A new application of logarithmic differentiation is presented, which provides an alternative elegant proof of two basic rules of differentiation: the product rule and the quotient rule. The proof can intrigue students, help promote their critical thinking and rigorous reasoning and deepen their understanding of previously encountered concepts. The…

Place value underpins much of what people do in number. In this article, the author describes some simple tasks that may be used to assess students' understanding of place value. This set of tasks, the Six Tasks of Place Value (SToPV), takes five minutes to administer and can give direct insight into a student's understanding of the number system…

"Improving Mathematics in the Early Years and Key Stage 1" reviews the best available evidence to offer five recommendations for developing the maths skills of 3-7-year olds. Recommendations include integrating maths into different activities throughout the day -- for example, at registration and snack time -- to familiarise children…

The purpose of this study was to examine the cognitive predictors of calculations and number line estimation with whole numbers and fractions. At-risk 4th-grade students (N = 139) were assessed on 6 domain-general abilities (i.e., working memory, processing speed, concept formation, language, attentive behavior, and nonverbal reasoning) and…

Background: Evidence exists that there are two main underlying cognitive factors in mathematical difficulties: working memory and number sense. It is suggested that real math difficulties appear when both working memory and number sense are weak, here referred to as the double deficit (DD) hypothesis. Aims: The aim of this study was to test the DD…

This study examined the influence of professional development on elementary school teachers' perceptions of and use of an internet-based formative assessment tool focused on students' number sense skills. Data sources include teacher-participants' pre and post survey, open ended response on post survey, use of the assessment tool and their written…

This study evaluated the effects of a mathematics software program, the Building Blocks software suite, on young children's mathematics performance. Participants included 247 Kindergartners from 37 classrooms in 9 schools located in low-income communities. Children within classrooms were randomly assigned to receive 21 weeks of computer-assisted…

This note can be used to illustrate to the student such concepts as periodicity in the complex plane. The basic construction makes use of the Tent function which requires only that the student have some working knowledge of binary arithmetic.

In this article, the author provides results from a 3-year, longitudinal study that examined two novice bilingual teachers' mathematics teaching practices and their professional opportunities to learn to teach. Primary data sources included videotaped mathematics lessons, teacher interviews, and field notes of their teacher preparation methods…

Two-Way Immersion (TWI) programs have demonstrated positive outcomes in students' academic achievement in English, yet less is known about content teaching and learning in the non-English language in these programs. This study uses math instruction as a lens to identify pedagogical strategies and challenges in the teaching of math in Korean to…

This document contains all of the Minnesota kindergarten academic standards in the content areas of Arts, English Language Arts, Mathematics, Science and Social Studies. For each content area there is a short overview followed by a coding diagram of how the standards are organized and displayed. This document is adapted from the official versions…

This Framework builds upon the foundation of the 2010 Massachusetts Curriculum Framework for Mathematics as well as versions of the Massachusetts Mathematics Framework published since 1995. The current Framework incorporates improvements suggested by Massachusetts educators after six years of experience in implementing the 2010 standards in their…

Rational numbers and particularly fractions are difficult for students. It is often claimed that the "natural number bias" underlies erroneous reasoning about rational numbers. This cross-sectional study investigated the natural number bias in first and fifth year secondary school students. Relying on dual process theory assumptions that…

In providing a continued focus on tasks and activities that help to illustrate key ideas embedded in the new Australian Curriculum, the focus in this issue is on Measurement in the Measurement and Geometry strand. The small unit of work on measurement presented in this article has activities that can be modified to meet the requirements of…

The purpose of this study was to identify the use of number sense strategies by pre-service teachers studying at the department of elementary education. Compared to the previous one; new mathematics curriculum places more emphasis on various strategies such as estimation strategies, computational estimation strategies, rounding and mental…