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Quantitative analysis of the Factors Influencing College Success in Mathematics (FICSMath) Survey data indicates that high school mathematics teachers' abilities to teach for conceptual understanding is a significant and positive predictor of student performance in singlevariable college calculus. To explore these findings further, we gathered and analyzed interview data gained from a representative sample of high school precalculus teachers from across the U.S., identified by their students as requiring high levels of conceptual understanding (n=13). Seventeen themes were identified and then combined into five overarching phenomenological themes. These overarching themes suggest that teachers who teach for high conceptual understanding (a) support relational understanding during problem solving, (b) require students to learn how to study to build on prior knowledge and learn from mistakes, (c) use mathematical language and ask critical questions to support learning, (d) focus on content knowledge necessary to make connections, and (e) use technology to support learning concepts but limit calculator use. Comparison of these results to quantitative findings further illuminate that intentional development of disciplinary knowledge, cognition, and language are noteworthy points of intersection for teachers and researchers alike. [ABSTRACT FROM AUTHOR]

In this paper, we present findings from a preliminary analysis of transcript data in the High School Longitudinal Study (HSLS:09), a large-scale longitudinal investigation of academic achievement among U.S. high school students. Using proportional flow diagrams of course-taking patterns, we illustrate differences in calculus completion associated with non-malleable student characteristics such as ethnicity, gender, and socioeconomic status (SES), as well as malleable student characteristics, such as knowledge of mathematics in ninth grade, the level of mathematics course they take in ninth grade, and self-efficacy. Confirming and extending findings from prior literature, we conclude that “tracks” through high school mathematics curriculum, together with students' ethnicity, SES, and self-efficacy, converge as important factors associated with which of the approximately 19% of high school students complete calculus in high school. [ABSTRACT FROM AUTHOR]

We delineate some types of structured practice (modeling, requests, feedback, and space-making) that help students learn to pose appropriate questions and to initiate exploration of those questions. Developing skills requires practice, so we suggest ways to embed structured practice into existing class sessions. Including structured practice is nuanced, instructor-specific, and depends on context. Therefore, we give examples of implementation in an inquiry-based learning (IBL)-influenced calculus class, in a partially IBL mathematics for liberal arts class, and in a completely IBL class for gifted high school students. [ABSTRACT FROM PUBLISHER]

This study investigates how the use of calculators during high school mathematics courses is associated with student performance in introductory college calculus courses in the USA. Data were drawn from a nationally representative sample of 7087 students enrolled in college calculus at 134 colleges and universities. They included information about students' demographics, standardized test scores, and high school mathematics course enrollment and performance. Factor analysis reduced ten items describing high school calculator usage to two composites: how extensively calculators were employed and teacher-imposed restrictions on their use. Hierarchical linear models predicted students' college calculus grades, reported by their professor, while controlling for differences between colleges and student backgrounds. The more extensively students had used calculators in high school, the lower their grade in college calculus. However, students earned higher college calculus grades to the extent that their high school teachers had limited calculator use on quizzes and exams and had restricted calculator use until paper-and-pencil methods had been mastered, which offset the negative association of extensive calculator use with grades. The effect sizes of both calculator composites were very small. Overall, the findings raise doubts about any substantial long-term effects on college mathematics performance of calculator use in high school. [ABSTRACT FROM AUTHOR]

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in their definition and exposition. We develop the beginning concepts of differential and integral calculus using only concepts and skills found in secondary algebra and geometry. It is our underlining objective to strengthen students' knowledge of these topics in an effort to prepare them for advanced mathematics study. The purpose of this reconstruction is not to alter the teaching of limit-based calculus but rather to affect students' learning and understanding of mathematics in general by introducing key concepts during secondary mathematics courses. This approach holds the promise of strengthening more students' understanding of limit-based calculus and enhancing their potential for success in post-secondary mathematics. [ABSTRACT FROM PUBLISHER]

The article describes an activity program for secondary education which asks students to find a formula related to antiderivatives.

