Python and pre-algebra
Locked
 
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I teach 6th
grade math and Python was suggested as a way to apply pre-algebra
concepts in a programming context. My programming background consists of
one C++ programming class. How do I begin? Are lesson plans and small
programs available, for example, where students could write and "drop
in" a script that includes integers and the output would not only
calculate it, but see the relevance of it in a real world situation? Or, perhaps, the
program controls a "wheelchair" robot and students would write scripts
to drive the robot at a certain speed considering the slope of a ramp? As you can see, I
am a novice, but I see great potential and am willing to learn. Thanks, _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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Many subscribers to edu-sig have developed interesting approaches over the years. There's a lot of interest in turtle art and/or turtle graphics. There's this tendency to divide algebra from geometry, whereas some teachers think it's important to keep lexical and graphical connected.
To that end, my pre-algebra tends to focus on numeric sequences that have a clear geometric meaning (like triangular and square numbers, but I also take it into volume and growth sequences in space -- polyhedral numbers some call these sequences).
You'll get the flavor my approach from the Oregon Curriculum Network web site, this page in particular, and this essay in particular: I'm guessing others will chime in. Python's 'How to Think Like a Computer Scientist' literature, a free syllabus, is not inconsistent with developing skills in algebra.
If you want to be more serious and formal about "object oriented" and link in a notion of "math objects", I recommend spiraling through the same or similar material with that in mind.
They may not be ready for vector objects tomorrow, but perhaps the day after. Polyhedrons are stellar objects because they're both abstract and concrete in their properties and behaviors.
Algebra and geometric shapes are good friends, or should be, starting with such as V + F == E + 2. Kirby On Wed, Jun 29, 2011 at 4:15 PM, <[hidden email]> wrote:
_______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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Welcome Mary.
Mary first posted her question on my blog post about ISTE, so I sent her here, thinking of the work that many of you have been doing. In addition to Kirby, Andy Harrington has been looking at Python and algebra and I know there were others.
I hope some of us can help you out. Cheers, Vern On Thu, Jun 30, 2011 at 12:50 AM, kirby urner <[hidden email]> wrote:
-- Vern Ceder [hidden email], [hidden email] The Quick Python Book, 2nd Ed - http://bit.ly/bRsWDW _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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In reply to this post by mary.dooms
On Wed, June 29, 2011 7:15 pm, [hidden email] wrote:
> > I teach 6th grade math and Python was suggested as a way to apply > pre-algebra concepts in a programming context. My programming background > consists of one C++ programming class. How do I begin? Python is one of several excellent options. Others are Logo, Smalltalk, and APL, all of which are available at no cost. I worked on a free APL for 8-bit computers before the Free Software movement got started, and I have friends working on APLs for current computers to put under the GPL. Assuming that your students know no Python, you could use the Sugar Labs Turtle Art approach to math and programming to get started. Turtle Art was designed for children to use for math, programming, and art, and has natural ways to move to Logo, Python, or Etoys/Smalltalk. FORTH, too, but most people don't want to know that. ^_^ (FORTH love if honk then) The question is, which pre-algebra concepts? Do you have a curriculum standard or a particular textbook in mind? Are there other topics of interest? I can write TA or mixed TA/Python examples, and show students how to do the same, and we could work together on lesson plans to share in the Sugar Labs Replacing Textbooks program. There are others with an interest in doing this. > Are lesson plans and small programs available, for example, Probably. There are well over 100,000 digital learning resources on the Net. You can find some of them on pages linked from http://wiki.sugarlabs.org/go/Open_Education_Resources We will need a substantial number of teachers to review them, compare them, and select those that do the best job making concepts clear in ways that will stay with students. > where students could write and > "drop in" a script that includes integers and the output would not only > calculate it, but see the relevance of it in a real world situation? There are many ways to do that. One of the weirder ones is my Turtle Art Turing