We discuss aspects of the role and practice of mathematics in education from elementary school to university.
What will you be worth if you don´t know enough math? (Peter Tillberg)
- (Q1) Is knowledge of mathematics as important as reading and writing, for everyone?
- (Q2) What is the net result of 12 years of school mathematics, for most people?
- Mathematics education is important to everyone, but most students learn very little and use less.
- in this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures…mathematical competence opens doors to productive futures and lack of mathematical competence keeps those doors closed
- NCTM challenges the assumption that mathematics is only for the select few…attitudes that suggest only certain students are capable of mastering mathematics should be deprecated … everyone needs to understand mathematics
- all students, regardless of their personal characteristics, backgrounds, or physical challenges, must learn significant mathematics with depth and understanding…there is no conflict between equity and excellence
- the mathematics taught in modern classrooms should be the skills that are most important to the students’ lives and careers
- school mathematics curricula should focus on deepening students’ appreciation of mathematics as a discipline and as a human creation.
- a circulatory definition of what mathematics to teach to what students
- all students have to learn all the unspecified math skills required for life and career
- appreciation of mathematics as a discipline should be indoctrinated.
- mathematics is considered to be so important for everybody that knowledge has to be limited to practically zero.
- To understand fully the nature of “rigorous proof” in mathematics, you will view the film “The Proof” in which Andrew Wiles’ describes the seven-year-long process that led to the proof of Fermat’s Last Theorem.
- prekindergarten-to-eighth-grade math curriculums should be streamlined and put focused attention on skills like the handling of whole numbers and fractions and certain aspects of geometry and measurement
- by the end of the third grade, students should be proficient in adding and subtracting whole numbers and two years later, they should be proficient in multiplying and dividing them
- by the end of the sixth grade students should have mastered the multiplication and division of fractions and decimals
- fractions are especially troublesome for Americans…the catchword for math teachers today should be “fractions” (Francis Fennell, president of the National Council of Teachers of Mathematics)
- the current “talent-driven approach to math, that either you can do it or you can’t, like playing the violin” needs to be changed
- what should be avoided in mathematics is an approach that continually revisits topics year after year without closure…
- US math textbooks are far too long – often 700-1000 pages…Excessive length makes our books unnecessarily expensive and tends to undermine coherence and focus.
Mathematics = Music
- playing piano is necessary to succeed in life and career
- all students are capable of mastering the piano.
In a piano education based on these principles, all students would learn to play the C-scale on the piano, like “handling” whole numbers, but not much more.
- mathematics is not as important as reading and writing, for everybody
- acknowledging the relative unimportance of mathematics for everybody, the need of some who can understand and use mathematics in the information society, can be met
A Critical Analysis
- school teaches mathematics in a way that makes it appear as something very powerful and everywhere present, but at the same time invisible and beyond comprehension for students and teachers. Using terminology from Slovene philosopher Slavoj Zizek, mathematics can thus be understood as the sublime object of an ideology sustained by school mathematics (similar to the God of a religion or the King in a monarchy).
- school asks students/teachers to confess that mathematics is a universal and powerful tool, but admits that few students/teachers learn to use the tool
- the failure of school mathematics is used to motivate more resources to school mathematics
- school practices mathematics as an instrument for discipline, selection and sorting and to keep students busy.
- to develop activities increasing the interest/understanding of the value, role and importance of mathematics in everyday life, professional life, science and society.
What Mathematics Does Obama (or Bush) Need to Know?
- counting: voters, income, expenses, budget deficits, soldiers, age, megabytes, pixels
- performance: speed, miles/gallon, squaremeter/dollar, income/capita, bullets/second
- listen to President Bush learns mathematics:
- modern information society is based on mathematics
- mathematics education is in a (permanent) state of crisis
- mathematics education has changed little the last 100 years
Typical statements (of questionable truth value) about mathematics influencing opinions, are:
- A mystery lurks beneath the magic carpet of science, something that scientists have not been telling, something too shocking to mention except in rather esoterically refined circles: that at the root of the success of twentieth-century science there lies a deeply ‘religious’ belief — a belief in an unseen and perfect transcendental world that controls us in an unexplained way, yet upon which we seem to exert no influence whatsoever. What this world is, where it is, and what it is to us is what this book is about. (John D. Barrow )
- Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. (Bertrand Russell)
- The advancement and perfection of Mathematics are intimately connected with the prosperity of the State. (Napoleon I)
- Nature’s great book is written in mathematical symbols. (Galileo)
- All science requires Mathematics. The knowledge of mathematical things is almost innate in us… This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon. (Roger Bacon)
- Learning to think in mathematical terms is an essential part of becoming a liberally educated person. (Kenyon College Math Department Web Page)
- To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature. … If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. (Richard Feynman)
Proof of the mathematical nature of Romanesque Cauliflower