Background: Valid assessment of the understanding of Newton's mechanics is highly relevant to both physics classrooms and research. Several tests have been developed. What remains missing, however, is an efficient and fair test of conceptual understanding that is adapted to the content taught to secondary school students and that can be validly…

The relationship between mathematical creativity (MC) and mathematical problem-solving performance (MP) has often been studied but the causal relation between these two constructs has yet to be clearly reported. The main purpose of this study was to define the causal relationship between MC and MP. Data from a representative sample of 480…

This paper concerns communities of learners and teachers that are formed, develop and interact in university mathematics environments through the theoretical lens of "Communities of Practice." From this perspective, learning is described as a process of participation and reification in a community in which individuals belong and form…

In this study, we developed an instrument for assessing teachers' mathematics content knowledge (MCK) on ratio and proportion and examined the profile of Indonesian primary teacher's MCK on this topic. The MCK items were administered to 271 Indonesian in-service primary teachers with a variety of educational backgrounds and teaching experiences.…

This study examines students' procedural and conceptual achievement in fraction addition in England and Taiwan. A total of 1209 participants (561 British students and 648 Taiwanese students) at ages 12 and 13 were recruited from England and Taiwan to take part in the study. A quantitative design by means of a self-designed written test is adopted…

In this work we explored proof schemes used by 41 middle school students when confronted with four mathematical propositions that demanded verification of accuracy of statements. The students' perception of mathematically complete vs. convincing arguments in different mathematics branches was also elicited. Lastly, we considered whether the…

A reverse engineering approach to automatic item generation (AIG) was applied to a figure-based publicly released test item from the Organisation for Economic Cooperation and Development (OECD) Programme for International Student Assessment (PISA) mathematical literacy cognitive instrument as part of a proof of concept. The author created an item…

This study was conducted with 93 freshmen and 82 senior prospective mathematicians and mathematics teachers in order to investigate how they construct and evaluate proofs and whether there are any significant differences in their proof construction (with respect to department and grade) and proof evaluation (with respect to department)…

A method called the Remainder Method is proposed for the calculation of sample quantiles of a given order, for example, quartiles, hexatiles, octatiles, deciles and percentiles assuming that all the observations are distinct. Proof is given for a special case of deciles. The criterion "equisegmentation" is proposed, namely that the number of…

It is believed by some that most tests are multidimensional, meaning that they measure more than one underlying construct. The primary objective of this study is to illustrate how variations in the secondary ability distribution affect the statistical detection of dimensionality and to demonstrate the difference between substantive and statistical…

The usual formula for variance depending on rounding off the sample mean lacks precision, especially when computer programs are used for the calculation. The well-known simplification of the total sums of squares does not always give benefit. Since the variance of two observations is easily calculated without the use of a sample mean, and the…

The suppressor variable, a variable wholly uncorrelated with a criterion, but which nevertheless improves prediction because of its relationship with a predictor, is critically examined. For a suppressor so defined, formal identities are shown with part, partial, and multiple correlational procedures. It is demonstrated that if maximum prediction…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) Improving Decimal Number Conception by Transfer from Fractions to Decimals (Irita Peled and Juhaina Awawdy Shahbari); (2) The Development of Student Teachers' Efficacy Beliefs in Mathematics during…