Robert Hansen (RH) posted Jan 9, 2014 6:44 PM (http://mathforum.org/kb/message.jspa?messageID=9359319) - GSC's responses interspersed: > I reviewed the Shute book here a while ago? > > http://mathforum.org/kb/message.jspa?messageID=7372302 > > The Dolciani books were longer because they had a few > more topics in them than the Shute book did. > I know little or nothing in detail about the US books (Dolciani, Shute, the 'doorstopper books' mentioned by Domenico Rosa, etc, etc) - I recall we had various books here in India, most of which were, I found, in general rather unsatisfactory (though some were admittedly better than others). I assume that many of the Indian books were 'take offs' from various US or British books, as that has been the Indian style for long.
In any case, most students graduating from Indian schools went out of school with a 'fear and loathing' of math, except a few who may have been influenced by excellent teachers who managed get 'mathematical thinking' across to them (the students) before they were overwhelmed by that 'fear and loathing' of math. (This was the condition during my schooldays, and I believe this state prevails today as well - and, from whatever I see here at Math-teach, this is the condition that prevails in the USA as well). > > The later books actually have fewer topics than the > Dolciani books but are substantially longer because > of how they are typeset and they go simply crazy with > pictures. Not only does this create a book that is > twice as long as need be, it breaks up the text (the > story) into scattered bits. > > The Shute book is written better than the Dolciani > book (modern books aren?t even written). > > My ideal Algebra 1 book would have the following > topics? > > 1. What is Algebra? (this is the first chapter the > student sees. I would ask Devlin to write this). > 2. Variables and Formulas (Introduce the notion of > variables using arithmetic formulas) > 3. Introduction to Algebraic Notation (how we denote > multiplication and division in algebra, exponents) > 4. Numbers (a closer look at the number line, > integers, signed, zero, fractions, decimal, rational, > and a mention of irrational and real numbers) > 5. Linear Equations and Graphing (also the notion of > mapping) > 6. Polynomials (the conventions of polynomials and > polynomial arithmetic) > 7. Rational Expressions and Proportion > 8. Radicals and Roots > 9. Quadratics (2 variables, conic sections for fun) > > Interspersed are some chapters devoted to application > and solving at a algebra 1 level. > > 5a - Applications of Linear Expressions > 6a - Applications of Polynomial Arithmetic > 7a - Applications of Rational Expressions > 8a - Applications of Radicals and Roots > > The quadratics section will be less rigorous than in > Algebra 2 and is meant as an introduction. > > Bob Hansen > To my mind, the above should be *fairly adequate* as the "Algebra that should be mastered by the student by the time he/she leaves school" - IF the 'learning+teaching system' were also to inculcate an adequate awareness of the "HOWs?" and the "WHYs?" for each part and parcel of the topics covered in the above listing of "Algebra".
This is generally NOT done in any part of our educational systems - and it was not a part of the educational system when I was in school (and I do not believe it was a part of the US systems when RH was in school either). The only part of the educational system AS A WHOLE that does try to inculcate a sense of "the 'HOWs?' and the 'WHYs?'" in learners is the Montessori system - and that really has unfortunately been developed only for the primary levels in the school systems.
Nowhere else in our school systems - or, indeed, in any of the other 'systems' that we've developed over the centuries - are the participants in those systems enoouraged to seek the answers of such questions. To a minor extent, the question "HOW?" may be 'allowed'(**) - but the question "WHY?" is very rarely, if ever, addressed in our systems. (Indeed, the question "WHY?" is not even tolerated in general - though many individual teachers in the educational systems do try individually to encourage such 'question-asking'; I would charadterise such teachers as the 'great teachers') Onw serious difficulty is that the system - educational; other - would probably soon be overwhelmed if the question "WHY?" were actively encouraged. [**I believe the question "HOW?" is allowed in our systems largely because it is needed so that those systems may be operated by the 'slaves' - all of us - in the system].
I've read the posts here up to Joe Niederberger's dt Jan 12, 2014 12:53 AM (http://mathforum.org/kb/message.jspa?messageID=9362188). In none of them, I'm afraid, do I see much awareness that the educational system in fact often tends to repress/suppress the question-asking faculty in most learners.
For instance, I've acknowledged quite early in this post that the curriculum sketched in RH's "ideal" Algebra should be quite adequate by and large. However, the real and underlying issue hasn't been addressed at all: if a sound (but otherwise traditional) Algebra book were to be written quite proficiently covering all of that 'ideal' - it would still not address the fundamental issue of most students coming out of school 'fearing and loathing math (inccluding Algebra)'.
> On Jan 8, 2014, at 3:47 PM, Richard Strausz > <Richard.Strausz@farmington.k12.mi.us> wrote: > > > I'm not familiar with either Shute's book or > > Leinwand's. Would you give a few examples of things > > that Leinwand included that Shute didn't? > >> > >> A follow-up question: knowing what you know now, > >>are there any topics that Shute left out that he > >>should have included? If you have taught from > >>Shute's book, are there any things you would would > >>try to add in? > >> > > Thanks - Richard