In this paper we follow a hypothetical mathematician who is working on a problem that is eventually solved. We treat this problem as if it were difficult for the mathematician. In following the mathematician's work, we note both what she does and what she doesn't do in the process. By the latter, we consider the times when progress is not being…

By some estimates, over 1.2 billion tons of soil was blown across the Great Plains during the height of the Dust Bowl. The so-called "black blizzards" these massive dust storms caused suffocated cattle, sickened children, and destroyed thousands of family farms. Formerly prosperous farmers, unsure why they had such bad luck, wondered if…

This paper describes a model of mathematics bianshi teaching using one problem with several solutions, changes, and applications in an inquiry-based classroom. Based on the model of mathematics bianshi teaching, the author discusses a class-room experience where one Chinese mathematics teacher takes a simple plane geometry problem to guide…

This article extends initial ideas on what hope is, why it matters to democracy, and how to teach it in schools, which were first presented by Sarah M. Stitzlein in her book "Learning How to Hope: Reviving Democracy through Our Schools and Civil Society" (Oxford University Press, 2020). It accounts for recent obstacles to hope,…

A problem-solving experiment is a learning activity that uses experimental design to solve an authentic problem. It combines two evidence-based teaching strategies: problem-based learning and inquiry-based learning. The use of problem-based learning and scientific inquiry as an effective pedagogical tool in the science classroom has been well…

The comprehensive practical activity curriculum can be said to be created to cater to children's curiosity and nature of exploration. Through the creation of problem situations, children are guided not only to explore what the world is, but also to pay close attention to what the world will be and cultivate children's key competencies in the real…

One of the most effective forms of professional learning happens when teachers conduct collaborative inquiry in their own classrooms around difficult and challenging topics -- even topics that are potentially divisive. In this article, the authors describe how they have seen this powerful process at work in their district in Pitt County, North…

This article is based upon Peter Sullivan's (2021) structured inquiry approach to teaching mathematics, in which the authors take a deep dive into the technique of "Spotlighting" in the "Explore" phase of this model to assist in optimal learning experiences for students. Working from the premise that students are best placed to…

The static equilibrium properties of a spool, resting on an incline and subject to the tension exerted by a string wrapped around the core cylinder, are studied by means of Newtonian mechanics. The overall behaviour of this system is imagined to be similar to that of a doggie kept on a leash. Starting from the well-known mechanical properties of…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

Research has shown that the ways in which teachers engage in professional development activities vary widely. identified three levels of teacher appropriation within professional development, with their inquiry stance indicative of teachers engaging in self-sustaining practices. In our project, we modified the demonstration lesson format so that…

Encouraging students' ability to reason can be looked at through the lens of both oral and written representations. In 2022, the author participated in the first intake of the Teacher Excellence Program run by the Victorian Teaching Academy. Being part of an in-depth professional learning program challenged the author's teaching practices to focus…

Connections among the mathematics, science, and engineering disciplines have been recognized and affirmed in national standards. For example, the application of mathematical ideas and skills within science has been highlighted in national science standards for over 20 years. More recently, the Next Generation Science Standards (NGSS; NGSS Lead…

Since the content of the Theory of Interest course in an actuarial science program is tied to an external exam, instructors may be hesitant to attempt to use inquiry-based learning. In this paper, I outline how and why I did so, including descriptions of the materials that I wrote. I found that student performance on the final exam improved…

Historically, math education at the high school and introductory college levels has focused on computational skills. With the advancement of computational technologies, problemsolving and other higher-order thinking skills should become the focal point. This article discusses ways in which the University of Minnesota has integrated problem-solving…