Some reasons why simple ideas in projective geometry should have a place in the elementary school curriculum are suggested. Then, seven lessons on projective geometry that were taught to a class of 10-year-olds are described. (MNS)

A sample lesson is given in which students apply mathematics on a hypothetical trip. (MK)

Research on effective teaching is described. Comparisons of expert and novice teachers reveal a profile of expertise in elementary mathematics instruction. How lessons are planned and presented is discussed. (MNS)

Five reasons why graph work is effective are given, followed by suggestions for making bar, picto-, and line graphs. (MS)

Suggested is a format for sequencing instructional activities during the typical elementary school mathematics period to elicit better teaching and more learning. To illustrate each component of the format, a lesson on fractions appropriate for fourth or fifth grade is outlined. (CW)

The following five steps are designed to help teach a directed mathematics lesson: (1) introducing, (2) presenting, (3) analyzing, (4) practicing, and (5) applying. It is noted that teaching a directed lesson means to help students master specific mathematical skills, as well as to formulate concepts and understand principles. (MP)

The relationship in the Pythagorean Theorem is introduced to low-ability seventh graders using Cuisenaire rods. The sequence of instruction is described. (MNS)

A 12-lesson course using a microcomputer with second graders was developed by a parent and a teacher. In addition to the course outline, specific suggestions for conducting the course are given. (MNS)

A teaching sequence for the division algorithm is detailed. (MP)

Manipulative materials designed to instruct pupils on fractions are presented. The use of unit holders in teaching fundamental concepts of fractions and equivalent fractions are reviewed. (MP)

The use of silent instruction as a tool to present mathematics to young elementary school students is reviewed. (MP)

A lesson using Logo was found to be effective when working with concepts of division. It emphasizes relationships between arithmetic and geometry in a novel way, and has been used with students in grades two and four. (MNS)

A useful approach for developing insights and discovering patterns is to examine numbers in relation to the number of their divisors. A teaching procedure for this approach is presented, with questions, answers, and homework suggestions. (MNS)

Activities are presented to give students a picture of decimal concepts of tenths and hundredths. Three models (linear, regional, and value) are described, followed by four activities. (MNS)

A plan used successfully in the classroom to introduce pupils in grades one through six to calculators is outlined. It comprises a sequence of activities designed to help teachers have a good start when they take the first steps introducing calculators to students. (MP)