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.

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…

Manipulative-based instructional sequences have proven to be successful with students with disabilities. However, instruction must not only support the acquisition of conceptual and procedural knowledge but also build on students' strengths. This article describes how teachers can use manipulative-based instructional sequences to support the…

To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…

The presented article is dedicated to a new way of teaching substitution in algebra. In order to effectively master the subject matter, it is necessary for students to perceive the equal sign equivalently, to learn to manipulate expressions as objects, and to perceive and use transformations based on defining their own equivalences. According to…

Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…

Background: Empirical studies have revealed students' development of computational thinking (CT) and mathematical thinking (MT) during programming-based mathematical problem-solving, highlighting specific CT concepts or practices that serve as learning goals or outcomes. However, implementing programming-based mathematics instruction requires…

ABN (Abierto Basado en Números--Open Calculation Based on Numbers) is a method for teaching basic arithmetic operations in primary education that has become popular in recent years and that is based on the decomposition of numbers through manipulative materials that encourage mental calculation. Currently there is limited number of tools that can…

This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…

In this paper we consider implications of the current world-wide inclusion of computational thinking in relation to children's development of algebraic thinking. Little is known about how newly developed visual programming environments such as Scratch could enhance early algebra learning. The study is based on examples of programming activities…

The results of this study revealed students' solution strategies progressed from inefficient strategies e.g., counting on fingers to more efficient strategies with mathematical connections. These findings should enable educators to gain more insight to use Number Talks to help student develop computational fluency with numbers.

In this study, I present how eight U.S. college calculus instructors with different patterns of inquiry practices used instructional situations to frame instructional tasks for introducing derivatives graphically to students. During four interviews, the instructors proposed up to eight tasks for introducing derivatives physically, graphically,…

Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely…

Creating and developing mathematical models to solve real-world problems is a complex task and students often have difficulties in tackling it successfully. The design and implementation of sequences that help students autonomously develop their ability to solve modelling tasks could be a useful scaffolding tool to foster modelling learning. In…

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…