This article focuses on how middle and high school students understand and use counterexamples, as well as how teachers can bring counterexamples into their classrooms. The authors believe purposeful incorporation of counterexamples into classrooms can greatly benefit students. The third of the Common Core State Standards for Mathematics (CCSSM)…

Reinhart's (2000) article "Never Say Anything a Kid Can Say!" shared the lessons he learned as he journeyed from a teacher-centered model of instruction to one that puts students at the center of the teaching and learning process. Within his narrative, he itemized the strategies he used and learned from, balanced recommendations with…

In this research, a new test for understanding simple fractions has been developed for students at the beginning of lower secondary education. In many countries, mathematics education in Grade 5 builds on elementary students' developing concepts of fractions. Understanding fractions causes many difficulties for students, and research on mental…

The formulation of learning objectives is considered an important task for teaching at all educational levels. However, teachers tend to trivialize learning objectives and consider them as part of an administrative requirement. This study sought to characterize the specific learning objectives for two school mathematics tasks posed by primary…

The present study examined the effects of the non-digital game-based instructional method and the cognitive level of questions in determining students' achievement in mathematics, particularly in Isometric Transformation. The study used a quasi-experimental design and involved 116 participants (i.e., form two students) from two local secondary…

The design of inquiry-based tasks and problem situations for daily mathematics teaching is still a challenge. In this article, we study the implementation of two tasks as part of didactic scenarios for inquiry-based mathematics teaching, examining teachers' classroom orchestration supported by these scenarios. The context of the study is the…

Often, mathematics teachers do not incorporate whole-class discourse of students' various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students' thinking and develop their collective construction of mathematics. This study explores the…

The aim of this pseudo-longitudinal study is to investigate pre-service teachers' beliefs about (1) the nature of mathematics and (2) mathematics teaching and learning and the development of both beliefs over the course of their studies. A quantitative belief questionnaire was completed by 142 participants divided into three groups based on their…

Non-digital games are a tool that can help children to build and improve problem solving skills in early mathematics learning. Teachers need to design a learning activity using non-digital games taken account problem solving skills in the learning activities. However, the application of problemsolving skills in early mathematics learning…

Research has shown assistance can provide many benefits to novices lacking the mental models needed for problem solving in a new domain. However, varying approaches to assistance, such as subgoals and next-step hints, have been implemented with mixed results. Next-Step hints are common in data-driven tutors due to their straightforward generation…

Interpreting statistical graphs and making inferences based on the graphs are a precursor for formal statistical inferences. To support student inferences, both teachers and future teachers should have adequate knowledge regarding students' thinking on graphs as well as their potential misinterpretations and difficulties in interpreting graphs. In…

Existing computational thinking (CT) research focuses on programming in K-12 education; however, there are challenges in introducing it into the formal disciplines. Therefore, we propose the introduction of non-programming plugged learning in mathematics to develop students' CT. The research and teaching teams collaborated to develop an…

The authors describe how professors can work with schools (teachers and/ or administrators) to create and implement a tutoring program designed to promote the learning of Algebra 1 by students with learning disabilities as well as provide a learning experience for undergraduates majoring in special education. From the professors' perspective, we…

The methods and techniques used by teachers have an important place on the basis of many students' negative perspectives and failures towards mathematics. Integrating technology into mathematics learning environments is inevitable since it is of great importance to create rich learning environments to increase students' interest and understanding…

In this article, we conduct a qualitative systematic review of studies examining the use of digital games to promote students' mathematical reasoning in primary and lower secondary schools. Digital games now have a prominent role in students' leisure time, as has mathematical reasoning in curricula around the world. This study investigates how the…