Algebra in Education
It should no longer be regarded as a species of original sin on the part of the inquisitive pupil if he asks his algebra teacher, on the very first day, “What is it all about?” or “What is the use of studying algebra?” As a rule, such a pupil would be unable, even with the most powerful microscope, to find a satisfactory answer to these questions in his textbook…
Whither Algebra? Will it continue to travel on the road that leads to educational suicide, or will it establish its rightful place in the sun as one of the most significant and indispensable domains of human thought and endeavor?
— William Betz (1930), German/American mathematician-educator, author, teacher (East Rochester High School)
There is a stage in the curriculum when the introduction of algebra may make simple things hard, but not teaching algebra will soon render it impossible to make hard things simple.
— David Tall & Michael O. J. Thomas, contemporary mathematicians (1991)
The logic of the subject [algebra], which, both educationally and scientifically speaking is the most important part of it, is wholly neglected. The whole training consists in example-grinding. What should have been merely the help to attain the end has become the end itself. The result is that algebra, as we teach it, is neither an art nor a science, but an ill-digested farrago of rules, whose object is the solution of examination problems.
— George Chrystal (1885), Scottish mathematician, textbook author
Doing algebra is a way of thinking and…it is a way of thinking that is different from arithmetical thinking. Those formulas and equations, involving all those x’s and y’s, are merely a way to represent that thinking on paper. They no more are algebra than a page of musical notation is music.
— Keith Devlin (2011), contemporary mathematician
Reformation must begin at the other end. First, you must make up your mind as to those quantitative aspects of the world which are simple enough to be introduced into general education; then a schedule of algebra should be framed which will bout find its exemplification in these applications.
— Alfred North Whitehead (1916), influential English mathematician, logician, philosopher
The proper field for the display of mathematical genius, is in the region of invention. But what is requisite for an elementary work, is to collect, arrange and illustrate, materials already provided…
Algebra requires to be treated in a more plain and diffuse manner…; because it is to be attended to, early in the course, while the mind of the learner has not been habituated to a mode of thinking so abstract, as that which will now become necessary.
He has also a new language to learn, at the same time he is settling the principles upon which his future inquiries are to be conducted. These principles ought to be established, in the most clear and satisfactory manner which the nature of the case will admit of.
— Jeremiah Day (1814), mathematician-educator, author, President of Yale College, principal co-author of the influential Yale Report of 1828
There is a very large percentage that halt on the bridge over from arithmetic to algebra.
— William Torrey Harris (1902), American educator and educational philosopher, US Commissioner of Education, Committee of Ten member
Teaching algebra to a broad spectrum of the population raises issues of relevance and of equity. If algebra is interpreted just as symbolic manipulation, then it has little relevance to everyday life….Indeed, it can be a source of alienation of students from learning mathematics.
The challenge, therefore, has been to reconceptualise algebra as a subject that does have relevance to students and to do this in a way that the students themselves can perceive the relevance.
— Kaye Stacey & Helen Chick (2004), contemporary mathematicians
The examples which a beginner should choose for practice should be simple and should not contain very large numbers. The powers of the mind cannot be directed to two things at once; if the complexity of the numbers used requires all of the student’s attention, he cannot observe the principle of the rule which he is following.
— Augustus De Morgan (1832), influential British mathematician, logician, inaugural president of the London Mathematical Society