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This paper examines the extent to which an intervention program on the use of practical work affected the following two variables: instructional techniques and mathematical ability. An attempt was made to correlate these two variables with age, educational attainment, and teaching experience to determine if there exists a relationship with and without the effect of the intervention. Differences and relationships between these two variables before and after the intervention were significant. However, these two variables were not correlated with age, educational attainment and teaching experience before and after the intervention. Generally, the results and discussion in this paper may serve as a catalyst from which necessary remediation and modification of school and in-service programs could emanate. (Contains 4 tables.)

This paper examines the extent to which an intervention program on the use of practical work affected the following two variables: instructional techniques and mathematical ability. An attempt was made to correlate these two variables with age, educational attainment, and teaching experience to determine if there exists a relationship with and without the effect of the intervention. Differences and relationships between these two variables before and after the intervention were significant. However, these two variables were not correlated with age, educational attainment and teaching experience before and after the intervention. Generally, the results and discussion in this paper may serve as a catalyst from which necessary remediation and modification of school and in-service programs could emanate. (Contains 4 tables.)

This paper examines the extent to which an intervention program on the use of practical work affected the following two variables: instructional techniques and mathematical ability. An attempt was made to correlate these two variables with age, educational attainment, and teaching experience to determine if there exists a relationship with and without the effect of the intervention. Differences and relationships between these two variables before and after the intervention were significant. However, these two variables were not correlated with age, educational attainment and teaching experience before and after the intervention. Generally, the results and discussion in this paper may serve as a catalyst from which necessary remediation and modification of school and in-service programs could emanate. (Contains 4 tables.)

This paper examines the extent to which an intervention program on the use of practical work affected the following two variables: instructional techniques and mathematical ability. An attempt was made to correlate these two variables with age, educational attainment, and teaching experience to determine if there exists a relationship with and without the effect of the intervention. Differences and relationships between these two variables before and after the intervention were significant. However, these two variables were not correlated with age, educational attainment and teaching experience before and after the intervention. Generally, the results and discussion in this paper may serve as a catalyst from which necessary remediation and modification of school and in-service programs could emanate. (Contains 4 tables.)

This paper examines the extent to which an intervention program on the use of practical work affected the following two variables: instructional techniques and mathematical ability. An attempt was made to correlate these two variables with age, educational attainment, and teaching experience to determine if there exists a relationship with and without the effect of the intervention. Differences and relationships between these two variables before and after the intervention were significant. However, these two variables were not correlated with age, educational attainment and teaching experience before and after the intervention. Generally, the results and discussion in this paper may serve as a catalyst from which necessary remediation and modification of school and in-service programs could emanate. (Contains 4 tables.)

This paper examines the extent to which an intervention program on the use of practical work affected the following two variables: instructional techniques and mathematical ability. An attempt was made to correlate these two variables with age, educational attainment, and teaching experience to determine if there exists a relationship with and without the effect of the intervention. Differences and relationships between these two variables before and after the intervention were significant. However, these two variables were not correlated with age, educational attainment and teaching experience before and after the intervention. Generally, the results and discussion in this paper may serve as a catalyst from which necessary remediation and modification of school and in-service programs could emanate. (Contains 4 tables.)

The study of three-dimensional objects is undertaken in the Mexican curriculum throughout all levels of basic education. However, few studies relate to the mathematics knowledge needed to teach those ideas. This report represents an approach to the study of such knowledge. The approach is based on an account, developed from class observations, of three six grade teachers and their use of mathematics knowledge in teaching their students to calculate the volume of prisms, in two schools in Mexico City. The results provide evidence related to some sub-domains of mathematics knowledge for teaching. While there are some strengths related to this knowledge, teachers also showed that there is room for improvement. This speaks to the need to develop training spaces (both for preservice and in-service teachers) where the analysis and discussions stimulate learning of both the geometric and pedagogical knowledge needed for teaching practice. [Funding for this project was provided by Conacyt/SEP/SEB. This paper is presented in both English and Spanish. For the complete proceedings, see ED583608.]

