Problem Posing: A Neglected Component in Mathematics Courses for Prospective Elementary and Middle School Teachers

The purpose of this article is to describe a scheme which is designed to guide the prospective teacher beyond the point of proficiency as a student solving given problems. By experiencing several stages of inquiry, the scheme provides a mechanism where by the prospective teacher advances toward assuming the role of a teacher posing his or her own problems. Although the scheme has been developed within the context of a standard mathematics course for preservice teachers, the ideas set forth are equally appropriate for incorporation within a science course for prospective teachers.     

Applying NAEP to Improve Mathematics Content and Methods Courses for Preservice Elementary and Middle School Teachers

This study explored how mathematics content and methods courses for preservice elementary and middle school teachers could be improved through the integration of a set of instructional materials based on the National Assessment of Educational Progress (NAEP). A set of eight instructional modules was developed and tested. The study involved 7 university instructors and 542 preservice teachers (PSTs) from three different universities. A quasi‐experimental nonequivalent groups design was used for this study in which the following data sources were collected and analyzed. Three versions of a Learning Mathematics for Teaching test were given to assess PSTs‘ mathematical content knowledge for teaching: (a) Elementary Number Concepts and Operations—Content Knowledge; (b) Elementary Geometry—Content Knowledge; and (c) Middle School Number Concepts and Operations—Content Knowledge. In addition, the Mathematics Teacher Efficacy Beliefs Instrument was given to assess PSTs’ teacher efficacy beliefs. Test results were analyzed using paired samples t‐tests. Findings suggest that use of instructional materials, based on NAEP, with PSTs results in increases in their mathematical content knowledge for teaching and in their teaching efficacy beliefs.     

Data Collection and Elementary School Mathematics

The curriculum standards of the National Council of Teachers of Mathematics advocate the inclusion of data collection activities throughout the middle school. This paper presents activities that implement these recommendations. Activities include data collection in the home, school and community and encourage students to summarize, interpret, and draw inferences from the data they collect individually and in cooperative groups. Four types of data collection activities are presented - observations, surveys, experiments and sampling. Every activity requires minimal planning/preparation by the teacher yet involves students in a variety of roles. Further, each activity can be adapted to different classroom settings.     

Calculators in Elementary School Mathematics Instruction

Due to the increased availability of hand-held calculators, teachers at all grade levels must now face the prospect of having to change both how they teach mathematics as well as what mathematics they teach. Since most teachers did not learn mathematics with the help of technology, they need time to adjust to both a new learning environment and a new teaching one. Through federal funds, the Texas Education Agency has created mathematics staff development modules which help teachers learn about calculators, mathematics, and the integration of calculators in mathematics instruction. This article presents games based upon those included in the staff development modules. Each game was designed to promote exploration of mathematical relationships via a calculator, specifically, Texas Instrument's Math Explorer.     

Scientific Methodology and Elementary School Mathematics

Investigations provide an exciting and relevant background for the study of mathematics. In this article children's conceptions of the laws of motion, introduced by Eckstein and Shemesh (1993), are extended with an emphasis placed upon the benefits to mathematics education. The focus is on the principle that the faster an object is moving when it is dropped, the greater the distance it will travel away from the drop point. The problems faced by a class of elementary school children who focus upon this experiment are described, and the impact of these problems upon the decisions made by the class are discussed. The use of mathematics in support of this experiment, particularly concepts of probability and statistics, are discussed, as well as suggestions for alternative methods of evaluating children's performance.