High School Mathematics Courses Research Articles

Intended and Unintended Effects of State-Mandated High School Science and Mathematics Course Graduation Requirements on Educational Attainment.

Mathematics and science course graduation requirement (CGR) increases in the 1980s and 1990s might have had both intended and unintended consequences. Using logistic regression with Census and American Community Survey (ACS) data (n = 2,892,444), we modeled CGR exposure on (a) high school dropout, (b) beginning college, and (c) obtaining any college degree. Possible between-groups differences were also assessed. We found that higher CGRs were associated with higher odds to drop out of high school, but results for the college-level outcomes varied by group. Some were less likely to enroll, whereas others who began college were more likely to obtain a degree. Increased high school dropout was consistent across the population, but some potential benefit was also observed, primarily for those reporting Hispanic ethnicity.

Productive and ineffective efforts: how student effort in high school mathematics relates to college calculus success

Relativizing the popular belief that student effort is the key to success, this article finds that effort in the most advanced mathematics course in US high schools is not consistently associated with college calculus performance. We distinguish two types of student effort: productive and ineffective efforts. Whereas the former carries the commonly expected benefits, the latter is associated with negative consequences. Time spent reading the course text in US high schools was negatively related to college calculus performance. Daily study time, however, was found to be either a productive or an ineffective effort, depending on the level of high school mathematics course and the student's performance in it.

고등학교 수학 교과서에서의 반례에 대한 학습가능성 탐색

In recent years, there has been increasing interest in the pedagogical importance of counter-examples that contradict statements about mathematics education research and the curriculum revision process for high school mathematics courses. Using a literature research method, this study analyzed views about counter-examples according to a method of approach to statements and the classification of counter-examples and their criteria. The study also described the learnability of the content of counter-examples presented in Korean secondary school mathematics textbooks. The results showed that generating many counter-examples enables learners to understand mathematical concepts exactly, construct links between mathematical contents, and have flexible thoughts about mathematical objects. Considering the learnability of counter-examples, the contents of counter-examples in school mathematics textbooks are needed for mathematics teachers and students to generate numerous counter-examples and verify the justification of generating counter-examples in various manners.

Predictors of Placement in Lower Level Versus Higher Level High School Mathematics

Educators and researchers have long been interested in determinants of access to honors level and college prep courses in high school. Factors influencing access to upper level mathematics courses are particularly important because of the hierarchical and sequential nature of this subject and because students who finish high school with only lower level courses lack readiness for college and have severely diminished chances for admission to college. Our research analyzes a district-level transcript data set. We examine whether probabilities of enrollment in upper level mathematics courses in high school vary by demographic characteristics, before and after controlling for prior achievement. Before controlling for prior achievement, minority and low-income students have significantly lower odds of placement in upper level mathematics courses; after controlling for prior achievement, the disparities disappear.

Ask Marilyn in the mathematics classroom: probability questions

Since 1986, Marilyn Vos Savant, who is listed in the Guinness Book of World Records Hall of Fame for the highest IQ, has had a weekly column that is published in Parade Magazine. In this column, she answers readers’ questions on a wide variety of subjects including mathematics and particularly probability. Many of the mathematically oriented questions are directly relevant to high school and undergraduate college level mathematics courses. For nearly 20 years, I have incorporated many of these questions into a variety of mathematics courses that I teach. In this note, I will discuss some of the questions that I use dealing with probability.

Call for Manuscripts: Maximizing Learning for ALL: Teaching Entry-Level High School Mathematics Courses

Call for Manuscripts: Maximizing Learning for ALL: Teaching Entry-Level High School Mathematics Courses

Algebra readiness for students with learning difficulties in grades 4–8: Support through the study of number

Developing proficiency in algebra is the focus of instruction in high school mathematics courses and is a minimum expectation for high school completion for all students including those with learning difficulties. However, the foundation for success is laid in grades 4–8 (aged 9–14). In this paper, we assert that students' development of algebraic reasoning skills and knowledge is influenced by their understanding of numeracy. We propose that students in grades 4–8 need targeted instruction on three interconnected numeracy concepts. First, we propose that students need a strong conceptual foundation of number and number systems to facilitate computation, estimation and problem solving across number systems. Second, we identify students' understanding of basic number properties as foundational to lawful application of operations. Finally, we note that procedural proficiency, including computational fluency and conceptual understanding, provides a foundation for generalised application of algorithms for solving arithmetic and algebraic problems. Combined, these skills and knowledge enable students to employ algebraic reasoning by generalising their knowledge for solving abstract problems.

