School subjects differ in their histories, epistemologies, and relations to state and federal policies. Though educational policymaking is shaped by how education leaders view school mathematics--what mathematics is, how mathematics is learned, and what counts as equitable and high-quality mathematics education--policy research often takes a…

Understanding negative numbers can be challenging for many students, as these concepts may seem less tangible than counting objects, which are commonly represented by positive numbers. In addition, the multiplication of two negative numbers resulting in a positive might appear inconsistent and puzzling to young learners who are used to seeing the…

Nowadays, mathematics teachers in K-12 strive to promote their students' mathematical knowledge and computational thinking (CT) skills. There is an increasing need for effective CT-embedded mathematics learning material and a better understanding of students' views toward them. In this work, we present the results of a research study, which…

In this article, we outline the process undertaken to establish and evaluate a mathematics centre at the Ravensburg-Weingarten University of Applied Sciences. Firstly, we outline some of the current research into centre evaluation. Secondly, we give a brief overview of our centre, including details on staffing, teaching format, goals, etc.…

This study aims to examine the changes in students' mental constructions of function transformation based on the designed activities, classroom discussions, exercises (ACE) teaching cycle in the light of the action, process, object, schema (APOS) theoretical framework. The study was conducted by seven volunteer students who were enrolled in…

Task design is an important element of effective mathematics teaching and learning. Past research in mathematics education has investigated task design in mathematics education from different perspectives (e.g., cognitive and cultural) and offered a number of (theoretical) frameworks and sets of principles. In this study, through a narrative…

The goal of the paper is to understand to what degree the student success depends on teaching practices and materials, and to what degree it is due to differences in background, including prior knowledge, skills, preparation, abilities, etc. We analyzed the existing research on outcomes of the SAT and ACT in the United States and the Unified…

The problem of adverse effects of prior knowledge in mathematics learning has been amply documented and theorized by mathematics educators as well as cognitive/developmental psychologists. This problem emerges when students' prior knowledge about a mathematical notion comes in contrast with new information coming from instruction, giving rise to…

When presented with a problem in mathematics class, students often function as problem performers rather than problem solvers (Rigelman 2007). That is, rather than understanding the problem, students focus on using an operation to complete it. Students' tendencies to act as problem performers can prevent them from suggesting problem-solving…

Psychologists and mathematics educators have long viewed flexibility as critical to students' mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified…

The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across…

The present study addressed the effectiveness of an educational math game for improving proportional reasoning in prevocational education, and examined the added value of support in the form of reflection. The study compared four conditions: the game with reflection prompts, the game with reflection prompts plus procedural information, the game…

According to the National Center for Education Statistics (2016), the number of public school students in the United States who were English learners (ELs) was estimated at 4.5 million. However, in 2005, the national standardized testing scores (Fry 2007) show that about 51 percent of eighth-grade EL students were behind other students in reading…

This research aims to investigate, compare, and describe the achievement and enhancement of students' mathematical communication skills (MCS). It based on the prior mathematical knowledge (PMK) category (high, medium and low) by using Treffinger models (TM) and conventional learning (CL). This research is an experimental study with the population…

We synthesize ideas from the foregoing articles in this special issue and from the broader literature on transfer to explore several themes. In many ordinary life circumstances, transfer proceeds easily, but formal learning often shows much less transfer than educators would like, making failure to transfer a focus of investigation. Transfer, like…