High School Mathematics Courses Research Articles

Cognitive and Affective Changes as Determinants for Taking Advanced Mathematics Courses in High School

Using data from the Longitudinal Study of American Youth, this analysis tested whether changes during middle and high school in mathematics‐related cognitive and affective factors influence participation in the most advanced mathematics course work, with control over confounding factors associated with student background. No significant interaction effects between cognitive and affective factors were found. Although changes in cognitive factors had more comprehensive effects on participation than those in affective factors, changes in attitude toward mathematics had the most important effect on participation. Among cognitive factors, growth in basic skills and quantitative literacy was more important to participation than growth in algebra and geometry.

Language performance at high school and success in first year computer science

We describe the first part of a study investigating the usefulness of high school language results as a predictor of success in first year computer science courses at a university where students have widely varying English language skills. Our results indicate that contrary to the generally accepted view that achievement in high school mathematics courses is the best individual predictor of success in undergraduate computer science, success in English at the first-language level in high school correlates better with actual performance. We discuss the implications of this for universities whose medium of teaching is English, operating in social contexts where many students are not native English speakers.

Sound Off! Trade in Your Pendulum for a Personal Spacecraft

Over my fifteen–year career in mathematics education, I have seen major changes in the way textbooks are written and used as well as in how state standards are written and tested. Many of the mathematics teachers with whom I have spoken are excited about the momentum brought about by the increase in research and the publication of the NCTM Standards documents in 1989, 1991, 1995, and 2000. These include recommendations in curriculum, instruction, assessment, and professional responsibilities. I have witnessed curriculum changes that include shifts in emphasis, inclusion of new topics, exclusion of outdated topics, and the integration of content within high school mathematics courses. Instructional changes have included a shift toward using more hands–on materials at the high school level, an increase in awareness of the role of multiple representations, a shift from occasional use of scientific calculators to frequent use of graphing calculators, and an emphasis on the role of the student as an active learner in the mathematics classroom. Assessment changes include less emphasis on tests as the be–all and end–all of assessment and a shift toward having students explain their reasoning as a part of the assessment process.

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.

EXPLORING MATHEMATICS OUTSIDE THE CLASSROOM THROUGH THE FIELD TRIP ASSIGNMENT

ABSTRACT This article describes the Field Trip Assignment, which was developed for a mathematics modeling course for prospective teachers. The objective of the assignment was to motivate students to make connections between mathematics and real-life phenomena while considering how to make those connections explicit to their future students. For the Field Trip Assignment, students designed a field trip that would be suitable for middle and high school mathematics courses. In groups of three, students chose a site, developed a project based on the site, conducted a test-run of the field trip, and shared their experiences with their peers. Through this assignment, students not only explored the applications of mathematics in various authentic settings, but also, as future teachers, they were exposed to the complexities of planning field trips. As part of the assignment, students posted their completed projects on Blackboard so that their peers could use them as resources when planning field trips for their future students.

Equal Arcs, Triangles, and Probability

Typical high school mathematics courses too often postpone probability until the end of the year. Traditional textbooks relegate this area of mathematics to a section toward the end of the book, and teachers offer it to their students if time permits. I try to connect and integrate probability into the curriculum when appropriate.

Attributions About Achievement and Intentions About Further Study in Social Context

This project examined sources and consequences of attributions for achievement for boys and girls at co-ed (N = 663) and single-sex schools (N = 697). Overall attributions emphasised long and short term effort, over other personal (ability, liking) and social reasons (parents, teachers) or feeling good or bad on the day. Attributions were substantially similar for girls and boys, with particular variations in attributions to effort and ability at co-ed and not single-sex schools. Results suggested an illusory glow for boys more than girls in attributions to ability and effort for doing well in Mathematics and English, and traditional gender stereotyping in attributions to poor ability for not doing well in Mathematics. Results showed weak associations between attributions about effort and ability with intentions for Mathematics and English courses in senior high school. Findings suggest further research about personal and social sources of attributions in co-ed schools, and question the practical significance of attributions for achievement motivation.