Machine for addition. ^_^ http://wiki.sugarlabs.org/go/Activities/TurtleArt/Tutorials/Turtle_Art_Turing_Machine More directly to your needs, Pippy is a Sugar activity that shows a number of Python examples that students can edit. For example, Fibonacci a, b = 0, 1 while b< 1001: print b, a, b = b, a+b Changing the 0, 1 in the first line changes this from a generator of Fibonacci numbers to a generator of the related Lucas numbers. There is a Pascal's Triangle program. Plotted mod 2, it reveals a Sierpinski fractal. Relevant Python resources include NumPy and PyGame. > Or, perhaps, the program controls a "wheelchair" robot and students would > write scripts to drive the robot at a certain speed considering the slope > of a ramp? See the Etoys tutorial challenge for programming a "car", and the robot program in Uruguay with robots controlled by Sugar software. http://www.flickr.com/photos/christophd/4827926508/ XO turned into a robot thanks to the Butiá project > As you can see, I am a novice, but I see great potential and am willing to > learn. Delighted to meet you. > Thanks, > > Mary _______________________________________________ > Edu-sig mailing list > [hidden email] > http://mail.python.org/mailman/listinfo/edu-sig > -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://wiki.sugarlabs.org/go/Replacing_Textbooks _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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On Thu, Jun 30, 2011 at 8:03 PM, <[hidden email]> wrote:
> > On Wed, June 29, 2011 7:15 pm, [hidden email] wrote: > > > > I teach 6th grade math and Python was suggested as a way to apply > > pre-algebra concepts in a programming context. My programming background > > consists of one C++ programming class. How do I begin? > > Python is one of several excellent options. Others are Logo, Smalltalk, > and APL, all of which are available at no cost. I worked on a free APL for > 8-bit computers before the Free Software movement got started, and I have > friends working on APLs for current computers to put under the GPL. > APL was my first love at Princeton, back when most people (including me) had to use punch cards. It was the interactivity I loved, among other aspects. Logo the same way. Grew into dBase later, always interactive, a dialog. Languages divide into those which respond, conversationally, and those which must be looked at as non-conversational. Python joined the ranks of the conversationals. > > Assuming that your students know no Python, you could use the Sugar Labs > Turtle Art approach to math and programming to get started. Turtle Art was > designed for children to use for math, programming, and art, and has > natural ways to move to Logo, Python, or Etoys/Smalltalk. FORTH, too, but > most people don't want to know that. ^_^ (FORTH love if honk then) I was a math teacher in a day school for humans of the female persuasion, as one of the trusted male faculty (most were not male), but this was long before the Free Software movement (GNU / GPL), was still at the start of the first computer revolution. No Internet yet, at least not for ordinary civilians like me. I dreamed of hypertext (read Computer Lib / Dream Machines by Ted Nelson) and joined IGC with a guest account at New Jersey Institute of Technology. Proto-internet, pre-listserv. In the meantime, snailmailers were proto-typing listservs via Action Linkage. Anyone remember? You'd mail your post to the anchor, who'd photocopy the lot and mail back out to subscribers. The whole listserv phenomenon, happening through snailmail. Lots of ethnography as yet unwritten. Mid 1980s. 'A Network Nation' by Turoff and Starr Roxanne Hiltz. http://web.njit.edu/~turoff/Vita/vita2005.html#a30 I lived behind Loew's Theater on Journal Square, the main PATH station in Jersey City. By 1985, I was back in Portland, having been raised there through 2nd grade. > > The question is, which pre-algebra concepts? Do you have a curriculum > standard or a particular textbook in mind? Are there other topics of > interest? > > I can write TA or mixed TA/Python examples, and show students how to do > the same, and we could work together on lesson plans to share in the Sugar > Labs Replacing Textbooks program. There are others with an interest in > doing this. > Then I worked at McGraw-Hill (after some stuff in between), 28th floor, Rockefeller Center, Manhattan, editing textbooks, testing educational computer games, contributing curriculum writing (Logo, BASIC). Back then, we thought computers were soon to take the math teaching world by storm. Little did we suspect that the North Americans would be conquered by Texas Instruments, leaving the innovation vista to other cultures and/or subversive counter-cultures still operational in some areas. OLPC (One Laptop per Child) was one attempt to break the TI lock on teacher imaginations. For the most part, it failed in North