Relationship Between Professional Development,Teachers' Instructional Practices,and the Achievement of Students in Science and Mathematics

The purpose of this study was to examine the relationship between different types of professional development, teachers' instructional practices, and the achievement of students in science and mathematics. The types of professional development studied included immersion, examining practice, curriculum implementation, curriculum development, and collaborative work. Data regarding teachers' instructional practices and the amount of professional development were collected using teacher surveys. Ninety‐four middle school science teachers and 104 middle school mathematics teachers participated in the study. Student achievement was measured using eighth grade state science and mathematics achievement test data. Regression analyses suggested that for both science and mathematics teachers, examining practice and curriculum development were significantly related to the use of standards‐based instructional practices. Only curriculum development for mathematics teachers was significantly related to student achievement. Implications of results for the professional development of science and mathematics teachers are discussed.     

The Cumulative and Residual Impact of a Systemic Reform Program on Teacher Change and Student Learning of Science

This longitudinal, five‐year study of teachers and students who had participated in a systemic reform program in science explored if (1) teacher change in practice realized during a three‐year program is sustained one, two, and three years following the program, (2) student performance on state science assessments two years following studying with teachers at this school still demonstrated significant differences from students who attended the control school, and (3) student performance continued to be enhanced for both White and Minority students. Student achievement was assessed using the Discovery Inquiry Test in Science during sixth through eighth grades and the Ohio Graduation Test was used in 10th grade. The same students completed the test in grades 6–8 and 10th grade. Students from the Program school significantly outperformed students who attended the control school on the 10th grade state assessment in science. Findings in this study revealed the ability for sustained, whole‐school, professional development programs to have a cumulative and residual impact on teacher change and student learning of science.     

Issues and Challenges for Middle School Mathematics Teachers in Inclusion Classrooms

The purpose of this qualitative study was to investigate typical middle school general education mathematics teachers' beliefs and knowledge of students with learning disabilities and inclusive instruction and to gain an understanding of the process of inclusion as it is implemented in middle school classrooms. In‐depth interviews, surveys, and classroom observations were conducted with seven teachers. The constant comparative method was used to analyze all interview and observation data. The findings reveal that even teachers who believe that inclusion is being successfully implemented are unclear about their responsibilities towards included students and the learning characteristics and specific mathematics teaching approaches that would be effective. The general educators feel that they were grossly under‐prepared during preservice and inservice for the realities of inclusion teaching. The study provides insights that can be used to enhance preservice and inservice programs for teachers and underscores the necessity for building teamwork and collaboration among general and special education middle school teachers.     

Exploring the Link between Reformed Teaching Practices and Pupil Learning in Elementary School Mathematics

This study examined the classroom practices of beginning elementary school teachers' instruction of mathematics and how it connected to their pupils' learning. The Reformed Teaching Observation Protocol (RTOP) was used to measure the extent to which beginning teachers used reformed teaching practices. As a measure of pupil learning, we utilized assessment scores specific to the mathematics unit observed and correlated them with teachers' RTOP scores. We found that beginning teachers who implemented reformed teaching practices tended to have pupils who scored higher on the district mathematics test with a statistically significant correlation of 0.56 (p < .05). Implications of these findings and others are discussed in terms of using the RTOP to improve practice at the elementary school level and for future school‐based research.     

Calculator Use on NAEP: A Look at Fourth‐ and Eighth‐Grade Mathematics Achievement

This article summarizes research conducted on calculator block items from the 2007 fourth‐ and eighth‐grade National Assessment of Educational Progress Main Mathematics. Calculator items from the assessment were categorized into two categories: problem‐solving items and noncomputational mathematics concept items. A calculator has the potential to be used as a problem‐solving tool for items categorized in the first category. On the other hand, there are no practical uses for calculators for noncomputational mathematics concept items. Item‐level performance data were disaggregated by student‐reported calculator use to investigate the differences in achievement of those fourth‐ and eighth‐grade students who chose to use calculators versus those who did not, and whether or not the nation's fourth and eighth graders are able to identify items where calculator use serves as an aide for solving a given mathematical problem. Results from the analysis show that eighth graders, in particular, benefit most from the use of calculators on problem‐solving items. A small percentage of students at both grade levels attempted to use a calculator to solve problems in the noncomputational mathematics concept category (items in which the use of a calculator does not serve as a tool to solve the problem).     

