The decomposition of numbers when solving subtraction tasks is regarded as more powerful than counting-based strategies. Still, many students fail to solve subtraction tasks despite using decomposition. To shed light upon this issue, we take a variation theoretical perspective (Marton, 2015) seeing learning as a function of discerning critical…

The basic notions of combinatorics, including systematic listing and permutations, are important topics of mathematics that are recommended to be learned eventually from elementary schools. However, there is little research in mathematics education regarding elementary students' combinatorial strategies. The purpose of this research is to…

Students who exhibit mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly choose effective problem-solving strategies (McIntosh et al., 1997, https://ro.ecu.edu.au/ecuworks/6819). Due to its dispositional nature, mature number sense is typically measured through in-depth interviews or tests of…

Relational understanding constitutes students' awareness of appropriate procedures to solve problems along with logical reasoning. It is pivotal to help students solve problems in mathematics. It is necessary that the teaching of mathematics be directed to achieve relational understanding. Accordingly, students are capable of solving complicated…

Mathematical word problem-solving skills are crucial for students across their lives, yet solving such tasks poses challenges for many. Therefore, understanding the characteristics of mathematical word problems that are associated with students' performance is important. The objective of this systematic review and meta-analysis was to evaluate the…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

This paper shares how fourth grade students solved a unique type of number line task. Instead of giving students the unit and asking them to locate a fraction on the number line, students were given two points on the number line and asked to either find 1, or another number on the number line. This type of task is called "reconstructing the…

The present study aimed to test the effect of the problem-posing instruction experimentally based on the extended active learning framework on the development of Turkish middle school sixth-grade students' (N = 19) problem-posing and -solving skills with whole-number operations. The training programme was completed in 13 lessons over a seven-week…

Instructional routines, like "Number Talks" and "Notice and Wonder," engage students in doing and then talking about their mathematical thinking. Number Talk routines are short mathematical discussions where students mentally solve and share the strategies they used to make sense of the problem. In comparison, the Notice and…

Place value is one of the 'big ideas' in number and plays a critical role in helping students develop their number sense, problem solving and computation skills. Yet, the elegant simplicity of our place value system belies the abstract nature of the construct. This paper presents data from 606 Year 3-6 students (ages 8-12) from two metropolitan…

The authors describe a lesson--"You Decide"--which challenges students but also provides opportunities for success for those who may struggle. They show how this lesson has been helpful for teachers in revealing some misconceptions that often exist in primary students' thinking. In this article, they share data on the apparent relative…

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…

We investigated whether three interventions -- studying incorrect worked examples, studying correct worked examples, or receiving feedback -- improved children's 0-1,000 (Experiment 1) and adults' 1 thousand--1 billion (Experiment 2) number-line estimation precision relative to a no intervention control group. At pretest, participants estimated…

As elementary students begin to program using tangible blocks, they must coordinate their use of counting with the movements, directions, and numbers they use to move a character. In our study, we analyzed 13 first graders' first attempts at coordinating these elements when playing a programming game on the iPad that used tangible programming…

In this article, we present research on eight kindergarten and eight first-grade students' understandings of the arithmetic properties of commutativity, additive identity, and additive inverse during a classroom teaching experiment, selected from a larger study that included 88 students. In this study, we explore the students' types of…