The Effects of Non‐CAS Graphing Calculators on Student Achievement and Attitude Levels in Mathematics: A Meta‐Analysis

Forty‐two studies comparing students with access to graphing calculators during instruction to students who did not have access to graphing calculators during instruction are the subject of this meta‐analysis. The results on the achievement and attitude levels of students are presented. The studies evaluated cover middle and high school mathematics courses, as well as college courses through first semester calculus. When calculators were part of instruction but not testing, students' benefited from using calculators while developing the skills necessary to understand mathematics concepts. When calculators were included in testing and instruction, the procedural, conceptual, and overall achievement skills of students improved.     

Preservice Teachers of High School Mathematics: Success,Failure, and Persistence in the Face of Mathematical Challenges

The goal of this study was to identify variables related to success and resilience in an undergraduate, high school mathematics teacher education program. Over a five‐year period, we tracked the academic performance and achievement motivation goals of multiple cohorts of students. Students who successfully completed their degrees had higher grade point average (GPAs) upon entering the program, earned higher grades in their first college mathematics course, and failed fewer courses than students who left the program or university. Learning and performance motivational goals did not predict success in the program. Performance goals decreased over time. Nearly half the successful students repeated one or more mathematics courses. Ten students completed their degrees, obtained a teaching license, and are teaching despite the need for multiple repetitions of the same mathematics courses. These persistent students did not differ from their peers in motivational goals. Our results suggest that although students with higher GPAs and initial mathematics grades were more likely to complete the program, students who experienced challenges in mathematics courses were able to succeed. We discuss the implications of these results for recruiting, advising, and retention of students in mathematics education programs.     

Teaching Probability in Intermediate Grades∗;†

This paper discusses three alternative models for structuring homework assignments in college level mathematics. A distributive model which incorporates both early and late review of previously learned material into the daily assignment schedule is explicated in detail. The relative efficacy of the conventional method for assigning homework and the distributive method in promoting achievement and favourable attitudes toward mathematics in a first semester course in calculus was investigated in a controlled experiment. Significant (p < 0.03) interactions between mathematical ability and assignment model were found on three of four unit tests. In each case, pupils with the weaker pre‐calculus background profited more from the distributive assignment schedule. There were no significant interactions or differences on a comprehensive post‐test or on attitudes toward mathematics. Implications for research and practice in college level mathematics, physics, and engineering courses are suggested.     

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.     

Kinks in the STEM Pipeline: Tracking STEM Graduation Rates Using Science and Mathematics Performance

In an effort to maintain the global competitiveness of the United States, ensuring a strong Science, Technology, Engineering and Mathematics (STEM) workforce is essential. The purpose of this study was to identify high school courses that serve as predictors of success in college level gatekeeper courses, which in turn led to the successful completion of STEM degrees. Using a purposive sample of 893 students who had declared a STEM major between the fall of 2006 and the spring of 2008, data were collected on students' high school grades, college grades, national test scores, grade point average, gender, and ethnicity. Using analysis of variance, correlations, multiple discriminant function analysis, and multiple regression models we found that high school calculus, physics, and chemistry (respectively) were predictors of success in STEM gatekeeper college courses. Then using those courses, we constructed a predictive model of STEM degree completion. The implications of this study highlight and reinforce the importance of providing rigorous mathematics and science courses at the high school level, as well as provide some evidence of a potential mediated model of the relationship between high school performance, college performance, and graduating with a STEM degree.     

Diagrams and math notation in e-learning: growing pains of a new generation

Current e-learning environments are ill-suited to college mathematics. Instructors/students struggle to post diagrams and math notation. A new generation of math-friendly e-learning tools, including WebEQ, bundled with Blackboard 6, and NetTutor's Whiteboard, address these problems. This paper compares these two systems using criteria for ideal math-friendly e-learning systems. NetTutor's Whiteboard is, apparently, the only system allowing two-way communication of both diagrams and math notation between instructor and students. This paper also summarizes a case study of two community college mathematics courses (calculus and algebra) using NetTutor over two semesters. Pilot studies, interviews and experimental problems revealed that NetTutor's Whiteboard is effective for 2-way communication of diagrams and math notation in college courses. Learning difficult concepts was comparable to face-to-face courses.     

Measurement Instruction in the Context of Scientific Investigations With Diverse Student Populations

The purpose of this study was to investigate the impact of a hands‐on science curriculum, which integrates mathematics and supports English language development, on third‐grade students' mathematics achievement—specifically the measurement subscale of the statewide assessment. The data drew from a larger five‐year research and development project consisting of reform‐based science curriculum units and teacher workshops designed to promote effective science instruction while integrating mathematics and supporting English language development. The third‐grade curriculum places a strong emphasis on measurement skills in the context of science inquiry. The third‐grade students' performance on the measurement subscale of the statewide mathematics assessment in the treatment schools was compared with that of comparison schools using a hierarchical linear model. Students at the treatment schools performed significantly higher than students at the comparison schools. The results provide evidence that an integrated approach to mathematics and science instruction can benefit diverse student groups.     

