The Effects of a Mathematics Infusion Curriculum on Middle School Student Mathematics Achievement

Increasing mathematical competencies of American students has been a focus for educators, researchers, and policy makers alike. One purported approach to increase student learning is through connecting mathematics and science curricula. Yet there is a lack of research examining the impact of making these connections. The Mathematics Infusion into Science Project, funded by the National Science Foundation, developed a middle school mathematics‐infused science curriculum. Twenty teachers utilized this curriculum with over 1,200 students. The current research evaluated the effects of this curriculum on students' mathematics learning and compared effects to students who did not receive the curriculum. Students who were taught the infusion curriculum showed a significant increase in mathematical content scores when compared with the control students.     

Secondary Options and Post‐secondary Expectations: Standards‐based Mathematics Programs and Student Achievement on College Mathematics Placement Exams

Research on student achievement within the University of Chicago School Mathematics Project (UCSMP) and Core‐Plus Mathematics Project (CPMP) at the secondary level is beginning to accumulate, however, much less is known about how prepared these students are for post‐secondary education. Therefore this study involving students within one tracked school district used multiple linear regression to examine the role of differential experience within two secondary Standards‐based mathematics programs, gender, and prior mathematics achievement on college algebra and calculus readiness placement test scores. Results show that there are no significant differences between students who had completed three and four years of the CPMP curriculum. UCSMP students with four or five years of experience significantly outperformed CPMP students on both assessments. Prior achievement was a significant predictor of student achievement on both examinations. Male students outperformed female students on the algebra placement exam. Students who had studied from both CPMP and UCSMP significantly outperformed students who had studied from CPMP for four years on the calculus readiness examination.     

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.     

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).     

Using Similarities and Differences: A Meta‐Analysis of Its Effects and Emergent Patterns

The purpose of the study was to update previous meta‐analytic findings on the effectiveness of using similarities and differences as an instructional strategy. The strategy includes facilitating student comparison, classification, use of analogies, and use of metaphors. Previously, Marzano, Pickering, and Pollock reported a mean effect size of 1.61. For the present meta‐analysis, literature was searched to locate experimental studies meeting the following inclusion criteria: published between 1998 and 2008; examined effects of facilitating student comparison, classification, use of analogies, and use of metaphors; measured student academic achievement as an outcome; involved students in kindergarten through grade 12; and provided data necessary to compute effect sizes. Based on the eligible research, the overall mean effect size (Hedges' g) was .65, confirming earlier results indicating that using similarities and differences positively influences student achievement. Type of control group, however, moderated the effect. Larger effect sizes were associated with control groups receiving textbook‐guided instruction versus those receiving interactive instruction. Emergent patterns were observed for the positive influence of long‐term instruction, systematic instruction, supportive cuing, and opportunity for reflection and discussion. Results support recommendations to guide students through analogical reasoning about, and classification of, important concepts and relationships in content‐area instruction.     

The Relationships Between Parental Influence and Student Achievement in Seventh Grade Mathematics

Parental influence has been identified as an important factor affecting student achievement, but the variables addressed by various parent-school partnership programs vary, and lack literature support. This deficiency was ameliorated in this study through an analysis of a national data base from the Longitudinal Study of American Youth (LSAY). AH parental variables investigated in LSAY were considered in this study, and significant variables of students' achievement in seventh grade mathematics were selected through the Backward Elimination Procedure in the Statistical Analysis System (SAS). The results show that those variables significant at α= .05 have accounted for around 22% variability of the student achievement. A further analysis of the empirical results seems to indicate that parent education and encouragement are strongly related to improved student achievement. However, parents should attempt to understand students' feeling, and expect students to take the full responsibility for their successes in the school.     

Assessing the Use of Graphing Calculators in College Algebra: Reflecting on Dimensions of Teaching and Learning

This article considers various aspects of teaching and learning stemming from the integration of graphing calculator use in a semester-long college algebra course. The project examined four class sections, in which two instructors each taught one section using graphing calculators and one section using a traditional approach. Achievement and attitude data showed no significant differences for treatment or instructor; a significant difference in achievement was found for gender. Students in the calculator sections responded to an open-ended questionnaire about their use of the calculator and were generally supportive of the technology. Students were in agreement about specific topics for which the technology was most useful. Overall, findings indicated that the technology use had a positive impact on various dimensions of student learning.     

Complex Applications of HLM in Studies of Science and Mathematics Achievement: Cross‐Classified Random Effects Models

Hierarchical linear models have become a familiar method for accounting for a hierarchical data structure in studies of science and mathematics achievement. This paper illustrates the use of cross‐classified random effects models (CCREMs), which are likely less familiar. The defining characteristic of CCREMs is a hierarchical data structure defined by multiple random factors at higher levels. We illustrate CCREMs using data for approximately 10,000 students from more than 250 high schools who attended one of 27 four‐year postsecondary institutions. The appropriate use of CCREMs helps to ensure unbiased estimates of effects and credible inferences.     

