20 juillet 2011

ARITHMETICS FOR PARENTS, by Ron Aharoni

It is plain fascinating how much meaningful information is hidden behind simple arithmetic facts. There is so much that children may miss! There is so much to be learned in order to acquire a working grasp of the concepts of the elementary mathematics.
The book will be helpful to and enjoyed by teachers, parents who attend to their kids' study and, of course, the home schooling parents. It's a treasure trove of ideas usually missed out in textbooks and teacher manuals.

For example, some texts in English :

Ron Aharoni : “I reached this field (Mathematical education) almost by chance, but now I am deeply involved. It is a truly fascinating subject, in which I feel mostly as a student, learning from the teachers whom I am supposed to guide. They usually know, intuitively, how to approach children, a knowledge that cannot be found in the academy. A book of mine on the subject, "Arithmetic for Parents", appeared in Schocken press, in 2004.”

ARITHMETICS FOR PARENTS

- Presentation on SingaporeMath.Com

- Présentation sur le site de l’éditeur / The publisher’s website : http://www.sumizdat.org/

- By Alexander Bogomolny, at his award-winning math web resource Cut The Knot:
The book under review is an outcome of a rare experiment: an university math professor (a high caliber professor at that from one of the best universities in the world) who has responded to a challenge to teach in elementary school shares the acquired insights about teaching young children and their mathematics. The book is a very enjoyable read, the advice proffered is sound, the pedagogy is illustrated by numerous examples. I highly recommend the book to the grown ups concerned with young children education (...) 

In the Introduction, the author outlines the sequence of events that led him to taking up teaching elementary grades in a small town on the Northern outskirts of Israel and describes the surprise experiences that came out of that experiment. The greatest surprise was in that the teaching of elementary grades provided him - a professional mathematician - an opportunity to learn mathematics: not any new facts of course but the subtleties inherent in the elementary mathematics. (As an aside, this part supplies a crashing argument in the hotly discussed topic as to whether or not elementary school teachers can be expected to possess math expertise.)

The first part is a collection of interrelated essays that discuss the fundamental role of abstraction in mathematics, the mathematical beauty, the peculiar economy of thought and expression that characterizes mathematics and the its hierarchical organization. There are also chapters on the whole numbers, the decimals and general thoughts of what might be expected to be learnt in elementary school. Mathematical economy is beautifully classified as being achieved in three ways: Order (by looking for patterns), Generalization (by abstracting common features from different areas) and Concise Representation (the decimal system serving as an example.)

The second part is deftly subtitled The Road to Abstraction as conveying an abstraction is a fundamental need and principle of teaching mathematics. The author's methodology is to start with familiar and diversify the examples to help students grasp the abstraction as a common feature of several examples and prevent them from attaching unintended importance to auxiliary details. He has harsh words for a textbook where all examples of "real world" fractions referred to pieces of pizza. Students taught from that textbook had difficulty dividing a square into equal parts. Further on, he emphasizes the role of the teacher as a mediator and importance of naming math objects: operations and their parts (e.g., a quotient). He also argues against using calculators in elementary grades.

The third part is the largest - it takes about two thirds of the book. The third part opens with a chapter on the meaning of arithmetic operations. For example, there is a real (for children) difference between questions such as,
1.     There are five apples of which 2 have been eaten. How many apples have been left?
2.     In a family of 5 siblings, 2 are boys. How many girls are in the family?
3.     Joseph has 5 toys, Reena has 2. How many more toys does Joseph have?
All are naturally solved by subtraction 5 - 2 = 3. However, in the first, subtraction means a removal of two items. In the second, it means classification of objects into two types and counting each type separately. In the third, subtractions means comparison.
With the same attention to detail and profound insights, he then talks of the nature and rules of calculations, of fractions, decimals, and ratios. 

It is plain fascinating how much meaningful information is hidden behind simple arithmetic facts. There is so much that children may miss! There is so much to be learned in order to acquire a working grasp of the concepts of the elementary mathematics.
The book will be helpful to and enjoyed by teachers, parents who attend to their kids' study and, of course, the home schooling parents. It's a treasure trove of ideas usually missed out in textbooks and teacher manuals.

See also :
What's Sophisticated about Elementary Mathematics?
Plenty—That's Why Elementary Schools Need Math Teachers

By Hung-Hsi Wu

Improving mathematics instruction is a priority in the United States, but there's little agreement on how to do it. Here's an idea that is rarely discussed: starting no later than fourth grade, math should be taught by math teachers (who teach only math). Teaching elementary math in a way that prepares students for algebra is more challenging than many people realize. Given the deep content knowledge that teaching math requires—not to mention the expertise that teaching reading demands—it's time to reconsider the generalist elementary teacher's role.


American Educator, Fall 2005

Table of Contents
A professional mathematician shares his insights about effective instructional practice, how children learn, the importance of a coherent, systematic curriculum—and mathematics—after taking up the challenge of teaching in an Israeli elementary school.
The Role of Curriculum
By William H. Schmidt
Knowing Mathematics for Teaching (PDF)
Who Knows Mathematics Well Enough to Teach Third Grade, and How Can We Decide?
By Deborah Loewenberg Ball, Heather C. Hill, and Hyman Bass
There is general agreement that teachers' knowledge of the mathematical content to be taught is the cornerstone of effective mathematics instruction. But the actual extent and nature of the mathematical knowledge teachers need remains a matter of controversy. A new program of research into what it means to know mathematics for teaching—and how that knowledge relates to student achievement—may help provide some answers.
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