Points and Viewpoints: Some comment on accelerated mathematics

1958 ◽  
Vol 51 (4) ◽  
pp. 292-293
Author(s):  
Daymond J. Aiken
Keyword(s):  
Gifted Students ◽  
Secondary Mathematics ◽  
Accelerated Programs ◽  
Accelerated Mathematics ◽  
Modern Mathematics

There are two definite trends in secondary mathematics today: the introduction of modern mathematics into the curriculum, and the introduction of accelerated programs to gifted students. It is my belief that we should take a closer look at the second trend.

Strategies of Proof in Secondary Mathematics

1970 ◽  
Vol 63 (8) ◽  
pp. 637-645
Author(s):  
Henry Van Engen
Keyword(s):  
High School Students ◽  
Secondary Teachers ◽  
Undergraduate Students ◽  
Secondary Mathematics ◽  
Solution Set ◽  
Methods Courses ◽  
School Students ◽  
Undergraduate Major ◽  
Internal Logic ◽  
Modern Mathematics

It has been the experience of the author that graduate and undergraduate students are not very knowledgeable about direct and indirect strategies of proof used in mathematics. In methods courses for secondary teachers, the author has observed that even those students who have an undergraduate major in modern mathematics are not at all conscious as to why books usually check the elements of a solution set to an equation before asserting that it is indeed the solution set. Neither are they aware, even at an intuitive level, of the “internal” logic of indirect proof. This lack of awareness leads one to question whether it is possible for them to do a passable job of teaching high school students how to prove theorems.

Mathematical Giftedness, Problem Solving, and the Ability to Formulate Generalizations: The Problem-Solving Experiences of Four Gifted Students

2003 ◽  
Vol 14 (3) ◽  
pp. 151-165 ◽  
Author(s):  
Bharath Sriraman
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Gifted Students ◽  
Secondary Mathematics ◽  
Ninth Grade ◽  
Higher Order ◽  
Combinatorial Problems ◽  
Mathematical Tasks ◽  
Mathematically Gifted ◽  
Dirichlet Principle

Complex mathematical tasks such as problem solving are an ideal way to provide students opportunities to develop higher order mathematical processes such as representation, abstraction, and generalization. In this study, 9 freshmen in a ninth-grade accelerated algebra class were asked to solve five nonroutine combinatorial problems in their journals. The problems were assigned over the course of 3 months at increasing levels of complexity. The generality that characterized the solutions of the 5 problems was the pigeonhole (Dirichlet) principle. The 4 mathematically gifted students were successful in discovering and verbalizing the generality that characterized the solutions of the 5 problems, whereas the 5 nongifted students were unable to discover the hidden generality. This validates the hypothesis that there exists a relationship between mathematical giftedness, problem-solving ability, and the ability to generalize. This paper describes the problem-solving experiences of the mathematically gifted students and how they formulated abstractions and generalizations, with implications for acceleration and the need for differentiation in the secondary mathematics classroom.

scholarly journals Possible interactions with mathematically gifted students: Views of prospective teachers

2020 ◽  
Vol 10 (2) ◽  
pp. 121-132
Author(s):  
Gönül Yazgan-Sağ
Keyword(s):  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Classroom Environment ◽  
Descriptive Analysis ◽  
History Of Mathematics ◽  
Gifted Students ◽  
Secondary Mathematics ◽  
Video Camera ◽  
Mathematically Gifted ◽  
Study Results

Teachers' interactions with mathematically gifted students in the classroom environment, and the elements of this interaction have become prominent recently. This qualitative study's purpose is to reveal the views of prospective secondary mathematics teachers about these interactions. The study participants were seven prospective teachers attending the fourth year of a secondary mathematics teaching programme in a public university in Turkey during the 2018-2019 academic year. These prospective teachers participated in a 90-minute focus group interview which was recorded with a video camera. During the interview, the researcher brought up possible classroom environment scenarios that could occur with mathematically gifted students who may have the characteristics that the participants described. The prospective teachers' views about the kinds of behaviours they can exhibit, and what methods they can reveal in these theoretical interactions were analysed with the descriptive analysis method. The study results indicated that the participants exhibited different approaches to situations they might encounter in the classroom. For example, some prospective mathematics teachers asserted that mathematically gifted students should be assisted in the classroom context; others stated that such students should be supported with out-of-class activities rather than helping them in the classroom. Besides, the participants suggested that the history of mathematics and advanced mathematics subjects could also be used to educate mathematically gifted students.

Enrichment or Acceleration?

1970 ◽  
Vol 63 (6) ◽  
pp. 471-473
Author(s):  
Joseph E. Holmes
Keyword(s):  
High School ◽  
Advanced Placement ◽  
Mathematics Teachers ◽  
College Freshmen ◽  
Secondary Mathematics ◽  
First Year ◽  
Accelerated Programs ◽  
Accelerated Program ◽  
Secondary Mathematics Teachers ◽  
Difference Of Opinion

There has been much difference of opinion among secondary mathematics teachers during the last several decades as to just how the curriculum should be changed. There appears to have been, however, general agreement that changes were necessary. This agreement has given rise to the so-called accelerated programs in which students are enabled to study the usual (but modernized) high school courses at an earlier stage. In many cases this acceleration allows the student to be exposed to a full year of calculus while still in high school. Many of the student who have followed this route are unable to qualify for Advanced Placement credit and are required to repeat the first year of calculus as college freshmen. This indicates that we have allowed some students to enter an accelerated program who are not really ready.

Evaluation of a Summer-School Program for Highly Gifted Secondary-School Students: The German Pupils Academy

2002 ◽  
Vol 18 (3) ◽  
pp. 214-228 ◽  
Author(s):  
Heinz Neber ◽  
Kurt A. Heller
Keyword(s):  
Secondary School ◽  
Summer School ◽  
Secondary School Students ◽  
Social Cognitive ◽  
Gifted Students ◽  
School Program ◽  
School Students ◽  
Positive Effects ◽  
Regulatory Strategies ◽  
Cognitive Framework

Summary The German Pupils Academy (Deutsche Schüler-Akademie) is a summer-school program for highly gifted secondary-school students. Three types of program evaluation were conducted. Input evaluation confirmed the participants as intellectually highly gifted students who are intrinsically motivated and interested to attend the courses offered at the summer school. Process evaluation focused on the courses attended by the participants as the most important component of the program. Accordingly, the instructional approaches meet the needs of highly gifted students for self-regulated and discovery oriented learning. The product or impact evaluation was based on a multivariate social-cognitive framework. The findings indicate that the program contributes to promoting motivational and cognitive prerequisites for transforming giftedness into excellent performances. To some extent, the positive effects on students' self-efficacy and self-regulatory strategies are due to qualities of the learning environments established by the courses.

How to Teach Gifted Students: Practical Advice

PsycCRITIQUES ◽  
2006 ◽  
Vol 51 (12) ◽  
Author(s):  
Russell Eisenman
Keyword(s):  
Gifted Students ◽  
Practical Advice
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