The National Council of Teachers of Mathematics (NCTM, 2014) highlights that effective teaching practices promote students' reasoning and sense making through various problem-solving strategies. Rather than telling students what to do and how to solve problems, teachers are expected to engage learners in accessible real-life problem situations…

Frequently, the shadow of financial insolvency is present in economies, whether between countries, companies or the general population (people) who contract the obligation of a loan, credit or other debt. Debt restructuring is one of the most effective financial tools to face this. Through mathematical modeling with algorithms designed for the…

By modeling learning students enjoy learning and doing mathematics in new ways. This study aimed firstly to produce senior high school mathematics modeling tasks, lesson plan, and student worksheet for valid mathematical learning; secondly, to produce senior high school mathematics modeling, lesson plan, and student worksheet for practical…

The purpose of this study was to explore students' mathematical practices while working on modeling problems using 3 interactive computer simulations. Three fifth grade students' interactions with computer-based modeling simulation were examined to identify how children defined and prioritized and coordinated variables and parameters in…

A new visual representation for insight problems permits 22 new quantitative measures; which leads to a detailed diagnosis of a person's (or team's) creative weaknesses; which then leads to prescribing targeted, effective counter-techniques for each weakness. Currently, only two measures are consistently used for insight problem solving: the…

We make a case for including difference equations, in particular the discrete logistic equation, in basic differential equations courses. Contrasting the behavior of discrete and continuous models enriches students' understanding of both modeling and differential equations. To facilitate sharing discrete population models with students, some…

Most children, when presented with the option between two drink items, will choose the one with "more." But what exactly do children consider when they recognize one object as having more than another? Is it the perceived surface area or volume of an object? Depending on children's cognitive development, the aspect of measurement on…

We examine the challenges of teaching probability through the use of modelling. We argue how an integrated modelling approach might facilitate a coordinated understanding of distribution by marrying theoretical and data-oriented perspectives and present probability as more connected to the social lives of modern-day students. Research is, however,…

Have you ever noticed trash collecting in streams or waterways? How does trash influence our environment, and what can be done to enact change? These are questions middle school students explored as the authors launched the Great Pacific Garbage Patch (GPGP) task. The Great Pacific Garbage Patch activity involves an urgent environmental issue that…

One promising approach for connecting undergraduate content coursework to secondary teaching is using teacher-created representations of practice. Using these representations effectively requires seeing teachers' use of mathematical knowledge in and for teaching (MKT). We argue that Rowland's (2013) Knowledge Quartet for MKT, in particular, the…

In this dissertation study, I report on six middle school students' construction and interpretation of graphs and associated dynamic situations. Constructing and interpreting graphs represents a critical moment in middle school mathematics due to its opportunity to provide a powerful foundation for learning. Nevertheless, researchers have…

To be literate in a society where the information shared online is often exploited, learners should be exposed to multiple aspects of contemporary predictive modeling. This article explores an activity in which grade 10 students learned how a famous AI algorithm (the Apriori algorithm) uses conditional probability to automate the process of…

The teaching of mathematical modeling is limited in P-12 classrooms. Little is known in regards to how to support teachers to successfully enact modeling activities. Teachers do not always appreciate the value of modeling activities in mathematics learning and often feel unprepared to implement modeling in their classrooms. Teachers often struggle…

This paper investigates students' mathematical modeling activity in data-rich modeling tasks. It aims at gaining insight into how students develop meaning when modeling data-rich situations and the mathematical models produced. A tendency to model a particular dataset, rather than the phenomenon that the dataset is a particular instance of, has…

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.