America. The resistance was too great. No breakfast cereal boxes featured the XO. Nothing on the backs of Kellogs or General Mills. No donated G1G1 commercials during Saturday Morning cartoons. http://www.youtube.com/watch?v=yFmQP3JimAE&feature=related http://youtu.be/XSH_5YP0tU8 Few ever got a clue. Teachers fell further and further behind. The situation was so bad in Hillsboro (personal anecdote), home of Intel in Oregon (Aloha plant) that the police got into the home schooling business, tried to do outreach to tomorrow's gangland by setting up a Linux Lab in West Precinct (where I came in, as a contract instructor). The schools had proved incompetent to do their jobs (educating for the future), so the Chief of Police was stepping in (he was 2nd generation Chinese immigrant). I lectured about this Hillsboro experiment to the London Knowledge Lab on my way to the Shuttleworth Foundation meeting with Helen King et al, our benevolent dictator, Guido, another member of our merry party (Scheme also represented). This was a meeting about South Africa, making long term plans even then (government officials were part of Mark's entourage). > > > Are lesson plans and small programs available, for example, > > Probably. There are well over 100,000 digital learning resources on the > Net. You can find some of them on pages linked from > > http://wiki.sugarlabs.org/go/Open_Education_Resources > > We will need a substantial number of teachers to review them, compare > them, and select those that do the best job making concepts clear in ways > that will stay with students. The South African model was shaping up to serve auto-didacts. Kids who could self teach would stand the best chance. The teachers were proving hopeless. Adult teachers could not be expected adapt to these technologies in sufficient time in sufficient number. Those were the facts on the ground. It's not like anyone wanted it to be this way. One had to make the best of a bad situation. > > > where students could write and > > "drop in" a script that includes integers and the output would not only > > calculate it, but see the relevance of it in a real world situation? > > There are many ways to do that. One of the weirder ones is my Turtle Art > Turing Machine for addition. ^_^ > > http://wiki.sugarlabs.org/go/Activities/TurtleArt/Tutorials/Turtle_Art_Turing_Machine > > More directly to your needs, Pippy is a Sugar activity that shows a number > of Python examples that students can edit. For example, > > Fibonacci > a, b = 0, 1 > while b< 1001: > print b, > a, b = b, a+b > > Changing the 0, 1 in the first line changes this from a generator of > Fibonacci numbers to a generator of the related Lucas numbers. There is a > Pascal's Triangle program. Plotted mod 2, it reveals a Sierpinski fractal. "Generator" also has a technical meaning in Python, such that one might actually write a Fibonacci generator (of the GeneratorType). > > Relevant Python resources include NumPy and PyGame. > > > Or, perhaps, the program controls a "wheelchair" robot and students would > > write scripts to drive the robot at a certain speed considering the slope > > of a ramp? > > See the Etoys tutorial challenge for programming a "car", and the robot > program in Uruguay with robots controlled by Sugar software. Alan Kay was at that Shuttleworth meeting in Kensington. I'm sure there've been many follow-up meetings which I've not been privy to, plus I've continued to meet with Oregon-based colleagues. I also work with an outfit in Sonoma County, where Python is concerned. > > http://www.flickr.com/photos/christophd/4827926508/ > XO turned into a robot thanks to the Butiá project > > > As you can see, I am a novice, but I see great potential and am willing to > > learn. > > Delighted to meet you. > Ed writes a lot of good posts on many a math-related list. I recommend paying attention to his thinking (I know I do). Kirby _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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On Fri, July 1, 2011 1:41 am, kirby urner wrote:
> On Thu, Jun 30, 2011 at 8:03 PM, <[hidden email]> wrote: >> >> On Wed, June 29, 2011 7:15 pm, [hidden email] wrote: >> > >> > I teach 6th grade math and Python was suggested as a way to apply >> > pre-algebra concepts in a programming context. My programming >> background >> > consists of one C++ programming class. How do I begin? >> >> Python is one of several excellent options. Others are Logo, Smalltalk, >> and APL, all of which are available at no cost. I worked on a free APL >> for >> 8-bit computers before the Free Software movement got started, and I >> have >> friends working on APLs for current computers to put under the GPL. >> > > APL was my first love at Princeton, back when most people (including > me) had to use punch cards. You and jazz guitarist Stanley Jordan. He wants to create an APL-based computer music education