The professional lexicons of middle school mathematics teachers in communities around the world were documented as part of The International Classroom Lexicon Project. This vocabulary captured teachers' naming of classroom pedagogical practice. Reported in this paper are attributes of the lexicons of teachers from Australia and Chile. A comparison…

Place value is one of the 'big ideas' in number and plays a critical role in helping students develop their number sense, problem solving and computation skills. Yet, the elegant simplicity of our place value system belies the abstract nature of the construct. This paper presents data from 606 Year 3-6 students (ages 8-12) from two metropolitan…

Automatic short answer grading is an important research direction in the exploration of how to use artificial intelligence (AI)-based tools to improve education. Current state-of-the-art approaches use neural language models to create vectorized representations of students responses, followed by classifiers to predict the score. However, these…

In this paper, the SOLO taxonomy is used to identify different levels of student understanding of the statistical concepts associated with sampling distribution. This study was part of a research project investigating students' conceptual understanding of concepts of hypothesis testing taught with the support of simulation learning activities. The…

Learning objectives, especially those well defined by applying Bloom's taxonomy for Cognitive Objectives, have been widely recognized as important in various teaching and learning practices. However, many educators have difficulties developing learning objectives appropriate to the levels in Bloom's taxonomy, as they need to consider the…

Supporting students of all levels to move beyond empirical arguments, which employ example based reasoning to endorse universal truths and are thus mathematically invalid, remains a challenging goal in mathematics education. Arguments that make use of generic examples are both mathematically valid and accessible for even young learners. However,…

Maslow's hierarchical needs theory has a unique approach to classifying human needs into five different levels. Some researchers agree that Maslow's need theory followed a "low-high" order and that there is a dominance level for five needs in a hierarchical structure. At the same time, some researchers argue that Maslow's needs are…

This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…

Describing and measuring instructional quality of mathematics lessons is a common goal amongst mathematics education researchers. Such work takes several forms such as classifying and coding instructional moves and student activity or providing high-level rubric-based scores in relation to categories. In this work, we share an innovative mixed…

In this paper, we present the development of an investigation on the promotion of covariational reasoning in high school students (14-15 years old) in Mexico. The study consists of designing and applying a sequence of didactic activities that simulate a real situation virtually. The activities are organized through a Hypothetical Learning…

Despite the unquestionable academic interest on corpus-based approaches to language education, the use of corpora by teachers in their everyday practice is still not very widespread. One way to promote usage of corpora in language teaching is by making pedagogically appropriate corpora, labelled with different types of problems (for instance,…

This paper uses the commognitive framework to analyse how a group of four primary school students classify odd and even numbers. The findings show how students' reasoning is grounded in their personal uses of "odd" and "even". The students attend to different features of "oddness" and "evenness" and agree on…

Knowledge components (KCs) have many applications. In computing education, knowing the demonstration of specific KCs has been challenging. This paper introduces an entirely data-driven approach for: (1) discovering KCs; and (2) demonstrating KCs, using students' actual code submissions. Our system is based on two expected properties of KCs: (1)…

Some children experience more difficulty than others becoming literate, often at great emotional, intellectual, social, and economic cost to themselves, but also to those who love and care for them, and for society at large. The causes of those difficulties and what to do about them have been the source of much research and sometimes heated…

Creativity is a dynamic process which generates ideas that are both novel and of value. However there is little understanding in what drives creativity in students and how to help teachers or education experts to detect creative thinking. This paper begins to address this gap by providing a platform and experiments for studying how creative…