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…

Prompting people to estimate climate change numbers before showing them the true value can shift learners' attitudes and conceptions. Yet, interventions created for such a learning experience are not easily accessible to the general public. The purpose of this preregistered study was to address this research gap by developing and testing an openly…

The purpose of the present study was to investigate how inclusion of computational creativity exercises (CCE) based on Epstein's Generativity Theory (1996, 2005; Epstein, Schmidt, & Warel, 2008) in post-secondary computer science [CS] courses affected students' class grades, learning of computational thinking and CS knowledge, self-efficacy,…

Learning curves have proven to be a useful tool for understanding how a student learns a given skill as they progress through a curriculum. A learning curve for a given Knowledge Component (KC) is a plot of some measure of competence as a function of the number of opportunities the student has had to apply that KC. Consider the case where each…

Student modeling can help guide the behavior of a cognitive tutor system and provide insight to researchers on understanding how students learn. In this context, Bayesian Knowledge Tracing (BKT) is one of the most popular knowledge inference models due to its predictive accuracy, interpretability and ability to infer student knowledge. However,…

This paper compares the counting and whole number knowledge and skills of primary school children in Australia and Germany at the end of Grade 1 and Grade 2. Children's learning was assessed using the Early Numeracy Interview and associated Growth Point Framework. The findings highlight substantial differences between the two groups that vary for…

This paper proposes to use communalism, an asset-driven strategy effective with Black learners, with racially mixed study groups. This study found that students who studied in racially mixed groups performed better when told that individuals would receive a reward for scoring the highest in their group. Also, the White students' perceptions of how…

"Let's Count" is an early mathematics program that has been designed by The Smith Family and the authors to assist educators in early childhood contexts in socially disadvantaged areas of Australia to work in partnership with parents and other family members to promote positive mathematical experiences for young children (3-5 years). A…

Pat was a 19-year-old attending a Special School for the Intellectually Disabled in Indonesia. She was interviewed by the first author regarding her mental calculation strategies when solving 1- and 2-digit addition and subtraction problems. Results indicate that she was able to see ten as a unit composed of ten ones and was facile in using…

The introduction of the "Early Years Learning Framework and the Australian Curriculum-Mathematics" in Australian preschools and primary schools has caused early childhood educators to reconsider what may be appropriate levels of mathematics knowledge to expect from children as they start school. This paper reports on initial data from an…

The "Extending Mathematical Understanding" (EMU) Program is a specialised mathematics program that aims to accelerate the learning of Grade 1 students who struggle with learning school mathematics. Forty-two students participated in an EMU Program in 2010 as part of the "Bridging the Numeracy Gap" (BTNG) project. Analysis of…

In this article we describe the results of a special final course, at the main teachers' college in Mexico, which had two related main objectives: one was to find out the Mathematical Knowledge for Teaching (MKT) held by student teachers (ST) at the end of their instructional preparation. The other was to discern ways to improve this knowledge and…

A fundamental goal of educational research is identifying students' current stage of skill mastery (complete/partial/none). In recent years a number of cognitive diagnosis models have become a popular means of estimating student skill knowledge. However, these models become difficult to estimate as the number of students, items, and skills grows.…

Student modeling is a widely used approach to make inference about a student's attributes like knowledge, learning, etc. If we wish to use these models to analyze and better understand student learning there are two problems. First, a model's ability to predict student performance is at best weakly related to the accuracy of any one of its…

Students in a college introductory statistics class were evaluated with conceptual and computational tests and the relationship between their levels of knowledge on the two forms of testing was assessed. There were significant correlations between their abilities to perform computations and to answer more conceptual questions on individual tests…