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Comment by learn1ng2learn | Hacker News Reader

> This is not surprising as Maria Montessoris understanding of geometry and pre-numeric Math is nowadays considered to be quite poor.

Could you elaborate on this? Or point to any references? Thanks

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Keep in mind that Montessoris theory is ~100 years old; it kept up very well but there are shortcomings; IMO especially in the realm of pre-numeric mathematics.

The base of the critique is that Montessori does not provide a conclusive, foundational Layer of (Pre-)Mathematics - a model of more or less depending sub-skills - which would enable A) Educators to better understand their pupils or what they need to further their skills[1] B) enable the invention of new Material. She basically states that children need Material X, Y and Z, but not how and why the work with the material enables them to start using math.

[1] = Which is very important for pupils with different learning paths and/or disabilities.

Is there anything you would recommend instead? Or any resources you have on hand to get more information?

You mean of the critique of Maria Montessoris education in general?

Then i'd refer you the 1914s Text from Kilpatrick (From the same time than Montessori, a progressive Educator himself) https://archive.org/details/montessorisystem00kilprich

I just chuckeled as i re-read his accounts of her arithmetics material:

"On the whole, the arithmetic work seemed good, but not remarkable; probably not equal to the better work done in this country. In particular there is very slight effort to connect arithmetic with the immediate life of the child. Certainly, in the teaching of this subject, there is for us no funda- mental suggestion. "

Mind you, that's from 1914. Pedagogics have improved since then...

Or do you mean a better understanding how pre-numeric mathematic works? Most efforts are built around Piagets Teachings (Not very scientific as he "just" observed his own three children) https://en.wikipedia.org/wiki/Piaget%27s_theory_of_cognitive...

One sample of such a adaptations for pre-numerics (not Geometry) are the works of Carin de Vries (sadly only in German): http://oops.uni-oldenburg.de/1014/1/vridia10.pdf

I call BS.

Kilpatrick was a disciple of Dewey; both were known haters of Maria Montessori and her work, and never gave any specific criticism of her system, just appeals to their own authority; they basically rejected her purpose in education (developing the faculty of reason, learning writing, reading, arithmetics, and geometry) because of their progressive-education, anti-reason dogma.

There isn't much difference between the insights of Montessori and Piaget. Piaget worked with Montessori early in his career. The experimental nursery school in Geneva, La Maison des Petits, where Piaget carried out his first studies of children in the 1920s, was a modified Montessori institution, and Piaget was the head of the Swiss Montessori Society for many years.

Jean Piaget was a great scientist who conducted systematic experiments with countless children. Your claim that he only observed his own 3 children is a lie. Scientists at the University of Geneva to this day carry on with his research and experiments.

That last reference you provide is some obscure German PhD thesis which does not reference Montessori's work at all; it has a major focus on teaching mentally retarded children, as well as teaching mathematics out of books to children older than the ones that go to Montessori schools (commonly age 3-6).

Kilpatrick contra Montessori: I'd call the 70 page critique quite specific. Quote: "The Montessori child learns self-reliance by free choice in relative isolation from the directress. He learns in an individualistic fashion to respect the rights of his neighbors. The kindergarten child learns conformity to social standards mainly through social pressure focused and brought to bear in a kindly spirit by the kindergartner." Clearly the writings of a hater ;)

  > There isn't much difference between the insights of Montessori and Piaget.

How a child learns, what big influence self interest and self control are is quite similar between the both. I personally also agree. The immense impact and usefulness of Piagets stages of cognitive development are orginally his and not to be found in Montessoris Teachings.

  > Piaget was a great scientist who conducted systematic experiments with countless children. Your claim that he only observed his own 3 children is a lie.

Well, it's a hyperbole based on Ginsburg & Opper, 2004. I included the hyperbole b/c i thought it might come up after i brought up Piagets name. His well-respected and often built upon work is often criticized because of lack of initial sample size, reliance on language as critical examination tool and some stages don't develop in all and/or most children like he predicted.

His work was still a giant leap.

  > That last reference you provide is some obscure German PhD thesis which does not reference Montessori's work at all; it has a major focus on teaching mentally retarded children, as well as teaching mathematics out of books to children older than the ones that go to Montessori schools (starting at age 3).

The Author of this thesis is one of the most respected scientists in germany relating to pre-numeric Mathematics. Teachers for mentally retarded children had to think about pre-numeric mathematics long before it became fashionable for younger kids. She based her work on Piaget and Vygotsky. Its quite my point that she didn't base it on Montessori.

More nonsense.

Evidence contra your second claim, that Piaget's "stages of cognitive development orginally his and not to be found in Montessoris Teachings": Montessori's theory of the sensitive stages [1] and the planes of development [2].

I'm not going to continue to argue with someone who willfully spreads lies (malicious "hyperbole") and poppycock.

[1] http://rmschool.org/content/sensitive-periods

[2] https://ami-global.org/montessori/quotes/four-planes-develop...

I said: " The immense impact and usefulness of Piagets stages of cognitive development are orginally his and not to be found in Montessoris Teachings"

Montessori via your source on mathematics: "Mathematics: Formation of the concepts of quantity and operations (addition, subtraction, multiplication, and division) from the uses of concrete learning materials. (birth to 6)" Quite general.

Piaget has a few sub-skills concerning Quantities:

  * conservation (xxx has the same amount of x'es as x x x)
  * classification (x is a letter and lowercase)
  * seriation (x X y Y could be orderes XY; xy, but also Xx, Yy)
  * transitivity and others

This insights are very useful if you want to make - for an example - a pre-numeric mathematical game concerning quantities.

Montessori does not provide such deep insights into pre-numeric mathematics.

Rubbish.

You pretend to "infer", from a one-sentence description of how the Montessori method uses concrete materials to teach the basic arithmetic operations, that somehow other mathematical principles are absent from the Montessori pedagogy.

Of course these principles are demonstrated and taught in Montessori schools, also with concrete learning materials.

You may not know much about Montessori, or you may have an axe to grind, or ...? Either way, you should stop making demonstrably false statements about her pedagogy (and about Piaget).

You've crossed into incivility in this thread and broken the HN guidelines by calling names. That's not ok, regardless of how wrong someone else is. Indeed, assuming your position is correct, it's important not to discredit it by commenting like this.

Would you mind reading the site guidelines and following them scrupulously when commenting here? We're trying for a better outcome than scorched earth followed by heat death, which seems to be the default for internet forums.

https://news.ycombinator.com/newsguidelines.html

Ok.

My father worked with Piaget, so I lack tolerance for someone who deliberately spreads lies about Piaget's work.

I can certainly understand that. Still, patient correction is probably a better way to honour him.

Thank you, that's a helpful perspective.

Well, could you reference something more scientific and recent? You just dissed Montessori's saying it's quite poor, and some backing to that would be great.

I would agree of course, 100 years over it's bound to be primitive to what we know now. Since you say in a previous comment you are a member of the German Education and Science Union I was hoping you could point us the right way

I second this ask: the parent's claim is new to me.

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