Gender differences in mathematics achievement in Jordan: A differential item functioning analysis of the 2015 TIMSS

This study is within the framework of the United Nations sustainable development goals related to equitable quality education. The total score on the 2015 Trends in International Mathematics and Science Study that indicated eighth‐grade girls in Jordan significantly outperformed boys is hiding many details related to the quality of mathematics learning that reflect a gender gap. Data were analyzed using the Mantel–Haenszel differential item functioning analysis procedure to investigate test items that favored either boys or girls. The results showed that boys were more likely than girls to correctly answer the more difficult, unfamiliar, life‐related mathematical problems. In contrast, girls were more likely than boys to correctly answer the familiar, less difficult, and not life‐related problems. Some recommendations were suggested to diminish this gender gap that goes each way.     

New Perspectives on the Gender Stereotyping of Mathematics

Historically, mathematics has been stereotyped as a male domain, and there is considerable evidence to support this belief. In the last 30 years, mathematics education researchers have uncovered a range of factors contributing to the documented achievement and participation differences that favored males and sought to redress them. Mathematics as a male domain, one of the subscales of the Fennema-Sherman Mathematics Attitude Scales (1976), has been used widely to assess the extent to which mathematics is stereotyped as a masculine sphere. It has been argued that some of the items comprising the subscale are anachronistic and that the subscale scores can no longer be interpreted reliably. In this article we outline the development of two new instruments-the mathematics as a gendered domain instrument and the who and mathematics instrument-that have been designed to overcome the limitations of the original Fennema-Sherman mathematics as a male domain subscale. We also present findings from the administration of the two instruments in Australia, where they were developed, and in the United States, the site of the trials of the original Fennema-Sherman scales. The results indicate that females feel more strongly than males about some aspects of gender stereotyping in mathematics although, in general, most students feel that mathematics is gender neutral.     

New Perspectives on the Gender Stereotyping of Mathematics

Historically, mathematics has been stereotyped as a male domain, and there is considerable evidence to support this belief. In the last 30 years, mathematics education researchers have uncovered a range of factors contributing to the documented achievement and participation differences that favored males and sought to redress them. Mathematics as a male domain, one of the subscales of the Fennema-Sherman Mathematics Attitude Scales (1976), has been used widely to assess the extent to which mathematics is stereotyped as a masculine sphere. It has been argued that some of the items comprising the subscale are anachronistic and that the subscale scores can no longer be interpreted reliably. In this article we outline the development of two new instruments-the mathematics as a gendered domain instrument and the who and mathematics instrument-that have been designed to overcome the limitations of the original Fennema-Sherman mathematics as a male domain subscale. We also present findings from the administration of the two instruments in Australia, where they were developed, and in the United States, the site of the trials of the original Fennema-Sherman scales. The results indicate that females feel more strongly than males about some aspects of gender stereotyping in mathematics although, in general, most students feel that mathematics is gender neutral.     

Gender‐Related Beliefs and Mathematics Performance of Preservice Primary Teachers

The aim of this study was to examine whether there are gender differences in mathematics achievement and in beliefs about mathematics of preservice teachers over a period of four years. Data were collected from preservice teachers (156 males and 155 females) from the Ad?yaman University Faculty of Education in Turkey. The Mathematics as a Gendered Domain instrument was used to investigate preservice teachers' beliefs about the gender differences in mathematics. The results indicated that gender had no effect on mathematics performances of the preservice primary teachers. Findings of this research show that most of the male and female preservice primary teachers do not gender‐stereotype mathematics and believe that mathematics is gender neutral, although there are gender differences on some types of items of instrument.     

