As students contribute to social and sociomathematical norms, they will often reorganize their own understandings. As such, the purpose of this article is to describe the ways in which prospective elementary teachers contributed to the norms that were established and "re"-established throughout an entire semester in an undergraduate…

Freshmen with declared life-science majors typically matriculate with a determination to succeed. However, inadequately-prepared students are easily overwhelmed and at risk of abandoning their aspirations for a STEM career. The investigator designed and taught weekly recitations for approximately 850 students during a five-year span, and…

In a 2-year longitudinal study, 66 children were assessed in Grades 3 and 4 with a within-method-and-time design on metacognition (including the computerized Evaluation and Prediction Assessment [EPA2000]) and mathematics. Moreover, half of the children were trained in Grade 3 in the metacognitive skill of predicting their abilities in solving…

The present study evaluated the effectiveness of an instructional intervention (schema-based instruction, SBI) that was designed to meet the diverse needs of middle school students by addressing the research literatures from both special education and mathematics education. Specifically, SBI emphasizes the role of the mathematical structure of…

A course in the Calculus sequence is arguably the most difficult course in which inquiry-based learning (IBL) can be achieved with any degree of success within the curriculum in part due to: (1) the plethora of majors taking Calculus to which the sequence relates to their majors in what is considered an "applied" manner; and (2) the…

Comparing multiple examples typically supports learning and transfer in laboratory studies and is considered a key feature of high-quality mathematics instruction. This experimental study investigated the importance of prior knowledge in learning from comparison. Seventh- and 8th-grade students (N = 236) learned to solve equations by comparing…

The main objective of this study is (a) to explore the relationship among cognitive style (field dependence/independence), working memory, and mathematics anxiety and (b) to examine their effects on students' mathematics problem solving. A sample of 161 school girls (13-14 years old) were tested on (1) the Witkin's cognitive style (Group Embedded…

"The power of two" is a Royal Institution (Ri) mathematics "master-class". It is a two-and-a half-hour interactive learning session, which, with varying degree of coverage and depth, has been run with students from Year 5 to Year 11, and for teachers. The master class focuses on an historical episode--the Josephus…

Early in my career someone else reported that the best indicator of success in calculus-based physics (CBP) at our school was whether students had taken mathematics in a certain region of New Brunswick. I sat down with a very longtime mathematics teacher and asked him what he thought students should know in mathematics after high school to succeed…

This paper is a whimsical survey of the various explanations which might account for the biblical passage in I Kings 7:23 that describes a round object--a bronze basin called Solomon's Sea--as having diameter ten cubits and circumference thirty cubits. Can the biblical pi be any number other than 3? We offer seven different perspectives on this…

We introduce a simple game made up of a board of coins on a triangular lattice. We then study the possibility of turning the board from one pattern of heads and tails to some other pattern. Given that a solution exists we find a precise answer to the number of solutions possible. We then generalize this to more complex boards with coins of many…

We present an alternative method to that of Scott (D. Scott, "When is an ordinary differential equation separable?", "Amer. Math. Monthly" 92 (1985), pp. 422-423) to teach the students how to discover whether a differential equation y[prime] = f(x,y) is separable or not when the nonlinearity f(x, y) is not explicitly factorized. Our approach is…

We describe a method to extract roots of a reducible quintic over the real field, which makes use of a simple division. A procedure to synthesize such quintics is given and a numerical example is solved to extract the roots of quintic with the proposed method.

This paper presents a qualitative case study of statistical practice in a university-based statistical consulting centre. Naturally occurring conversations and activities in the consulting sessions provided opportunities to observe questions, problems, and decisions related to selecting, using, and reporting statistics and statistical techniques…

These proceedings contain the papers of the 16th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2019), held during November 7-9, 2019, which has been organized by the International Association for Development of the Information Society (IADIS) and co-organised by University Degli Studi di Cagliari, Italy.…