Observes some children as they went through middle school from two perspectives: as a parent, and as a college mathematics teacher. Contemplates why American children learn so little arithmetic in the middle grades. (ASK)

Introduces some of the basic techniques of cryptography along with examples of how cryptography can be employed in teaching mathematics and used as a cross curricular theme. (Author/ASK)

This article describes the impact of thinking about addition and subtraction facts instead of rotely memorizing them.

Learning mathematics has traditionally been thought of as a sequential progression. Children learn to count to 10, then to 20, and then to 100. They learn to add without regrouping and then with regrouping. The authors teach addition before multiplication and the two-times table before the six-times table. They usually teach division as a separate…

This article proposes an instructional idea where students can figure out an individual's secret personal information using the power of mathematics, particularly the power of algebraic thinking. The proposed examples in this article start with a personalized context that other people do not know and end up with generalized patterns of solutions.…

Algebraic reasoning stands as a formidable gatekeeper for students in their efforts to progress in mathematics and science, and to obtain economic opportunities (Ladson-Billings, 1998; RAND, 2003). Currently, mathematics education research has focused on algebra in order to provide access and opportunities for more students. There is now a growing…

The aim of this series of four articles is to look critically, and in some detail, at the primary strategy approach to written calculation, as set out on pages 5 to 16 of the "Guidance paper" "Calculation." The underlying principle of that approach is that children should use mental methods whenever they are appropriate, whereas for calculations…

This article discusses the difficulties preservice teachers experience when they try to make sense of the standard long-division algorithm, describes a realistic context that we have found productive in helping our students think about why the algorithm works and the role of place value in the algorithm, and suggests the applicability of this…

For boys and girls who are prepared in the essential elements of arithmetic this later book proposes extended instruction in percentage and commercial transactions, and in the elements of geometry. It is one of a series of handbooks for pupils, and consists of progressive lessons, arranged mainly in topics, either reviewing the treatment in…

For boys and girls who are prepared in the essential elements of arithmetic this later book proposes extended instruction in percentage and commercial transactions, and in the elements of geometry. It is one of a series of handbooks for pupils, and consists of progressive lessons, arranged mainly in topics, either reviewing the treatment in…

For boys and girls who are prepared in the essential elements of arithmetic this, the Fifth Book of the Series, proposes additional instruction in concrete measurements, percentage, interest, and commercial matters. This Series purports to be only a systematic arrangement of lessons for children studying the subject. It consists of graded lessons…