One expected outcome of physics instruction is for students to be capable of relating physical concepts to multiple mathematical representations. In quantum mechanics (QM), students are asked to work across multiple symbolic notations, including some they have not previously encountered. To investigate student understanding of the relationships…

The ability to relate physical concepts and phenomena to multiple mathematical representations--and to move fluidly between these representations--is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered.…

Multiple representations can enhance students' understanding of mathematical concepts and complex information but can also pose well-documented challenges for students. Whereas instructional designs have been optimized to support students' "learning" with multiple representations, little is known about supportive "teaching"…

Teaching and learning undergraduate statistics has been a most challenging task for undergraduate psychology majors (Salkind, 2017). A seasoned statistics instructor consulted with a seasoned instructional designer on a method to improve a particularly demanding course using a performance improvement approach to address learning difficulties she…

Students expose various intuitions in probability comparison and calculation tasks. Large volumes of research looked into these intuitions by categorizing learners' strategies, but fewer studies considered how these intuitions may be associated with learners' judgments. Even fewer examined the mixed effects of multiple intuitions held by the same…

Research shows the salient place of mathematical teaching talk, including the mathematical-linguistic practices of naming and explaining, in the enactment of students' mathematical talk and learning with understanding in the classroom. Our study was developed to examine the noticing of two groups of secondary-school mathematics teachers in one-day…

In this study, it was aimed to examine the probability problems which were posed based on continuous sample space and discrete sample space. Participants of the study consisted of 48 university students selected by using the convenience sampling method. Eight tasks related to continuous and discrete variables were designed by the researcher. Eight…

Mathematical language (or the content-specific words in mathematics) has repeatedly shown to be related to mathematical abilities in preschool and in the early grades of primary education. Research in this field has predominantly focused on young children's quantitative and spatial language. At the same time, recent research has discovered that…

The ability to understand mathematics is a faculty crucial to be possessed by pre-service teachers who will enter into the education sphere. It is one of the professional competencies essential for teachers since satisfactory lessons' delivery engenders more comprehensible instruction in teachers' students. Qualitative research employs a…

Background/purpose: Awareness of the mathematical skills and knowledge children possess in their early years is widely accepted. This includes various common positive aspects, not only for educators but also for researchers and policymakers. This study presents a systematic review conducted to meticulously identify empirical studies published in…

Proportional reasoning failures seem to constitute most errors in probabilistic reasoning, yet there is little empirical evidence about its role for attaining probabilistic knowledge and how to effectively intervene with students who have less proportional reasoning skills. We examined the contributions of students' proportional reasoning skill…

This study analyzes the relationship between the entry path to a degree and the prior statistical competence of students taking a Statistics and Probability course at an online university. We assessed students' prior knowledge by administering a pretest of the information covered in the course analyzed. The sample includes 108 students from…

Problems teaching probability in Tonga (in the South Pacific) led to the question on how language and culture affect the understanding of probability and uncertainty. The research uses a discursive approach to identify the endorsed narratives which underlie Tongans' reasoning in situations of uncertainty. I aim to justify the claim that the Tongan…

This paper investigates two specific probabilistic biases which middle graders usually exhibit when reasoning about probability and randomness on assessment items. We discuss how students' reasoning about key probability concepts undergirds statistics literacy related to randomness, independence, and the likelihood of future events based on past…

Learning the fundamentals of probability and random variables can be a struggle for many students. Games by their nature require active participation and reward mastery, lending naturally to the framework of active learning. In this study, we designed and evaluated the efficacy of a lab activity using a game where strategy hinges on sums of dice…