This position paper examines the phenomenon of the McNamara Fallacy to analyse flawed conceptions of "success" in mathematics learning, normalised assessment structures and their implications for mathematics education. The established presence of the McNamara Fallacy and the ramifications of this statistical fallacy provide a foundation…

The National Council of Teachers of Mathematics (NCTM), has made an effort to increase the use of technology and the use of calculators into the classroom and curriculum. As a result, many studies and articles have been written on the subject of calculator use in the classroom. A review of over 600 studies revealed that it is not curricula that…

Research Question: This paper examines the overarching question of to what extent different analytic choices may influence the inference about country-specific cross-sectional and trend estimates in international large-scale assessments. We take data from the assessment of PISA mathematics proficiency from the four rounds from 2003 to 2012 as a…

Wollack et al. (2015) suggested the erasure detection index (EDI) for detecting fraudulent erasures for individual examinees. Wollack and Eckerly (2017) and Sinharay (2018) extended the index of Wollack et al. (2015) to suggest three EDIs for detecting fraudulent erasures at the aggregate or group level. This article follows up on the research of…

This longitudinal study examined the influence of prekindergarten teacher characteristics and classroom instructional processes during mathematical activities on the growth of mathematics learning scores in prekindergarten, kindergarten, and first grade. Participants attended state-funded and Head Start prekindergarten programs. Mathematical…

In this article, the authors applied profile analysis to Maths exam data to demonstrate how different exam forms, differing in difficulty and length, can be reported and easily interpreted. The results were presented for different groups of participants and for different institutions in different Maths domains by evaluating the balance. Some…

Students must leave elementary school with a firm understanding of fractions and decimals in order to make satisfactory progress in advanced mathematics. Firm understanding includes manipulation of rational numbers using different models of representation such as area and length. Research has demonstrated that a graduated sequence such as…

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

Objective: Remedial mathematics courses are widely considered a barrier to student success in community college, and there has been a significant amount of work recently to reform them. Yet, there is little research that explicitly examines whether increasing learning in remedial classes improves grades or completion rates. This study examines the…

This dissertation aims to investigate the effect size measures of differential item functioning (DIF) detection in the context of cognitive diagnostic models (CDMs). A variety of DIF detection techniques have been developed in the context of CDMs. However, most of the DIF detection procedures focus on the null hypothesis significance test. Few…

This study investigated the effect of van Hiele Phase-based Instruction (VHPI) on Ghanaian Pre-service Teachers' (PTs') geometric thinking in terms of the van Hiele Levels. A pre-test post-test quasi-experimental design was employed. There were 75 PTs each in the experimental group and the control group. Van Hiele Geometry Test (VHGT) was…

This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…

Many studies have argued the negative effects of external rewards on internal motivation while others assert that external motivation does not necessarily undermine intrinsic motivation. At a private university, students were given the option to earn bonus points for achieving mastery in the online homework systems associated with Statistics and…

This study investigated the effectiveness of statistical adjustments applied to rater bias in many-facet Rasch analysis. Some changes were first made in the dataset that did not include "rater × examinee" bias to cause to have "rater × examinee" bias. Later, bias adjustment was applied to rater bias included in the data file,…

The National Senior Certificate (NSC) examination in South Africa is a standardised assessment whose main function is to determine whether Grade 12 learners have mastered subject knowledge at the culmination of their secondary education. Alongside this, the National Benchmark Test Project (NBTP) was introduced to develop the National Benchmark…