Gender Differences in Risk-Taking Behavior and their Relationship to SAT-Mathematics Performance

This study focused on the relationship of an individual's risk-taking behavior and his/her performance on the mathematics section of the Scholastic Aptitude Test (SAT-M). Previous research in this area has found that on multiple choice tests, calculated guessing (risk-taking) plays a role in the score one obtains. Risk-taking behavior was defined by the number of items omitted by the student on the instrument designed for the purpose of assessing this behavior. The data were obtained from 89 students who were attending two colleges in upstate New York. The data consisted of SAT-M scores and performance scores on a mathematics test designed to assess risk-taking. A t-test performed on the number of omissions revealed that females omit more items and thus manifest less risk-taking behavior. A significant difference in favor of females omitting more items was found at the p < .01 level. A multiple regression design was employed, and gender and risk-taking behavior were found to be significantly related at the p<.01 level to a student's performance on the SAT-M.     

The Effect of a Modified Moore Method on Attitudes and Beliefs in Precalculus

As part of a study on the effects of teaching with a Modified Moore Method (MMM), a survey containing 20 items from Schoenfeld's (1989 ) investigation of attitudes and beliefs about mathematics was administered to students in undergraduate precalculus classes. The study included one section of precalculus taught with an MMM, a student‐centered and inquiry‐based teaching method, and two sections taught using traditional lecture methods. The survey was administered one week into the semester, following the drop/add date, and during the last week of classes. In this paper, we discuss the findings of the attitudes and beliefs portions of the survey and correlations with scores on a common final exam. We looked for differences between the MMM and traditional sections as well as gender differences. There were only a few differences in the attitudes and beliefs among the students, although there were more changes for females than males and all the significant differences were positive. The correlation between attitudes and beliefs and final exam scores was much stronger in the traditionally taught classes than in the MMM class. When separated by gender, only the reported attitudes and beliefs of the females in the traditional class significantly correlated with final exam scores.     

How Much Do Mathematics Skills Improve With Age? Evidence From LTT NAEP

The Long‐Term Trend (LTT) mathematics assessment of the National Assessment of Educational Progress (NAEP) used the same set of items from 1982 through 2004, including 20 items that were administered to 9‐ and 13‐year‐olds, 29 items that were administered to 13‐ and 17‐year‐olds, and 4 items that were administered at all three ages. This study used these items to identify areas of mathematics that had substantial gain from one age level to the next and to identify patterns of gain by age and how those patterns changed over time. Findings included the facts that older students usually did better on items than younger students, although item context and wording was often as important as mathematical knowledge in explaining differences in performance by age. LTT NAEP included a unique set of estimation items and analysis of performance on those items showed that students at all levels could identify an appropriate estimate only when numbers were small and the context for the estimate was familiar. The LTT data also indicated that addition and subtraction skills of 9‐year‐olds increased and the estimation skills of 13‐ and 17‐year olds improved in some contexts from 1982 through 2004.     

Perceptions of Mathematics and Gender

This study examined students’ perceptions about gender and the subject of mathematics, as well as gender and mathematics learning. Secondary school students and pre‐service elementary teachers were surveyed using the Mathematics as a Gendered Domain and Who and Mathematics instruments developed by Leder and Forgasz ( Leder, 2001 ). The data indicate that, similar to findings from the 1970s, students believe that mathematics is gender neutral, although females hold this belief more strongly than males. Female secondary school students hold beliefs in gender neutrality more strongly than female pre‐service teachers. Data for secondary school students indicate that both males and females see differences in the way boys and girls act and are treated in mathematics classes (e.g., boys cause more distractions while girls care more about doing well). The data also show that secondary school males who believe they are good mathematics students tend to have more gender‐neutral perceptions than those who believe they are average or below average. No such pattern appears for secondary school females.     

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.     

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.     

An overview of the gender factor in mathematics in TIMSS-2003 for the Asia-Pacific region

This paper highlights the gender factor in the Trends in Mathematics and Science Study in 2003 (TIMSS-2003) of eight participating countries from the Asia-Pacific region: Chinese Taipei, Hong Kong-SAR, Indonesia, Japan, Republic of Korea, Malaysia, Singapore, and the Philippines (Chinese Taipei and Hong Kong-SAR will be referred to as countries in this paper.) in mathematics. The focus is on gender-related data encompassing the overall performance of students from the participating countries and their performance in the content and cognitive domains. At grade 8 level, the gender difference in the overall performance of students mirrored the international average and favored girls in all countries of the Asia-Pacific region (except in Japan and the Republic of Korea). The regional data also showed that, in general, the Philippines and Singapore can be considered to be at one extreme with gender differences favoring girls in both content and cognitive domains, and the Republic of Korea and to some extent Japan are at the other extreme with the gender differences favoring boys. At grade 4 level, girls from the Philippines and Singapore also performed better than the boys whereas the boys from Japan and Chinese Taipei did slightly better than the girls.     