program. At Yale in 1963 we only had octal and FORTRAN. Later on, Yale hired Alan Perlis away from Carnegie-Mellon to be Chairman of the Computer Science Department. He made APL the first language for all CS students. > It was the interactivity I loved, among > other aspects. Logo the same way. Grew into dBase later, always > interactive, a dialog. Languages divide into those which respond, > conversationally, and those which must be looked at as non-conversational. > Python joined the ranks of the conversationals. LISP was the first. On the other hand, Waterloo University in Canada created a FORTRAN interpreter for use in classes, to go with its APL, Pascal, and others. >> Assuming that your students know no Python, you could use the Sugar Labs >> Turtle Art approach to math and programming to get started. Turtle Art >> was >> designed for children to use for math, programming, and art, and has >> natural ways to move to Logo, Python, or Etoys/Smalltalk. FORTH, too, >> but >> most people don't want to know that. ^_^ (FORTH love if honk then) > > I was a math teacher in a day school for humans of the female > persuasion, as one of the trusted male faculty (most were not male), > but this was long before the Free Software movement (GNU / GPL), > was still at the start of the first computer revolution. No Internet > yet, at least not for ordinary civilians like me. My father was using timesharing, and allowed me on at 300 bps. > I dreamed of hypertext (read Computer Lib / Dream Machines > by Ted Nelson) I met Ted when he gave an invited speech at the APL91 Conference at Stanford. > and joined IGC with a guest account at New > Jersey Institute of Technology. Proto-internet, pre-listserv. In > the meantime, snailmailers were proto-typing listservs via > Action Linkage. Anyone remember? You'd mail your post to > the anchor, who'd photocopy the lot and mail back out to > subscribers. The whole listserv phenomenon, happening > through snailmail. Pierre de Fermat operated as listserv for all of the top mathematicians of Europe before the journals got started. > Lots of ethnography as yet unwritten. > > Mid 1980s. > > 'A Network Nation' by Turoff and Starr Roxanne Hiltz. > http://web.njit.edu/~turoff/Vita/vita2005.html#a30 > > I lived behind Loew's Theater on Journal Square, the main > PATH station in Jersey City. By 1985, I was back in Portland, > having been raised there through 2nd grade. > >> >> The question is, which pre-algebra concepts? Do you have a curriculum >> standard or a particular textbook in mind? Are there other topics of >> interest? >> >> I can write TA or mixed TA/Python examples, and show students how to do >> the same, and we could work together on lesson plans to share in the >> Sugar >> Labs Replacing Textbooks program. There are others with an interest in >> doing this. >> > > Then I worked at McGraw-Hill (after some stuff in between), 28th floor, > Rockefeller Center, Manhattan, editing textbooks, testing educational > computer games, contributing curriculum writing (Logo, BASIC). We need you to do that again as we find out what children can learn with computer aid at earlier stages of development than we thought. > Back then, we thought computers were soon to take the math teaching > world by storm. Little did we suspect that the North Americans would be > conquered by Texas Instruments, leaving the innovation vista to > other cultures and/or subversive counter-cultures still operational > in some areas. Thousands of dollars for a computer, under $100 for a calculator. No contest. HP was content with the engineering market and didn't want to challenge TI to a retail war. > OLPC (One Laptop per Child) was one attempt to break the TI lock > on teacher imaginations. For the most part, it failed in North America. > The resistance was too great. No breakfast cereal boxes featured > the XO. Nothing on the backs of Kellogs or General Mills. No > donated G1G1 commercials during Saturday Morning cartoons. > http://www.youtube.com/watch?v=yFmQP3JimAE&feature=related > http://youtu.be/XSH_5YP0tU8 Ah, but what will happen when we have free digital textbook replacements, so that netbooks cost less than printed textbooks? Better education at lower cost. Can politicians resist that? > Few ever got a clue. Teachers fell further and further behind. > > The situation was so bad in Hillsboro (personal anecdote), home > of Intel in Oregon (Aloha plant) that the police got into the home > schooling business, tried to do outreach to tomorrow's gangland > by setting up a Linux Lab in West Precinct (where I came in, as > a contract instructor). I have an idea for going after homeschooling networks with OLPCs and Sugar, also. > The schools had proved incompetent to do their jobs (educating > for the future), so the Chief of Police was stepping in (he was > 2nd generation Chinese immigrant). > > I lectured about this Hillsboro experiment