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 the resolution of problems in chemical kinetics and catalysis the mathematical models relate the independent variable that is usually time, with the dependent variable which is normally the concentration of a reactant. They conform to linear models, whose parameters such as the ordering to origin and the slope are kinetic parameters, applying…

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…

As the authors are proponents for engineering education that is done well, they have provided an explanation of truss design using the Method of Joints that combines the application of practical hands-on learning with sound mathematical and scientific theory. The Method of Joints will allow students to design trusses to meet specified criteria…

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.

This article presents a proposal to analyze student perceptions, through a mathematical model, using a previously designed and validated questionnaire. This approach attempts to describe and explain the different positions and interpretations which inhabit students regarding the notion of professorial quality. For this, a question that sums up the…

This article provides information to educational leaders about how to address the challenge of supporting students who are emergent multilingual--i.e., those identified as English Learners (ELs) by their schools--in middle grades mathematics classes. The ideas in this article draw on research and collaborations with hundreds of teachers across the…

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…

We present our experience with an open-ended lab activity that we designed for students with a Calculus 1 background. With the goal of learning how scientists study transport in streams, the students collected data on how a pulse of leaves travels down a nearby stream. Students who had little to no experience with data with two independent…

This article provides an overview of a modeling sequence that culminates in student reinvention of a bifurcation diagram. The sequence is the result of years of classroom-based research and curriculum development grounded in the instructional design theory of Realistic Mathematics Education. The sequence of modeling tasks and examples of student…

In times of rapid technological innovation and global challenges, the development of science, technology, engineering and mathematics (STEM) competencies becomes important. They improve the personal scientific literacy of citizens, enhance international economic competitiveness and are an essential foundation for responsible citizenship, including…

Many introductory physics courses begin with the teaching of motion and kinematics. This naturally leads to the use of constant acceleration equations to solve various problems involving common motions (free fall being a notable example). Students can sometimes get the impression that these equations are the only thing they need to remember in…