Teachers and teacher educators have been sharing strategies and resources for implementing mathematics routines in National Council of Teachers of Mathematics (NCTM) journals for years. A less commonly shared mathematics routine, especially with young learners, is "Clothesline Math" (Shore, 2017, 2018). In this routine, teachers create…

The aim of this study was to investigate second-grade elementary school students' performance related to their counting skills, place value understanding, and addition operation in natural numbers. A total of 205 second-grade elementary school students from Turkey participated in this study. The data were collected through a 'Personal Information…

Math fact fluency--the ability to quickly and accurately recall basic addition, subtraction, multiplication, and division facts--is a foundational mathematical skill. "Zaner-Bloser Building Fact Fluency (BFF)" was designed to build students' conceptual understanding of arithmetic operations and increase procedural fluency among…

The development of mathematical reasoning is a key proficiency for mathematics within the Australian Curriculum. However, reasoning can be difficult for teachers to assess, particularly with pen and paper tests. In this study, interview tasks were designed across three curriculum areas at three different levels to assess student reasoning through…

Problem solving has been the focus of the Common Core State Standards for Mathematical Practice. Helping students acquire critical-thinking and problem-solving skills has become the primary goal of mathematics education across all grade levels. However, research has found that many students struggle with word problems because of poor text…

This study addresses first graders' conceptual knowledge exhibited in addition strategies in relation to instructional practices and teachers' beliefs in a suburban Alabama school. To address the purpose of the study, the central question was "What is the nature of the relationship between curricular practices and beliefs and students'…

The purpose of this article is to show how the philosophical theory of inferentialism can be used to understand students' conceptual development in the field of mathematics. Based on the works of philosophers such as Robert Brandom, an epistemological theory in mathematics education is presented that offers the opportunity to trace students'…

Mastering traditional algorithms has formed mathematics teaching in primary education. Educational reforms have emphasized variation and creativity in teaching and using computational strategies. These changes have recently been criticized for lack of empirical support. This research examines the effect of teaching two differently structured…

Understanding rational numbers is a complex task for primary and secondary school students. Previous research has shown that a possible reason is students' tendency to apply the properties of natural numbers (inappropriately) when they are working with rational numbers (a phenomenon called "natural number bias"). Focusing on rational…

Each child will not become senior mathematicians in the future but all children have the right to get learning opportunities which he/she can develop his/her mathematical understanding at school. The success of children in mathematics is closely related to how they are taught mathematics. At this point, the role of teaching mathematics stands out…

How do students cope with and make sense of polysemy in mathematics? Zazkis (1998) tackled these questions in the case of 'divisor' and 'quotient'. When requested to determine the quotient in the division of 12 by 5, some of her pre-service teachers operated in the domain of integers and argued for 2, while others adhered to rational numbers and…

Ensuring students correctly understand the notion of equality is a fundamental problem in teaching mathematics. Is it possible to teach arithmetic in such a way that students do not misinterpret the equal sign "=" as indicating the result of an arithmetic operation and, consequently, viewing the arithmetic operation symbols (+, -, or x)…

The paper describes one problem solving strategy -- the Use of false assumption. The objective of the paper is to show, in accordance with Phylogenesis and Ontogenesis Theory, that it is worthwhile to reiterate the process of development of the concept of a variable and thus provide to pupils one of the ways helping them to eliminate usual…

This paper presents an assessment of the understanding of the decimal numeral system in students with Down Syndrome (DS). We followed a methodology based on a descriptive case study involving six students with DS. We used a framework of four constructs (counting, grouping, partitioning and numerical relationships) and five levels of thinking for…

Counting all and counting on are distinct counting strategies that can be used to compute such quantities as the total number of objects in two sets (Wright, Martland, and Stafford 2010). Given five objects and three more objects, for example, children who use counting all to determine quantity will count both collections; that is, they count…