Students’ ratings of teacher practices

In this paper, we explore a novel approach for assessing the impact of a professional development programme on classroom practice of in-service middle school mathematics teachers. The particular focus of this study is the assessment of the impact on teachers’ employment of strategies used in the classroom to foster the mathematical habits of mind and mathematical self-efficacy of their students. We describe the creation and testing of a student survey designed to assess teacher classroom practice based primarily on students’ ratings of teacher practices.     

Integrating Science,Mathematics, and Technology in Middle School Technology‐Rich Environments: A Study of Implementation and Change

The GTECH project, funded through a grant from the GTE Foundation, prepared school teams of science, mathematics and technology teachers and an administrator to set goals for their local schools regarding implementation of electronic technology and integration of content across curricular areas. A variety of teacher‐centered staff development strategies were used to enable participants to achieve local school objectives, model and encourage active learning environments involving technology, develop integrated curriculum and provide training to their peers. GTECH staff provided workshops and summer institutes based on teacher feedback and classroom observations. Data from the Stages of Concerns Questionnaire assisted the staff in designing effective staff development activities. Over the 2‐year period, teacher teams developed and implemented integrated instructional materials and developed skills in using HyperStudio, PowerPoint, telecommunications applications, and instructional resources from the Internet. They also linked instruction to new state and national standards in science, mathematics, and technology. GTECH teachers reported that their students have expanded their knowledge and skill in problem solving, teamwork, technical expertise, and creativity.     

Crutch or Catalyst: Teachers' Beliefs and Practices Regarding Calculator use in Mathematics Instruction

This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands.     

Planning District‐Wide Professional Development: Insights Gained From Teachers and Students Regarding Mathematics Teaching in a Large Urban District

This paper describes the mechanism used to gain insights into the state of the art of mathematics instruction in a large urban district in order to design meaningful professional development for the teachers in the district. Surveys of close to 2,000 elementary, middle school, and high school students were collected in order to assess the instructional practices used in mathematics classes across the district. Students were questioned about the frequency of use of various instructional practices that support the meaningful learning of mathematics. These included practices such as problem solving, use of calculators and computers, group work, homework, discussions, and projects, among others. Responses were analyzed and comparisons were drawn between elementary and middle school students' responses and between middle school and high school responses. Finally, fifth‐grade student responses were compared to those of their teachers. Student responses indicated that they had fewer inquiry‐based experiences, fewer student‐to‐student interactions, and fewer opportunities to defend their answers and justify their thinking as they moved from elementary to middle school to high school. In the elementary grades students reported an overemphasis on the use of memorization of facts and procedures and sparse use of calculators. Results were interpreted and specific directions for professional development, as reported in this paper, were drawn from these data. The paper illustrates how student surveys can inform the design of professional development experiences for the teachers in a district.     

Middle‐School Mathematics Teachers' Beliefs in NCTM's Vision

This study examined the extent to which seventh‐ and eighth‐grade mathematics teachers are aware of National Council of Teachers of Mathematics (NCTM) standards documents, Curriculum and Evaluation Standards for School Mathematics and Principles and Standards for School Mathematics and agree with NCTM's vision of school mathematics as expressed in these documents. Quantitative data were collected through the Mathematics Standards Belief Survey (MSBS), a survey specifically designed to measure teachers' overall belief in NCTM's vision as well as in certain philosophical tenets of NCTM. Of the 82 seventh‐ and eighth‐grade mathematics teachers in the identified school district of Nevada, 73 (89.0%) participated in this study. The data revealed that, among seventh‐ and eighth‐grade mathematics teachers, secondary‐certified teachers had significantly higher MSBS scores than elementary‐certified teachers. A number of other findings were made, including significant differences among mean belief scores in the philosophical tenets of NCTM.     