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).     

Controlling Choice: Teachers,Students, and Manipulatives in Mathematics Classrooms

This research study examines the instructional practices of 10 middle grades teachers related to their use of manipulatives in teaching mathematics and their control of mathematics tools during instruction. Through 40 observations of teaching, 30 interviews, and an examination of 67 written documents (including teachers' plans and records), profiles were developed that describe how teachers used and controlled manipulatives during instruction. Results showed that teachers used a variety of manipulatives and other mathematics tools over the course of the year‐long study. Teachers reported using a mathematics tool (manipulative, calculator, or measuring device) in 70% of their lessons, and this self‐report was verified by observations in which teachers used mathematics tools in 68% of their lessons. During a 3‐ to 4‐month period of “free access,” in which students had some measure of control in their selection and use of the mathematics tools, the students used manipulatives spontaneously and selectively. During free access, teachers exhibited various behaviors, including posting lists of items on containers, assigning group leaders to manage tools, and negotiating the control of the mathematics tools during instruction.     

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.     

“Do we teach subjects or students?” Analyzing science and mathematics teacher conversations about issues of equity in the classroom

Teachers involved in a Master's level course in diversity participated in virtual, synchronous, anonymized discussions around issues of ethnic and racial diversity, gender, and stereotypes that could impact their students’ participation in fields related to science, technology, engineering, and mathematics (STEM). Guided by theoretical frameworks from Social Cognitive Career Theory (SCCT) and Critical Race Theory (CRT), a convenience sample of 14 science and mathematics teachers participated in a series of virtual chats using open‐ended questioning and facilitated by two university instructors. Using conversation and critical discourse analyses, three primary themes emerged: understanding of issues related to stereotypes, encouragement of females and minorities to pursue careers in STEM, and the place for diversity discussions in science and mathematics classrooms. The teachers felt burdened by curricular and administrative constraints that inhibit their ability to participate in thought‐provoking critical conversations. The paper concludes with a discussion of ways teachers can assist in the STEM career identity development of their underrepresented females and students of color and calls for research that combines the key findings in SCCT and CRT to build confidence and capacity for teachers to effectively confront issues of racism, sexism, and stereotyping in science and mathematics classrooms.     

Revisiting the STEBI‐B: Measuring Self‐Efficacy in Preservice Elementary Teachers

The Science Teaching Efficacy Belief Instrument‐Preservice (STEBI‐B) has been used in many studies to measure science teaching self‐efficacy and outcome expectancy in preservice elementary teachers. Since its development in 1990, there have been no studies that have re‐examined its internal validity and reliability. The purpose of this study was to do so. Two hundred ninety preservice elementary teachers participated in this study. The STEBI‐B was administered at the beginning of science methods courses. A factor analysis established that the two subscales, Personal Science Teaching Efficacy Belief (PSTE) and Science Teaching Outcome Expectancy (STOE), on the STEBI‐B were homogeneous, and loadings were comparable to those reported by Enochs and Riggs (1990) . Two items on the STOE were found to exhibit cross‐loading on the factor analysis, as well as low item‐total correlations. These two items were modified and the revised instrument administered to 86 new participants. Both revised items loaded more clearly on the STOE subscale, and item‐total correlations were stronger. Comparison of means analyses showed that gender, number of science courses taken, and school science experiences had significant associations with PSTE. The STEBI‐B continues to be employed in hundreds of studies to measure science teaching self‐efficacy. It is important to continue to monitor its reliability and validity, as well as check on associations with various background variables. The modified STEBI‐B is included in an appendix with this article.     

