The growing use of programming in mathematics classrooms presents a challenge linked to implementation in general and task design in particular. This article presents design ideas for mathematical problems incorporating programming in which the focus remains mainly on learning mathematics and less on learning programming. The article starts by…

This article provides a brief overview of the instructional strategy known as team-based learning (TBL). It then focuses specifically on the use of one of its integral components in a biblical studies classroom--namely, the "4S application task." The 4S application task, which is one of the fundamental pieces of the learning experience…

The Cell Phone modeling task centers on a Fermi real-world estimation question. The task and rubric can be used at different grade levels to focus on the modeling process and classroom community. Finding time and space to engage students, especially novice modelers, in mathematical modeling can be a challenge, yet the benefits of modeling are…

Problem solving requires the application of critical reading and thinking skills and the use of relevant strategies to reach a solution. Independent learners are able to apply taught strategies across contexts and often complete challenging tasks unassisted. The purpose of this paper is to explain how a process of analysis of assignments and…

In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the…

When one sets out to solve a mathematics problem, a feeling of satisfaction and accomplishment comes with finding the answer and knowing it is correct. In contrast, a student performing the correct process to solve an algebra equation and getting an answer such as 3 = 0 may be left perplexed and not understanding what--if anything--he or she did…

This article presents the analysis and discussion of solving geometry tasks by Portuguese Basic Education students, using material from the Poly-UNiverse in Teacher Training Education (PUNTE) project. The teaching experience developed was aimed at testing and disseminating new resources, and innovative and transdisciplinary methodologies in the…

We present in this paper a pair of approaches to support mathematics educators and learners in formulating original tasks. In particular, we facilitate the posing of rich mathematical problems by using two novel methods that were created by a mathematics department at a K-12 school in the United States, and further developed alongside our students…

When a Year 7 student physically reacted to a prompt of another student by anxiously drumming the desk with his ruler, exclaiming "uuuuhh", the initial thought of the observing researcher, Laura, was: "this is an interesting account". This started a reflective journey of first applying robust research methodologies to the…

Mathematical modeling involves using mathematics to represent, analyze, and make predictions or decisions about real- world situations. Garfunkel and Montgomery (2016) elaborate on six components of the mathematical modeling process, including identifying the problem, making assumptions and identifying variables, doing the math, analyzing and…

The National Council of Teachers of Mathematics (NCTM 2014) takes a clear stance that each and every student should have rich experiences in mathematics classrooms. In 2015, the Every Student Succeeds Act noted that Universal Design for Learning (UDL) is an evidence-based, scientifically valid framework that fosters access to instruction for all…

In response to increasing teacher interest in how to design and implement effective challenging tasks, James presents the Launch/Explore/Discuss model that builds on the work of leading Australian educators and researchers Peter Sullivan, Doug Clarke, and Charles Lovitt.

The fear of making mistakes and avoidance of risks can create disabling anxiety and limit learning opportunities. However, it is possible to teach mathematics in ways that not only reduce student agency but also have the effect of excluding some students. This article proposes approaches that are intended to both foster student decision making and…

We implemented a STEM task that highlights the engineering cycle and engages students in productive struggle. Students problem solved in productive ways and saw tangible benefits of revising their work to achieve mathematical goals.

Three mathematics education researchers discuss their findings on the use of diagrams in math instruction for English language learners. The authors show how diagrams can help students who are English learners better develop mathematical thinking and communicate their mathematical understanding.