Describing Reasoning in Early Elementary School Mathematics

NCTM's Standards documents (1989, 2000) call for increased attention to the development of mathematical reasoning at all levels. In order to accomplish this, teachers need to be attentive to their students' reasoning and aware of the kinds of reasoning that they observe. For teachers at the early elementary level, this may pose a challenge. Whatever explicit discussion of mathematical reasoning they might have encountered in high school and university mathematics courses could have occurred some time ago and is unlikely to have included the reasoning of children. The main intent of this article is to give teachers examples of ways to reason mathematically so that they can recognize these kinds of reasoning in their own students. This knowledge can be beneficial both in evaluating students' reasoning and in evaluating learning activities for their usefulness in fostering reasoning.

The effect of block scheduling high school mathematics courses on student achievement and teachers' use of time: implications for educational productivity

Block scheduling involves the reallocation of instructional time into longer class sessions to encourage more active teaching strategies, reduce fragmentation inherent in single-period schedules, and improve student performance. To the degree that such policies reallocate existing resources to realize higher levels of desired educational outcomes, the goal of productivity can be served. Despite widespread experimentation with various forms of block scheduling, there is conflicting evidence on the impact of these innovations on student achievement, and little evidence of their effect on classroom practice. This study explores these relationships. More specifically, the study draws on data from the National Education Longitudinal Study: 1988 to estimate the impact of block-scheduled mathematics courses on tenth-grade student achievement and teachers' use of class time. Findings suggest that while block scheduling is positively associated with teachers' use of multiple instructional methods and more individualized instruction, this scheduling reform has a negative impact on students' tenth-grade mathematics scores, controlling for other factors. Implications for educational productivity are discussed.

The Influence of Social Capital on Mathematics Course Selection by Latino High School Students

This study examined the processes involved in high school mathematics course selection among Latino students. Of particular interest in this study were an investigation of how parental involvement affects these processes. The findings in this research generally provide evidence to support the notion that social capital is associated with more informed educational decisions. Introduction of ethnicity and socioeconomic variables complicate the findings by showing that aspects of parental involvement may be effective for White students but not for Latinos. Although social capital is effective for upper socioeconomic Latinos at increasing the likelihood of algebra and advanced mathematics enrollment, it tends to be less effective for lower socioeconomic Latinos. Future research should point toward a continued examination of the nature of our stratified society and how social capital varies across social class groups. Future initiatives should be directed at schools to develop programs, interventions, and partnerships with Latino families to help parents recognize and take advantage of their own resources to guide their children toward higher education.

The Influence of Social Capital on Mathematics Course Selection by Latino High School Students

This study examined the processes involved in high school mathematics course selection among Latino students. Of particular interest in this study were an investigation of how parental involvement affects these processes. The findings in this research generally provide evidence to support the notion that social capital is associated with more informed educational decisions. Introduction of ethnicity and socioeconomic variables complicate the findings by showing that aspects of parental involvement may be effective for White students but not for Latinos. Although social capital is effective for upper socioeconomic Latinos at increasing the likelihood of algebra and advanced mathematics enrollment, it tends to be less effective for lower socioeconomic Latinos. Future research should point toward a continued examination of the nature of our stratified society and how social capital varies across social class groups. Future initiatives should be directed at schools to develop programs, interventions, and partnerships with Latino families to help parents recognize and take advantage of their own resources to guide their children toward higher education.

Mathematics skill and male–female wages

Using data from the National Longitudinal Survey of Youth (NLSY; 1993), this paper analyzes the extent of wage differentials between men and women and the impact of mathematics and verbal skills on the wages of men and women across different levels of education and occupations. The results show that mathematics skills lead to significant wage premiums across all groups of workers. Separate analyses by gender show that women with superior mathematics skill experience wage gains that are comparable to or higher than the wage premiums enjoyed by men. Although women earn significantly lower wages than men do across all levels of education and occupational categories, the gender wage gap is not significant among professional men and women with above-average mathematics skills. One way of reducing the gender wage gap would be to encourage girls to invest more in high school mathematics courses in order to improve their quantitative skills.

Effect of Part-Time Work on High School Mathematics and Science Course Taking

The effect of part-time work intensity on high school course work completed in mathematics and science and its indirect effect on 12th-grade achievement was explored. Longitudinal data from a nationally representative sample were used to test the models through path analysis. Socioeconomic status and previous achievement were included as exogenous variables for control purposes, and part-time work intensity was hypothesized to negatively affect course work completed in the 2 subjects, as well as 12th-grade achievement through course work during high school. Results suggest that, controlling for the background variables, there was a significant negative effect of part-time work intensity on course work and that its indirect effect on 12th-grade achievement through course work was larger than its direct effect.

