A One-Line High School Algebra Proof of the Unimodality of the Gaussian Polynomials [ k n ] for k < 20

It was once suggested that beginning the study of freshman high school algebra is not totally unlike embarking upon the sea of matrimony. Both are milestones in one's life, involving opportunities for excitement, adventure, growth, and rich and lasting reward; but, nonetheless, both tend to necessitate some different approaches to problems, some new ways of thinking, and certainly, in more than a few cases, some amount of adjustment. Without intending to attach social implication to algebra, we as teachers cannot fail to recognize that the first exposure to high school algebra can be a foreboding experience to many elementary school graduates, particularly in the light of the statistical evidence for the high fatality rate of students taking algebra for the first time.

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“Plus” Work for “Plus” Pupils

The Arithmetic Teacher ◽

10.5951/at.6.5.0251 ◽

1959 ◽

Vol 6 (5) ◽

pp. 251-256

Author(s):

Eunice Lewis ◽

Ernest C. Plath

Keyword(s):

High School ◽

Binary System ◽

Sixth Grade ◽

Number System ◽

College Of Education ◽

Base Number ◽

High School Algebra ◽

Second Year ◽

The University

One plus one equals “10” for the members of a special arithmetic class at the University School, College of Education, Norman, Oklahoma. Of course, the members of this class were working with a number system of base two, commonly referred to as the binary system. Students also readily stated that three plus three equals “12” if the base is four. Changing the base number was not only fascinating to these highly talented fifth and sixth grade youngsters, but also provided a launching platform for the development of complicated formulas (patterns to them) which are normally developed in a second year high-school algebra course.

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Aspects of Teacher Discourse and Student Achievement in Mathematics

Journal for Research in Mathematics Education ◽

10.5951/jresematheduc.8.3.0195 ◽

1977 ◽

Vol 8 (3) ◽

pp. 195-204

Author(s):

Lyle R. Smith

Keyword(s):

High School ◽

Student Achievement ◽

First Year ◽

Teacher Discourse ◽

High School Algebra ◽

Several Variables ◽

The Mean ◽

Achievement In Mathematics ◽

Algebra Class

Each of 20 high school algebra teachers taught a lesson on direct variation to one first-year algebra class. The students (N=455) had not previously been taught this topic in class. Before the lessons were taught, each teacher was given a list of lesson objectives. Immediately after each lesson, a posttest that focused on the lesson objectives was administered. The teachers were not shown the posttest before they taught their lessons. Correlations were found between the mean posttest scores for the classes and several variables pertaining to teacher discourse.

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Why Mechanical Manipulation?

Mathematics Teacher ◽

10.5951/mt.37.5.0215 ◽

1944 ◽

Vol 37 (5) ◽

pp. 215-216

Author(s):

William S. Tobey

Keyword(s):

High School ◽

Mathematics Teacher ◽

Direct Response ◽

High School Algebra ◽

Mechanical Manipulation ◽

February Issue

Just how difficult it is to purge our thinking mechanism of early implanted misconceptions is brutally manifest in Mr. Richter's splendid and most timely article in the February issue of The Mathematics Teacher. He states that it has been found that those aspects of algebra which involve thinking are retained to a much greater degree than those involving mechanical manipulations. To Mr. Richter and to most of us, who studied our high school algebra before the days when an over indulgent public became possessed with the mistaken notion that somehow the schools could literally implant education into a neutral mind, there really are no mechanical manipulations in algebra. No mental growth occurs from a manipulation that is not in direct response to some reasoned decision. Lapses in adherence to this principle in the forms of rules, such as invert divisor, transpose, change signs, cancel, and the like, are the cancerous infestations which, during our recent prodigious experiment in the field of untrained and inadequately and inexpertly supervised teaching, have brought down upon us the present widespread and generally warranted criticism.

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What the Word “Function” Means to Algebra Teachers

Mathematics Teacher ◽

10.5951/mt.36.5.0212 ◽

1943 ◽

Vol 36 (5) ◽

pp. 212-218

Author(s):

Lee J. Cronbach

Keyword(s):

High School ◽

Present Article ◽

College Mathematics ◽

High School Algebra ◽

Definition Of ◽

Word Function ◽

Technical Terms

Teachers are well aware of the fact that the pupil who can repeat the definition of a word may not really understand what that word means. Since understanding of technical terms in a subject like mathematics is essential, it is important for the teacher to determine whether the pupil has really mastered basic words. In one of a series of studies, the writer sought to construct a test which would determine how well pupils understand the word function, a term generally considered basic in work in advanced high school algebra and college mathematics. While attempting to build the test, it was found that teachers often did not agree as to whether a given expression should be called a function; this suggested that it might be important to determine just what is being taught as the meaning of function, since agreement as to what is being tested is necessary before a test can be constructed. The present article reports an attempt to determine what typical teachers of algebra mean when they speak of a function.

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