to the London Knowledge > Lab on my way to the Shuttleworth Foundation meeting with > Helen King et al, our benevolent dictator, Guido, another member > of our merry party (Scheme also represented). I met Guido at a BayPiggies meeting (Bay Area Python Interest Group) at Google, where I mentioned to the audience that both Guido and I were trying to compile sugar-jhbuild, and reporting to one of the mailing lists, and that I had not been able to do it. He chimed in from the audience that he had failed to build it also. > This was a meeting about South Africa, making long term plans even > then (government officials were part of Mark's entourage). The Shuttleworth Foundation funded development of a suite of digital learning resources for high school math and sciences for South Africa. >> > Are lesson plans and small programs available, for example, >> >> Probably. There are well over 100,000 digital learning resources on the >> Net. You can find some of them on pages linked from >> >> http://wiki.sugarlabs.org/go/Open_Education_Resources >> >> We will need a substantial number of teachers to review them, compare >> them, and select those that do the best job making concepts clear in >> ways that will stay with students. > > The South African model was shaping up to serve auto-didacts. > > Kids who could self teach would stand the best chance. I would like to see how much of that we can help children learn, given that they learn languages and cultures, among other things, with no formal instruction. > The teachers were proving hopeless. Adult teachers could not be > expected adapt to these technologies in sufficient time in sufficient > number. Those were the facts on the ground. I don't think that that is necessarily so, and I intend to have our Replacing Textbooks project create a sufficient set of teacher training materials also. On some points, however, we might have to wait until some of our XO students enter teachers colleges. > It's not like anyone wanted it to be this way. One had to make the > best of a bad situation. > >> >> > where students could write and >> > "drop in" a script that includes integers and the output would not >> only >> > calculate it, but see the relevance of it in a real world situation? >> >> There are many ways to do that. One of the weirder ones is my Turtle Art >> Turing Machine for addition. ^_^ >> >> http://wiki.sugarlabs.org/go/Activities/TurtleArt/Tutorials/Turtle_Art_Turing_Machine >> >> More directly to your needs, Pippy is a Sugar activity that shows a >> number of Python examples that students can edit. For example, >> >> Fibonacci >> a, b = 0, 1 >> while b< 1001: >> print b, >> a, b = b, a+b >> >> Changing the 0, 1 in the first line changes this from a generator of >> Fibonacci numbers to a generator of the related Lucas numbers. There is >> a Pascal's Triangle program. Plotted mod 2, it reveals a Sierpinski >> fractal. > > "Generator" also has a technical meaning in Python, such that one > might actually write a Fibonacci generator (of the GeneratorType). > >> >> Relevant Python resources include NumPy and PyGame. >> >> > Or, perhaps, the program controls a "wheelchair" robot and students >> would >> > write scripts to drive the robot at a certain speed considering the >> slope >> > of a ramp? >> >> See the Etoys tutorial challenge for programming a "car", and the robot >> program in Uruguay with robots controlled by Sugar software. > > Alan Kay was at that Shuttleworth meeting in Kensington. I'm sure > there've been many follow-up meetings which I've not been privy to, plus > I've continued to meet with Oregon-based colleagues. I met Alan Kay at the 40th anniversary of Doug Engelbart's Mother of All Demos at Stanford. I had met Doug previously, and was apparently the first to show him an XO. > I also work with an outfit in Sonoma County, where Python is concerned. > >> >> http://www.flickr.com/photos/christophd/4827926508/ >> XO turned into a robot thanks to the Butiá project >> >> > As you can see, I am a novice, but I see great potential and am >> > willing to learn. >> >> Delighted to meet you. >> > > Ed writes a lot of good posts on many a math-related list. I recommend > paying attention to his thinking (I know I do). Thanks, Kirby. > Kirby > _______________________________________________ > Edu-sig mailing list > [hidden email] > http://mail.python.org/mailman/listinfo/edu-sig > -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://wiki.sugarlabs.org/go/Replacing_Textbooks _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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In reply to this post by kirby urner-4
On Thu, Jun 30, 2011 at 10:41:45PM -0700, kirby urner wrote:
