This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled…

A study with prospective teachers without prior mathematical modeling experience sheds light on how their newly developed conceptual understanding of modeling manifested itself in their work on the final task of a modeling module within a pedagogy course in secondary mathematics curriculum and assessment. The main purpose of the module was to…

In recent years the use of expert judgement to set and maintain examination standards has been increasingly criticised in favour of approaches based on statistical modelling. This paper reviews existing research on this controversy and attempts to unify the evidence within a framework where expertise is utilised in the form of comparative…

To meet the demand of the incoming school curriculum reform focusing on competency-based learning in Vietnam, this paper reports on an innovation project on developing secondary mathematics preservice teachers' (PSTs) mathematical literacy and preparing them to teach mathematics contextually. We developed a curriculum and studied the effectiveness…

Data science is emerging as a field that is revolutionizing science and industries alike. Work across nearly all domains is becoming more data driven, affecting both the jobs that are available and the skills that are required. As more data and ways of analyzing them become available, more aspects of the economy, society, and daily life will…

The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…

The senior school Mathematics syllabus is often restricted to the study of single variable differential equations of the first order. Unfortunately most real life examples do not follow such types of relations. In addition, very few differential equations in real life have exact solutions that can be expressed in finite terms. Even if the solution…

In a study with ninth-grade mathematics students on learning the concept of variance, students experienced either direct instruction (DI) or productive failure (PF), wherein they were first asked to generate a quantitative index for variance without any guidance before receiving DI on the concept. Whereas DI students relied only on the canonical…

Exploring and deriving proofs of closed-form expressions for series can be fun for students. However, for some students, a physical representation of such problems is more meaningful. Various approaches have been designed to help students visualize squares of sums and sums of squares; these approaches may be arithmetic-algebraic or combinatorial…

Modelling of statistical data is a well established analytical strategy. Statistical data can be modelled to represent, and thereby predict, the forces acting upon a structure or system. For the rapidly changing systems in the world of education, modelling enables the researcher to understand, to predict and to enable decisions to be based upon…

This paper describes a quantitative model for the optimal assignment of students to courses for their complete high school careers. The model--the Automatic Curriculum Planning Program (ACPP)--can assign curriculum to a complete set of students based on their derived student grouping. Following a review of the literature on techniques for…

Discusses students' exploration of a particular rational function in the context of people waiting in line for service. The concepts of domain, range, and asymptotes are also developed in that context as is the effect of changes in input variables on function outputs. (Author/NB)

Examines the impact of a school-based assessment system on the implementation of an applications/modeling-based curriculum at the senior secondary level. The persistence of high task scaffolding in assessment tasks throughout the course and the concerns of teachers about the reliability and ownership of assessment in unsupervised conditions…

A model, easily constructed by students, is used to assist in seeking basic Pythagorean identities used to prove more complex ones. (MNS)

In this workshop, we will continue to reflect on a models and modeling perspective to understand how students and teachers learn and reason about real life situations encountered in a mathematics and science classroom. We will discuss the idea of a model as a conceptual system that is expressed by using external representational media, and that is…