks, one of South African and the other of German origin. These two textbooks are used in different language-based streams in a school in Gauteng, South Africa. A qualitative content analysis on how the topic of…

Identifying and expressing relations between quantities is a key aspect of understanding and using functions. We are aiming to understand the development of functions understanding throughout school years in Israel. A survey instrument was developed with teachers and given to 20 high and average achieving students from each of years 7-11 and to 10…

In many scientific contexts, students need to be able to use mathematical knowledge in order to engage in scientific reasoning and problem-solving, and their understanding of scientific concepts relies heavily on their ability to understand and use mathematics in often new or unfamiliar contexts. Not only do science students need high levels of…

The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…