The study of how children learn numbers has yielded one of the most productive research programs in cognitive development, spanning empirical and computational methods, as well as nativist and empiricist philosophies. This paper provides a tutorial on how to think computationally about learning models in a domain like number, where learners take…

In the primary grades, engaging in counting collections provides students with regular opportunities to make sense of numbers in dynamic ways, build social skills, and communicate about mathematics. This article aims to guide elementary educators through a team's process of planning and implementing counting collections in kindergarten. Counting…

The multiplication principle (MP) is foundational for combinatorial problem-solving. From a units-coordination perspective, applying the MP with justification entails establishing unit relationships between the number of options at each independent stage of a counting process and the total number of combinatorial outcomes. Existing research…

Our study on 328 five- to six-year-old kindergarteners (mainly White European living in France, 152 girls) shows that children who do not count on their fingers and undergo finger counting training exhibit drastic improvement in their addition skills from pre-test to post-test (i.e., accuracy from 37.3% to 77.1%) compared to a passive control…

The same and different routine offers an opportunity to build a strong foundation for future grades while also deepening the experiences of prekindergarten and transitional kindergarten students. Students have opportunities to make sense, share ideas, and engage in the ideas of others. We conjecture this type of experience supports students and…

The aim of the present study is to explore strategies in enumerating units of three dimensional (3D) arrays. We analyse enumeration strategies of students in grade 3 (ages 8 to 9) in situations of cubical and spherical representations of units of 3D arrays. By exploring students' strategies in these two situations, we find that difficulties in…

Our work investigated how six primary school students used a non-traditional method for adding and subtracting: the ABN method, a Spanish acronym for Open (method) Based on Numbers. Commognitive theory [Sfard, A. 2008. "Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing." New York: Cambridge…

Background/purpose: This study aimed to investigate the differences among the equations used in estimating the reliability coefficient using the half-split method. These equations demonstrate Spearman-Brown's, Rulon's, Guttman's, Mosier's, Flanagan's, and Horst's. Materials/methods: The study instrument was a 43-item scale for evaluating the…

An elementary method to calculate the area, centroid and volume of rotation of the Koch curve is presented. Classroom extensions are provided to allow students to investigate the method used.

This paper presents a series of basic computational problems that are mathematically and/or graphically appealing, and provides an idea of places one might go in trying to understand what is happening, integrating mathematics, computation, and graphics. The real point of this paper is to make a case, through those examples, for computation as an…

Ben Zunica describes a lesson in which computational thinking has been successful in assisting students to understand the process of simplifying surds. The strengths and limitations of this approach are discussed. The author concludes that computational thinking can assist in solidifying understanding of a range of mathematical processes for…

The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical…

Coordination of theoretical probability and relative frequency estimates is challenging in probability teaching and learning. Modeling is one of the ways of teaching and learning that facilitates inquiry between these two perspectives. Given that, we designed a modeling activity to support fifteen secondary students in investigating theoretical…

Properties of curved functions considered to be parallel over their domains are investigated. Parallel curves in a given plane may appear identical but are actually not superimposable and thus are not congruent. Translational shifted functions in a plane are not parallel curves because the shortest perpendicular distance between them is not…

Every application of integration by parts can be done with a tabular method. The trick is to identify and consider each new integral in the table before deciding how to proceed. This paper supplements a classic introduction to integration by parts with a particular tabular method called Row Integration by Parts (RIP). Approaches to tabular methods…