The study of three-dimensional objects is undertaken in the Mexican curriculum throughout all levels of basic education. However, few studies relate to the mathematics knowledge needed to teach those ideas. This report represents an approach to the study of such knowledge. The approach is based on an account, developed from class observations, of three six grade teachers and their use of mathematics knowledge in teaching their students to calculate the volume of prisms, in two schools in Mexico City. The results provide evidence related to some sub-domains of mathematics knowledge for teaching. While there are some strengths related to this knowledge, teachers also showed that there is room for improvement. This speaks to the need to develop training spaces (both for preservice and in-service teachers) where the analysis and discussions stimulate learning of both the geometric and pedagogical knowledge needed for teaching practice. [Funding for this project was provided by Conacyt/SEP/SEB. This paper is presented in both English and Spanish. For the complete proceedings, see ED583608.]

The study of three-dimensional objects is undertaken in the Mexican curriculum throughout all levels of basic education. However, few studies relate to the mathematics knowledge needed to teach those ideas. This report represents an approach to the study of such knowledge. The approach is based on an account, developed from class observations, of three six grade teachers and their use of mathematics knowledge in teaching their students to calculate the volume of prisms, in two schools in Mexico City. The results provide evidence related to some sub-domains of mathematics knowledge for teaching. While there are some strengths related to this knowledge, teachers also showed that there is room for improvement. This speaks to the need to develop training spaces (both for preservice and in-service teachers) where the analysis and discussions stimulate learning of both the geometric and pedagogical knowledge needed for teaching practice. [Funding for this project was provided by Conacyt/SEP/SEB. This paper is presented in both English and Spanish. For the complete proceedings, see ED583608.]

The purpose of this research is to determine the impact of augmented reality technology and geometry teaching on elementary school mathematics teacher candidates' technology acceptance and to examine participants' views on augmented reality. The sample of the research was composed of 40 elementary school mathematics teacher candidates who were freshman students in the faculty of education of a university which located in the central Anatolian region of Turkey during the fall semester of 2016-2017 academic year. Participants in the study were given a training seminar on teaching geometry via augmented reality (AR). They were provided with the opportunity to develop teaching materials for AR. At the end of this process, their opinions on the use of these materials were taken. Both qualitative and quantitative research methods were used in the research. The quantitative data of this study were collected by the Technology Acceptance and Use Scale for Information and Communication Technologies and the qualitative data were collected through semi-structured interviews. The themes and codes related to the usefulness of geometry teaching supported by augmented reality teaching emerged by means of qualitative content analysis. The t-Test, one of the parametric tests, was used to analyze the quantitative data. The data obtained from the semi-structured interview forms were classified under 9 categories and 35 themes. As a result of data analyses, it was found that the teacher candidates' attitudes towards the effectiveness geometry instruction supported by the augmented reality technology were positive but as regards' teacher candidates' intentions to use augmented reality technology, it was observed that some of them had reservations because of technological limitations, such as recognition of signs and freezing of the augmented reality environments. Keywords: augmented reality (AR), geometry teaching, mathematics teacher candidate, technology acceptance and use

This investigation traced changes in anxiety for teaching mathematics (ATM) among pre-service elementary school teachers (n=36) enrolled in a mathematics methods course by analyzing their weekly journal entries. Journal entries were coded for high level of ATM (ATM-high) or absence of ATM (ATM-absent) during the first class session, as well as high level or absence of ATM and classroom context throughout the semester. Results of analysis of initial ATM-high (n=8) and initial ATM-absent (n=8) journal entries found variability in ATM levels among both groups throughout the semester. Initial ATM-absent pre-service teachers consistently reported high levels of interest in teaching mathematics. Similarly, when those reporting high initial ATM described interest in developing creative strategies for teaching mathematics, their ATM was reduced. For initial ATM-high pre-service teachers, when ATM became severe during the semester, it interfered with learning new course material. Implications for developing mathematics methods course curriculum are discussed. (Author)

A computer-assisted instructional (CAI) course at Pennsylvania State University uses an IBM 1500 system to introduce education majors to strategies for teaching elementary school mathematics. CAI is employed to provide individualized instruction on the theoretical aspects of the subject. The course is divided into 16 modules, each of which contains an outline of the content and a set of instructional objectives. Sequences of instructional episodes are designed for each objective; these are flow-charted, thus providing documentation not only of curricular material but also of the instructional logic. The advantages of the course as it is structured are that it offers self-paced individualized instruction and that it gives feedback for continuous modification of the program. In addition, the CAI course constitutes an instructional laboratory in which basic instructional research can be carried out. (LB)