The Effects of Metacognitive Reflective Assessment on Fifth and Sixth Graders' Mathematics Achievement

The purpose of this experimental study was to investigate the effects of metacognitive reflective assessment instruction on student achievement in mathematics. The study compared the performance of 141 students who practiced reflective assessment strategies with students who did not. A posttest‐only control group design was employed, and results were analyzed by conducting one‐way analysis of variance (ANOVA) and nonparametric procedures. On both a posttest and a retention test, students who practiced reflective strategies performed significantly higher than students who did not use the strategies. A within‐subjects ANOVA was also conducted six weeks following the intervention to assess how the factor of time affected retention levels. No significant difference was found between the posttest and retention test results for the experimental groups or the control group.     

The Effects of Project‐Based Learning on Students' Academic Achievement,Attitude, and Retention of Knowledge: The Subject of “Electricity in Our Lives”

The aim of this study is to analyze the effects of project‐based learning on students' academic achievement, attitude, and retention of knowledge in relation to the subject of “Electricity in Our Lives” in a fourth‐grade science course. The study was conducted in a quasi‐experimental design as a “pre‐test, post‐test with control group.” In the experimental group, the unit was taught through the project‐based learning method. The measuring tools were administered to both groups before and after the applications. To perfectly analyze the “process” of the method, seven different learning assessment “forms” were administered to the students. The findings of the forms indicated that the students learn to construct their own learning and to evaluate changes in their own behavior through the application of the method. The application of different methods between both groups had a statistically significant effect in terms of academic achievement, (F(1,112) = 46.78, p = .000) and of retention of knowledge (F(1,112) = 35.24, p = .000). However, there were no statistically significant effects from being in different groups for the attitudes of students (F(1,112) = .99, p = .321). For the students, being in the project‐based learning groups resulted in better academic achievement and retention of knowledge than being in the traditional teaching group.     

The Effect of Calculator‐Based Ranger Activities on Students' Graphing Ability

Middle school students can learn to communicate with graphs in the context of appropriate Calculator‐Based Ranger (CBR) activities. Three issues about CBR activities on graphing abilities were addressed in this study: (a) the effect of CBR activities on graphing abilities; (b) the extent to which prior knowledge about graphing skills affects graphing ability; (c) the influence of instructional styles on students' graphing abilities. Following the use of CBR activities, students' graphing abilities were significantly more developed in three components _ interpreting, modeling, and transforming. Prior knowledge of graphing skills on the Cartesian coordinate plane had little effect on students' understanding of graphs. Significant differences, however, were found in students' achievement, depending on instructional styles related to differentiation, which is closely connected to transforming distance‐time graphs to velocity‐time graphs. The result of this study indicates that the CBR activities are pedagogically promising for enhancing graphing ability of physical phenomena.     

The Role of Interactions Between Student and Classroom Context in Developing Adaptive Self‐Efficacy in One Sixth‐Grade Mathematics Classroom

Research and theory suggest several instructional practices that could enhance student self‐efficacy. However, little is known about the ways these instructional practices interact with individual students to create opportunities or challenges for developing adaptive self‐efficacy. In this study, we focused on two sources of efficacy, mastery experiences, and social persuasion, and examined how these sources were structured for three students with different levels of mathematics achievement and self‐efficacy within a sixth‐grade mathematics classroom. Analyses within each case showed that each student experienced success and received social persuasion differently. On the other hand, analyses across the cases suggest that not only the amount but also the form (i.e., with and without assistance) of successful experiences and the type of performances (e.g., stating definitions, explaining solution procedures, sharing problem‐solving strategies, and making comments on others' ideas) through which the student experienced mastery may have played important role in developing self‐efficacy. Consistently, the amount and form of teacher feedback was different for each focal student. Examining these differences provide insight into each student's self‐efficacy assessed over the course of the study as well as the kind of support each student needed to develop adaptive self‐efficacy.     

The Effect of Journal Writing on Achievement in and Attitudes Toward Mathematics

A teaching experiment was conducted to investigate the effect of journal writing on achievement in and attitudes toward mathematics. Achievement variables included conceptual understanding, procedural knowledge, problem solving, mathematics school achievement, and mathematical communication. Subjects were selected from first intermediate students (11–13 years) attending the International College, Beirut, Lebanon, where either English or French is the language of mathematics instruction. The journal-writing (JW) group received the same mathematics instruction as the no-journal-writing (NJW) group, except that the JW group engaged in prompted journal writing for 7 to 10 minutes at the end of each class period, three times a week, for 12 weeks. The NJW group engaged in exercises during the same period. The results of ANCOVA suggest that journal writing has a positive impact on conceptual understanding, procedural knowledge, and mathematical communication but not on problem solving, school mathematics achievement, and attitudes toward mathematics. Gender, language of instruction, mathematics achievement level, and writing achievement level failed to interact with journal writing. Student responses to a questionnaire indicated that students found journal writing to have both cognitive and affective benefits.