Ralph Pantozzi

#iTeachMath "The first thing to be required in a system of popular instruction is that it should be intelligible; that children and youth should understand what they learn.

We have not the least hesitation in saying, that two or three years, in the education of almost every individual in this country, have been thrown away upon studying what they did not understand." (1841)

#iTeachMath "The first thing to be required in a system of popular instruction is that it should be intelligible; that children and youth should understand what they learn.

New standard! #iTeachMath “we have no documented cases of students dying from timed practice”

Out in Missouri not long ago a class of country school children voted in lieu of regular lessons to spend a term in discovering and if possible removing the causes of recurrent typhoid fever on a neighboring farm. 1/5

Oddly enough, too, the children who solved the problem learned more reading, writing and arithmetic than did other children of the same age, grade and mentality who had had routine lessons in two near-by rural schools. 4/5

Out in Missouri not long ago a class of country school children voted in lieu of regular lessons to spend a term in discovering and if possible removing the causes of recurrent typhoid fever on a neighboring farm. 1/5

They were, in other words, to have no reading or writing or arithmetic or geography at all except as these formal subjects came incidentally into the course of the adventure. So they set to work with their teacher to find out what the possible causes of typhoid are. 2/5

Maybe we should start a new Society for the Diffusion of Useful Knowledge

and the evangelical Religious Tract Society, on the one side, and the cheap, seditious unstamped political papers on the other.

Maybe we should start a new Society for the Diffusion of Useful Knowledge

“We don't need an analysis of DI to know that we teachers are not realising our dream. Most of us don't walk into the classroom each day with unwavering confidence that today all 30 of our children are going to understand everything we're preparing to share with them.

1956 trashing 1936 teaching of mathematics #iTeachMath

Teachers had only to make sure that their pupils could follow directions, and then assign textbook lessons and correct papers"

#iTeachMath Arithmetic really can't get much love in any century: "Years ago in most schools (and even today in many schools) the whole program was highly formalized. The material presented was frequently above the maturity levels of the pupils and it was often extremely uninteresting to them.

Drill was the prime method of instruction. The typical pupil understood but little of his lessons in arithmetic and he enjoyed none of it. He moved through the grades getting little understanding of, and hence deriving little benefit from, the study of arithmetic

Traditional Math: "Arithmetic is commonly learnt by rote, and is never thoroughly learnt; it is almost always an unpleasant task both to teacher and pupil, and conduces very little to the general improvement of the mind. 1/8

, merely because the entire abstraction or separation of a science from all others happens to be best for some other purposes. 8/8

Traditional Math: "Arithmetic is commonly learnt by rote, and is never thoroughly learnt; it is almost always an unpleasant task both to teacher and pupil, and conduces very little to the general improvement of the mind. 1/8

Although we should not forget that we ought to teach knowledge for the purpose of improving all our faculties, still we must remember that we should also teach it because it is wanted for use in the world; 6/8

Traditional Math: "Arithmetic is commonly learnt by rote, and is never thoroughly learnt; it is almost always an unpleasant task both to teacher and pupil, and conduces very little to the general improvement of the mind. 1/8

Their authors are satisfied if they present a proposition, regarding number, under one point of view, when it is ten to one if the child can apprehend it thoroughly unless it be presented in many lights, and under many varieties of language. 4/8

Traditional Math: "Arithmetic is commonly learnt by rote, and is never thoroughly learnt; it is almost always an unpleasant task both to teacher and pupil, and conduces very little to the general improvement of the mind. 1/8

An endeavor has, therefore, been made to prepare this Treatise in such a manner that the pupils shall be entertained in their progress, and shall be led on to discover most things for themselves, and to exert and improve their mental faculties. 2/8

1936 says, what are you talking about? Our drills are not meaningless! #iTeachMath

1956 trashing 1936 teaching of mathematics #iTeachMath

"There was no need for a manual of this kind twenty years ago. At that time arithmetic was generally viewed as a tool subject or as a drill subject, and the teaching process was not very complicated.