Changing the Order of Factors Does Not Change the Product but Does Affect Students’ Answers, Especially Girls’ Answers

Clelia Cascella,Chiara Giberti,Giorgio Bolondi

doi:10.3390/educsci11050201

Clelia Cascella, Chiara Giberti + Show 1 more

Open Access

https://doi.org/10.3390/educsci11050201

Copy DOI

Abstract

This study is aimed at exploring how different formulations of the same mathematical item may influence students’ answers, and whether or not boys and girls are equally affected by differences in presentation. An experimental design was employed: the same stem-items (i.e., items with the same mathematical content and question intent) were formulated differently and administered to a probability sample of 1647 students (grade 8). All the achievement tests were anchored via a set of common items. Students’ answers, equated and then analysed using the Rasch model, confirmed that different formulations affect students’ performances and thus the psychometric functionality of items, with discernible differences according to gender. In particular, we explored students’ sensitivity to the effect of a typical misconception about multiplication with decimal numbers (often called “multiplication makes bigger”) and tested the hypothesis that girls are more prone than boys to be negatively affected by misconception.

Highlights

Differences in mathematical performance between boys and girls have received increasing attention over the years
In contrast to most of the current literature based on gender differences displayed over the entire test, as previously recommended, for example, by [14], we explored gender differences at item level, i.e., comparing the probability of encountering each item successfully by boys and girls matched on ability, via Rasch differential item functioning analysis (DIF)
We focus on the misconception related to decimal numbers, according to which the result of a multiplication is always bigger than factors multiplied

Summary

Introduction

Differences in mathematical performance between boys and girls have received increasing attention over the years. Most of the research studies carried out on this topic have used national or international large-scale assessment results and have operationalised gender differences as a reason behind the gap in mathematics test scores observed in relation to the entire test (e.g., [2,3,4,5]) This perspective merely glances at gender differences, providing a snapshot of the gap between genders at some point or relating gender differences to other factors such as background and metacognitive aspects but failing to provide didactic information about the nature of these differences (differences that usually disadvantage girls more than boys), or explaining whether these differences are typically related to just some items or may concern all the test items. Part of the literature explores gender differences in relation to specific sub-domains of mathematical ability (for example, arguing that boys outperform girls in spatial ability and, more generally, in geometry items; e.g., [6,7]), other works at item level find a correlation between item difficulty and gender differences (e.g., [8,9]), and, some studies examine the influence of item type in relation to gender

Objectives

Methods

Results

Conclusion