Predictive factors of students’ motivation to succeed in introductory mathematics courses: evidence from higher education in the UAE

The purpose of the study is to examine whether there is a significant relationship between students’ motivation to succeed in introductory mathematics courses offered by universities in the United Arab Emirates (UAE) as the dependent variable of the research and another five independent variables including cognitive mathematics self-concept, affective mathematics self-concept, extrinsic motivation as expectations of future career and income, students’ age and the number of mathematics courses taken by students. The rationale of the study is based on the significance of mathematics achievements for students and academic institutions in particular, as well as for the society in general. The study is designed based on a quantitative research methodology and a sample of 685 students participated in completing a survey questionnaire. The sample is drawn from students who were registered in different introductory mathematics courses at four academic institutions of higher education in the UAE. The quantitative correlation analysis among students’ motivation, cognitive mathematics self-concept, affective mathematics self-concept, extrinsic motivation, students’ age and the number of mathematics courses taken by students reveals theoretically consistent interrelationships. The quantitative multiple regression analysis indicates that the five independent variables explain 71.3% of the variation in students’ motivation to succeed in introductory mathematics courses.     

Geometry‐Related Children's Literature Improves the Geometry Achievement and Attitudes of Second‐Grade Students

Use of mathematics‐related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi‐experimental study of two second‐grade classrooms assessed whether daily inclusion of geometry‐related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the hypothesis, only the students in the classroom with a strong emphasis on geometry‐related children's literature showed a significant improvement in their attitudes about geometry over time. While both classes improved their geometry performance over the 4 weeks of the study, the class with a strong emphasis on geometry‐related literature improved significantly more (51.2%) than the control class (33.47%). Children's literature can provide a useful and interesting context in which students can develop their understanding of geometry.     

Applications of a sequence of points in teaching linear algebra,numerical methods and discrete mathematics

Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, Using a sequence of number pairs as an example in teaching mathematics. Math. Comput. Educ., 39 (2005), pp. 198–205; Y. Shi, Case study projects for college mathematics courses based on a particular function of two variables. Int. J. Math. Educ. Sci. Techn., 38 (2007), pp. 555–566) have presented some interesting examples which can be used in teaching high school and college mathematics classes. In this article, we further discuss a few interesting ways to apply this sequence of points in teaching college mathematics courses such as linear algebra, numerical methods in computing, and discrete mathematics. In addition to using them in individual courses, these studies may also be combined together to offer seminars or workshops to college mathematics students. Studies like these are likely to promote student interests and get students more involved in the learning process, and therefore make the learning process more effective.     

Seeking mathematics success for college students: a randomized field trial of an adapted approach

Many students enter the Canadian college system with insufficient mathematical ability and leave the system with little improvement. Those students who enter with poor mathematics ability typically take a developmental mathematics course as their first and possibly only mathematics course. The educational experiences that comprise a developmental mathematics course vary widely and are, too often, ineffective at improving students’ ability. This trend is concerning, since low mathematics ability is known to be related to lower rates of success in subsequent courses. To date, little attention has been paid to the selection of an instructional approach to consistently apply across developmental mathematics courses. Prior research suggests that an appropriate instructional method would involve explicit instruction and practising mathematical procedures linked to a mathematical concept. This study reports on a randomized field trial of a developmental mathematics approach at a college in Ontario, Canada. The new approach is an adaptation of the JUMP Math program, an explicit instruction method designed for primary and secondary school curriculae, to the college learning environment. In this study, a subset of courses was assigned to JUMP Math and the remainder was taught in the same style as in the previous years. We found consistent, modest improvement in the JUMP Math sections compared to the non-JUMP sections, after accounting for potential covariates. The findings from this randomized field trial, along with prior research on effective education for developmental mathematics students, suggest that JUMP Math is a promising way to improve college student outcomes.     

Case study projects for college mathematics courses based on a particular function of two variables

Based on a sequence of number pairs, a recent paper (Mauch, E. and Shi, Y., 2005, Using a sequence of number pairs as an example in teaching mathematics, Mathematics and Computer Education, 39(3), 198–205) presented some interesting examples that can be used in teaching high school and college mathematics classes such as algebra, geometry, calculus, and linear algebra. In this paper, this study is generalized further to develop a few interesting case study proposals that can be used for student projects in college mathematics courses such as real functions, analytic geometry, and complex variables. In addition to using them in individual courses, these studies may also be combined to offer seminars or workshops to college mathematics students. Projects like these are likely to promote student interest and get students more involved in the learning process, and therefore make the learning process more effective.     