> On Thu, Jun 30, 2011 at 8:03 PM, <[hidden email]> wrote: > > > > On Wed, June 29, 2011 7:15 pm, [hidden email] wrote: > > > > > > I teach 6th grade math and Python was suggested as a way to apply > > > pre-algebra concepts in a programming context. My programming background > > > consists of one C++ programming class. How do I begin? > > > > Python is one of several excellent options. Others are Logo, Smalltalk, > > and APL, all of which are available at no cost. I worked on a free APL for > > 8-bit computers before the Free Software movement got started, and I have > > friends working on APLs for current computers to put under the GPL. > > > > APL was my first love at Princeton, back when most people (including > me) had to use punch cards. It was the interactivity I loved, among > other aspects. Logo the same way. Grew into dBase later, always > interactive, a dialog. Languages divide into those which respond, > conversationally, and those which must be looked at as non-conversational. > Python joined the ranks of the conversationals. > > > > > Assuming that your students know no Python, you could use the Sugar Labs > > Turtle Art approach to math and programming to get started. Turtle Art was > > designed for children to use for math, programming, and art, and has > > natural ways to move to Logo, Python, or Etoys/Smalltalk. FORTH, too, but > > most people don't want to know that. ^_^ (FORTH love if honk then) > > I was a math teacher in a day school for humans of the female > persuasion, as one of the trusted male faculty (most were not male), > but this was long before the Free Software movement (GNU / GPL), > was still at the start of the first computer revolution. No Internet > yet, at least not for ordinary civilians like me. > > I dreamed of hypertext (read Computer Lib / Dream Machines > by Ted Nelson) and joined IGC with a guest account at New > Jersey Institute of Technology. Proto-internet, pre-listserv. In > the meantime, snailmailers were proto-typing listservs via > Action Linkage. Anyone remember? You'd mail your post to > the anchor, who'd photocopy the lot and mail back out to > subscribers. The whole listserv phenomenon, happening > through snailmail. Lots of ethnography as yet unwritten. > > Mid 1980s. > > 'A Network Nation' by Turoff and Starr Roxanne Hiltz. > http://web.njit.edu/~turoff/Vita/vita2005.html#a30 > > I lived behind Loew's Theater on Journal Square, the main > PATH station in Jersey City. By 1985, I was back in Portland, > having been raised there through 2nd grade. > > > > > The question is, which pre-algebra concepts? Do you have a curriculum > > standard or a particular textbook in mind? Are there other topics of > > interest? > > > > I can write TA or mixed TA/Python examples, and show students how to do > > the same, and we could work together on lesson plans to share in the Sugar > > Labs Replacing Textbooks program. There are others with an interest in > > doing this. > > > > Then I worked at McGraw-Hill (after some stuff in between), 28th floor, > Rockefeller Center, Manhattan, editing textbooks, testing educational > computer games, contributing curriculum writing (Logo, BASIC). > > Back then, we thought computers were soon to take the math teaching > world by storm. Little did we suspect that the North Americans would be > conquered by Texas Instruments, leaving the innovation vista to > other cultures and/or subversive counter-cultures still operational > in some areas. > > OLPC (One Laptop per Child) was one attempt to break the TI lock > on teacher imaginations. For the most part, it failed in North America. > The resistance was too great. No breakfast cereal boxes featured > the XO. Nothing on the backs of Kellogs or General Mills. No > donated G1G1 commercials during Saturday Morning cartoons. > http://www.youtube.com/watch?v=yFmQP3JimAE&feature=related > http://youtu.be/XSH_5YP0tU8 > > Few ever got a clue. Teachers fell further and further behind. > > The situation was so bad in Hillsboro (personal anecdote), home > of Intel in Oregon (Aloha plant) that the police got into the home > schooling business, tried to do outreach to tomorrow's gangland > by setting up a Linux Lab in West Precinct (where I came in, as > a contract instructor). I hope you don't mind me chiming in here. I grew up in Hillsboro, Oregon. I graduated from Glencoe High School in 1985. I am an early Saturday Academy alumni (I believe Kirby knows about Saturday Academy). Since you all are talking about use of computers in teaching children mathematics, I thought I would mention my own personal experience as a learner in the early days of microcomputers. When I was in 7th grade (1979) in Brown Junior High in Hillsboro, I was in a "talented and gifted" track and was given a semester to do any science-related project I wanted to do, and then display my work in science-fair format at the end of the semester. My dad suggested I learn computer programming, which I originally thought was beyond my abilities. He took me to the Byte Shop (anyone remember that store?) and bought me a book called "BASIC from the Ground