Measuring Reform Practices in Science and Mathematics Classrooms: The Reformed Teaching Observation Protocol

The National Science Foundation has funded 22 Collaboratives for Excellence in Teacher Preparation. Despite the remarkable allocation of resources to this effort, it has proven exceptionally difficult to demonstrate the effectiveness of collaborative reform. In large part, this has resulted because of the difficulty of defining and measuring reform. The Reformed Teaching Observation Protocol (RTOP) was designed by the Evaluation Facilitation Group of the Arizona Collaborative for Excellence in the Preparation of Teachers (ACEPT). It is a 25‐item classroom observation protocol that is (a) standards based, (b) inquiry oriented, and (c) student centered. This instrument has provided the definition for reform and the basis for evaluation of the ACEPT collaborative. The data upon which this report is based were collected over a period of more than 2 years from 153 public school, college, and university mathematics and science classrooms. A trained team of observers consisting of two faculty members and seven graduate students was able to achieve exceptionally high levels of interrater reliability. Internal consistency, as estimated by Cronbach's alpha, was also remarkably high. Correlation coefficients ranging from 0.88 to 0.97 between RTOP scores for classrooms, and mean normalized gain scores for students in those classrooms on achievement measures demonstrate that reform, as defined by ACEPT and measured by the RTOP, has been effective.     

大学数学与中学数学教学内容衔接研究

数学教育是一个完整的科学体系,对大学数学教育与中学数学教育进行衔接研究具有重要意义,而教学内容的衔接是二者衔接的一个重要方面.本文根据大学数学和中学数学教学中较普遍使用的经典教材,对大学数学和中学数学教学内容从数学符号使用、教学内容重叠、教学内容遗漏三个方面进行详细归纳总结,对于大学数学教学和大学数学教材的编写具有一定借鉴作用.     

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.     

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.     

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.     

Promoting Preservice Elementary Teachers' Awareness of Learning and Teaching Mathematics Conceptually Through KTEM

In this article, we describe preservice elementary teachers' reactions to Liping Ma's (1999) book, Knowing and Teaching Elementary Mathematics (KTEM), from five universities. Ma's discussion of solely teaching elementary mathematics procedurally and its consequences awakens the preservice teachers' memories of learning elementary mathematics. Ma's analysis of and solution to the problem ignites strong emotions in the preservice elementary teachers and promotes a desire to teach elementary mathematics conceptually. Through the analysis of writing assignments, we summarize how reading and reflecting on KTEM gives preservice teachers an opportunity to examine their beliefs about teaching and learning elementary mathematics conceptually.     

Exploring Pi Using the Computer in Middle School Mathematics

The National Council of Teachers of Mathematics (NCTM) in its Curriculum and Evaluation Standards for School Mathematics encourages a middle school curriculum that integrates technology. It recommends that students should be able to identify and use functional relationships and make connections among seemingly diverse concepts and topics. In this activity of exploring the derivation of Pi, students take a constructivist role by collecting data and making conjectures. Using the data they construct graphs and tables and discourse about appropriate algebraic representations. The computer is used as an instructional aid enabling the students to view the data in a variety of forms. They are encouraged to communicate about the connections among the various representations.