Providing students the autonomy and choice to learn when productive struggle becomes unproductive is a core teaching belief in the author's classroom. The author teaches in a multiage classroom where he has 16 first- and second-grade students, ages 6, 7, and 8. Like other educators, he believes in the importance of productive struggle. The author…

The use of different registers to represent mathematical concepts enhances understanding. For example, rational numbers can assume pictorial, symbolic and natural language representations and this kind of change improves learning. Based on these assumptions, a teaching experiment for the learning of rational numbers by 2nd grade students was…

A vast majority of elementary students struggle with the core, pre-algebraic concept of mathematical equivalence. The Improving Children's Understanding of Equivalence (ICUE) intervention integrates four research-based strategies to improve outcomes for second grade students: (1) introducing the equal sign before arithmetic, (2) non-traditional…

Computational thinking requires high cognitive load as students work to manage multiple tasks in their problem-solving environment. Through research in K-2 classrooms on computational thinking, we noticed that students lack the representational fluency needed to move from one form to another--such as moving from physical to more abstract…

Research has shown that a profound place value understanding is crucial for success in learning mathematics. At the same time, a substantial number of students struggles with developing a sustainable place value understanding. In this regard, two aspects of the place value system appear especially relevant: First, the knowledge of the decimal…

Block building activities help develop students' spatial reasoning, but few studies focus on the development of block building skills beyond preschool. We worked with four kindergarten, four first grade, and four second grade students to learn more about their Lego block building. We compared students' accuracy, building strategies, and spatial…

This study examines four of the most commonly-used core mathematics curricula in the USA for evidence of support for research-based instructional strategies for mathematics vocabulary in first and second grade. Content analyses of the teachers' editions of two units for each grade level were analyzed per curriculum (n = 16). Statistically…

We conducted a skills analysis on written expression curriculum-based measurement (WE-CBM) tasks completed by 117 second-grade students. As part of the skills analysis, we scored two WE-CBM tasks (i.e., narrative and expository) for correct and incorrect writing sequences, common writing errors, and sentence structures. Although a majority of…

How people see the world, even how they research it, is influenced by beliefs. Some beliefs are conscious and the result of research, or at least amenable to research. Others are largely invisible. They may feel like "common knowledge" (though myth, not knowledge), unrecognized premises that are part of the surrounding culture. As we…

Elementary school students struggle in interpreting the equal sign as a symbol denoting equivalence. Although many have advocated using a pan-balance scale to help students develop this understanding, less is known about what features associated with this model support learning. To attempt to control and examine these features, the investigators…

The current investigation systematically contrasted teaching with cognitively demanding (challenging) tasks using a task-first lesson structure with that of a teach-first lesson structure in a primary school setting (Year 1 and 2). The findings indicate that there is more than one way of incorporating challenge tasks into mathematics lessons to…

Communications studies and psychology offer analytical and methodological tools that when combined have the potential to bring novel perspectives on human interaction with technologies. In this study of children using simple and complex mathematics applications on tablet computers, cognitive load theory is used to answer the question: how…

This study that adopts descriptive and inferential research methods investigated the status of elementary grade pupils' English proficiency, particularly the Grades 1, 2 and 3 pupils who are simultaneously taking up subjects in the Mother Tongue and English that are integrated in their curricula. The research population was sourced from a single…

Advances in technology have led to continuous innovation in teaching and learning methods. For instance, the use of tablet PCs (TPCs) in classroom instruction has been shown to be effective in attracting and motivating students' interest and increasing their desire to participate in learning activities. In this paper, we used a TPCs game--an iPad…

This study examined the impact of independent practice of multiple-criteria text that targeted high-frequency words, decodability, and meaningfulness. Second-grade students, including at-risk students, were randomly assigned within classroom to a treatment group that read multiple-criteria text ("n" = 34), or contrast group that read…