A computer-assisted instructional (CAI) course at Pennsylvania State University uses an IBM 1500 system to introduce education majors to strategies for teaching elementary school mathematics. CAI is employed to provide individualized instruction on the theoretical aspects of the subject. The course is divided into 16 modules, each of which contains an outline of the content and a set of instructional objectives. Sequences of instructional episodes are designed for each objective; these are flow-charted, thus providing documentation not only of curricular material but also of the instructional logic. The advantages of the course as it is structured are that it offers self-paced individualized instruction and that it gives feedback for continuous modification of the program. In addition, the CAI course constitutes an instructional laboratory in which basic instructional research can be carried out. (LB)

A computer-assisted instructional (CAI) course at Pennsylvania State University uses an IBM 1500 system to introduce education majors to strategies for teaching elementary school mathematics. CAI is employed to provide individualized instruction on the theoretical aspects of the subject. The course is divided into 16 modules, each of which contains an outline of the content and a set of instructional objectives. Sequences of instructional episodes are designed for each objective; these are flow-charted, thus providing documentation not only of curricular material but also of the instructional logic. The advantages of the course as it is structured are that it offers self-paced individualized instruction and that it gives feedback for continuous modification of the program. In addition, the CAI course constitutes an instructional laboratory in which basic instructional research can be carried out. (LB)

A computer-assisted instructional (CAI) course at Pennsylvania State University uses an IBM 1500 system to introduce education majors to strategies for teaching elementary school mathematics. CAI is employed to provide individualized instruction on the theoretical aspects of the subject. The course is divided into 16 modules, each of which contains an outline of the content and a set of instructional objectives. Sequences of instructional episodes are designed for each objective; these are flow-charted, thus providing documentation not only of curricular material but also of the instructional logic. The advantages of the course as it is structured are that it offers self-paced individualized instruction and that it gives feedback for continuous modification of the program. In addition, the CAI course constitutes an instructional laboratory in which basic instructional research can be carried out. (LB)

A computer-assisted instructional (CAI) course at Pennsylvania State University uses an IBM 1500 system to introduce education majors to strategies for teaching elementary school mathematics. CAI is employed to provide individualized instruction on the theoretical aspects of the subject. The course is divided into 16 modules, each of which contains an outline of the content and a set of instructional objectives. Sequences of instructional episodes are designed for each objective; these are flow-charted, thus providing documentation not only of curricular material but also of the instructional logic. The advantages of the course as it is structured are that it offers self-paced individualized instruction and that it gives feedback for continuous modification of the program. In addition, the CAI course constitutes an instructional laboratory in which basic instructional research can be carried out. (LB)

In this paper the authors present three design principles they use to develop preservice teachers' mathematical content knowledge for teaching in their mathematics content and/or methods courses: (1) building on currently held conceptions, (2) modeling teaching for understanding, (3) focusing on connections between content knowledge and other types of knowledge. The authors share results of individual research projects and teaching approaches focusing on helping preservice elementary teachers develop such knowledge. Specific examples from different content areas (whole number, fractions, angle, and area) are discussed. (Contains 8 figures.)

For boys and girls who are prepared in the essential elements of arithmetic this later book proposes extended instruction in percentage and commercial transactions, and in the elements of geometry. It is one of a series of handbooks for pupils, and consists of progressive lessons, arranged mainly in topics, either reviewing the treatment in earlier books, or completing the subject, or preparing for the next book. Teaching suggestions are included. [Cover title varies: "Graded Arithmetics. Book Seven--Grade VIII."]

For boys and girls who are prepared in the essential elements of arithmetic this later book proposes extended instruction in percentage and commercial transactions, and in the elements of geometry. It is one of a series of handbooks for pupils, and consists of progressive lessons, arranged mainly in topics, either reviewing the treatment in earlier books, or completing the subject, or preparing for the next book. Teaching suggestions are included. [Cover title varies: "Graded Arithmetics. Book Seven--Grade VIII."]

