Tilings, Patterns and Technology

In this paper we discuss various situations where tilings and patterns, with the aid of technology, facilitate the teaching of mathematics and serve as tools in understanding and developing new mathematical ideas. We also illustrate how technology makes possible cultural connections in the study of mathematics using Islamic tilings and patterns

Integrating Computational Thinking With Abstraction In Context: A Project Proposal

The concepts of Computational Thinking (CT) and its link to mathematics provide an assumption that the affordance of CT can be extended to mathematics (Wing, 2006). Correspondingly, their interplay suggests a potential approach in helping the learners abstract concepts that are new to them. In this light, the researcher will present her proposed dissertation project that aims to fill in the gaps concerning CT and mathematics education. The proposed research intends to find out the CT skills and practices that the students will manifest as they perform the unplugged CT task involving the addition of rational algebraic expressions (RAE). Moreover, the research will also describe how CT, through the unplugged Use-Modify-Create (UMC) progression (Lee et al., 2011), mediates in vertically reorganizing the students’ previous constructs into forming the concepts about adding RAEs. Data collection will commence in September 2023 in-class in which three triads of junior high school students, ages 13-15, will perform the CT-integrated tasks. The researcher will examine the written outputs and scratch pads of the students, review the recordings, and backread through the transcripts. The data analysis will utilize the Recognizing, Building-with, Constructing (RBC) model of Abstraction in Context (AiC) to pinpoint the mathematical concepts, and identify the different actions and utterances of the students leading to the construction of the knowledge about adding RAEs (Hershkowitz et al., 2020). The researcher hypothesizes that the CT-integrated mathematical task is a context that incites students to reorganize prior mathematical constructs in forming the new abstract construct. Such results are vital in generating educational interventions for deepening understanding, correcting misconceptions, and conducting curricular reforms related to teaching and learning RAE

Using dynamic tools to develop an understanding of the fundamental ideas of calculus

Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the fundamental theorem of calculus. The lessons were designed on the basis of observed student difficulties and the existing scholarly literature. We show how a combination of dynamic tools and guide questions allows students to construct their understanding of these calculus ideas

App for Addition and Subtraction of Integers

This paper presents a mobile app, AlgeOps, created to assist students in understanding addition and subtraction of integers. The design of the app amalgamated the neutralization model (based on cancelling integers of opposite signs) and the number line model to offer a more holistic representation of integers. Furthermore, since AlgeOps presents two objects, boxes and balloons, the learning objective may be extended to adding and subtracting polynomials. Pre- and post-assessments, student observations and interviews with teachers and students revealed the app can increase performance, facilitate conceptual development, and increase engagement in tasks involving integer addition and subtraction