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Berman, Jeanette – Australian Primary Mathematics Classroom, 2011
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…
Descriptors: Comprehension, Grade 3, Number Systems, Number Concepts
Katz, Karin Usadi; Katz, Mikhail G. – Educational Studies in Mathematics, 2010
The view of infinity as a metaphor, a basic premise of modern cognitive theory of embodied knowledge, suggests in particular that there may be alternative ways in which one could formalize mathematical ideas about infinity. We discuss the key ideas about infinitesimals via a proceptual analysis of the meaning of the ellipsis "..." in the real…
Descriptors: Number Systems, Epistemology, Mathematics Education, Evaluation
Gibson, David – Mathematics Teaching, 2011
In the September 2010 issue of "Mathematics Teaching," Tom O'Brien offered practical advice about how to teach addition, subtraction, multiplication, and division and contrasted his point of view with that of H.H. Wu. In this article, the author revisits Tom's examples, drawing on his methodology while, hopefully, simplifying it and giving it…
Descriptors: Opinions, Number Systems, Methods, Teaching Methods
Cheng, Qiang; Wang, Jian – International Journal for Mathematics Teaching and Learning, 2012
As a key concept in early mathematics curriculum, number sense is crucial for children's learning of other mathematics concepts. An earlier curriculum with a strong focus on number sense development presumably helps children perform better in mathematics later on. Chinese students outperformed their United States (U.S.) peers on number sense at…
Descriptors: Mathematics Curriculum, Textbooks, Foreign Countries, Number Concepts
Skoumpourdi, Chrysanthi – European Early Childhood Education Research Journal, 2010
The aim of this paper is to investigate the role that auxiliary means (manipulatives such as cubes and representations such as number line) play for kindergartners in working out mathematical tasks. Our assumption was that manipulatives such as cubes would be used by kindergartners easily and successfully whereas the number line would be used by…
Descriptors: Mathematics Instruction, Problem Solving, Arithmetic, Learning Strategies
Navi, K.; Molahosseini, A. S.; Esmaeildoust, M. – IEEE Transactions on Education, 2011
The residue number system (RNS) has been an important research field in computer arithmetic for many decades, mainly because of its carry-free nature, which can provide high-performance computing architectures with superior delay specifications. Recently, research on RNS has found new directions that have resulted in the introduction of efficient…
Descriptors: Number Systems, Teaching Methods, Computer System Design, Computer Science Education
Murphy, Carol – British Educational Research Journal, 2011
Efforts to meet the needs of children's learning in arithmetic has led to an increased emphasis on the teaching of mental calculation strategies in England. This has included the adoption of didactical tools such as the empty number line (ENL) that was developed as part of the realistic mathematics movement in the Netherlands. It has been claimed…
Descriptors: Mental Computation, Foreign Countries, Arithmetic, Educational Strategies
Skoumpourdi, Chrysanthi – International Journal for Mathematics Teaching and Learning, 2010
The aim of this paper is to investigate the ways in which the number line can function in solving mathematical tasks by first graders (6 year olds). The main research question was whether the number line functioned as an auxiliary means or as an obstacle for these students. Through analysis of the 32 students' answers it appears that the number…
Descriptors: Grade 1, Mathematics Instruction, Problem Solving, Mathematical Applications
Friedlander, Alex – Mathematics Teaching in the Middle School, 2009
Infinity and infinitely small numbers pique the curiosity of middle school students. From a very young age, many students are intrigued, interested, and even fascinated by extremely large or extremely small numbers or quantities. This article describes an activity that takes this curiosity about infinity into the domain of adding the numbers of an…
Descriptors: Numbers, Mathematical Concepts, Grade 5, Arithmetic
Tsao, Yea-Ling; Lin, Yi-Chung – Journal of Case Studies in Education, 2011
The goal of this study was to investigate understanding of inservice elementary school teachers in Taiwan about number sense, teaching strategies of number sense and the development of number sense of students; and the profile of integrating number sense into mathematical instruction , and teaching practice. Data was gathered through interviews of…
Descriptors: Teaching Methods, Educational Practices, Investigations, Elementary School Teachers
Fazio, Lisa; Siegler, Robert – UNESCO International Bureau of Education, 2011
Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…
Descriptors: Class Activities, Learning Activities, Teaching Methods, Numbers
Kallai, Arava Y.; Schunn, Christian D.; Ponting, Andrea L.; Fiez, Julie A. – Society for Research on Educational Effectiveness, 2011
The aim of this study was to test a training program intended to fine-tune the mental representations of double-digit numbers, thus increasing the discriminability of such numbers. The authors' assumption was that increased fluency in math could be achieved by improving the analogic representations of numbers. The study was completed in the…
Descriptors: Experimental Groups, Control Groups, Numbers, Achievement Gains
Louis, Everett; Flores, Alfinio; Sophian, Catherine; Zbiek, Rose Mary – National Council of Teachers of Mathematics, 2010
How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organized around one big idea and supported by…
Descriptors: Number Systems, Mathematical Concepts, Mathematics Instruction, Pedagogical Content Knowledge
Copley, G. N. – Mathematics Teaching, 1972
The meaning of International Standard Book Numbers (ISBN) and the mathematics involved in the use of a check digit to catch errors in number transcription are discussed. (JM)
Descriptors: Arithmetic, Mathematics, Number Systems
Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott – Educational Leadership, 2007
Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…
Descriptors: Number Systems, Word Problems (Mathematics), Arithmetic, Algebra