The Effect of a Horseshoe Crab Citizen Science Program on Middle School Student Science Performance and STEM Career Motivation

The purpose of the present quasi‐experimental study was to examine the impact of a horseshoe crab citizen science program on student achievement and science, technology, engineering, and mathematics (STEM) career motivation with 86 (n = 86) eighth‐grade students. The treatment group conducted fieldwork with naturalists and collected data for a professional biologist studying horseshoe crab speciation and a mock survey. The comparison group studied curriculum related to horseshoe crabs in the science classroom. A series of measures related to self‐efficacy, interest, outcome expectations, choice goals, and content knowledge were given to participants before and after the intervention. It was hypothesized that students would report higher motivational beliefs regarding science and show higher levels of achievement following the intervention than the comparison group. Support was shown for most of the hypotheses. In addition, path analyses indicated that students' motivational beliefs influence content knowledge and outcome expectations, which in turn affect their career goals. These results have implications for incorporating authentic fieldwork within a formal school structure as an effective method for promoting student achievement and STEM career motivation.     

Gender and Racial Differences: Development of Sixth Grade Students' Geometric Spatial Visualization within an Earth/Space Unit

This study investigated sixth‐grade middle‐level students' geometric spatial development by gender and race within and between control and experimental groups at two middle schools as they participated in an Earth/Space unit. The control group utilized a regular Earth/Space curriculum and the experimental group used a National Aeronautics and Space Administration‐based curriculum. The quantitative data sources included the Lunar Phases Concept Inventory, Geometric Spatial Assessment, and the Purdue Spatial Visualization–Rotation Test. The results indicated the experimental males and females, and the students of color and white students in the experimental group showed significant gains in their understanding of geometric spatial visualization from pre‐ to post‐implementation. However, for the control group, the significant gains were limited to the males and the white students. The findings reveal that support is needed for males, females, and all racial groups to have the opportunity to develop their spatial reasoning, which in turn, increases students' scientific understanding.     

Radiation conditions for the linear water‐wave problem in periodic channels

We study the well‐posedness of the linearized water‐wave problem in a periodic channel with fixed or freely floating compact bodies. Floquet–Bloch–Gelfand‐transform techniques lead to a generalized spectral problem with quadratic dependence on a complex parameter, and the asymptotics of the solutions at infinity can be described using Floquet waves. These are constructed from Jordan chains, which are related with the eigenvalues of the quadratic pencil and which are calculated in the paper in some typical cases. Posing proper radiation conditions requires a careful study of spaces of incoming and outgoing waves, especially in the threshold situation. This is done with the help of a certain skew‐Hermitian form q , which is closely related to the Umov–Poynting vector of energy transportation. Our radiation conditions make the problem operator into a Fredholm operator of index zero and provides natural (energy) classification of outgoing/incoming waves. They also lead to a novel, most natural properties and interpretation of the scattering matrix, which becomes unitary and symmetric even at threshold.     

Peruvian Food Chain Jenga: Learning Ecosystems with an Interactive Model

A pilot study was conducted on a multimodal educational tool, Peruvian Food Chain Jenga (PFCJ), with 5th‐grade students (N = 54) at a public charter school. The goal was to compare the effectiveness of the multimodal tool to a more traditional presentation of the same materials (food chain) using an experimental/control design. Data collection included a pretest/posttest and a “What I Did/What I Learned” response sheet. Quantitative analysis of pretest/posttest results showed both groups improved from pretest to posttest; however, there was no statistically significant difference between posttest results of experimental and control groups. Qualitative analysis of student open‐ended responses indicated a difference between students who used the PFCJ and students in the control. The most striking difference occurred in how the students perceived the connectedness of species and the awareness of human impact. Our findings suggest that using a model such as PFCJ as a means of teaching and connecting scientific content with practices related to ecosystems is an effective method of engaging students in intelligent discussions about these topics.