"THE TEACHING OF MATHEMATICS IN THE ELEMENTARY AND THE SECONDARY SCHOOL" is an article from The Mathematics Teacher, Volume 1 . View more articles from The Mathematics Teacher . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-27949595

"THE TEACHING OF MATHEMATICS IN THE ELEMENTARY AND THE SECONDARY SCHOOL" is an article from The Mathematics Teacher, Volume 1 . View more articles from The Mathematics Teacher . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-27949595

"THE TEACHING OF MATHEMATICS IN THE ELEMENTARY AND THE SECONDARY SCHOOL" is an article from The Mathematics Teacher, Volume 1 . View more articles from The Mathematics Teacher . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-27949595

The challenges of teaching elementary mathematics and science, particularly in urban settings, have been well documented. While evidence exists that sustained professional development in mathematics and science can promote inquiry-oriented instruction and bolster student achievement, little has been written about the particular challenges associated with offering differentiated professional development through school-university partnerships. This paper examines the impact on student achievement and teacher practice when university teacher educators launched a 3-year science and mathematics professional development initiative in grades 3-5 at one of the university's elementary partner school campuses. Our intention was to create a ''constructivist'' professional learning initiative where the facilitator-researchers were responsive to teachers' ongoing needs and daily teaching challenges. After sharing results, we identify factors that may affect the ultimate success or failure of such initiatives in order to better understand how highly contextualized and differentiated professional development can be structured and sustained.

The challenges of teaching elementary mathematics and science, particularly in urban settings, have been well documented. While evidence exists that sustained professional development in mathematics and science can promote inquiry-oriented instruction and bolster student achievement, little has been written about the particular challenges associated with offering differentiated professional development through school-university partnerships. This paper examines the impact on student achievement and teacher practice when university teacher educators launched a 3-year science and mathematics professional development initiative in grades 3-5 at one of the university's elementary partner school campuses. Our intention was to create a ''constructivist'' professional learning initiative where the facilitator-researchers were responsive to teachers' ongoing needs and daily teaching challenges. After sharing results, we identify factors that may affect the ultimate success or failure of such initiatives in order to better understand how highly contextualized and differentiated professional development can be structured and sustained.

The challenges of teaching elementary mathematics and science, particularly in urban settings, have been well documented. While evidence exists that sustained professional development in mathematics and science can promote inquiry-oriented instruction and bolster student achievement, little has been written about the particular challenges associated with offering differentiated professional development through school-university partnerships. This paper examines the impact on student achievement and teacher practice when university teacher educators launched a 3-year science and mathematics professional development initiative in grades 3-5 at one of the university's elementary partner school campuses. Our intention was to create a ''constructivist'' professional learning initiative where the facilitator-researchers were responsive to teachers' ongoing needs and daily teaching challenges. After sharing results, we identify factors that may affect the ultimate success or failure of such initiatives in order to better understand how highly contextualized and differentiated professional development can be structured and sustained.

Includes bibliographies

The National Council of Teachers of Mathematics encourages the use of calculators in the classroom as a teaching and learning tool, as well as a computational tool. This paper evaluates the impact on teachers' approaches to teaching mathematics and students' attitudes toward mathematics as the result of participation in an in-service program designed to help third and fourth-grade teachers incorporate calculators into their instruction. Forty-two teachers from 14 rural Missouri school districts were invited to participate in three 1-day workshops held in the 1991-92 school year. The teachers were taught to use Texas Instrument Explorer calculators, encouraged to explore numbers and number relationships with the calculators, and asked to design five higher-level lessons to utilize the calculator. Results of a questionnaire used to assess changes in the teachers' (n=29) instructional approaches indicated no significant differences materialized in the teachers' teaching approaches and teachers hold misconceptions about such concepts such as division by zero. Pretest and posttest analysis of the students' (n=412) attitudes toward mathematics indicated that students developed a more positive attitude on scales dealing with value of division, willingness to do division, enjoyment of division, calculator use, and overall perception of mathematics. (MDH)

The National Council of Teachers of Mathematics encourages the use of calculators in the classroom as a teaching and learning tool, as well as a computational tool. This paper evaluates the impact on teachers' approaches to teaching mathematics and students' attitudes toward mathematics as the result of participation in an in-service program designed to help third and fourth-grade teachers incorporate calculators into their instruction. Forty-two teachers from 14 rural Missouri school districts were invited to participate in three 1-day workshops held in the 1991-92 school year. The teachers were taught to use Texas Instrument Explorer calculators, encouraged to explore numbers and number relationships with the calculators, and asked to design five higher-level lessons to utilize the calculator. Results of a questionnaire used to assess changes in the teachers' (n=29) instructional approaches indicated no significant differences materialized in the teachers' teaching approaches and teachers hold misconceptions about such concepts such as division by zero. Pretest and posttest analysis of the students' (n=412) attitudes toward mathematics indicated that students developed a more positive attitude on scales dealing with value of division, willingness to do division, enjoyment of division, calculator use, and overall perception of mathematics. (MDH)

