Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…

I explore some facts about the area, position, etc. of the Steiner ellipse using GeoGebra and numerical analysis. Students can use these for mathematical inquiry.

Problem-solving is an essential part of teaching, learning, and assessment of physics and mathematics. The continuing educational reforms have a deep impact on everyday teaching as well as working with talented students. In the Macedonian educational system, the curricula do not explicitly point out the connection between mathematics and physics,…

Many mathematics education researchers agree that students struggle to understand the key concepts in linear algebra courses. The purpose of this study was to examine in-service teachers' errors and misconceptions in the area of linear combinations. The participants were 73 Zimbabwean mathematics teachers who were enrolled in an in-service…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

This study investigated the methods that pre-service teachers employed while finding volume using integration and the reasons why they utilized these methods (problems); the accuracy of their solutions was also analyzed in this study. Case study design, a qualitative research method, was used for this study. 45 sophomore pre-service teachers…

This study investigated the role of the bar model method, a significant aspect of the Singapore mathematics curriculum, in the remediation of seventh-grade students' errors on algebra word problems. To accomplish this purpose, we first assessed students' errors on a written test involving algebra problems and identified ten students based on the…

The adverse influence of the presence of an irrelevant number and language inconsistency in a word problem is well known. Our study focused on the combination of these two variables and on the position of the irrelevant number in the word problem for Grade 6 pupils. The study has a mixed design. Item Response Theory was used to make equally able…

Evaluation of the cosine function is done via a simple Cordic-like algorithm, together with a package for handling arbitrary-precision arithmetic in the computer program Matlab. Approximations to the cosine function having hundreds of correct decimals are presented with a discussion around errors and implementation.

The present study aims to examine high school mathematics teachers' content knowledge of the logical structure of proof in geometry. For this purpose, three scenarios were established based on errors in proof deriving from the figural-concept interactions. Based on these scenarios, clinical interviews were held with five mathematics teachers, who…

Research in psychology and in mathematics education has documented the ubiquity of "intuition traps" -- tasks that elicit non-normative responses from most people. Researchers in cognitive psychology often view these responses negatively, as a sign of irrational behaviour. Others, notably mathematics educators, view them as necessary…

This paper explores analysis of feedback data collected from student consultations at two mathematics support centres at universities in Australia and Ireland. Unstructured text data was collected over six years and includes qualitative data on student queries collected during the consultations from mathematics and statistics related subjects.…

Learning to write formal mathematical proofs presents a major challenge to undergraduates. Students who have succeeded in algorithm-intensive courses such as calculus often find the abstract logic and nonprocedural nature of proof writing to be technically difficult, ambiguous and "filled" with potential errors and misconceptions. This…

The aim of the study is to examine prospective mathematics teachers' pedagogical content knowledge in terms of knowledge of understanding students and knowledge of instructional strategies which are the subcomponents of pedagogical content knowledge. The participants of this research consist of 98 prospective teachers who are studying in two…

In this paper a two-stage research study is described focused on problem solving relevant to place-value and on the use of the operations within the calculator environment. The findings show that in this specific environment and via appropriate tasks teachers are provided with a context to better understand what year 5 or 6 pupils know or do not…