It is increasingly recognised that to be informed citizens and to participate fully in the workforce requires an understanding of statistical data and risk. Such understanding is underpinned by statistical reasoning. It has been shown, however, that students have difficulty moving from concrete representations and procedural mathematical…

Progressing from additive to multiplicative thinking is a key outcome of school mathematics, making ratios an essential topic of study in junior secondary. In this study, 15 Australian Year 8 students were administered a ratio test followed by semi-structured interviews to explore their conceptions of ratio prior to formal instruction. In this…

Making connections within and between different aspects of mathematics is recognised as fundamental to learning mathematics with understanding. However, exactly what these connections are and how they serve the goal of learning mathematics is rarely made explicit in curriculum documents with the result that mathematics tends to be presented as a…

Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

Learn the most effective ways to teach elementary math, no matter how much experience you have with the subject. In this book, Fuchang Liu takes you through many common mistakes in math instruction and explains the misunderstandings behind them. He points out practices that should be avoided, helping you to adjust your lessons so that all students…

Here is the only reference book you will ever need for teaching primary school mathematics and statistics. It is full of exciting and engaging snapshots of excellent classroom practice relevant to "The New Zealand Curriculum" and national mathematics standards. There are many fascinating examples of investigative learning experiences,…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

Investigates the standard rounding rule for multiplication and division including its derivation from a basic assumption. Uses Monte-Carlo simulations to show that this rule predicts the minimum number of significant digits needed to preserve precision only 46.4% of the time and leads to a loss in precision 53.5% of time. Suggests an alternative…

Presented are several variations of a multiplication game which develops probability and statistical concepts while it reinforces students' arithmetic skills. (JP)

Presents a dice game that students can use as a basis for exploring mathematical probabilities and making decisions while they also exercise skills in multiplication, pattern identification, proportional thinking, and communication. (ASK)

Utilizing word problems relevant to the data processing field, this workbook presents a concept-oriented approach to competency development in ten areas of basic mathematics: (1) the expression of numbers as figures and words; (2) the multiplication, addition, and division of whole numbers, fractions, and decimals; (3) ratios and proportions; (4)…

Through the use of word problems relevant to the field of office occupations education, this workbook presents a concept-oriented approach to competency development in ten areas of basic mathematics: (1) the expression of numbers as figures and words; (2) the addition, subtraction, multiplication, and division of whole numbers, fractions, and…

Utilizing word problems relevant to automotive mechanics, this workbook presents a concept-oriented approach to competency development in 13 areas of basic mathematics: (1) the expression of numbers as figures and words; (2) the addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals; (3) scientific notation;…

Research Ideas for the Classroom is a three-volume series of research interpretations for early childhood, middle grades, and high school mathematics classrooms. Each volume looks at research from the perspective of the learner, the content, and the teacher, and chapters are co-authored by a researcher and a teacher. Chapter titles in the middle…