The National Council of Teachers of Mathematics encourages the use of calculators in the classroom as a teaching and learning tool, as well as a computational tool. This paper evaluates the impact on teachers' approaches to teaching mathematics and students' attitudes toward mathematics as the result of participation in an in-service program designed to help third and fourth-grade teachers incorporate calculators into their instruction. Forty-two teachers from 14 rural Missouri school districts were invited to participate in three 1-day workshops held in the 1991-92 school year. The teachers were taught to use Texas Instrument Explorer calculators, encouraged to explore numbers and number relationships with the calculators, and asked to design five higher-level lessons to utilize the calculator. Results of a questionnaire used to assess changes in the teachers' (n=29) instructional approaches indicated no significant differences materialized in the teachers' teaching approaches and teachers hold misconceptions about such concepts such as division by zero. Pretest and posttest analysis of the students' (n=412) attitudes toward mathematics indicated that students developed a more positive attitude on scales dealing with value of division, willingness to do division, enjoyment of division, calculator use, and overall perception of mathematics. (MDH)

The National Council of Teachers of Mathematics encourages the use of calculators in the classroom as a teaching and learning tool, as well as a computational tool. This paper evaluates the impact on teachers' approaches to teaching mathematics and students' attitudes toward mathematics as the result of participation in an in-service program designed to help third and fourth-grade teachers incorporate calculators into their instruction. Forty-two teachers from 14 rural Missouri school districts were invited to participate in three 1-day workshops held in the 1991-92 school year. The teachers were taught to use Texas Instrument Explorer calculators, encouraged to explore numbers and number relationships with the calculators, and asked to design five higher-level lessons to utilize the calculator. Results of a questionnaire used to assess changes in the teachers' (n=29) instructional approaches indicated no significant differences materialized in the teachers' teaching approaches and teachers hold misconceptions about such concepts such as division by zero. Pretest and posttest analysis of the students' (n=412) attitudes toward mathematics indicated that students developed a more positive attitude on scales dealing with value of division, willingness to do division, enjoyment of division, calculator use, and overall perception of mathematics. (MDH)

The accompanying report deals with the mathematical training of prospective teachers in elementary schools as described in the reports submitted by the International Commission of the Teaching of Mathematics to the Fifth International Congress of Mathematicians, held at Cambridge, England, in August, 1912. A comparative study of the facts presented in these reports is of interest for those engaged in the training of teachers in this country, if only because they indicate that the standards elsewhere are as chaotic as they are here. The requirements of the normal schools, or corresponding institutions vary from a review of the elementary-school arithmetic to the mathematics required for entrance to colleges and universities; or, from another point of view, from an emphasis on the purely professional needs limited to the immediate requirements of the elementary schools, to academic and cultural aims founded on the principle that the more a teacher knows about the subject, in addition to the purely professional training, the more successful will be his teaching. But, great as is the variety of standards and aims in Europe, almost every standard finds a parallel in this country, owing to the absence of uniformity--a condition almost paralleled in England and Switzerland. But, if a generalization may be permitted, it would be true to say that the academic standards in the best systems are higher in the more advanced countries of Europe than they are in the United States. Countries included in this report are: (1) Belgium; (2) Denmark; (3) England; (4) France; (5) Germany; (6) Hungary; (7) Italy; (8) Russia; (9) Sweden; (10) Switzerland; and (11) the United States. A bibliography is included. (Contains 2 footnotes.) [This bulletin was written with the editorial cooperation of David Eugene Smith, William F. Osgood, and J.W.A. Young. Best copy available has been provided.]

