This case study narrative reports on the journey of *Sammy as her mindset as a learner of mathematics is challenged. Often students who are mathematically highly capable are viewed as being privileged, they are rarely placed with the cohort of struggling students. Children like Sammy who are mathematically highly capable or gifted, however, are…

Over the past few decades, there has been extensive debate as to whether humans represent number abstractly and, if so, whether perceptual features of a set such as cumulative surface area or contour length are extracted more readily than number from the external world. Here we show that 7-month-old infants are sensitive to smaller ratio changes…

Calculus students' difficulties in understanding integration have been extensively studied. Research shows that the difficulty lies with students understanding of the definition of the definite integral as a limit of a Riemann sum and with the idea of accumulation inherent in integration. We have created a set of manipulatives and activities…

The emergence of a proof image is often an important stage in a learner's construction of a proof. In this paper, we introduce, characterize, and exemplify the notion of proof image. We also investigate how proof images emerge. Our approach starts from the learner's efforts to construct a justification without (or before) attempting any…

Teachers often express to Marulyn Burns their worry about the need to "cover the curriculum." In response, she draws on one of her favorite quotes: "You don't want to cover a subject; you want to uncover it." This quote is from "The Having of Wonderful Ideas and Other Essays on Teaching and Learning" by Eleanor…

The dice game Farkle provides an excellent basis for four activities that reinforce probability and expected value concepts for students in an introductory statistics class. These concepts appear in the increasingly popular AP statistics course (Peck 2011) and are used in analyzing ethical issues from insurance and gambling (COMAP 2009; Woodward…

Understanding the roles of random selection and random assignment in experimental design is a central learning objective in most introductory statistics courses. This article describes an activity, appropriate for a high school or introductory statistics course, designed to teach the concepts, values and pitfalls of random selection and assignment…

We introduce a family of puzzles that can help students understand permutation groups. In addition these puzzles provide a basis to investigate other puzzles and their groups of permutations.

This paper explores the usefulness of understanding quotients as measures of relative size in mathematics. The paper characterizes the types of thinking displayed by high school mathematics teachers on two novel tasks designed to reveal teachers' meanings in contexts where making comparisons of relative size is productive. [For the complete…

In response to an open-ended assessment task, 282 children of 6 to 8 years of age revealed their understandings of mass measurement. Each of the Year 1 and 2 children in 13 classes from 3 schools represented their knowledge of mass measurement in drawing and / or writing. Responses ranged from portrayals of activities they had undertaken or…

"Current Studies in Educational Disciplines 2021" is published annually from the selected papers invited by the editors. This edition includes 6 sections and 14 papers from the field of Environmental Education, Science Education, Educational Technology, Mathematics Education, Assessment in Education and STEM Education. All submissions…

Purpose: Universal language can be viewed as a conjectural or antique dialogue that is understood by a great deal, if not all, of the world's population. In this paper, a sound argument is presented that mathematical language exudes characteristics of worldwide understanding. The purpose of this paper is to explore mathematical language as a tool…

Multiplicative thinking is a "big idea" of mathematics that underpins much of the mathematics learned beyond the early primary school years. This article reports on a recent study that utilised an interview tool and a written quiz to gather data about children's multiplicative thinking. Our research has so far revealed that many primary…

Very little is known about children's discussion of mathematics topics during unstructured play. Ginsburg, Lin, Ness, and Seo [2003. Young American and Chinese children's everyday mathematical activity. Mathematical Thinking and Learning, 5(4), 235-258. Retrieved from…

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice…