This study explores, from both constructivist and cognitive perspectives, teacher guidance in student-centered classrooms when addressing a common learning difficulty with equivalent fractions--lines or pieces--based on number line models. Findings from three contrasting cases reveal differences in teachers' facilitating and direct guidance…

Studies reveal that students as well as teachers have difficulties in understanding and learning of decimals. The purpose of this study is to investigate students' as well as pre-service teachers' solution strategies when solving a question that involves an estimation task for the value of a decimal number on the number line. We also examined the…

This research was designed to investigate the conceptualisations and thinking strategies Indigenous Australian students use in counting tasks. Eighteen Aboriginal students, in years 1 to 11 at a remote community school, were interviewed using standard counting tasks and a "counting" task that involved fetching "maku" (witchetty…

Early number sense is a strong predictor of later success in school mathematics. A disproportionate number of children from low-income families come to first grade with weak number competencies, leaving them at risk for a cycle of failure. The present study examined the effects of an 8-week number sense intervention to develop number competencies…

Teachers and researchers have known for decades that the use of storybooks can have a positive impact on students' experiences with mathematics. This article describes how first graders in an urban public school actively engage with mathematics by using the story "Bean Thirteen" as a context for developing number sense. This…

Mrs. Fisher's class was learning about arithmetic functions by pretending to operate real-world "function machines" (Reeves 2006). Functions are a unifying mathematics topic, and a great deal of emphasis is placed on understanding them in prekindergarten through grade 12 (Kilpatrick and Izsák 2008). In its Algebra Content Standard, the…

This article outlines the author's efforts to build her knowledge of students' understandings of mathematics whilst catering for different abilities within a Year 1 classroom, using the freely available "Assessment for Common Misunderstandings tools." "The Assessment for Common Misunderstandings" materials have been…

Math relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across…

This study explores the effects of counting objects and reciting numbers in preschool on 1st-grade math performance. Data on 3,125 low-income preschoolers' (4-to 5-year-olds) counting abilities (orally reciting numerals in chronological order and counting blocks) were collected during a fall session (between September 15 and December 15) and were…

The study aimed to investigate students' conceptions on the notion of absolute value and their abilities in applying the specific notion in routine and non-routine situations. A questionnaire was constructed and administered to 17-year-old students. Data were analysed using the hierarchical clustering of variables and the implicative method, while…

Knowing number facts up to 10 become crucial if we want students to solve addition and subtraction problems using more abbreviated strategies. Otherwise, students will keep counting one-by-one until they get an answer. One of important number facts is number pairs that make ten because it is an important "benchmark" that students will…

When asked to "find three forks", adult speakers of English use the noun "fork" to identify units for counting. However, when number words (e.g. "three") and quantifiers (e.g. "more", "every") are used with unfamiliar words ("Give me three blickets") noun-specific conceptual criteria are unavailable for picking out units. This poses a problem for…

This article deals with a short history of mathematics and mathematical scientists during the ancient and medieval periods. Included are some major developments of the ancient, Indian, Arabic, Egyptian, Greek and medieval mathematics and their significant impact on the Renaissance mathematics. Special attention is given to many results, theorems,…

The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the…

Lorna Quinnell and Merrilyn Carter examine the use of symbols in teaching mathematics and outline the difficulties students experience in "reading symbols and abbreviations." We are sure teachers will appreciate the way the authors have examined the use of symbols and abbreviations in NAPLAN testing and organized them into five distinct…