The accompanying report deals with the mathematical training of prospective teachers in elementary schools as described in the reports submitted by the International Commission of the Teaching of Mathematics to the Fifth International Congress of Mathematicians, held at Cambridge, England, in August, 1912. A comparative study of the facts presented in these reports is of interest for those engaged in the training of teachers in this country, if only because they indicate that the standards elsewhere are as chaotic as they are here. The requirements of the normal schools, or corresponding institutions vary from a review of the elementary-school arithmetic to the mathematics required for entrance to colleges and universities; or, from another point of view, from an emphasis on the purely professional needs limited to the immediate requirements of the elementary schools, to academic and cultural aims founded on the principle that the more a teacher knows about the subject, in addition to the purely professional training, the more successful will be his teaching. But, great as is the variety of standards and aims in Europe, almost every standard finds a parallel in this country, owing to the absence of uniformity--a condition almost paralleled in England and Switzerland. But, if a generalization may be permitted, it would be true to say that the academic standards in the best systems are higher in the more advanced countries of Europe than they are in the United States. Countries included in this report are: (1) Belgium; (2) Denmark; (3) England; (4) France; (5) Germany; (6) Hungary; (7) Italy; (8) Russia; (9) Sweden; (10) Switzerland; and (11) the United States. A bibliography is included. (Contains 2 footnotes.) [This bulletin was written with the editorial cooperation of David Eugene Smith, William F. Osgood, and J.W.A. Young. Best copy available has been provided.]

The accompanying report deals with the mathematical training of prospective teachers in elementary schools as described in the reports submitted by the International Commission of the Teaching of Mathematics to the Fifth International Congress of Mathematicians, held at Cambridge, England, in August, 1912. A comparative study of the facts presented in these reports is of interest for those engaged in the training of teachers in this country, if only because they indicate that the standards elsewhere are as chaotic as they are here. The requirements of the normal schools, or corresponding institutions vary from a review of the elementary-school arithmetic to the mathematics required for entrance to colleges and universities; or, from another point of view, from an emphasis on the purely professional needs limited to the immediate requirements of the elementary schools, to academic and cultural aims founded on the principle that the more a teacher knows about the subject, in addition to the purely professional training, the more successful will be his teaching. But, great as is the variety of standards and aims in Europe, almost every standard finds a parallel in this country, owing to the absence of uniformity--a condition almost paralleled in England and Switzerland. But, if a generalization may be permitted, it would be true to say that the academic standards in the best systems are higher in the more advanced countries of Europe than they are in the United States. Countries included in this report are: (1) Belgium; (2) Denmark; (3) England; (4) France; (5) Germany; (6) Hungary; (7) Italy; (8) Russia; (9) Sweden; (10) Switzerland; and (11) the United States. A bibliography is included. (Contains 2 footnotes.) [This bulletin was written with the editorial cooperation of David Eugene Smith, William F. Osgood, and J.W.A. Young. Best copy available has been provided.]

The accompanying report deals with the mathematical training of prospective teachers in elementary schools as described in the reports submitted by the International Commission of the Teaching of Mathematics to the Fifth International Congress of Mathematicians, held at Cambridge, England, in August, 1912. A comparative study of the facts presented in these reports is of interest for those engaged in the training of teachers in this country, if only because they indicate that the standards elsewhere are as chaotic as they are here. The requirements of the normal schools, or corresponding institutions vary from a review of the elementary-school arithmetic to the mathematics required for entrance to colleges and universities; or, from another point of view, from an emphasis on the purely professional needs limited to the immediate requirements of the elementary schools, to academic and cultural aims founded on the principle that the more a teacher knows about the subject, in addition to the purely professional training, the more successful will be his teaching. But, great as is the variety of standards and aims in Europe, almost every standard finds a parallel in this country, owing to the absence of uniformity--a condition almost paralleled in England and Switzerland. But, if a generalization may be permitted, it would be true to say that the academic standards in the best systems are higher in the more advanced countries of Europe than they are in the United States. Countries included in this report are: (1) Belgium; (2) Denmark; (3) England; (4) France; (5) Germany; (6) Hungary; (7) Italy; (8) Russia; (9) Sweden; (10) Switzerland; and (11) the United States. A bibliography is included. (Contains 2 footnotes.) [This bulletin was written with the editorial cooperation of David Eugene Smith, William F. Osgood, and J.W.A. Young. Best copy available has been provided.]

