As engineering and Science, Technology, Mathematics, and Engineering (STEM) rise in popularity, engineering and STEM standards in some US states as well as the Next Generation Science Standards are starting to emerge. However the ability to engineer is difficult to test with a standardized test. Either the definition of engineering (having…

How can we teach inquiry? In this paper, I offer practical techniques for teaching inquiry effectively using activities built from routine textbook exercises with minimal advanced preparation, including rephrasing exercises as questions, creating activities that inspire students to make conjectures, and asking for counterexamples to reasonable,…

In this article, I present a collection of puzzles appropriate for use in a variety of undergraduate courses, along with suggestions for relevant discussion. Logic puzzles and riddles have long been sources of amusement for mathematicians and the general public alike. I describe the use of puzzles in a classroom setting, and argue for their use as…

In this paper, the knowledge dimension for Revised Bloom's taxonomy (RBT) is unpacked for integral calculus. As part of this work, the 11 subtypes of the knowledge dimension are introduced, and through document analysis of chapter 4 of the RBT handbook, these subtypes are defined. Then, by consulting materials frequently used for teaching integral…

When presented with a problem in mathematics class, students often function as problem performers rather than problem solvers (Rigelman 2007). That is, rather than understanding the problem, students focus on using an operation to complete it. Students' tendencies to act as problem performers can prevent them from suggesting problem-solving…

Problem solving is one of the main competences we seek to teach students at school for use in their future lives. However, when dealing with mathematical problems, teachers encounter a wide variety of difficulties. To foster students' problem-solving skills, the authors developed "strategy keys." Strategy keys can serve as material to…

Problem-solving skills in creative, open-ended domains are both important and little understood. These domains are generally ill-structured, have extremely large exploration spaces, and require high levels of specialized skill in order to produce quality solutions. We investigate problem-solving behavior in one such domain, the…

Abilities in scientific thinking and reasoning have been emphasized as core areas of initiatives, such as the Next Generation Science Standards or the College Board Standards for College Success in Science, which focus on the skills the future will demand of today's students. Although there is rich literature on studies of how these abilities…

This paper focusses on the process of learning mathematics in primary school from the perspectives of 62 girls aged seven to 11. For many of these Singaporean girls, English is not the dominant home language, but they all learn mathematics in English. Despite the fact that achievement in mathematics is high nationally, girls appear to be less…

Transboundary challenges such as climate change, loss of biodiversity, energy transformation and the Covid-19 pandemic put vast pressures on generating solutions. They also call for updated teaching providing the required capabilities for international business (IB) and -entrepreneurship (IE) students. This paper presents a teaching initiative…

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…

This study compared the outcomes of student learning between an online Pre-Calculus course and a face-to-face Pre-Calculus course. Participants for this study included nine online and 14 face-to-face students from an urban community college in the Southeastern region of the United States. The study data were written responses from the subjects to…

Psychologists and mathematics educators have long viewed flexibility as critical to students' mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified…

Teacher education programs all around the world are challenged with the emergency transition to remote teaching due to the COVID-19 pandemic. Human-centered design can help generate creative solutions to the pedagogical problems that teacher educators face during this transition. In this paper, we present a case of the Advanced Learning…

In this study, we analyzed the imprecise (i.e., less mathematically precise) responses that 148 third- to fifth-grade Chinese students made on selected-response problems that were part of a spontaneous mathematical focusing task, the Quantitative Relations Test for Chinese Children (QRTC[superscript 2]). The purpose for this analysis was to…