There is widespread concern about the reduction in the number of students in Australia studying calculus-based mathematics courses in the final year of secondary education. Over the last 20 years in New South Wales, we have seen a dramatic increase in the number of students studying general mathematics in place of calculus courses. The concern arises because students graduating from high school with no calculus are often not well equipped for many aspects of university-level study. This paper explores one potential reason for this in New South Wales, namely the scaling algorithm used to derive the Australian Tertiary Admission Rank. At a time when we are encouraging students to study higher mathematics, this paper contributes to the discussion by illustrating some empirical evidence, based on an analysis of published output from the application of the scaling algorithm used to derive Australian Tertiary Admission Ranks, as to why students may be opting for lower level mathematics at the Year 12 level in great numbers. [ABSTRACT FROM AUTHOR]

The proof of the chain rule from calculus is usually omitted from a beginning calculus course. Six different rationales and motivations are presented here to help students understand some of the rule's details and the reason the rule is valid. [ABSTRACT FROM AUTHOR]

The article offers an insight to secondary school students to develop conceptual understanding of the vertex formula used for solving graph quadratic equations. Topics discussed include the need for understanding features of quadratic equations such as shape and symmetry of quadratic graphs and table of quadratic equations, the understanding for determining x-coordinate of the vertex as the mean of the two x-intercepts' coordinates and the verification of the vertex formula.

The article describes a lesson plan and activity program for secondary education students to solve linear equations.

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. [ABSTRACT FROM AUTHOR]

This paper focuses on the belief systems towards teaching calculus of 29 upper secondary mathematics teachers. Firstly, we discuss different educational trends in teaching calculus, and the theoretical approach based on the construct of belief systems. Afterwards we describe the method of our study used to analyse the belief systems of the calculus teachers. Referring to findings of our research, we firstly focus on central and peripheral beliefs and thus discuss the structure of the teachers' belief systems. Further, we compare the teachers' belief systems to established educational trends of teaching calculus. Finally, we conclude the paper by reflecting on our main findings and by discussing possible directions of further research. [ABSTRACT FROM AUTHOR]

The article focuses on the science, technology, engineering, and mathematics (STEM) project assigned by calculus teacher Dori Ray to his students at Unionville High School in Kenneth Square, Pennsylvania to build three-dimensional solids of known cross-section of layers of hand-cut foam. It presents the process of the project and the activities they undertook to build the 3D model. It notes that undergraduate persistence in STEM education has increased as a result of teachers and students' inspiration from the interdisciplinary approach with STEM projects. It emphasizes that high school students should train themselves for career fields that may have not yet existed.

The article offers the author's perspective on the curriculum for calculus in the 21st century in the U.S. He mentions that combining calculus with computing is an important advancement in mathematics, as it provides creative ways of teaching mathematics to students. He also talks about the usual proofs in calculus and how teachers can help improve students' understanding of the course.

This study sought to examine calculus students’ mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students’ mathematical performances and their preferred modes of thinking. Data were collected from 183 Advanced Placement calculus students in five high schools. Students’ visual preferences were not influenced by gender. Statistically significant differences in visual preference scores were found among high- and low-performing students. Thus, the results suggest that stronger preference for visual thinking was associated with higher mathematical performances. [ABSTRACT FROM PUBLISHER]

Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students' conceptions of rate, focussing on the influence of representation and context on their expression of their understanding of rate. This analysis shows that different representations of functions provide varying levels of rate-related information for individual students. Understandings of rate in one representation or context are not necessarily transferred to another representation or context. Rate is an important, but commonly misunderstood, mathematical concept with many everyday applications (Swedosh, Dowsey, Caruso, Flynn, & Tynan, ). It is a complicated concept comprising many interwoven ideas such as the ratio of two numeric, measurable quantities but in a context where both quantities are changing. In mathematics classes, this is commonly expressed as change in the dependent variable resulting from a unit change in the independent variable, and variously described as constant or variable rate; average or instantaneous rate. In addition, rate may be seen as a purely abstract mathematical notion or embedded in the understanding of real-world applications. This paper explores the research question: Are students' expressions of their conceptions of rate affected by either context or mathematical representation? This question was part of a larger study (Herbert, ) conducted with Grade 10 students from the Australian state of Victoria. [ABSTRACT FROM AUTHOR]

In the above mentioned article [1] unfortunately the names of the translators of Toeplitz's lecture were omitted. The correct title is:The Problem of University Courses on Infinitesimal Calculus and TheirDemarcation from Infinitesimal Calculus in High SchoolsOtto ToeplitzTranslated into English by Michael N. Fried and Hans Niels Jahnke [ABSTRACT FROM PUBLISHER]

The article presents an approach for reshuffling calculus in high school education. It discusses the importance of linear approximation in studying calculus as well as explores its aid in students to calculate derivatives. Illustrations of calculating derivatives through computing limits, continuity, and differentiation, are provided. The extent to which students need to study limits to understand derivatives is examined.