These eleven essays range across a variety of topics. They concern: (1) philosophy and the curriculum, with comments on accountability, humanism, programmed learning, hierarchies, structure, idealism, existentialism, realism, experimentalism, and essentialism; (2) philosophy in the mathematics curriculum, with comments on mathematics laboratories, programmed learning, contracts, management systems, and learning centers; (3) objectives and learning activities in the mathematics curriculum, focusing on objectives and on using various types of materials; (4) providing for individual differences and designing the mathematics curriculum, with sections on slow learners, talented pupils, learning activities, other ways of providing for individual differences, and scope; (5) principles of learning and the mathematics curriculum, with comments on purpose, interest, problem solving, meaningful learning, individual differences, mathematics concepts, decision-making, and evaluation; (6) mathematics and the learner; (7) change in education; (8) inservice education and the computer; (9) innovation, technology, and the mathematics curriculum; (10) knowledge of results, with comments on evaluation procedures, behaviorism, and humanism; and (11) evaluating achievement in mathematics, including the use of observations, checklists, teacher-made tests, standardized tests, work samples, parent-teacher conferences, tape recorders, pupils' responses, and pupil-teacher conferences. Some chapters provide selected references. (MNS)

This publication is a collection of articles which are related to elementary school mathematics. The authors note that the book was written primarily for elementary school principals, mathematics specialists and supervisors, and elementary school teachers. The articles discuss such topics as major issues in mathematics education, instructional procedures for teaching mathematics, inservice programs, and future directions for elementary school mathematics. (FL)

This report contains case studies of two teachers who attempt to go beyond traditional mathematics curriculum and instruction. There are important differences in the contexts of teaching and in the approaches to studying teaching and learning in these two classrooms. Case study 1 describes a teacher who draws upon professional experiences to initiate change in the classroom. The authors describe elements of the teacher's mathematics teaching, using NCTM Curriculum and Evaluation Standards as a framework for analysis, then analyze the teacher's views about instructional issues, focusing on connections between beliefs and practice. Case study 2 describes a teacher involved in a Mathematics Study Group in a Professional Development School. The authors chronicle the changes in this teacher's thinking and practice during a 3-year period, focusing on her views about, and understanding of, mathematical content, the nature and role of discourse about mathematics, and what constitutes evidence of mathematical learning. The authors also explore the role of collaboration among teachers and between teachers and university participants in discussing the kinds of changes these teachers made. (Contains 15 references.) (Author)

This report contains case studies of two teachers who attempt to go beyond traditional mathematics curriculum and instruction. There are important differences in the contexts of teaching and in the approaches to studying teaching and learning in these two classrooms. Case study 1 describes a teacher who draws upon professional experiences to initiate change in the classroom. The authors describe elements of the teacher's mathematics teaching, using NCTM Curriculum and Evaluation Standards as a framework for analysis, then analyze the teacher's views about instructional issues, focusing on connections between beliefs and practice. Case study 2 describes a teacher involved in a Mathematics Study Group in a Professional Development School. The authors chronicle the changes in this teacher's thinking and practice during a 3-year period, focusing on her views about, and understanding of, mathematical content, the nature and role of discourse about mathematics, and what constitutes evidence of mathematical learning. The authors also explore the role of collaboration among teachers and between teachers and university participants in discussing the kinds of changes these teachers made. (Contains 15 references.) (Author)

This report contains case studies of two teachers who attempt to go beyond traditional mathematics curriculum and instruction. There are important differences in the contexts of teaching and in the approaches to studying teaching and learning in these two classrooms. Case study 1 describes a teacher who draws upon professional experiences to initiate change in the classroom. The authors describe elements of the teacher's mathematics teaching, using NCTM Curriculum and Evaluation Standards as a framework for analysis, then analyze the teacher's views about instructional issues, focusing on connections between beliefs and practice. Case study 2 describes a teacher involved in a Mathematics Study Group in a Professional Development School. The authors chronicle the changes in this teacher's thinking and practice during a 3-year period, focusing on her views about, and understanding of, mathematical content, the nature and role of discourse about mathematics, and what constitutes evidence of mathematical learning. The authors also explore the role of collaboration among teachers and between teachers and university participants in discussing the kinds of changes these teachers made. (Contains 15 references.) (Author)

