This study aimed to explore if there are any differences in word problem solving skills of fourth grade students using animated-cartoon story vs. text-only story vs. non-story. For this purpose, word problems-embedded animated cartoon stories were created on computers and the same stories were written in text format on paper. The word problems…

This study focuses on proportional division, a specific problem type of proportions and proportional relationships, which embeds a part-part-whole relationship. We investigated how students in grades 6 to 9 solved and perceived three proportional division problems. Analysis of the students' performance on the tasks revealed three types of…

Mathematics evidenced un/manifested in/active, un/changeable, im/pure and primordial nature; therefore, it is illimitable to define as finite. It exists in the engineering of this universe. Philosophy of Mathematics studies abstract entities such as assumption and implication. Mathematics educators regard it as deductive tool and relate to solving…

The purpose of this study was to measure the mathematics-vocabulary performance of 3rd graders to determine if performance differences existed among English learners (ELs) and non-ELs with and without mathematics difficulty (MD). Using screening data from a large-scale intervention study, we categorized students into four groups based on equation…

Intelligent Tutoring Systems (ITSs) for Math still use traditional data input methods: computers' keyboard and mouse. However, students usually solve math tasks using paper and pen. Therefore, the gap between the manner the students work and the requirements imposed by these typing-based systems expose students to an extraneous cognitive load,…

Background: With the recent pivot to online instruction and/or to mixed online/face-to-face (i.e., hybrid) models of teaching necessitated by the novel coronavirus pandemic, the uses of technology to support instruction would seem to have great importance. Whereas effective integration of technology in mathematics classrooms requires recognition…

In this paper, we highlight examples from school mathematics in which invariance did not receive the attention it deserves. We describe how problems related to invariance stimulated the interest of both teachers and students. In school mathematics, invariance is of particular relevance in teaching and learning geometry. When permitted change…

One of the major aims of STEM education is the development of mathematical thinking. The common misconception is that "doing mathematics" is the same as getting involved in "mathematical thinking". Rallying to such argument, many would agree that mathematics should be taught as a thinking activity. Thus, this study endeavours…

Estimation is such an important yet sometimes overlooked skill. Enhancing estimation skills through exposing students to enumeration ('how many') problems where they are required to estimate before calculating is a critical aspect of developing number sense (Reys et al., 2012). This article describes a 'how many' problem undertaken with a small…

I examined how well a self-diagnosis activity engages students in knowledge-integration processes, and its impact on students' mathematical achievements. The self-diagnosis activity requires students to self-diagnose their solutions to problems that they have solved on their own--namely, to identify where they went wrong and to explain the nature…

Myths about early education abound. Many beliefs people hold about early math have a grain of truth in them, but as a whole are not true--they are largely myths. But the myths persist, and many harm children. In this article, we address ubiquitous math myths that may be negatively affecting many young students. We conclude that avoiding the myths…

Research indicates that standards-based mathematics instruction positively supports students' academic development. Although standards documents identify accepted best practices, they do not speak to the impact that students' expectations of the mathematics classroom has on the successful implementation of standards-based instruction at the…

A second-grade class visits Saint John's Food Pantry each year and spends the morning learning about the needs of the community. Then students pitch in and help the staff for a few hours. When the children return to school, they create signs advertising a canned food drive, and they place collection boxes at various locations around the school.…

Productive mathematical conversations are a significant component of developing students' mathematical understanding and ability to effectively communicate their thinking, and the types of questions teachers ask can either hinder or advance that development. Seeking to understand students' thinking while monitoring their initial work on a task…

What do nonroutine algebra problems look like for a second-year algebra course, and where can such problems be found? Starting from the belief that even challenging, nonroutine problems should be solvable with the resources that students possess, Benjamin Dickman proceeded to formulate a small collection of tasks to push students into integrating…