Exploring the Feasibility of Dual-Credit Mathematics Courses in High School via a Web-Enhanced, Blended Model

Exploring the Feasibility of Dual-Credit Mathematics Courses in High School via a Web-Enhanced, Blended Model

Exploring the Feasibility of Dual-Credit Mathematics Courses in High School via a Web-Enhanced, Blended Model

The wveb Mathematics Project is a collaborative program offering college-level courses to high school students. Results of a matched-pair study comparing on- and off-campus students in algebra indicate that both sections show a significant gain in score on the math act test, with no difference in gain found between sections.

Outcomes of Mathematics Placement: An Analysis of Advising and Enrollment Data

The mathematics placement process at the University of Northern Colorado includes brief faculty-student interviews, during which faculty members suggest mathematics courses for students in their first year at the university. Data from a sample of 1466 students admitted in the fall of 2007 were analyzed to assess the effectiveness of the placement interview. Logistic regression was used to model student success in the first university mathematics course as a function of variables available from university records or self-reported by students. The analysis indicated that, among the available variables, by far the most important factor in modeling success was high school grade point average. Whether or not a student followed the recommendation advice, and a student's most recent (usually high school) mathematics course and grade were also useful variables for modeling success.

Conceptualizing RTI in 21st-Century Secondary Science Classrooms: Video Games' Potential to Provide Tiered Support and Progress Monitoring for Students with Learning Disabilities

Secondary schools across the United States are adopting response to intervention (RTI) as a means to identify students with learning disabilities (LD) and provide tiered instructional interventions that benefit all students. The majority of current RTI research focuses on students with reading difficulties in elementary school classrooms. Recommendations for practice that stem from this empirical work are not generalizable to high school classrooms, where adolescents with LD experience unique learning challenges. This is especially true in secondary science classes, where an emphasis on complex vocabulary and sophisticated phenomenological investigations places added cognitive requirements on these students. This article presents a foundation for conceptualizing the role of technology in RTI implementation at the secondary level. We examine how video games can enhance RTI instructional practices by providing multiple tiers of academic supports and realtime progress monitoring in secondary science classrooms. The article illustrates how evidence-based practices can be included in the games in a manner that increases intervention fidelity and assessment reliability. While this article focuses on science video games, we contend that there is considerable conceptual overlap among high school science, technology, engineering, and mathematics (STEM) courses that will allow for further expansion of this discussion. The article concludes with recommendations for future research.

Call for Manuscripts: Maximizing Learning for ALL: Teaching Entry-Level High School Mathematics Courses

The Mathematics Teacher is eager to publish articles about teaching mathematics at the entry level. These courses are critical to fostering students' pursuit of and love for learning mathematics through the high school years and beyond.

Call for Manuscripts: Entry Level High School Mathematics Courses: Maximizing Learning for ALL

The Mathematics Teacher is eager to publish articles about teaching mathematics at the entry level. These courses are critical to fostering students' pursuit of and love for learning mathematics through the high school years and beyond.

Removing Remediation Requirements: Effectiveness of Intervention Programs

Remediation of incoming college freshman students is a national concern because remediated students are at higher risk of failing to complete their degrees. Some Oklahoma higher education institutions are working to assist K–12 systems in finding ways to reduce the number of incoming college freshman students requiring remediation. This study investigated one such undertaking in which 12th-grade students took mathematics courses modeled after the East Central University ATLAS developmental mathematics program in an effort to enhance their performance on college admissions and placement assessments. A key feature of ATLAS is its use of an artificial intelligence–based learning system called ALEKS to hone mathematical skills. This study compared the efficacy of ATLAS-patterned high school mathematics courses with non-ALEKS-based mathematics courses or no mathematics course in removing remediation requirements for college-bound high school seniors. Results support the effectiveness of taking a senior-year high school mathematics course in reducing the number of college-bound high school seniors requiring mathematics remediation and also suggest that the ATLAS program may provide an alternative for some students to remove their college mathematics remediation requirements while still in high school.

Call for Manuscripts: Entry-Level High School Mathematics Courses: Maximizing Learning for ALL

The Mathematics Teacher is eager to publish articles about teaching mathematics at the entry level. These courses are critical to fostering students' pursuit of and love for learning mathematics through the high school years and beyond.

Applying cognitive science to education: thinking and learning in scientific and other complex domains

