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    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeApr 25th 2016
    • CommentRowNumber2.
    • CommentAuthorThomas Holder
    • CommentTimeApr 26th 2016

    I have added some references at mathematics education.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 26th 2016

    Is Conceptual Mathematics by Lawvere and Schanuel really intended for the high-school level? I thought that those lectures had been tried out on college students, and didn’t know that anything had been tried out for high-school students.

    • CommentRowNumber4.
    • CommentAuthorfastlane69
    • CommentTimeApr 26th 2016
    • (edited Apr 26th 2016)

    Is Conceptual Mathematics by Lawvere and Schanuel really intended for the high-school level?

    Depends on the high school: public probably not, private maybe, home-schooling or self-taught may be more likely.

    Honestly, there is nothing in the book that a HS student can’t handle EXCEPT finding it’s applicability to their lives; that is what keeps HS students away from these or any other abstract concepts the most IMO.

    • CommentRowNumber5.
    • CommentAuthorThomas Holder
    • CommentTimeApr 26th 2016
    • (edited Apr 26th 2016)

    I glimpsed shortly through the text and haven’t found a pasage which kind of readership they intend to address. Maybe I am a bit optimistic here but that would be the text I would recommend to a brave teacher whereas for undergraduate education it seems to me to be to slowed paced. I am also not familiar with the US educational system to know what ’being a college student’ amounts to. If you think the decription is too misleading it should be altered of course! I found it appropriate as a pointer because Lawvere always stressed the importance of teaching for mathematics or even philosophy!

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 26th 2016

    Is it maybe the book Sets for Mathematics rather than the book Conceptual Mathematics which you want to wonder about whether it may be handed to young students?

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 26th 2016
    • (edited Apr 26th 2016)

    It’s definitely my understanding that the contents of the book were tried out on lectures to undergraduate students. But I don’t have the book to hand, so I can’t point to page numbers yet to back that up.

    The book may definitely seem slow-paced in the beginning, but from the student POV that appearance could be deceiving unless one is prepared to take the exercises seriously. This is anyway what (the late) Schanuel has said.

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeApr 26th 2016

    It looks to me that these are lectures for undergraduate students of mathematics rather than for arbitrary majors.

    • CommentRowNumber9.
    • CommentAuthorThomas Holder
    • CommentTimeApr 26th 2016

    Technically, Todd might be right - the front matter has It serves two purposes: to provide a skeleton key to mathematics for the general reader or beginning student; and to furnish an introduction to categories for computer scientists, logicians, physicists, linguists, etc. who want to gain some familiarity with the categorical method . I, personally, wouldn’t give it to anyone but bright high school kids or general readers. It’s true they are making a lot of fine points and certainly convey the Lawverian outlook on mathematics but from the mixture of extreme smartness and extreme didactics these groups can profit most.

    • CommentRowNumber10.
    • CommentAuthortrent
    • CommentTimeApr 26th 2016

    there is nothing in the book that a HS student can’t handle EXCEPT finding it’s applicability to their lives; that is what keeps HS students away from these or any other abstract concepts the most IMO.

    In some cases (especially cases when people are young and don’t have well developed value systems and exeriences, or when one is dealing with something radically outside of one’s frame of reference, like anthropologists contacting an perviously uncontacted tribe) - rather than trying to map things to people’s existing value system and experiences - it is better to try to elucidate how the natives in a given realm understand things, and the mechanisms through which they ascribe/perceive value. (This is - strangely, given its detachedness in contrast to the almost obnoxious pressing of values on people in what follows - quite like Steve Jobs famous idea that people don’t know what they want, you have to show them what they want. The difference is that whereas Jobs supposes that what he is presenting is alteritous and better and acts accordingly, this “anthropological”/”natural daoist” approach simply supposes that what one is presenting is alteritous and acts accordingly).

    Grothendieck has passages in Récoltes et Semailles about the beauty and value of letting things flourish as they naturally are, acclimating to other realms rather than bringing the other realms to you. One might say that this takes a lot of maturity … and it does … but young people demonstrate that they have this ability for example when learning to appreciate strange(ly beautiful) new genres of music, styles of fashion etc as they naturally are. Actually, I’d even say that young people are more interested in moving into and bringing into existence interesting new worlds than in connecting things to past experience.

    • CommentRowNumber11.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 26th 2016

    Nice observations, trent. Actually I do find though that there are plenty of concrete examples in Conceptual Mathematics, such as the Chinese restaurant, which find applicability in daily life.

    ’Alteritous’ is a word which is new to me and is not in my OED, nor did I see a definition online. But based on the resemblance to ’alterity’, not to mention other words beginning with alter-, I’d guess it means “having a quality of otherness” – in a sui generis kind of way. This reminds me a little of Rudolf Otto’s or Karl Barth’s description of God as “wholly Other”, ganz Andere or totaliter aliter, the numinous or holy to be approached only on its own terms.

    • CommentRowNumber12.
    • CommentAuthorzskoda
    • CommentTimeApr 28th 2016
    • (edited Apr 28th 2016)

    Various people enlarged the entry mathematics education in a ways which I am not quite happy with, and I think the material should rather be distributed to other (including new) pages. The books on mathematics subjects tailored for teachers (I also added few, temporarily) and elementary students are not properly books about mathematics education! Educational science is a science and one wants to keep on the page about that science discussions of that science, not merely books on the other subjects (like geometry) which are well written from the point of view of that science.

    Second the Idea section said that it is a page to “collect materials” about teaching (P.S. I like “about teaching” which is very different from the materials “for teaching”, as the latter sometimes has nothing about teaching), like if it were not a worthy subject to have ideas, definitions, results, schools of thought and other section and then at the very end references (now all the sections are what should eventually be subsections of references).

    If nobody complaints I will later open pages for pedagogically written “materials” on elementary mathematics. Pages like introductions to mathematics, introductions to geometry may be written for that purposes.Still in those, one should emphasise which books are of innovative pedagogical value and which are just introductions (I think we should not do much about the plenty in the latter group; if something is not cutting edge scientifically it should have some special educational of historical role at least).

    I am going also to add the link to a major software now used in mathematics education, geogebra.

    • CommentRowNumber13.
    • CommentAuthorzskoda
    • CommentTimeApr 28th 2016

    I added some content at mathematics education (e.g. started an overview section).

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