Representing repeating nonterminating decimals as rational numbers is a topic introduced in the seventh-grade Common Core State Standards for Mathematics. According to Content Standard 7.NS.2.D., students should be able to represent a rational number as a decimal and understand that the decimal will either end in zeros or eventually repeat (NGO…

The teaching of mathematics does not only require the teacher to have knowledge about the subject, but the teacher also needs mathematical knowledge that is useful for the teaching and explaining thereof, as the teacher's knowledge effects the students' knowledge. A teacher should use appropriate mathematical explanation to be understood well by…

Thomas Kuhn (1962/2012) introduced the term "paradigm shift" to the scientific literature to describe how knowledge in science develops. The aims of this article are to identify paradigm shifts, or revolutions, that have occurred in mathematics, and to discuss their relevance to teaching mathematics in schools. The authors argue that…

This study was aimed to validate a digital tool for diagnosing mathematical proficiency in the Number and Algebra strand of 1,504 Thai seventh-grade students. Researchers employed a multidimensional approach, an extension of the Rasch model to measure its quality. A design-based research method was adopted to create the diagnostic tool which…

Exponential functions are an integral component of the secondary mathematics curriculum with which students struggle. Inherent difficulties students have had around the topic of exponential functions suggested a need for thinking about and examining the teaching and learning related to this content. This study presented the mathematical ideas made…

Online learning platforms integrating open educational resources (OERs) are increasingly adopted in secondary education as supplemental resources for teaching and learning. However, students report difficulties sustaining their engagement because of the self-paced nature of OER-supported learning environments. We noted that little attention has…

Mathematics courses should prepare students to use mathematics in a range of contexts, including science. However, students often struggle in applying mathematics in physics courses, even when they understand the mathematical content (Rebello et al., 2007). Often the root of this struggle is attributed to the "student" or the…

This study sought to answer the following questions: (1) Is it feasible to develop Academic Key Performance Indicators (KPIs) and collect data on them across member urban school districts? (2) Are comparisons between districts on academic performance measures valid and reliable? (3) Do districts collect and maintain requested KPI data in a way…

Few high school students associate mathematics with playfulness. In this paper, we offer a series of lessons focused on the underlying algebraic structures of the Rubik's Cube. The Rubik's Cube offers students an interesting space to enjoy the playful side of mathematics, while appreciating mathematics otherwise lost in routine experiences.

A selection of secondary school mathematics textbooks from twelve countries on five continents was analysed to better understand the support they might be in teaching and learning mathematical problem solving. Over 5700 tasks were compared to the information provided earlier in each textbook to determine whether each task could be solved by…

The researchers conducted a microanalysis of two purposefully sampled sessions of a tutor working with a student with a learning disability (LD) engaging with multi-step equations with and without fractions. During the tutoring sessions, the student experienced quick, independent success on equations without fractions, but struggled considerably…

Improving the strength of alignment between educational components is essential for quality assurance and to achieve learning goals. The purpose of the study was to investigate the strength of alignment between Senior Phase mathematics content standards and workbook activities on numeric and geometric patterns. The study contributes to…

The goal of this design-based research study was the creation and evaluation of a mini-unit intended to foster perceptually grounded understandings of the concept of slope in middle-school students. Central to this unit was an innovative device designed to create a productive pedagogical space between student intuition for steepness and formal…

One does not have to teach for very long to see students applying the wrong formula in the wrong situation (e.g., Kirshner and Awtry 2004; Tan-Sisman and Aksu 2016). Students can become overreliant on the power of the formula instead of thinking about the relationships it describes. It is not surprising that students can see formulas as a way to…

Mathematics is of major importance in science subjects. Unfortunately, students struggle with applying mathematics in science subjects, especially physics. In this qualitative study we demonstrate that transfer of algebraic skills from mathematics in physics class can be improved by using pre-knowledge effectively. We designed shift-problems…