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…

How can we prepare students for a world where data-driven decision-making shapes nearly every aspect of life? "Data Minds: How Today's Teachers Can Prepare Students for Tomorrow's World" helps K-8 educators infuse data literacy into everyday lessons across disciplines, without overwhelming existing curricula. Data literacy is an ability…

This article explores inquiry-based learning (IBL) pedagogy, particularly in mathematics education, examining how it differs from problem-based learning (PBL) and case-based learning (CBL). IBL is defined as a student-centered approach involving sequenced problems or tasks that build engagement and understanding through group work. While IBL, PBL,…

Inquiry-based learning (IBL) in mathematics is a student-centered approach that encourages exploration, problem-solving, and critical thinking, allowing students to actively engage with mathematical concepts and discover relationships through hands-on activities and collaborative learning. Despite the growing interest in IBL within mathematics…

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…

Carefully observing young children at play in a mathematically rich environment has led me to reflect on the way children naturally pose and solve interesting mathematical challenges. Here, three examples of the playful learning of six-year-old children illustrate the problem solving and persistence children can display. Teachers are encouraged to…

Conceptual challenge is often considered a necessary ingredient for promoting deep learning in an inquiry-based environment. However, challenge alone does not support conceptual development. In this paper, we draw on complexity theory as a theoretical lens to explore how a primary teacher facilitated students' conceptual change through repeated…

In this article, the authors present an inquiry activity presented to Year 7 students in a mathematics excellence class at a P-12 school in regional Queensland. Different students solved the activity (comparing the sugar content of fruit) using decimals, percentages, ratio and rates. By asking the students to solve a problem they were much more…

Descriptions of mathematical thinking have an extended lineage. Sometimes accurate and sometimes not, sometimes misinterpreted and sometimes not, characterizations of mathematical thought processes have inspired and at times misled people interested in designing or framing mathematics instruction. Challenges the field faces in conceptualizing…

As students learn to problem solve in authentic situations, they must also develop metacognitive tools to manage and regulate their problem-solving process. To foster process-focused metacognition utilized by mathematical thinkers and problem solvers, inquiry-based learning classroom practices and an adapted version of portfolio problems were…

The aspects of inquiry based learning (IBL) are vigorously and frequently in the focus of recent studies. With the use of inquiry in mathematics in the daily school practice, some further questions are arising there: What kind of problems can be useful for an analysis of students' competencies in the field of IBL and how to assess the performed…

In this paper I consider the notion of 'visible pedagogy' in refining a conceptualization of 'socially-just pedagogy' in the mathematics classroom. I explore reasons why the recent focus on promoting formative assessment and metacognition, embodied in Hattie's 'visible learning', has failed to bring about the fundamental shift in pedagogic…

Southern Cross University (SCU) educators and local teachers have developed a five-lesson instructional sequence built around fluke identification as a way of resolving the question: How fast do humpback whales travel up the east coast of Australia?

Background/Context: The problems that school district leaders identify and how they frame them have consequences--for both policy implementation and the ways that teachers respond. Although that is likely true in all community contexts (from rural to urban, inside and outside metropolitan centers), the influence of broader discourses associated…

In this paper we address practical questions such as: How do symbols appear and evolve in an inquiry-oriented classroom? How can an instructor connect students with traditional notation and vocabulary without undermining their sense of ownership of the material? We tender an example from linear algebra that highlights the roles of the instructor…