This report contains case studies of two teachers who attempt to go beyond traditional mathematics curriculum and instruction. There are important differences in the contexts of teaching and in the approaches to studying teaching and learning in these two classrooms. Case study 1 describes a teacher who draws upon professional experiences to initiate change in the classroom. The authors describe elements of the teacher's mathematics teaching, using NCTM Curriculum and Evaluation Standards as a framework for analysis, then analyze the teacher's views about instructional issues, focusing on connections between beliefs and practice. Case study 2 describes a teacher involved in a Mathematics Study Group in a Professional Development School. The authors chronicle the changes in this teacher's thinking and practice during a 3-year period, focusing on her views about, and understanding of, mathematical content, the nature and role of discourse about mathematics, and what constitutes evidence of mathematical learning. The authors also explore the role of collaboration among teachers and between teachers and university participants in discussing the kinds of changes these teachers made. (Contains 15 references.) (Author)

This report contains case studies of two teachers who attempt to go beyond traditional mathematics curriculum and instruction. There are important differences in the contexts of teaching and in the approaches to studying teaching and learning in these two classrooms. Case study 1 describes a teacher who draws upon professional experiences to initiate change in the classroom. The authors describe elements of the teacher's mathematics teaching, using NCTM Curriculum and Evaluation Standards as a framework for analysis, then analyze the teacher's views about instructional issues, focusing on connections between beliefs and practice. Case study 2 describes a teacher involved in a Mathematics Study Group in a Professional Development School. The authors chronicle the changes in this teacher's thinking and practice during a 3-year period, focusing on her views about, and understanding of, mathematical content, the nature and role of discourse about mathematics, and what constitutes evidence of mathematical learning. The authors also explore the role of collaboration among teachers and between teachers and university participants in discussing the kinds of changes these teachers made. (Contains 15 references.) (Author)

This report contains case studies of two teachers who attempt to go beyond traditional mathematics curriculum and instruction. There are important differences in the contexts of teaching and in the approaches to studying teaching and learning in these two classrooms. Case study 1 describes a teacher who draws upon professional experiences to initiate change in the classroom. The authors describe elements of the teacher's mathematics teaching, using NCTM Curriculum and Evaluation Standards as a framework for analysis, then analyze the teacher's views about instructional issues, focusing on connections between beliefs and practice. Case study 2 describes a teacher involved in a Mathematics Study Group in a Professional Development School. The authors chronicle the changes in this teacher's thinking and practice during a 3-year period, focusing on her views about, and understanding of, mathematical content, the nature and role of discourse about mathematics, and what constitutes evidence of mathematical learning. The authors also explore the role of collaboration among teachers and between teachers and university participants in discussing the kinds of changes these teachers made. (Contains 15 references.) (Author)

This report contains case studies of two teachers who attempt to go beyond traditional mathematics curriculum and instruction. There are important differences in the contexts of teaching and in the approaches to studying teaching and learning in these two classrooms. Case study 1 describes a teacher who draws upon professional experiences to initiate change in the classroom. The authors describe elements of the teacher's mathematics teaching, using NCTM Curriculum and Evaluation Standards as a framework for analysis, then analyze the teacher's views about instructional issues, focusing on connections between beliefs and practice. Case study 2 describes a teacher involved in a Mathematics Study Group in a Professional Development School. The authors chronicle the changes in this teacher's thinking and practice during a 3-year period, focusing on her views about, and understanding of, mathematical content, the nature and role of discourse about mathematics, and what constitutes evidence of mathematical learning. The authors also explore the role of collaboration among teachers and between teachers and university participants in discussing the kinds of changes these teachers made. (Contains 15 references.) (Author)

This report contains case studies of two teachers who attempt to go beyond traditional mathematics curriculum and instruction. There are important differences in the contexts of teaching and in the approaches to studying teaching and learning in these two classrooms. Case study 1 describes a teacher who draws upon professional experiences to initiate change in the classroom. The authors describe elements of the teacher's mathematics teaching, using NCTM Curriculum and Evaluation Standards as a framework for analysis, then analyze the teacher's views about instructional issues, focusing on connections between beliefs and practice. Case study 2 describes a teacher involved in a Mathematics Study Group in a Professional Development School. The authors chronicle the changes in this teacher's thinking and practice during a 3-year period, focusing on her views about, and understanding of, mathematical content, the nature and role of discourse about mathematics, and what constitutes evidence of mathematical learning. The authors also explore the role of collaboration among teachers and between teachers and university participants in discussing the kinds of changes these teachers made. (Contains 15 references.) (Author)