Discussed is how the concept of equivalence can relate various segments of a mathematics program and help students develop an appreciation of the unity of mathematics. Activities and examples of equivalence at all grade levels are included. (KR)

Presented is an activity that explores the relationship between the size of a rectangle and the number of squares intersected by a diagonal. Students incorporate pattern recognition and the concept of the greatest common divisor in solving the problem. A sample worksheet is provided. (MDH)

Children's (n=70) solution strategies to a variety of multiplication and division word problems were analyzed to determine performance levels and strategies used. Solution strategies were classified at three levels: direct modeling with counting; no direct modeling with counting, additive, or subtractive strategies; and use of known derived facts.…

Describes four activities to develop visualization skills and the concept of dimensionality in which students (1) visualize transforming figures between the second and third dimensions; (2) identify the three-dimensional objects from their two-dimensional projections; (3) conjecture about the vertices, edges, and faces of zero- to four-dimensional…

Ontario's elementary and secondary school mathematics curriculum was implemented in Fall 2000 having been revised according to the key principles of the social-constructivist view of mathematics education. This change in pedagogy has implications for teaching and learning mathematics, the use of technology and the emphasis in problem-solving. In…

This article addresses some important issues in mathematics instruction at the middle and secondary levels, including the structuring of a district's mathematics program; the choice of textbooks and use of calculators in the classroom; the need for more rigorous lesson planning practices; and the dangers of teaching to standardized tests rather…

One of the most hotly contested issues in mathematics education today is the use of calculators in elementary schools. The National Council of Teachers of Mathematics (NCTM) has gone on record recommending the use of calculators in the earliest grades. NCTM's recommendation that calculators be introduced under the guidance of skilled teachers is…

"Everyday Mathematics," published by Wright Group/McGraw-Hill, is a core curriculum for students in kindergarten through grade 6 covering numeration and order, operations, functions and sequences, data and chance, algebra, geometry and spatial sense, measures and measurement, reference frames, and patterns. At each grade level, the…

Recognizing and responding to students' thinking is essential in teaching mathematics, especially when students provide incorrect solutions. This study examined, through a teaching scenario task, elementary preservice teachers' interpretations of and responses to a student's work on a task involving reflective symmetry. Findings revealed that a…

This article offers a personal vision and conceptual design for reimagining specialized science, technology, engineering, and mathematics (STEM) academies designed to nurture "decidedly different" STEM minds and ignite a new generation of global STEM talent, innovation, and entrepreneurial leadership. This design enables students to engage…

The current study investigated the discreet task completion hypothesis presented by C. H. Skinner (2002) by investigating how the rate of interspersing affects performance on and preferences for academic assignments. Specifically, 70 sixth-, seventh-, and eighth-grade students were presented with four assignment pairs of multiplication problems.…

In this article, the authors describe a varied day of stimulating mathematics with key stage 2 learners--all revolving around chocolate. They used a variety of stimuli organized around the chocolate theme. A whole day was spent on using and applying mathematics, and the exercise proved to be enjoyable for both staff and pupils. The children…

Everyone knows that teachers do not have unlimited time, a log of experience, or a deep understanding of all the mathematics they teach. To solve this problem, teachers often use textbooks, and the accompanying teacher's resource books, as sources of activities and advice about how to help students learn mathematics. The activity that prompted…

Multiplication, division and fractions are "hotspots" for students in the middle years with many students experiencing difficulty with these concepts. Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts. In this article the authors show how an open-ended array problem…

This article describes a professional development course intended to improve the content understanding of middle school mathematics teachers. The design of the course included three professional learning strategies: problem solving, examination of student thinking, and discussion of research. The concepts studied in the course included multi-digit…