There is a growing awareness that many children are not developing fast and accurate retrieval-based strategies for solving single-digit addition problems. In this study we individually assessed 166 third and fourth grade children to identify a group of children (called accurate-min-counters) who frequently solved simple single-digit addition…

This paper provides a set of five indicators of CAS use, which provide a means to analyse a student's written solution to determine whether they used CAS for solving a given problem. These indicators provide a way for researchers and teachers to determine CAS use without requiring classroom observation or the explicit recording of extra…

In this research, we examined how 200 students in seventh grade (around 12 years old) solved simple addition problems. A cluster approach revealed that less than half of the cohort displayed proficiency with simple addition: 35% predominantly used min-counting and were accurate, and 16% frequently made min-counting errors. Students who frequently…

This study explored the potential of a rich assessment task to reveal students' multiplicative thinking in respect to a hypothetical learning trajectory. Thirty pairs of students in grades 5 and 6 attempted the task. Twenty-two pairs applied multiplicative structure to find the number of items in arrays. However counting and computational errors…

Large-scale numeracy assessments are intended to facilitate the improvement of educational outcomes; however, it is not clear exactly how this is to be achieved. To move towards the goal of numeracy for all, it is necessary to systematically address issues that are known to be difficult, pervasive and persistent. This paper includes an analysis of…

A recent international study of pre-service teachers identified that proportional reasoning was problematic for pre-service teachers. Proportional reasoning is an important topic in the middle years of schooling and therefore it is critical that teachers understand this topic and can rely on their Mathematical Content Knowledge (MCK) when…

Counting strategies initially used by young children to perform simple addition are often replaced by more efficient counting strategies, decomposition strategies and rule-based strategies until most answers are encoded in memory and can be directly retrieved. Practice is thought to be the key to developing fluent retrieval of addition facts. This…

An experiment with 67 Australian junior high school students demonstrates that presentation of goal-free 2-move mathematics problems, reducing the use of means-ends analysis, prevents the stage effect (increase in errors at the subgoal stage) from occurring. Implications for enhancing learning are discussed. (SLD)

In contrast with younger children of the same reading age, reading-disabled (RD) children performed poorly when they were required to independently abstract grapheme-phoneme (g-p) rules and use them to pronounce pseudowords. Results suggest a phonologically based productive deficit which interferes with the learning of g-p rules. (RH)

This document contains the fifth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Sac and Zaz:…