In this speech on "The Future is Related to the Past", the parameters for mathematics education as determined by future society and by education systems are discussed, and implications for the learning of mathematics are considered. Responsibilities of mathematics educators are detailed. (DT)

Directions are given for the mechanical construction of hyperbolas, ellipses, conchoids, and lemniscates. (DT)

Introducing variety into the high school mathematics classroom by using activity units and small groups work is discussed. (DT)

A curriculum organization is described whereby 60 percent of the course time is spent on a prescribed syllabus of core topics and 40 percent of the time is for enrichment topics of the teacher's (or students') choice. Advantages of this type of organization and problems that teachers experience are discussed. (DT)

The rationale for using a camping situation in which children learn and do mathematics is discussed. (DT)

A number of outdoor practical activities involving measurement and shape are given. (DT)

Methods of guiding students in project-type activities that help to develop reading skills in mathematics (especially in the use of text and references materials) are suggested. (DT)

Brief descriptions of serious learning disorders which apply to mathematics are given. (DT)

Questions which stimulate discovery learning are asked concerning polygons and curves drawn on an integral lattice. (DT)

The long division algorithm approached as repeated subtractions is explained. (DT)

Early calculating methods and devices are discussed. These include finger products, the abacus, ancient multiplication algorithms, Napier's bones, and monograms. (MP)

A model of influences on curriculum is presented as an attempt to explain why changes to the curriculum in mathematics came about. The continuing revolution in mathematics in schools is also discussed. (MP)

The most significant feature of this program is the sorting of students into small groups managed by student teachers. This serves the purpose of teacher education as well as student remediation. (MP)

Five graded sets of examples of alphametrics are provided. The puzzles are suggested for use in developing the traits of considering all possibilities and systematic working. (MP)

The decline in enrollment in mathematics courses at universities is used as evidence of the increasing irrelevance of the mathematics done and taught at that level. (MP)