The Impact of Class Size on Instructional Strategies and the Use of Time in High School Mathematics and Science Courses

This study estimated the impact of class size on instructional practices and the use of time in high school mathematics and science courses. More specifically, the analysis examined the influence of class size on two categories of variables that measure the use of time: (a) time devoted to instruction (e.g., working with small groups, using innovative instructional practices, leading whole-group discussion, amount of homework assigned) and (b) time committed to noninstructional activities (e.g., conducting administrative tasks, maintaining order). The analysis also explored the influence of other factors such as characteristics of the class and the teacher. Findings revealed that class size has an impact on the use of class time, both instructional and noninstructional. The effect varied by subject area, type of student, and amount of time teachers spend planning for class.

The Impact of Class Size on Instructional Strategies and the Use of Time in High School Mathematics and Science Courses

This study estimated the impact of class size on instructional practices and the use of time in high school mathematics and science courses. More specifically, the analysis examined the influence of class size on two categories of variables that measure the use of time: (a) time devoted to instruction (e.g., working with small groups, using innovative instructional practices, leading whole-group discussion, amount of homework assigned) and (b) time committed to noninstructional activities (e.g., conducting administrative tasks, maintaining order). The analysis also explored the influence of other factors such as characteristics of the class and the teacher. Findings revealed that class size has an impact on the use of class time, both instructional and noninstructional. The effect varied by subject area, type of student, and amount of time teachers spend planning for class.

High School Mathematics Course Taking and Achievement Among College-Bound Students: 1987-1996

High School Mathematics Course Taking and Achievement Among College-Bound Students: 1987-1996

How High Is the Water Tower?

When are we ever going to need this math?” This question, frequently heard in high school mathematics courses, elicits an interesting, and perhaps unique, response from teachers at one California high school. To experience an indepth practical application of mathematics, the trigonometry and precalculus classes meet at the school's water tower and use some of the mathematics learned in classrooms. Students measure the height of the tower's topmost point, which is not only inaccessible but also invisible from the ground. In the process, they engage in some good teamwork, see how their mathematics courses fit together to facilitate a task that no one course can do alone, observe how mathematics can work around physical obstacles, use their scientific calculators for chained and multistage calculations, and gain a little more appreciation for the physical facilities of their school. Students also see that mathematical analysis can be easier and more accurate than direct measurement or scale drawings. And every time they see the water tower―which is hard to miss—they remember that their mathematics really is good for something. As a special benefit, several interested students help prepare the activity and coach their peers.

Gendered Perceptions of Talent and Planned Participation in Mathematics

An investigation of students’ perceptions of talent in relation to mathematics showed that gender stereotyped perceptions of talent were a determining factor in their planned mathematics courses in senior high school. Furthermore perception of talent affected students’ intended careers which also revealed gender imbalances in participation according to the level of mathematics required, as rated by six senior teacher educators from two universities in Sydney. The Year 10 students in Advanced and Intermediate courses were from coeducational government schools in an upper middle-class metropolitan area of Sydney. Actual performance on a standardised mathematics test was used to measure students’ achievement, and perception of talent and predicted mathematics participation were ascertained through use of a questionnaire. Despite similar performance on the test, boys perceived themselves as more talented than girls, and also planned to participate in the higher levels of mathematics more than girls, both in the Higher School Certificate and their intended career.

The Effect of Testing Frequency upon the Achievement of Students in High School Mathematics Course

The Effect of Testing Frequency upon the Achievement of Students in High School Mathematics Course

Solving Problems by Reading Mathematics

That was the first of eight recommendations by the National Coun cil of Teachers of Mathematics in its pol icy statement, An Agenda for Action: Recommendations for School Mathe matics in the 1980s. Although not specifi cally aimed at college remedial programs, this recommendation should have impli cations for them just as as it does for high school and elementary school mathe matics programs. In current high school mathematics courses and college remedial programs problem solving is typified by story problems or word problems, which are given as applications of algorithmic skills. Students anticipate which skill to use because most mathematics text books classify word problems by type. Word problems requiring systems of equations, for instance, are in the sec tion where systems of equations are dis cussed. In view of the concern that this approach is not enough to help students acquire skills in problem solving, a course was developed at the University of Georgia to improve remedial stu dents' problem-solving skills. A secondary goal of the course was to improve the remedial program in gen eral, since problem-solving experiences are not the only facets that have been