A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in…

Tychonov's 1935 solution of the heat equation, exhibiting nontrivial heat fluxes spontaneously appearing along an isolated conducting rod initially held at zero degrees, has intrigued some specialists for almost a century. No doubt those practicing heat engineers who took mathematics seriously were initially relieved to learn that the construction…

Research in psychology and education tend to use large-N group designs that necessitate reporting of mean measures analyzed mostly with null hypothesis statistical testing (NHST), but sometimes with Bayesian, or the estimation approaches in inferential statistics. These approaches all render the average person or student as the the putative…

Environmental education research often emphasizes the importance of community context, but conceptualization and measurement of environmental literacy has mostly occurred at the individual level, often focusing on individual behaviors. The environmental problems facing the world today require collective action--communities coming together to…

In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

The use of approximations in solving problems in sciences can be vital for students. Order of magnitude estimation also helps with physical understanding of the quantities involved in a calculation. For example, in the first exam in a first-year class in chemistry the student must find the mass in grams of an atom; a couple of students will…

In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the…

Research shows that when students engage with mathematical inquiry their problem-solving skills are strengthened. Demands in the revised Australian curriculum raised problem-solving of new senior secondary mathematics assessment, specifically in Queensland Problem-solving and Modelling Tasks (PSMTs). The challenge for Queensland was to scale…

Access to high-quality education at scale is limited by the difficulty of providing student feedback on open-ended assignments in structured domains like programming, graphics, and short response questions. This problem has proven to be exceptionally difficult: for humans, it requires large amounts of manual work, and for computers, until…

Peer feedback has been suggested as an avenue to leverage students as partners in their own learning and assessment across many disciplines. However, successful implementation of peer feedback activities may prove challenging if students believe that feedback requires more objective expertise than they possess. Summarizing participant…

Students often have limited opportunities in school to grapple with the ramifications of the increasing influence technology companies exert over their lives. Digital citizenship curricula could be the exception, but they typically emphasize personal safety and respectful behavior online, ignoring more participatory or justice-oriented notions of…

Design Thinking (DT) has recently been adopted in some higher education disciplines as an effective pedagogical approach to enable students to acquire the skills needed for solving real world problems. As a human-centered, iterative process, design thinking is characterized by working with others to understand, define and solve problems using…

The formation of a person's personality in his intellectual and moral improvement, the expansion of his independence, creativity and critical thinking is possible within his participation in the educational process. In the conditions of the Slovak Republic, the subject of civics plays an important role in this process. The aim of the paper is to…

The fields of quantitative and covariational reasoning boast a wide range of powerful theoretical tools, which are described carefully in the literature. Less frequent and explicit attention, however, has been paid to writing down detailed, practical guidance for operationalizing these theoretical constructs. Some guidance is provided by…

Probability is generally considered one of the most challenging areas to teach in mathematics education due to its intricate nature. However, the simulation-based teaching method can increase students' accessibility significantly to the probability problems because it enables students to resolve the problems with minimal mathematical skills. By…