Don Watson asked me to post this follow up, which again should be of interest to the forum. His website is at FoundationNotation.com.
---------------------------- In May 2014, Chris Burke posted a short article from me on a prototype called “Foundation” that turned two-dimensional Mathematics notation into a computer language. I had been trying to interest others in using it and working with me – since I had been retired for 18 years. That didn’t work and I had just made up my mind to go alone and turn it into a production system along with my systems engineer. That work has now been completed. The system uses a consistent virtual manipulative to justify all rules that are are used in the notation. The functionality of these virtual manipulatives has been redesigned and their code has been made more robust. We are adding virtual manipulatives from Grade 1 upwards in a consistent and incremental manner. Sometime in 2016 I hope we will finish the virtual manipulative needs of Elementary and Middle school. An on-line Teacher Guide has been provided for self-teaching. This self-teaching facility is based upon one I wrote in the late 1960s in APL where the computer taught students how to use itself – which was quite widely used. The result is something that educators want – a breakthrough product that uses the latest technology, is uniform throughout Grades 1 to 12; is easy to learn; and makes teaching the subject enjoyable for teachers who studied Arts because they didn’t like Mathematics. It took me a long time to figure out why nobody else had done something similar in the 30 years since Macintosh arrived as the first mass-produced two-dimensional screen. I now think it is because the man who is the father of Computer Science and Computer Intelligence and shortened the Second World War by 2 years, Alan Turing, said he didn’t need two dimensions – but he wasn’t teaching School Mathematics. We have started our promotion campaign by placing a two page advertisement in the Ontario Association for Mathematics Education Gazette this month and will sell the product as individual $10 teacher apps called “Foundation Notation” on Windows 8 and Macintosh, with an Ipad version to follow. There is also a paper at FoundationNotation.com called “Unlocking Mathematics for All Students” that documents the multiple benefits of Foundation, including my daughter’s experience in an 18 month pilot project with Foundation. On 13 May 2014 at 23:12, robert therriault <[email protected]> wrote: > I enjoyed the easy way Foundation linked the concepts of physical objects, > numbers and variables using automatic colouring and drag and drop > manipulation. Dragging a number on top of a dot and creating a pattern on > that many dots, as was shown in one of the videos seems simple but is a > really powerful way to give a new learner control over so many ideas of > quantity. The story of his grand daughter creating a 3 digit number bigger > than 100 (which was the biggest number she could think of) and then being > amazed at 545 dots can fill several screens, is learning in one of its most > joyful forms. > > I think that the visual interface when properly constructed allows the > user to shift their cognitive effort from trying to manipulate the concepts > within their head to focussing on the easy virtual manipulation of objects, > in turn allowing experience of the concept by exploring the rules as you > play. This was summed up by one student's reaction of amazement that they > had learned math, but that their head did not hurt. > > I am surprised that Don Watson, in the quote below thought that teaching > had been neglected with J. Within the lab section of the environment I see > many 'Livetexts' that reveal a teaching tool that is both expository and > exploratory. I don't see the language itself abandoning the teaching aspect > as much as I see many of the practitioners focussing on facility of the > language over developing instruction for others. Perhaps that is a tide > that is beginning to turn...slowly. > > In any case, thank you Chris for providing us with Don's ideas. Very > stimulating stuff. > > Cheers, bob > > On May 13, 2014, at 6:51 PM, chris burke <[email protected]> wrote: > > > When he moved on to J, a > > powerful nature was his priority and Mathematics teaching was left > behind. > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
