This study investigates college students' understanding of arithmetic fraction operations as defined by the Common Core State Standards in grades three through six Mathematics. This study is meant to extend upon an extensive body of research regarding elementary and middle grades students' understanding of fraction operations and see if recognized erroneous thinking among younger students persist among college students. Among these misconceptions include: fraction equivalence, common denominators, the algorithm and the concept of division, whole number bias, and incorrectly applying fraction operations. The results of this study suggest that college students have the same misunderstandings and misconceptions as elementary students in regards to fraction operations.

Is reasoning about religious ritual tethered to ordinary, nonreligious human reasoning about actions? E. Thomas Lawson and Robert N. McCauley’s ritual form hypothesis (rfh) constitutes a cognitive approach to religious ritual – an explanatory theory that suggests people use ordinary human cognition to make specific predictions about ritual properties, relatively independent of cultural or religious particulars. Few studies assess the credibility ofrfhand further evidence is needed to generalize its predictions across cultures. Towards this end, we assessed culturally Chinese “special patient” rituals in Singapore. Our findings strongly supportrfhpredictions for special patient ritual repeatability, reversibility, sensory pageantry and emotionality.

People with disabilities are underrepresented in STEM as well as information, communication, and technology (ICT) careers. The underrepresentation of individuals with disabilities in STEM may reflect systemic issues of access. Curricular materials that allow students to demonstrate their current fraction knowledge through multiple means and provide opportunities to share and explain their thinking with others may address issues of access students face in elementary school. In this study, we employed a sequential mixed-methods design to investigate how game-enhanced fraction intervention impacts students’ fraction knowledge, engagement, and STEM interests. Quantitative results revealed statistically significant effects of the program on students’ fraction understanding and engagement but not their STEM interest. Qualitative analyses revealed three themes—(1) Accessible, Enjoyable Learning, (2) Can’t Relate, and (3) Dreaming Bigger—that provided contextual backing for the quantitative results. Implications for future research and development are shared.

Efforts to improve teachers’ knowledge of tools and strategies are often intertwined with their beliefs regarding mathematics teaching and learning. Yet, few studies have examined the impact of professional development designed to bolster teachers’ knowledge of and beliefs about young children’s mathematical development. In this study, we evaluated whether participants’ beliefs changed significantly after engaging in online professional learning on teaching math to young children, overall orientations of participants’ teaching practices and shifts over time, and how changed beliefs might coincide with changed orientations to practice. We employed a multilevel mixed methods design, with quantitative results showing changes in participants’ overall beliefs based on survey data. We discuss how trends in perceived instructional practices coincide with beliefs found to be statistically significant in the quantitative analysis and the potential for online professional development to influence beliefs. Considerations for design of online professional learning and implications for future research are shared.

College students view mathematics, specifically fraction arithmetic, as a series of tricks that can lead them to the correct answer. This view of mathematics is a direct reflection of their lack of conceptual understanding of fraction arithmetic and their reliance on procedural understanding. College students have an imprecise remembrance of fraction arithmetic and instead rely on tricks they vaguely remember and cannot explain. This reliance on procedural processes that they do not fully understand causes them to make mistakes in their arithmetic. If we do not require students to think critically about the mathematical processes they are completing when first taught a subject and require this critical thought as students progress through mathematics courses, mathematics loses meaning and our students will not have the ability to think critically or conceptually about mathematics.