This learning module provides students with practice in applying mathematical operations to vocational agriculture. The module consists of unit objectives, definitions, information, problems to solve, worksheets suitable for various levels of vocational agriculture instruction, and answer keys for the problems and worksheets. This module, which…

Almost all experimental investigations on concepts of time (T), distance (D) and velocity (V) since 1946 have been based on the Piagetian theory. However, there are several controversial points in Piaget's investigations. In the experiment described in this paper, developmental changes of concepts concerning relation of T, D, and V were examined…

This document consists of eleven bulletins which present answers to questions about research on the teaching and content of elementary school mathematics, K-8. The bulletins are revisions of a set originally published in 1970 and revised in 1975. Specific research findings on eleven topics are cited with selected references. Titles are: (1)…

This monograph concerns the geometry curriculum as it should be in an effective and complete mathematics program in grades K-9. The first section makes an impelling argument for teaching substantial amounts of geometry in grades K-9: for practical life skills, for developing number and measurement concepts, for problem-solving experiences, for…

This preapprenticeship preparation curriculum consists of 13 learning modules. Covered in the modules are the following: the nature and scope of apprenticeships, a pretest to assess students' mathematical skills, the General Aptitude Test Battery, interviews for an apprenticeship program, whole numbers, common fractions, decimal fractions,…

The purpose of this booklet is to explain examination registration procedures and to introduce the Psychometric Entrance Examination so that students will know what to expect, what types of questions they will be asked, and how they will be expected to answer. The aim of the examination is to evaluate a variety of cognitive abilities: verbal,…

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…

This paper presents some initial findings from a multi-year project that is exploring the growth of mathematical understanding in a variety of construction trades training programs. In this paper, we focus on John, an entry-level plumbing trainee. We explore his understandings for multiplication, fractions and units of imperial measure as he…

One of a series of pre-apprenticeship phase 1 training modules dealing with math skills, this self-paced student module covers the addition and subtraction of common fractions and mixed numbers. Included in the module are the following: cover sheet listing module title, goals, and performance indicators; introduction; study guide/check list with…

Presented is an overview of the 1979 Illinois Inventory of Educational Progress (IIEP) for fourth-grade mathematics. The IIEP is a systematic effort by the Illinois State Board of Education to collect information on the educational achievement of Illinois students in certain areas and to make that information available to education…

Presented is the final report of a one-year project on the structure of high school mathematics knowledge sponsored by the National Institute of Education (NIE). The main body contains conclusions on a conceptual framework for representing high school mathematics. Results are presented through discussion of three domains from the secondary school…

Eight activity packages, designed to teach students mathematical topics which are inappropriate to teach through a paper and pencil approach, are presented. The materials were created so that students: (1) can follow the instructions with little supervision; (2) are physically engaged in the activity, either measuring, counting, drawing pictures…

This guide outlines an Option X course on problem solving techniques. The 16 learner objectives identified in the Mathematics Program Guide stress applications orientation to concepts about numbers and operations and common plane and solid figures. Techniques covered include working with diagrams, organizing information, using patterns,…

Problem solving is viewed as an ability required throughout life, and how we function is seen to be directly related to how well we solve problems. In this document, the issue of a steady decline in students' abilities in the area of mathematical problem solving is confronted and a program designed to teach students the necessary skills in this…

The National Assessment of Educational Progress (NAEP) administered the selected supplemental mathematics exercises to 13-year-old students during October and November 1975 and to 17-year-old students during March and April 1976. This assessment represents a specially modified supplement to 1972-73 full-scale mathematics assessment and was…