Prior findings on the effects of active learning environments were limited by both research design and data-analysis techniques, such as lack of controls over confounding factors and misuse of statistical modeling. We (1) investigated the effects of active learning environments on student achievement and motivation and (2) overcame the limitations…

Literature portrays advanced mathematics lecturing as a uniform teaching style, often criticized for offering minimal opportunities for student participation. In this paper we present results from a comparative case study of two instructors' facilitation of student participation in Real Analysis lectures. Analyzing fieldnotes from several observed…

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…

As higher education seeks to define and justify itself in a "post-pandemic" world, it is important to understand the role of centripetal and centrifugal forces. The centrifugal approach suggests engagement facing outward and away from the classroom, from curricula, and from campus in favor of service learning, internships, political…

Learner metacognition can positively impact learning. However, little is known about how to effectively design gamebased learning environments such that metacognition is promoted in learners. Previous research does not provide sufficiently structured and empirically verified insights for designers and researchers to make informed design decisions.…

Learning the meaning of number words is a lengthy and error-prone process. In this review, we highlight outstanding issues related to current accounts of children's acquisition of symbolic number knowledge. We maintain that, despite the ability to identify and label small numerical quantities, children do not understand initially that number words…

Proportional reasoning is an important type of reasoning that students need to develop and was thus chosen as the context for my research of multiple-choice (MC) items. My investigations of ways to improve the function of MC items so that they reduced guessing, better addressed higher order thinking and assessed partial knowledge, influenced my…

The Times Tables Drill, in which students recite multiplication facts at high speed, is based on a 200 year-old American military education practice. Emphasising "commands," "obedience," "rules," "silence," "separation," "surveillance," "speed," "competition,"…

Many universities have been designing and implementing online instruction for years, but the COVID-19 pandemic created an unexpected impetus for the expansion of virtual learning. Instructors and students who may not have previously chosen or experienced online instruction found themselves in need of safe, virtual options, and it appears that the…

This book discusses a number of ways in which out-of-school science education can uniquely engage learners with 'wicked' global problems such as biodiversity loss and climate change. The idea for the volume originated in discussions among members of the ESERA special interest group on "Science Education in Out-of-School contexts". It…

Successful lessons are explicit, yet also inspire active learning and opportunities to respond. As the one shaping lessons, can you do better? Probably, and you're not alone. Research shows teachers consistently offer students far fewer than the recommended opportunities to respond, leaving all students--including those with special needs and…

There has been great progress towards Reinforcement Learning (RL) approaches that can achieve expert performance across a wide range of domains. However, researchers have not yet applied these models to learn expert models for educationally relevant tasks, such as those taught within tutoring systems and educational games. In this paper we explore…

This book introduces, rationalizes and describes some ways to circumvent the challenges of providing 'hands-on' learning when programmes with practice-based focuses have to be offered via distance learning. It presents a framework to help deconstruct the many aspects of 'learning to become' a professional or practitioner. Then, it demarcates the…

Your students may recognize the words determine, explain, and summarize in the above standard, but would they understand and be able to apply these concepts? Students encounter these and other academic vocabulary words throughout their school years, but too often, they don't have a firm grasp of these words' meanings or what skills they require.…

The array is a powerful tool that builds students' understanding in multiplication. Students' interactions with the array changes through the course of an instructional sequence, which can be viewed as a process of "reification." In this paper, I report the findings of a research study conducted with 45 Year 5 students in Sydney. The…