<a href="http://sugarlabs.org/go/User:Gdk/4th_Grade_Maths">http://sugarlabs.org/go/User:Gdk/4th_Grade_Maths</a> <a href="http://gregdek.livejournal.com/45211.html">http://gregdek.livejournal.com/45211.html</a> I think what is missing in the approach outlined by Greg here (and in curriculum frameworks in general) is no real consideration of the deep structure of maths or of how children learn maths, the psychology of children's reasoning There is already constructionist software on the xo (turtle art, etoys, scratch) so what would be wrong with having some other programs with narrow but clear learning objectives? Is it complementary or oppositional? I think I complement these sorts of objectives with other, richer approaches in my teaching. But I think Papert presents it as more oppositional in his writings, eg. The Childrens Machine (Papert) and also in Cynthia Solomons book, Computer Environments for Children. Greg's approach seems much the same as Patrick Suppes to me, as explained in these writings It might be worthwhile is to complement Greg's approach to the sort of ideas outlined in the following books: Children Doing Mathematics by Terezinha Nunes and Peter Bryant (1996), 268pp <a href="http://books.google.com.au/books?id=CSINjqKYc1gC&dq=nunes+bryant+%22children+doing+mathematics%22&printsec=frontcover&source=bl&ots=YXzWaP18k-&sig=Hn14LWozl4ebbtlAb_ygmZZ5Gsk&hl=en&sa=X&oi=book_result&resnum=1&ct=result#PPP1,M1">http://books.google.com.au/books?id=CSINjqKYc1gC&dq=nunes+bryant+%22children+doing+mathematics%22&printsec=frontcover&source=bl&ots=YXzWaP18k-&sig=Hn14LWozl4ebbtlAb_ygmZZ5Gsk&hl=en&sa=X&oi=book_result&resnum=1&ct=result#PPP1,M1</a> They are psychologists who are interested in children's reasoning ... Keith Devlin recommends this book for its treatment of multiplication (Multiplication is not repeated addition). This book is entirely devoted to an understanding of number Knowing and Teaching Elementary Mathematics by Liping Ma (2000), 166pp <a href="http://books.google.com.au/books?id=EjkKBotJcyIC&dq=Liping+Ma&printsec=frontcover&source=an&hl=en&sa=X&oi=book_result&resnum=4&ct=result">http://books.google.com.au/books?id=EjkKBotJcyIC&dq=Liping+Ma&printsec=frontcover&source=an&hl=en&sa=X&oi=book_result&resnum=4&ct=result</a> This book asserts and documents the claim that maths is better taught in China than in the USA because Chinese teachers have a more profound understanding of maths knowledge. One thing that appeals to me here is that it contains concrete examples of a good way and a not so good way of teaching various maths concepts. IMO it would be a mistake to ignore the information contained in these books because it violates one of Greg's principles - they are not free