Developing students' competence in algorithmic thinking is emerging as an objective of mathematics education, but despite its inclusion in mathematics curricula around the world, research into students' algorithmic thinking seems to be falling behind in this curriculum reform. The aim of this study was to investigate how the mathematical modelling…

This paper reports on a teaching experiment on mathematical modelling in an upper secondary school class that investigates how the constructs of "model eliciting" and "emergent modelling" may be brought together to inform teaching and learning. A prominent role is covered by the process of task design, seen as a complex process…

A widely used instrument was implemented to ascertain the mathematical modelling competency displayed by a cohort of South African learners in grade 10 and grade 12 of the school mathematics programme in South Africa. The cohort comprised 471 grade 10 and 200 grade 12 learners from schools serving learners from low socio-economic status…

In this study, we follow students' modeling and covariational reasoning in the context of learning about big data. A three-week unit was designed to allow 12th grade students in a mathematics course to explore big and mid-size data using concepts such as trend and scatter to describe the relationships between variables in multivariate settings.…

This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in…

In this study, we test an information-processing model (IPM) of problem solving in science education, namely the working memory overload model, by applying catastrophe theory. Changes in students' achievement were modeled as discontinuities within a cusp catastrophe model, where working memory capacity was implemented as asymmetry and the degree…

Explains a model to analyze direct teaching cost per student at the class level in the final two years of secondary schooling in Victoria, Australia. The model provides predictions for class size and unit cost for each learning area for various enrollment levels. Cost predictions for foreign-language classes were twice that of English classes.…

The concept under investigation was the reliability of estimates of mean scores of groups under various assumptions of multiple-matrix sampling when reliabilities are computed according to procedures based on generalizability theory. Four different cases were compared with respect to the generalizability coefficients depending upon whether pupils…

This study tested the multifaceted, hierarchical structure of self- concept (SC) against alternative models and determined whether academic SC can be discriminated from academic grades. Results supported the multidimensional interpretation of SC and demonstrated that general SC could be interpreted as distinct from but correlated with academic SC.…

The purpose of the study was to hypothesize and test a causal model of continuation in the mathematics study sequence. The causal model hypothesized (a) direct effects from parent attitudes and perceptions to student attitudes, spatial visualization skills, and mathematics achievement; and (b) direct effects from student attitudes, spatial…

This paper examines the sample-free test calibration claim, derived from Rasch's structural model for test items, by comparing item difficulty and log ability estimates between different samples of ability levels. Three tests from the Ball Aptitude Battery--Inductive Reasoning, Paper Folding; and Vocabulary--were administered to three samples of…

This paper introduces anthropologists to simultaneous equation models and to a powerful technique for estimating such models. Characteristically a simultaneous equations model consists of more than one equation and allows for interaction and joint determinancies between some of the variables. Basically these models apply to situations in which one…

This study investigates the extent to which the higher order factors of symbolic and semantic content are differentiated. The main concern is an expository description of the use of confirmatory factor analysis in establishing factorial validity. Reanalyzed data originally collected in 1968 involved a sample of 197 tenth, eleventh and twelfth…

The internal/external (I/E) frame of reference model describes relations among Verbal self-concept (VSC), Math self-concept (MSC), and corresponding achievement scores (VACH, MACH). In support of the model Marsh (1986) found that: (1) VSC and MSC were nearly uncorrelated; (2) the effect of VACH on VSC, and of MACH on MSC, were positive; but (3)…

This paper develops and estimates a model of the educational process. Most researchers have relied on a single equation, educational production function, which is an unrealistic formulation. A pupil's achievement, motivation, expectations, self-concept, and his perceived parents' and teachers' expectations are determined jointly, not…