Towards a Forward-Thinking College Calculus Program

A quasi-experimental design was used to investigate aptitude-treatment interaction in conditions of high instructional support (Personalized System of Instruction) and low instructional support (Lecture). A test for the homogeneity of regression coefficients indicated a significant (p <. 01) prior mathematics preparation x level of instructional support interaction. The most dramatic differences in post-course achievement favoring the high instructional support condition accrued to those students at the relatively lowest levels of prior mathematics preparation. Moreover, as level of prior mathematics preparation increased, the achievement differences between levels of instructional support tended to decrease. A verification analysis conducted on a separate sample yielded essentially the same interactive effect.

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Advanced Placement Oriented Calculus for High School Students

Journal for Research in Mathematics Education ◽

10.5951/jresematheduc.11.5.0347 ◽

1980 ◽

Vol 11 (5) ◽

pp. 347-355

Author(s):

Karen Mezynski ◽

Julian C. Stanley

Keyword(s):

High School ◽

High School Students ◽

Advanced Placement ◽

Opportunity To Learn ◽

Class Ii ◽

Class I ◽

College Level ◽

School Students ◽

Ap Calculus ◽

College Calculus

A supplementary calculus course was conducted to give highly able students the opportunity to learn the equivalent of two semesters of college calculus while still in high school. Two different student populations were sampled; the average age of the members of Class I was 14.9 years, whereas for members of Class II it was 16.7 years. Class I members had more previous exposure to fast-paced mathematics instruction than had members of Class II. Both classes took the College Board's AP Calculus Examination, Level BC, at the end of the course. The results of the AP examination indicated that most students learned college-level calculus well. Considerations for the establishment of similar programs are discussed.

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The Path to College Calculus: The Impact of High School Mathematics Coursework

Journal for Research in Mathematics Education ◽

10.5951/jresematheduc.49.3.0292 ◽

2018 ◽

Vol 49 (3) ◽

pp. 292-329 ◽

Cited By ~ 5

Author(s):

Philip Sadler ◽

Gerhard Sonnert

Keyword(s):

High School ◽

Hierarchical Models ◽

School Mathematics ◽

High School Mathematics ◽

Data Set ◽

Mathematics Preparation ◽

Mathematics Coursework ◽

College Calculus ◽

High Level ◽

The Impact

This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus—(a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? We used a data set of 6,207 students of 216 professors at 133 randomly selected U.S. colleges and universities, and hierarchical models controlled for differences in demography and background. Mastery of the mathematics considered preparatory for calculus was found to have more than double the impact of taking a high school calculus course on students' later performance in college calculus, on average. However, students with weaker mathematics preparation gained the most from taking high school calculus.

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Developing Meaning for Algebraic Symbols: Possibilities and Pitfalls

Mathematics Teaching in the Middle School ◽

10.5951/mtms.13.8.0478 ◽

2008 ◽

Vol 13 (8) ◽

pp. 478-483

Author(s):

John K. Lannin ◽

Brian E. Townsend ◽

Nathan Armer ◽

Savanna Green ◽

Jessica Schneider

Keyword(s):

High School ◽

Middle Grades ◽

Deep Understanding ◽

College Experiences ◽

Important Goal ◽

Symbolic Representations ◽

Mathematical Symbols ◽

The World ◽

Formal Algebra ◽

College Calculus

An important goal of school mathematics involves helping students use the powerful forms of representation that have been developed over the centuries through the work of mathematicians throughout the world. However, challenges exist in encouraging students to develop meaning for the mathematical symbols used in formal algebra. Research has demonstrated that students often fail to develop a deep understanding of the meaning of symbolic representations of variables (e.g., Booth 1984; Clement 1982), so much so that Thompson (1994) found that a limited understanding of the meaning of variables negatively impacts students who later take college calculus. The question arises as to how we can develop meaning for formal algebraic symbols in the middle grades so that instruction can build on this meaning throughout students' high school and college experiences.

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