Using the Mixture Rasch Model to Explore Knowledge Resources Students Invoke in Mathematic and Science Assessments

The purpose of this study was to investigate whether mixture Rasch models followed by qualitative item‐by‐item analysis of selected Programme for International Student Assessment (PISA) mathematics and science items offered insight into knowledge students invoke in mathematics and science separately and combined. The researchers administered an assessment constructed from PISA released items to 516 15‐year‐old middle school students in China. The findings suggest that while PISA attributes showed promise for providing insight into how students were classified in mathematics and science, when combined these attributes were not found. Our findings suggest that students do not seem to be applying attribute strengths to the dataset as a whole (i.e., mathematics and science items combined) in ways that differentiate them from students who appear weaker for those attributes.     

A Tutorial Program: Collaboration Between Preservice and Inservice Teachers

Many elementary school teachers face severe time constraints working individually with students who need extra help or attention in mathematics. Sometimes, children who need this attention do not receive it. At the same time, critics of teacher education programs contend that preservice teachers do not receive enough hands-on experience teaching children. The Mathematics Tutorial Program is one attempt to address both of these issues. In this program, elementary grade children are identified by their classroom teachers as needing extra help in mathematics. They are paired with preservice elementary school teachers. Each preservice teacher tutors one or more elementary children for two 30-minute sessions each week for 6 to 24 weeks. They use manipulatives and a hands-on approach. The tutors reported professional gains from their contacts with classroom teachers, mathematics educators, and elementary children. Classroom teachers involved with the program commented on the children's improved selfesteem and confidence in mathematics. The children eagerly looked forward to the time with their tutors.     

A longitudinal view of mathematics achievement of primary students: case studies from Japan, Singapore, and the United States

This paper shares results from a secondary analysis of data from the participation of Japanese, Singaporean, and U.S. students in the International Project on Mathematical Attainment (IPMA). IPMA was a longitudinal study to assess the mathematics achievement of primary students from their first year of schooling through the end of fifth grade. Tests were constructed to enable achievement on the same items to be assessed over multiple years, thus permitting the assessment of growth in achievement throughout primary school. Achievement is compared to the grade at which the content is introduced so that achievement can be related to students’ opportunity to learn.     

Enhancing Formative Assessment Practice and Encouraging Middle School Mathematics Engagement and Persistence

In the transition to middle school, and during the middle school years, students' motivation for mathematics tends to decline from what it was during elementary school. Formative assessment strategies in mathematics can help support motivation by building confidence for challenging tasks. In this study, the authors developed and piloted a professional development program, Learning to Use Formative Assessment in Mathematics with the Assessment Work Sample Method (AWSM) to build middle school math teachers' understanding of the characteristics of high‐quality formative assessment processes and increases their ability to use them in their classrooms. AWSM proved to be feasible to implement in the middle school setting. It improved teachers' practice of formative assessment, especially in their feedback practices, regardless of their pedagogical content knowledge at entry. Results from focus groups suggested that teachers were better able to implement ungraded practice and student self‐ and peer‐assessment after AWSM, and that students were more willing to engage in complex problem solving.     

Crossing the Barriers Between Preservice and Inservice Mathematics Teacher Education: An Evaluation of the Grant School Professional Development Program

A 2‐year school‐based mathematics professional development program is described and evaluated after its first year of implementation. Included in this program as its first course was a unique methods course in elementary education involving both preservice students and inservice teachers who cooperatively studied and applied reform pedagogy. The program resulted from the collaborative efforts of two institutions of higher education, a neighboring school district, the principal and teachers of one school within that district, and the state office of education. Evaluation of the first year of the program consisted of assessing the beliefs and perceptions of both preservice students and inservice teachers, along with an assessment of the mathematical achievement of the children within the classes of those teachers. Pre‐ and post‐assessments of the preservice students and inservice teachers' beliefs regarding reform pedagogy were administered using the IMAP [Integrating Mathematics and Pedagogy] Web‐Based Beliefs Survey (2006). Likert scale surveys were used to assess perceptions regarding course climate and participant relationships from both teacher groups. The mathematical achievement of children was assessed in three ways: The Wide Range Achievement Test‐3 ( Stone, Jastak, & Wilkinson, 1995 ), the Utah state criterion‐referenced assessment, and performance assessments developed specifically for use at the school. Data obtained from all sources indicated positive effects upon teachers and children, thus providing substantial evidence in support of both the value of the methods course itself and the overall professional development program. An additional evaluation will be conducted following the second year of the program.     

