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.     

Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable

This article reports results from a study focused on teachers' knowledge of students' understanding of core algebraic concepts. In particular, the study examined middle school mathematics teachers' knowledge of students' understanding of the equal sign and variable, and students' success applying their understanding of these concepts. Interview data were collected from 20 middle school teachers regarding their predictions of student responses to written assessment items focusing on the equal sign and variable. Teachers' predictions of students' understanding of variable aligned to a large extent with students' actual responses to corresponding items. In contrast, teachers' predictions of students' understanding of the equal sign did not correspond with actual student responses. Further, teachers rarely identified misconceptions about either variable or the equal sign as an obstacle to solving problems that required application of these concepts. Implications for teacher professional development are discussed.     

Science Self‐Efficacy and School Transitions: Elementary School to Middle School,Middle School to High School

This study examined the science self‐efficacy beliefs of students at the transition from elementary school (Grade 6) to middle school (Grade 7) and the transition from middle school (Grade 8) to high school (Grade 9). The purpose was to determine whether students' perceived competence is impacted at these important school transitions and if the effect is mediated by gender and ethnicity. Science self‐efficacy was measured through a modified Self‐Efficacy Questionnaire for Children, which was adapted to focus specifically on science self‐efficacy. Multiple ordinary least squares regression was used to analyze the data. Two models were developed, one using ninth grade as the comparison group and the other using sixth grade as the comparison group. In each model, the independent variables (grade level, gender, and ethnicity) were regressed on the dependent variable, science self‐efficacy. The most striking finding was the large and significant decline in science self‐efficacy scores for ninth graders at the transition to high school. We also found that females and Hispanic students had lower scores across grades as compared to males and Caucasians. How these results relate to existing studies, and implications for practice and future research are discussed.     

Prospective Elementary Teachers' Perceptions of Gender Differences in Children's Attitudes Toward Mathematics

Prospective elementary teachers hold preconceived ideas about elementary school students' attitudes toward mathematics. We found that there exists a gender bias with prospective teachers expecting girls to have negative attitudes toward mathematics and boys more likely to have positive attitudes toward mathematics. We found that these expectations exist for both prospective teachers in a traditional undergraduate degree program and prospective teachers in an alternative licensure graduate degree program. We also found that these expectations do change with the completion of a mathematics methods course and classroom experiences.     

Problem Solving: Teachers' Perceptions,Content Area Models,and Interdisciplinary Connections

Features of common problem-solving models in mathematics and science, as well as those found in business and industry today, are discussed. Commonalties in the models are used to advance a case for interdisciplinary or integrated instruction in mathematics, science and technology. The Integrated Mathematics, Science and Technology (IMaST) program's problem-solving model is presented as an example of a curriculum project that draws upon the commonalties in the problem-solving models as a basis for a seventh grade integrated curriculum.     

Middle School Mathematics Teachers’ Perceptions of the Common Core State Standards for Mathematics and Its Impact on the Instructional Environment

This study examines Middle School Mathematics Teachers’ (MSMTs') (N = 1,241) perceptions of the Common Core State Standards for Mathematics (CCSSM) and its impact on the instructional environment. A total of eight factors appear in the data. These factors include professional support, teachers’ use of district‐adopted and non‐district‐adopted curricular resources, influence of CCSSM assessment and teacher evaluation on the instructional environment, influence of the CCSSM on classroom instruction, teachers’ planning practices, and perceived rigor of the CCSSM. The data suggest that teachers’ use of digital resources located online was disconnected from their district‐adopted resources suggesting a lack of curricular coherence. MSMTs note that the CCSSM had caused them to incorporate more reform‐oriented practices such as exploration and productive struggle into their daily instruction. MSMTs also perceive that the CCSSM includes new content that is more rigorous than previous state standards. Sampled MSMTs state that while state assessments will measure CCSSM content, they are less likely to include more complex problems or the standards for mathematical practice. Teachers are more likely to read teacher resources than student textbook activities online and to use digital resources for remediation instead of inquiry activities. Over one‐third of MSMTs wanted more CCSSM professional development.     

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.     

Measuring K‐8 Teachers' Perceptions of Discourse Use in Their Mathematics Classes

This article documents the development and use of a survey instrument designed to measure K‐8 mathematics teachers ‘perceptions about discourse in mathematics classes. In particular, the 5‐point Likert‐type survey sought to address teachers ‘perceptions of their use of dialogic (dialogue to construct new meaning), univocal (conveying information), and general discourse in their mathematics classes. Factor analysis revealed three reliable factors that were compatible with the original constructs, these include: dialogic discourse (α₃= .67), univocal discourse (α₁= .83), and general discourse (α₂= .68). These results suggest a framework that could be used to uncover K‐8 teachers' perceptions of their use of discourse in mathematics instruction, especially if there is interest in tendencies toward univocal or dialogic discourse. In addition to research implications, the survey could be used to inform the design and implementation of teacher professional development that focuses on discourse in mathematics instruction.