In this article, Ajay Ramful and Siew Yin Ho explain the meaning of quantitative reasoning, describing how it is used in the to solve mathematical problems. They also describe a diagrammatic approach to represent relationships among quantities and provide examples of problems and their solutions.

This article examines whether the 7 abilities found in a previous study carried out by the authors to constitute fraction understanding of sixth grade elementary school students determine hierarchical levels of fraction understanding. The 7 abilities were as follows: (a) fraction recognition, (b) definitions and mathematical explanations for…

The authors analyzed the development of 4th-grade students' understanding of the transition from experimental relative frequencies of outcomes to theoretical probabilities with a focus on the foundational statistical concepts of variation and expectation. After observing the decreasing variation from the theoretical probability as the sample size…

In a classroom teaching experiment, we explored fifth graders' ability to identify relationships in and between two patterns--what we may refer to as functional relationships. Conventional functions curricula are dominated by defining relationships between two patterns via a rule, describing how to find y or f(x) given a particular value for x…

After teaching the concept of division with remainders for many years, Vanessa Battreal, Vanessa Brewster, and Juli Dixon noticed that interpreting remainders in contextualized problems is particularly challenging for elementary school students. To effectively interpret remainders, students must attend to problem context and consider carefully…

Calibration, or the correspondence between perceived performance and actual performance, is linked to students' metacognitive and self-regulatory skills. Making students more aware of the quality of their performance is important in elementary school settings, and more so when math problems are involved. However, many students seem to be poorly…

This research brief discusses the benefits of teachers using mathematical discourse--allowing students to explain, justify, and debate their individual techniques for solving math problems--to enhance learning. Using this strategy requires educators to discard traditional teacher-centered modes of instruction and adopt new student-centered modes…

Student learning is greatest in classrooms where students engage in problem solving tasks that are cognitively demanding. However, there are growing concerns that many Australian students are given limited opportunities to engage in these types of tasks. 108 upper primary school teachers were surveyed to examine task features and cognitive demand…

How much is 41 - 39? How about 100 - 3? Which of those computations was easier for you to do? It so happens that first graders are much more likely to solve 100 - 3 correctly than 41 - 39. Likewise, second graders are much more likely to solve 100 - 3 correctly than 201 - 199. Our data (Schoen et al. 2016) suggest that the latter problems are more…

The aim of this study is to identify how prospective teachers see mathematicians by the pictures they visualized. In accordance with this purpose phenomenology pattern which is one of the qualitative patterns was used. The study was carried out with 160 volunteered prospective teachers. The data collection tool to be used in this study consists of…

Understanding place value is a critical and foundational competency for elementary mathematics. Classroom teachers who endeavor to promote place-value development adopt a variety of established practices to varying degrees of effectiveness. In parallel, researchers have validated models of how young children acquire place-value understanding.…

Geometrical concepts play a crucial role in developing spatial thinking and reasoning. Further, curricular materials play a key role in shaping student-learning experiences in the classroom. The organisation of the content of textbooks plays a decisive role in how and when students are introduced to concepts, especially given the…

With an increased push to integrate coding and computational literacy in K-12 learning environments, teacher educators will need to consider ways they might support preservice teachers (PSTs). This paper details a tinkering approach used to engage PSTs in thinking computationally as they worked with geometric concepts they will be expected to…

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

Teachers at Jackson Elementary School in Hillsboro, Oregon, embrace a growth mindset and continuously try best practices that better reach all students. They collaborate and bounce ideas off one another, and they observe one another and provide feedback. They will even ask another teacher to model lessons with their students so they learn how to…