Are beginning calculus and engineering students adequately prepared for higher education? An assessment of students’ basic mathematical knowledge

Are students transitioning from the secondary level to university studies in mathematics and engineering adequately prepared for education at the tertiary level? In this study, we discuss the prior mathematical knowledge and skills demonstrated by Norwegian engineering (N?=?1537) and calculus (N?=?626) university students by using data from a mathematics assessment administered by the Norwegian Mathematical Council. The assessment examines students’ conceptual understanding, computation skills and problem solving skills on the basis of the mathematics curriculum of lower secondary education. We found that calculus students significantly outperformed engineering students, but both student groups struggled to solve the test, with the calculus and engineering groups scoring an average of 60% and 46%, respectively. Beginning students who fail to master basic skills, such as solving arithmetic and algebra problems, will most likely face difficulties in their further courses. Although few female students enrol in calculus and engineering programmes compared with male ones and are thus underrepresented, male and female students at the same ability level achieved comparable test scores. Furthermore, students reported high levels of intrinsic and extrinsic motivation, and a positive relationship was observed between intrinsic motivation and achievement.     

The impact of taking a college pre-calculus course on students’ college calculus performance

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.     

Mathematics achievement and interest in mathematics from a differential perspective

In this article, we present results of an empirical study with 500 German students of grades 7 and 8. The study focussed on students' mathematics achievement and their interest in mathematics as well as on the relation between these two constructs. In particular, the results show that the development of an individual student's achievement between grade 7 and grade 8 depends on the achievement level of the specific classroom and therefore on the specific mathematics instruction Interest in mathematics could be regarded a predictor for mathematics achievement Moreover, our findings suggest that the students show hardly any fear of mathematics independent of their achievement level.     

Factors Associated With Mathematics Achievement and Participation in Advanced Mathematics Courses: An Examination of Gender Differences From an International Perspective

This paper reports results of an exploratory study examining factors that might be associated with achievement in mathematics and participation in advanced mathematics courses in Canada, Norway, and the United States of America (USA). These factors, which were not directly related to schooling accounted for large degrees of variability, 24% to 39%, in mathematics achievement scores. Confidence in mathematics was the strongest predictor of achievement for students from Canada and Norway, whereas for the students from the USA, parents' highest education level was the highest predictor of achievement. Student home environment related variables were stronger predictors of achievement for females than for males in all three countries. The participation in advanced mathematics courses could be predicted with 72% to 76% accuracy by the same variables. In all of the three countries, the strongest predictors of participation in advanced mathematics courses were students' attitudes toward mathematics. Parents' education level, a socioeconomic related variable, was one of the strongest predictors of participation for Canadian female students and all students from the USA.     

The Hurricane Katrina Effect on Mathematics Achievement in Mississippi

Hurricane Katrina caused severe physical damage to the Gulf Coast states of Louisiana, Mississippi, and Alabama. Homes and businesses were destroyed. Natural habitats were annihilated, and many Americans were displaced for days, weeks, and even years. This study investigated the within‐subject effects and contrasts of poverty, rurality, and location within a Katrina distance impact zone on mathematics achievement in fifth‐grade, eighth‐grade, and Algebra I schools in Mississippi during the 2004–2007 school years. Through an analysis of publicly available school data, all school groups were found to have been impacted by Katrina, but the nonpoor/nonrural Algebra I schools within a 90‐mile radius of Katrina's point of landfall were affected the greatest. Interesting patterns in eighth‐grade mathematics achievement results were additionally found. Rural schools were impacted to a greater extent than their nonrural counterparts. Several findings in this study were startling and counterintuitive, but this initial analysis into the impact of Katrina on mathematics achievement in Mississippi illustrated that catastrophic natural disasters like Hurricane Katrina can cause more than just physical damage.     

Investigating the impact of an urban community school effort on middle school STEM-related student outcomes over time through propensity score matched methods

This study investigates the impact of an urban community school reform initiative that focuses on an immigrant and refugee population in middle school. A 6th–8th grade cohort of students in the community school are followed over time and compared to a propensity score matched group on overall GPA, mathematics, and science academic outcomes and traditional college preparedness indicators. Further, a deeper dive into the intersection of gender and race/ethnicity was examined on all outcomes. Findings revealed that students in the urban community school demonstrated significantly more preparedness to enroll in college and move into a STEM field if they desired compared to the matched students. All gender/racial groups in the community school performed significantly higher than those in the matched group. Further, all gender/racial groups of students in the urban community school defied standard academic achievement drops common over time in middle school, and instead increase overall, math, and science grades from 6th to 8th grade.     

An Exploratory Study of College Students' Views of Mathematical Thinking in a Historical Approach Calculus Course

Heuristic training alone is not enough for developing one's mathematical thinking. One missing component is a mathematical point of view. This study reports findings regarding outcomes of a historical approach calculus course to foster Taiwanese college students' views of mathematical thinking. This study consisted of 3 stages. During the initial phase, 44 engineering majors' views on mathematical thinking were tabulated by an open-ended questionnaire, and 9 randomly selected students were invited to participate in follow-up interviews. Students then received an 18-week historical approach calculus course in which mathematical concepts were problematized to challenge their intuition-based empirical beliefs about doing mathematics. Near the end of the semester, all participants answered the identical questionnaire, and we interviewed the same students to pinpoint any shifts in their views on mathematical thinking. We found that participants were more likely to value logical sense, creativity, and imagination in doing mathematics. Further, students were leaning toward a conservative attitude toward certainty of mathematical knowledge. Participants' focus seemingly shifted from mathematics as a product to mathematics as a process.     

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.