Background: The ability to translate concrete manipulatives into abstract mathematical formulas can aid in the solving of mathematical word problems among students, and metacognitive prompts play a significant role in enhancing this process. Aims: Based on the concept of semantic congruence, we explored the effects of metacognitive prompts and…

Recently, Lima lamented on the 'time-consuming and tiresome' pedagogical nature of repeated integration by parts, throwing down the challenge of providing a pencil-and-paper solution to a related problem in a few seconds. Lima put forth a simple formula as an alternative. In this work, I offer a response to Lima's challenge and his formula.…

This work is part of an investigation conducted in Italy, which aims to explore the effects of instruction on secondary school students' combinatorial reasoning. We gave a questionnaire adapted from Navarro-Pelayo's research to two groups of students with and without instruction on combinatorics in order to analyse the students' performances and…

STACK is an online testing system that can automatically assess mathematical formulae. When working with STACK on a smartphone, inputting mathematical formulae is time-consuming; therefore, to solve this problem a mathematical formula input interface for smartphones has been developed based on the flick operation. However, since the time of…

Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of…

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

Prior research suggests that introductory physics students have difficulty with graphing and interpreting graphs. Here, we discuss an investigation of student difficulties in translating between mathematical and graphical representations for a problem in electrostatics and the effect of increasing levels of scaffolding on students'…

The aim of the research is to examine the perspectives of teachers and preservice teachers in regard with models, mathematical models and mathematical modelling process in different variables terms and to compare them. In this research that is having quantitative research design survey method, which is one of the descriptive research technic,…

Aim of the study: This study examines numerical methods for solving the problems in gas dynamics, which are based on an exact or approximate solution to the problem of breakdown of an arbitrary discontinuity (the Riemann problem). Results: Comparative analysis of finite difference schemes for the Euler equations integration is conducted on the…

This study examined the effectiveness of 3 curriculum interventions focused on strengthening children's ability to solve area measurement problems and explored the instructional perspectives of the instructor who implemented the interventions. The interventions involved various degrees of emphasis on area measurement and knowledge of 2-dimensional…

This report describes the pilot conducted in the final phase of a project, Expanding Audio Access to Mathematics Expressions by Students With Visual Impairments via MathML, to provide easy-to-use tools for authoring and rendering secondary-school algebra-level math expressions in synthesized speech that is useful for students with blindness or low…

In this study we attempted to highlight the pedagogical role of activities to familiarize pre-schoolers with the measurement processes of container capacity. The sample of the study consisted of 20 subjects aged five-six, all coming from two Greek state kindergartens of the same area, bearing the same middle socioeconomic background. The research…

Many researchers, including Buriel (EJ 187 987), incorrectly compared the results in each study with null hypotheses of zero differences between means or zero population correlations. Instead, a test of difference between the mean differences in the two samples or the direct comparison of the two sample correlations is required. (Author/CP)

This study used species diversity indices developed in ecology as a measure of socioethnic diversity, and compared them to Coleman's Index of Segregation. The twelve indices were Simpson's Concentration Index ("ell"), Simpson's Index of Diversity, Hurlbert's Probability of Interspecific Encounter (PIE), Simpson's Probability of…

The communication of research findings among collegiate institutional researchers is considered in relation to the contribution of qualitative language in general, and catastrophe theory in particular. The qualitative language of catastrophe theory may help reduce the arbitrariness of description, through identification of qualitative features…