The Role of Teachers' Beliefs and Knowledge in the Adoption of a Reform‐Based Curriculum

Science as inquiry is a key content standard in the National Science Education Standards; however, few secondary science teachers successfully and consistently implement inquiry‐based instruction in their classrooms. This research examines the role of reform‐based curricular materials in influencing the classroom practices of 12 high school chemistry teachers and investigates the role of the teachers' knowledge and beliefs in their implementation of the reform‐based chemistry curriculum. Qualitative and quantitative data were collected in the form of beliefs interviews and classroom observations. The teachers' classroom practices were measured prior to and during the field test of the reform‐based chemistry curriculum. Analysis of the data revealed that teachers' classroom practice became more reform‐based in the presence of the new curriculum; however, the degree of change is related to the teachers' beliefs about teaching and learning, depth of chemistry knowledge, and years of teaching experience. Experienced, out‐of‐discipline teachers with transitional or student‐centered teaching beliefs demonstrated the most growth in reform‐based teaching practices. This study reinforces the need for reform‐based curriculum to assist teachers in implementing the intent of the National Science Education Standards.     

Knowing students as mathematics learners and teaching numbers 10–100: A case study of four 1st grade teachers from Romania

Researchers have increasingly linked teacher effectiveness with teacher knowledge of subject matter, curriculum, and teaching. Moreover, teacher knowledge of students has been regarded as another very significant component of teacher knowledge, influencing the classroom practice and student performance. Knowing students as mathematics learners means being aware of the ways students learn certain topics. This study examined the knowledge of students as mathematics learners displayed by four 1st grade teachers from Romania when designing and implementing a lesson on numbers 10–100. Findings show that knowledge of students as mathematics learners influenced the ways teachers planned and implemented their lesson. Teachers learned about students as mathematics learners from one series to another, and they tailored their use of manipulatives and classroom activities to meet the needs of their current students.     

Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: validation of the COACTIV constructs

Research interest in the professional knowledge of mathematics teachers has grown considerably in recent years. In the COACTIV project, tests of secondary mathematics teachers’ pedagogical content knowledge (PCK) and content knowledge (CK) were developed and implemented in a sample of teachers whose classes participated in the PISA 2003/04 longitudinal assessment in Germany. The present article investigates the validity of the COACTIV constructs of PCK and CK. To this end, the COACTIV tests of PCK and CK were administered to various “contrast populations,” namely, candidate mathematics teachers, mathematics students, teachers of biology and chemistry, and advanced school students. The hypotheses for each population’s performance in the PCK and CK tests were formulated and empirically tested. In addition, the article compares the COACTIV approach with related conceptualizations and findings of two other research groups.     

Urban Third Grade Teachers' Practices and Perceptions in Science Instruction with English Language Learners

The study examined relationships among key domains of science instruction with English language learning (ELL) students based on teachers' perceptions of their classroom practices (i.e., what they think they do) and actual classroom practices (i.e., what they are observed doing). The four domains under investigation included: (1) teachers' knowledge of science content; (2) teaching practices to support scientific understanding; (3) teaching practices to support scientific inquiry; and (4) teaching practices to support English language development during science instruction. The study involved 38 third‐grade teachers participating in the first‐year implementation of a professional development intervention aimed at improving science and literacy achievement of ELL students in urban elementary schools. Based on teachers' self‐reports, practices for understanding were related to practices for inquiry and practices for English language development. Based on classroom observations in the fall and spring, practices for understanding were related to practices for inquiry, practices for English language development, and teacher knowledge of science content. However, we found a weak to non‐existent relationship between teachers' self‐reports and observations of their practices.