The adverse influence of the presence of an irrelevant number and language inconsistency in a word problem is well known. Our study focused on the combination of these two variables and on the position of the irrelevant number in the word problem for Grade 6 pupils. The study has a mixed design. Item Response Theory was used to make equally able…

Improving children's "number sense" has been a core component of recent mathematics curricular and instructional reforms (CCSS, 2010; NCTM, 2000, 2014) in the United States. Students with mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient…

Australia has a National Numeracy Learning Progression (NNLP) that is strongly aligned with the Australian Curriculum: Mathematics. This article examines how a sub-element within this progression could be impacting students' learning of Science. This sub-element is firmly based on Mathematics education research as to how students build their…

Numeracy has increasingly become a topic of importance and concern in our contemporary society. Student success in numeracy is influenced by the positive attitudes and values they hold about mathematics. This outreach project sought to foster the development of such attitudes and values through the design, implementation, and evaluation of a…

The efficacy of a research-based fraction sense intervention for sixth graders with or at risk for mathematics difficulties (N = 52) was examined. The intervention aimed to build understanding of fraction magnitudes on the number line. Key concepts were taught with a narrow range of denominators to develop deep understanding. The intervention was…

International research suggests that early mathematical competence predicts later mathematical achievement. In this article, we explore the relationship between mathematical competencies at 4-5 years, as measured by teacher ratings, and later results on Years 3, 5, 7 and 9 "National Assessment Program -- Literacy and Numeracy" (NAPLAN)…

We administered specially-designed, free-response mathematics tasks to primary students (N = 583, ages five to 12 years old). Our focus was on whether (i) the children's responses could be reliably assessed, and (ii) the responses could provide insights into children's mathematical thinking. We used a contemporary comparative judgement technique,…

The efficacy of a research-based fraction sense intervention for sixth graders with or at risk for mathematics difficulties (N = 52) was examined. The intervention aimed to build understanding of fraction magnitudes on the number line. Key concepts were taught with a narrow range of denominators to develop deep understanding. The intervention was…

Teachers report that engaging students in solving contextual problems is an important part of supporting student understanding of algorithms for fraction division. Meaning for whole-number operations is a crucial part of making sense of contextual problems involving rational numbers. The authors present a developed instructional sequence to…

Some people recognize a palindrome when they see one, however fewer realize that a palindrome is a special case of a pattern and that these patterns are all around. Palindromes frequently occur in names, both of vehicles and people, and in music. The traditional mathematical curriculum has often left palindromes out of the common vernacular. Where…

Troy Thomas and Lynda Wiest share an engaging lesson on statistics involving analysis of real-world data on the top ten video game sales in the United States during a one-week period. Three upper-primary classes completed the lesson, providing insight into the lesson's effectiveness. The lesson description includes attention to the manner in which…

The study sought out to extend our knowledge regarding the origin of mathematical learning disabilities (MLD) in children by testing different hypotheses in the same samples of children. Different aspects of cognitive functions and number processing were assessed in fifth- and sixth-graders (11-13 years old) with MLD and compared to controls. The…

"Make It Count" was a large scale, government-funded, project aimed at improving the mathematics learning of Indigenous students. NAPLAN Numeracy test results were used as one measure of the effect of the program. In this paper we report on the performance on these tests of Indigenous students in schools involved in the project. Group…

Developing proficiency in algebra is the focus of instruction in high school mathematics courses and is a minimum expectation for high school completion for all students including those with learning difficulties. However, the foundation for success is laid in grades 4-8 (aged 9-14). In this paper, we assert that students' development of algebraic…

Mathematics education is replete with activities that explore real-world problems. A variety of these problems are added to lessons in the belief that merely applying mathematics knowledge to everyday contexts will enhance the transfer of that knowledge to other settings. However, these contexts are hypothetical rather than authentic. This…