Up" by David Ahl. Then he brought me to his work place (Tektronix, in Beaverton) and let me use a 4051 microcomputer (green storage tube display, large tape cassette drive). I was given no instruction except what was in the book, and was shown how to turn the computer on, etc. Once I got to the BASIC prompt I was pretty much on my own. Except for one thing - I wanted to make a "Star Trek"-like game, and needed to figure out how to move and rotate the spaceship. My dad took the time to teach me conversion between polar and cartesian coordinates, and proper use of sine and cosine. Unlike most of my peers, I never forgot those math skills. In fact, I recall all through my years of study on my way to an electrical engineering degree, being grateful again and again that I actually understood those concepts and didn't have to keep re-learning them, but could actually apply them in new situations. I continued programming in BASIC all through high school. I impressed my Physics teacher with an animated planetary motion simulation program written in GBASIC and run on an early IBM PC. So I consider myself an early success story in computer-based, independent, non-traditional math learning. I feel a need to "pay it forward" and help give other youth the experience and advantages I had when I was young. Ironically, it seems that the huge advances made in computing and networking can make it harder to use computers as teaching tools -- the rising generation considers them mostly entertainment, multimedia, and communication devices. The skills most often applied to see cool things happen on the computer is to google and download games, or to search You Tube for movie trailers. When basic math skills were required to make anything happen on that green screen, I was motivated to learn those math skills. On the other hand, of course, those huge advances can be put to excellent use and mathematics can be used to make things happen that were not possible in the early 1980s. And, with all of the free instruction available on the internet now, there's no excuse for ignorance. But, it's like drinking from the firehose. It still really helps to have a mentor. I'm striving to help people to get that same empowered feeling I got when, as a teenager, I made things happen on the computer and gained understanding in the process. I've written a beginning Python programming book (an updated attempt at the "BASIC from the Ground Up" that got me started), I've taught short, free seminars here in North Carolina and Virginia, and am doing what I can in my "spare time" to tutor youth, including my own children. Best wishes to all you fellow travelers! David H > > The schools had proved incompetent to do their jobs (educating > for the future), so the Chief of Police was stepping in (he was > 2nd generation Chinese immigrant). > > I lectured about this Hillsboro experiment to the London Knowledge > Lab on my way to the Shuttleworth Foundation meeting with > Helen King et al, our benevolent dictator, Guido, another member > of our merry party (Scheme also represented). > > This was a meeting about South Africa, making long term plans even > then (government officials were part of Mark's entourage). > > > > > > Are lesson plans and small programs available, for example, > > > > Probably. There are well over 100,000 digital learning resources on the > > Net. You can find some of them on pages linked from > > > > http://wiki.sugarlabs.org/go/Open_Education_Resources > > > > We will need a substantial number of teachers to review them, compare > > them, and select those that do the best job making concepts clear in ways > > that will stay with students. > > The South African model was shaping up to serve auto-didacts. > > Kids who could self teach would stand the best chance. > > The teachers were proving hopeless. Adult teachers could not be > expected adapt to these technologies in sufficient time in sufficient > number. Those were the facts on the ground. > > It's not like anyone wanted it to be this way. One had to make the > best of a bad situation. > > > > > > where students could write and > > > "drop in" a script that includes integers and the output would not only > > > calculate it, but see the relevance of it in a real world situation? > > > > There are many ways to do that. One of the weirder ones is my Turtle Art > > Turing Machine for addition. ^_^ > > > > http://wiki.sugarlabs.org/go/Activities/TurtleArt/Tutorials/Turtle_Art_Turing_Machine > > > > More directly to your needs, Pippy is a Sugar activity that shows a number > > of Python examples that students can edit. For example, > > > > Fibonacci > > a, b = 0, 1 > > while b< 1001: > > print b, > > a, b = b, a+b > > > > Changing the 0, 1 in the first line changes this from a generator of > > Fibonacci numbers to a generator of the related Lucas numbers. There is a > > Pascal's Triangle program. Plotted