An accessible introduction to some of the cognitive issues important for thinking and learning in scientific or other complex domains (such as mathematics, physics, chemistry, engineering, or expository writing), with practical educational applications and implementation methods. Many students find it difficult to learn the kind of knowledge and thinking required by college or high school courses in mathematics, science, or other complex domains. Thus they often emerge with significant misconceptions, fragmented knowledge, and inadequate problem-solving skills. Most instructors or textbook authors approach their teaching efforts with a good knowledge of their field of expertise but little awareness of the underlying thought processes and kinds of knowledge required for learning in scientific domains. In this book, Frederick Reif presents an accessible coherent introduction to some of the cognitive issues important for thinking and learning in scientific or other complex domains (such as mathematics, science, physics, chemistry, biology, engineering, or expository writing). Reif, whose experience teaching physics at the University of California led him to explore the relevance of cognitive science to education, examines with some care the kinds of knowledge and thought processes needed for good performance; discusses the difficulties faced by students trying to deal with unfamiliar scientific domains; describes some explicit teaching methods that can help students learn the requisite knowledge and thinking skills; and indicates how such methods can be implemented by instructors or textbook authors. Writing from a practically applied rather than predominantly theoretical perspective, Reif shows how findings from recent research in cognitive science can be applied to education. He discusses cognitive issues related to the kind of knowledge and thinking skills that are needed for science or mathematics courses in high school or colleges and that are essential prerequisites for more advanced intellectual performance. In particular, he argues that a better understanding of the underlying cognitive mechanisms should help to achieve a more scientific approach to science education.

'Model your genes the mathematical way'--a mathematical biology workshop for secondary school teachers

This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the lactose operon in Escherichia coli, one of the first known intracellular regulatory networks. The modelling approach utilizes Boolean networks and tools from discrete mathematics for model simulation and analysis. The workshop structure simulated the team science approach common in today's practice in computational molecular biology and thus represents a social case study in collaborative research. The workshop provided all the necessary background in molecular biology and discrete mathematics required to complete the project. The activities developed in the workshop show students the value of mathematical modelling in understanding biochemical network mechanisms and dynamics. The use of Boolean networks, rather than the more common systems of differential equations, makes the material accessible to students with a minimal mathematical background. High school students can be exposed to the excitement of mathematical biology from both the biological and mathematical point of view. Through the development of instructional modules, high school biology and mathematics courses can be joined without having to restructure the curriculum for either subject. The relevance of an early introduction to mathematical biology allows students not only to learn curriculum material in a innovative setting, but also creates an awareness of new educational and career opportunities that are arising from the interconnections between biological and mathematical sciences. The materials used in this workshop are available at a website created by the directors: http://polymath.vbi.vt.edu/mathbio2006/.

Student trajectories in high school mathematics: Issues of choice, support, and identity‐making

Abstract This study explores the range of experiences students have when making two kinds of decisions in relation to high school mathematics courses: what course to take, and how to and how much to apply themselves. Looking at the choices of students about to enter Grade 10, the first decision is their choice of courses. In mathematics, students leaving Grade 9 selected one course (usually), from five possibilities, for their Grade 10 year: an advanced‐placement Honours stream, an academic course with a traditional symbol‐manipulation approach, an academic course with a technology‐based applications approach, a non‐academic mathematics‐for‐citizenship course, and (as an imposed choice) repeating the Grade 9 mathematics course. The second point of decision‐making occurred within their mathematics and science courses—students constantly made choices about how, and how much, to apply themselves to the challenges of succeeding in the courses they had chosen. These students’ course choices, to a considerable ...

State Graduation Requirements, High School Course Taking, and Choosing a Technical College Major

Abstract I examine the changing patterns of enrollment of females and males in mathematics and science courses in high school between roughly the classes of 1982 and 1992. Course taking has increased in both subjects and, notably, the gender gap has closed. I also examine the impact of state graduation requirements on course taking patterns for males and females. Higher graduation requirements in mathematics and science are associated with increased course taking and the magnitude is similar for both females and males. Finally, I investigate the relationship between high school math and science course taking and college major choice for the latter cohort. Ability and taste are likely to affect both high school course selection and college major and students planning on choosing a technical major are more likely to choose to take additional math and science courses in high school. To address this issue of selection bias, I first include direct measures of ability and taste and then use variation in state graduation requirements to instrument for increased course taking. I find that the number of high school mathematics courses taken has a positive effect on the probability that a student chooses a technical major in college and that this result appears robust to correction for selection bias.

An empirical investigation of differences between mathematics specialists and non-specialists at the high school level in Cyprus: A Logistic regression Approach

AN EMPIRICAL INVESTIGATION OF DIFFERENCES BETWEEN MATHEMATICS SPECIALISTS AND NON-SPECIALISTS AT THE HIGH-SCHOOL LEVEL in Cyprus – The data obtained from high-school seniors for the Third International Mathematics and Science Study (TIMSS) for the country of Cyprus appear to be contradictory. Although Cypriot students did not perform well in mathematics in elementary school, middle school, and in the non-advanced sectors of high school, students in advanced mathematics courses in high school managed to perform exceptionally well. In seeking to account for this apparent disparity, the present study examines the differences between mathematics specialists and non-specialists at the high-school level and discusses the implications that these have for teaching practice. It shows how students educated in an environment that might not be optimal for producing high-achieving students in mathematics and science in elementary and middle school (according to the TIMSS) might nonetheless manage to excel in these fields at the end of their schooling. In conclusion, the authors address the implications of their study for similar educational systems in other developing countries.