This paper dealt with the design of learning tools, that was the development of learning implementation plan or Rencana Pelaksanaan Pembelajaran (RPP) based on Fun and Easy Math (FEM) approach in the form of a number line model. FEM was an approach in order to teach mathematics effectively to students in a fun and easy way according to the…

Supporting students of all levels to move beyond empirical arguments, which employ example based reasoning to endorse universal truths and are thus mathematically invalid, remains a challenging goal in mathematics education. Arguments that make use of generic examples are both mathematically valid and accessible for even young learners. However,…

In grade 3, students are expected to be able to represent a fraction on a number line by first identifying the interval from 0 to 1 as the unit and by partitioning the unit as needed on the basis of the denominator. This task extends these grade 3 fraction goals stated in the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010)…

Competence in fractions is important in achieving advanced mathematics such as algebra and calculus. To foster students' understanding of fractions, intervention studies have found number lines to be an effective representational tool. Yet, it is unclear whether or not number lines are equally effective regardless of the ways in which they are…

The objective of this research was to analyze the causes and consequences of the systematic process of teaching and learning of the division of whole numbers, a study aimed at students and teachers of the 3rd and 4th level of basic education. For its development the qualitative paradigm was used through the modality of field research. As…

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…

The purpose of this study is to examine the effects of concrete and technology-assisted learning tools on developing the conception of place value, mathematical achievement and arithmetical performance of primary school 4th graders. The study group was comprised of three different primary schools. There were no group differences prior to…

Yupana Inca Tawa Pukllay (YITP) is a ludic didactic resource based on semiotic alternation that, using the reading of numbers in the Inca numeral system, improves its equivalent Indo-Arabic reading. Twelve children from first to fourth grade of a bilingual (Spanish-Quechua), multi-grade elementary school in a small rural Peruvian community were…

Algebraic reasoning is foundational to all mathematical thinking. This is no less the case in the early years of school, where the capacity to recognise the structure of mathematical processes enables students to acquire deep conceptual understanding. It is through algebra, therefore, that students are able to explore and express mathematical…

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…

National and state assessments show that English language learners (ELs) in elementary and secondary grades score lower in mathematics compared with their matched English proficient peers (EPs). To provide information on strategies for enhancing learning opportunities for ELs in language inclusive classrooms, we analyze the efficacy of…

Background: The learning of rational numbers is a complex and difficult process that begins in the early grades. This teaching often focuses on the mastery of essential knowledge, including particular skills (e.g. using fractions to describe part--whole diagrams) and interpretations (e.g. sharing), which often results in an incomplete and…

This paper presents primary school teachers' perceptions associated with their engagement in a project aimed at building Year 3 and Year 4 students' number fact and computational fluency. Throughout the project, teachers were provided with classroom ideas and suggestions for engaging students in number fact practice and for generating student…

This study explored the impact of numbers used in instructional tasks on the construction and generalization of multiplicative reasoning by fourth grade students designated as having learning difficulties or disabilities in mathematics (SLDs). In particular, this study addressed the following research questions: (1) In what ways do SLDs'…

Students in the United States continue to struggle with fraction mastery despite the fact that understanding fractions is essential for further progress in mathematics (NAEP, 2008). This research project investigated the potential of using high-press mathematical discourse (Kazemi & Stipek, 2008) to investigate fourth graders' emerging…