Previous research has found that different presentations of the same concept can result in different patterns of transfer to isomorphic instances of the same concept. Much of this work has framed these effects in terms of advantages and disadvantages of concreteness or abstractness. We note that mathematics is a richly structured field, with…

During a time when students are accessing instruction virtually because of COVID-19, reflecting on the sixth of the Standards for Mathematical Practice (SMP 6) is a vital step for educators to take. Although the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010) identifies SMP 6 as Attend to precision, associated expertise…

This study examined the effects of two teaching treatments [multiple-representation instruction (MR) and traditional algorithmic instruction (TA)] on students' performance on mathematics problems that integrated fractions, decimals, and percent. Using a 2 × 2 crossover design, the effect of the teaching treatments and their sequences on student…

Mental models are representations of students' minds concepts to explain a situation or an on-going process. The purpose of this study is to describe students' mental model in solving mathematical patterns of generalization problem. Subjects in this study were the VII grade students of junior high school in Situbondo, East Java, Indonesia. This…

Background: Children have been found to report and demonstrate math anxiety as early as the first grade. However, previous results concerning the relationship between math anxiety and performance are contradictory, with some studies establishing a correlation between them while others do not. These contradictory results might be related to varying…

The phrase "interdimensional relationships" may conjure images of UFOs, alien beings, wormholes, and even mystical powers. These notions of interdimensionality were not out of bounds in the middle school learners' experiences described in this article. However, these notions do not entirely capture the mathematical relationships…

The traditional technique for converting repeating decimals to common fractions can be found in nearly every algebra textbook that has been published, as well as in many precalculus texts. However, students generally encounter repeating decimal numerals earlier than high school when they study rational numbers in prealgebra classes. Therefore, how…

The article is dedicated to solving extrema problems in teaching mathematics, without using calculus. We present and discuss a wide variety of mathematical extrema tasks where the extrema are obtained and find their solutions without resorting to differential. Particular attention is paid to the role of arithmetic and geometric means inequality in…

This paper synthesizes research from three separate studies, analysing how different representations of a mathematical concept may affect young children's engagement with mathematical activities. Children between five and seven years old engaged in counting objects, identifying triangles and completing repeating patterns. The implementation of…

Personal Best (PB) goals are defined as specific, challenging, and competitively self-referenced goals involving a level of performance or effort that meets or exceeds an individual's previous best. Much of the available research underpinning arguments for PB goal-setting is self-report-based; thus, the causal effect of PB goals on learning…

Background: The study focused on children with hearing disabilities, which was significant as almost 9 million children in sub-Saharan Africa, including Namibia, had hearing disabilities. The problem was the lack of prior research on the effects of assistive technology (AT) in primary education for the Deaf in Namibia, for guiding Namibian special…

General cognitive and specific number abilities that underlay arithmetic performance have been heavily investigated among typically developing students; however, the inquiry has rarely been applied to students with mild intellectual disability (MID). We examined whether domain-general cognitive abilities (i.e. working memory, processing speed, and…

We present first-grade, second-grade, and third-grade impacts for a first-grade intervention targeting the conceptual and procedural bases that support arithmetic. At-risk students (average age at pretest = 6.5) were randomly assigned to three conditions: a control group (n = 224) and two variants of the intervention (same conceptual instruction…

A challenge in digital learning games is assessing students' learning behaviors, which are often intertwined with game behaviors. How do we know whether students have learned enough or needed more practice at the end of their game play? To answer this question, we performed post hoc analyses on a prior study of the game "Decimal Point,"…

The history of the number zero is an interesting one. In early times, zero was not used as a number at all, but instead was used as a place holder to indicate the position of hundreds and tens. This article briefly discusses the history of zero and challenges the thinking where divisions using zero are used.