This study examined processes at the core of teacher professional development (PD) experiences that might positively impact teacher learning and more specifically teacher change. Four processes were considered in the context of a PD program focused on student mathematical errors: analysis of students' mathematical misconceptions as a lever for…

The floor function maps a real number to the largest previous integer. More precisely, floor(x)=[x] is the largest integer not greater than x. The square bracket notation [x] for the floor function was introduced by Gauss in his third proof of quadratic reciprocity in 1808. The floor function is also called the greatest integer or entier (French…

Current technologies incorporating sophisticated mathematical analysis software (calculation, graphing, dynamic geometry, tables, and more) provide easy access to multiple representations of mathematical problems. Realising the affordances of such technology for students' learning requires carefully designed lessons. This paper reports on design…

The Cartesian diver experiment certainly occupies a place of honour in old physics textbooks as a vivid demonstration of Archimedes' buoyancy. The original experiment, as described in old textbooks, shows Archimedes buoyancy qualitatively: when the increased weight of the diver is not counterbalanced by Archimedes' buoyancy, the diver sinks. When…

This article describes some problems of the maximum/minimum type, which are generally solved using calculus at secondary school, but which here are solved algebraically. We prove six algebraic properties and then apply them to this kind of problem. This didactic approach allows pupils to solve these problems even at the beginning of secondary…

Many problems of electric field strength on a boundary between two media require college-level mathematical analysis. However, when the boundary between media is represented by a sphere or a flat plane, these types of problems can be solved algebraically, placing them within reach of high school students. This article presents a solution analysis…

This paper describes and examines students' shared construction of meanings while learning about quadratic functions via digital artifacts that simulate real-world phenomena, like the motion of a ball on an inclined plane, focusing specifically on the role of the teacher in that construction process. The study follows the interactions of twenty…

The goal of this paper is to describe the teaching of initial multiplication concepts and skills, up to the multiplication table, in the Croatian educational system. As Stiegler and Hiebert (1999) concluded, teaching is a complex system rooted in a cultural script of a given society. To describe it without ignoring certain features of it that…

The Mathematics Performance Expectations (MPE) define the content and level of achievement students must reach to be academically prepared for success in entry-level, credit-bearing mathematics courses in college or career training. They were developed through a process that involved faculty from Virginia's two- and four-year colleges and…

Inspection of thousands of student responses to computer-marked assessment questions has brought insight into the errors made by adult distance learners of science. Most of the questions analysed were in summative use and required students to construct their own response. Both of these things increased confidence in the reliability of the…

The purpose of this causal-comparative study was to examine whether differences exist in the mathematics achievement of fifth grade gifted students based on the instructional delivery model used for mathematics instruction, cluster or collaborative, as defined by the Georgia Department of Education. The content area of mathematics, an area…

This study examined ways in which students make use of a graphing calculator and how use relates to comfort and understanding with mathematical symbols. Analysis involved examining students' words and actions in problem solving to identify evidence of algebraic insight. Findings suggest that some symbols and symbolic structures had strong…

Building students' ability to transfer physics fundamentals to real-world applications establishes a deeper understanding of underlying concepts while enhancing student interest. Forensic science offers a great opportunity for students to apply physics to highly engaging, real-world contexts. Integrating these opportunities into inquiry-based…

In this paper, we introduce a mathematical model for collaborative learning and the answering process for multiple-choice questions. The collaborative learning model is inspired by the Ising spin model and the model for answering multiple-choice questions is based on their difficulty level. An intensive simulation study predicts the possibility of…

Data visualizations have proliferated throughout the COVID-19 pandemic to communicate information about the crisis and influence policy development and individual decision-making. In invoking exponential growth, mathematical modelling, statistical analysis, and the like, these data visualizations invite opportunities for mathematics teaching and…