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).     

A Comparison of Concrete and Virtual Manipulative Use in Third‐ and Fourth‐Grade Mathematics

The primary purpose of this classroom experiment was to examine the effectiveness of concrete (hands‐on) manipulatives as compared with virtual (computer‐based) manipulatives on student review of fraction concepts in third grade and introduction of symmetry concepts in fourth grade. A pretest–posttest design was employed with a sample of 91 third‐grade students and 54 fourth‐grade students who were randomly assigned to complete a lesson using either concrete or virtual manipulatives. Students used a variety of manipulative materials during the lessons. Results of the posttest suggest that student learning was unchanged by lesson condition.     

Preparing Pre‐Service Teachers to Teach Mathematics in Inclusive Classrooms: A Three‐Year Case Study

Federal and state regulations mandating inclusion of students with disabilities in general education classes have made it essential to create pathways for pre‐service teachers to develop skills to teach content to diverse groups of students. The study uses a framework suggested by the relationship between teacher attitude and teacher behavior ( Fullan, 1982 ), teacher beliefs and practice, and self‐efficacy and behavioral change ( Bandura, 1977 ). The purpose of the study was to examine changes, if any, in three cohorts of general education teacher candidates' (n=13, n=8, n=5) attitudes toward teaching mathematics to students with disabilities after participating in focused instructional experiences which provided both information and vicarious positive teaching activities in special education. Data collected included pretest and posttest scores for each of the three cohorts and journal entries. Little or no change in attitude towards students with disabilities and mathematics, and efficacy to teach students with disabilities was observed for the year one and year two cohorts. In the third year the modules were combined with a structured field experience. The data collected from the third year cohort suggested a positive trend in attitude as measured by the survey data and field experience journal data. Future study with larger samples is needed.     

Teaching Multiple Modes of Representation in Middle‐School Science Classrooms: Impact on Student Learning and Multimodal Use

This quasi‐experimental study investigated how explicit instruction about multiple modes of representation (MMR) impacted grades 7 (n = 61) and 8 (n = 141) students’ learning and multimodal use on end‐of‐unit assessments. Half of each teacher's (n = 3) students received an intervention consisting of explicit instruction on MMR in science discourse, in addition to regular science instruction enhanced by a focus on MMR; comparison groups of students received regular science instruction. Three ordinary least squares regression models used student demographic variables and whether or not students received the intervention to predict students’ (a) gain scores on end‐of‐unit tests, (b) voluntary use of embedded MMR on unit tests, and (c) retention of science knowledge as measured by a state end‐of‐level criterion‐referenced assessment. Analyses showed that explicit instruction on MMR did not make a significant impact on student gain scores, the amount of embeddedness on unit tests, or end‐of‐level scores. However, Models 2 and 3 showed Hispanics and females used MMR more on end‐of‐unit tests than Whites or males, respectively, whether or not they received the intervention. Hispanics and females scored lower than Whites or males, respectively, on end‐of‐level, multiple‐choice assessments. Implications for classroom teachers and educational researchers in relation to these underserved populations are discussed.     

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.     

Fundamental Fraction Knowledge of Preservice Elementary Teachers: A Cross‐National Study in the United States and Taiwan

The purpose of this paper is to show the similarities as well as the differences of fundamental fraction knowledge owned by preservice elementary teachers from the United States (N= 89) and Taiwan (N= 85). To this end, we examined and compared their performance on an instrument including 15 multiple‐choice test items. The items were categorized into four different types of fundamental fraction constructs, including part–whole relationship, quotient, equivalence, and meanings of operations. Each item was embedded in the area, linear, or set model except for the items constructed out of the meaning of operations. Several items were featured with a pictorial illustration. Quantitative analysis showed that U.S. preservice teachers were significantly outperformed by their Taiwanese counterparts overall. The difference between the two groups was statistically significant on 12 of 15 items. Findings suggest that preservice elementary teachers from both countries need to be better prepared in their understanding of the meaning of fraction multiplication or division operations. Findings also suggest that U.S. preservice elementary teachers need to be more knowledgeable in dealing with fraction problems embedded in a linear model. Further research is suggested to study the issues raised from the findings.     

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.     

Re‐examining Test Item Issues in the TIMSS Mathematics and Science Assessments

As the largest international study ever taken in history, the Trend in Mathematics and Science Study (TIMSS) has been held as a benchmark to measure U.S. student performance in the global context. In‐depth analyses of the TIMSS project are conducted in this study to examine key issues of the comparative investigation: (1) item flaws in mathematics and science; (2) inability to reflect item score differences between adjacent grades; (3) ambiguity of the test items behind nonrandom guessing; and (4) unfair comparisons resulted from inconsistent item difficulties across the nations. The TIMSS item checking could help education stakeholders understand more profound assessment issues through the information triangulation.     

The Role of Reflection in Elementary Mathematics and Science Teachers' Training and Development: A Meta‐Synthesis

Meaningful and effective training and professional development programs for teachers are key to the improvement of teaching practices in our schools. In this paper, the authors offer a meta‐synthesis of the literature on the role of reflection for mathematics and science teachers within the context of professional development. The authors frame this review using Desimone's core components of professional development, a research‐based framework emphasizing components tied to positive outcomes (content focus, active learning, coherence, duration, and collective participation). A synthesis of literature in this area shows that few training and professional development programs include all five components of Desimone's core conceptual framework for effective professional development linked to positive outcomes. Further, the authors find in their review that increased contact hours included in a professional development program produce an increase in frequency, duration, and depth of reflective practice for teachers.