mod 2, it reveals a Sierpinski fractal. > > "Generator" also has a technical meaning in Python, such that one > might actually write a Fibonacci generator (of the GeneratorType). > > > > > Relevant Python resources include NumPy and PyGame. > > > > > Or, perhaps, the program controls a "wheelchair" robot and students would > > > write scripts to drive the robot at a certain speed considering the slope > > > of a ramp? > > > > See the Etoys tutorial challenge for programming a "car", and the robot > > program in Uruguay with robots controlled by Sugar software. > > Alan Kay was at that Shuttleworth meeting in Kensington. I'm sure > there've been many follow-up meetings which I've not been privy to, plus > I've continued to meet with Oregon-based colleagues. > > I also work with an outfit in Sonoma County, where Python is concerned. > > > > > http://www.flickr.com/photos/christophd/4827926508/ > > XO turned into a robot thanks to the Butiá project > > > > > As you can see, I am a novice, but I see great potential and am willing to > > > learn. > > > > Delighted to meet you. > > > > Ed writes a lot of good posts on many a math-related list. I recommend paying > attention to his thinking (I know I do). > > Kirby > _______________________________________________ > Edu-sig mailing list > [hidden email] > http://mail.python.org/mailman/listinfo/edu-sig Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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In reply to this post by mokurai-2
Thank you to everyone who has responded to my inquiry. I truly appreciate your willingness to help. Our math curriculum addresses the Illinois state standards, however within the next 3 years we will be moving to the Common Core. A breakdown of the curriculum is below: Advanced math (1 section) supported by McDougal-Littel Course 2 textbook http://www.classzone.com/cz/books/msmath_2_na/book_home.htm?state=IL
Fractions/Decimals/Percents Algebra (1 and 2 step equations, simplifying, distributive property, inequalities) Geometry (polygons, angles, surface area, volume) Ratios and Proportions Probability
Standard Math (3 sections) Supported by McDougal-Littel Course 1 textbook http://www.classzone.com/cz/books/msmath_1_na/book_home.htm?state=IL Problem Solving Strategies Fraction operations Decimal operations Geometry Number Sense (Prime factorization, GCF, LCM, Divisibility Rules) Our district is generally supportive to adding new software to the school computers, however requests are only honored during school breaks (winter, spring, summer) as they want to keep the computers available for student use and MAPS testing. (http://www.nwea.org/) :-( My plan is to begin with my advanced math students. On a side note, I have enjoyed reading the personal stories you have been sharing. Mine is that my first job out of college was working for the now defunct Teletype Corporation, a part of the now defunct Western Electric, a part of the now defunct Bell System, a part of the perhaps soon to be defunct AT&T?! I spent ten years in public relations, took time off to raise children, then returned to the workforce to teach middle school. Again, I appreciate your support, and I look forward to collaborating with you. From: [hidden email] To: "kirby urner" <[hidden email]> Cc: [hidden email] Sent: Friday, July 1, 2011 1:32:45 AM Subject: Re: [Edu-sig] Python and pre-algebra On Fri, July 1, 2011 1:41 am, kirby urner wrote: > On Thu, Jun 30, 2011 at 8:03 PM, <[hidden email]> wrote: >> >> On Wed, June 29, 2011 7:15 pm, [hidden email] wrote: >> > >> > I teach 6th grade math and Python was suggested as a way to apply >> > pre-algebra concepts in a programming context. My programming >> background >> > consists of one C++ programming class. How do I begin? >> >> Python is one of several excellent options. Others are Logo, Smalltalk, >> and APL, all of which are available at no cost. I worked on a free APL >> for >> 8-bit computers before the Free Software movement got started, and I >> have >> friends working on APLs for current computers to put under the GPL. >> > > APL was my first love at Princeton, back when most people (including > me) had to use punch cards. You and jazz guitarist Stanley Jordan. He wants to create an APL-based computer music education program. At Yale in 1963 we only had octal and FORTRAN. Later on, Yale hired Alan Perlis away from Carnegie-Mellon to be Chairman of the Computer Science Department. He made APL the first language for all CS students. > It was the interactivity I loved, among > other aspects. Logo the same way. Grew into dBase later, always > interactive, a dialog. Languages divide into those which respond, > conversationally, and those which must be looked at as non-conversational. > Python joined the ranks of the conversationals. LISP was the first. On the other hand, Waterloo University in Canada created a FORTRAN interpreter for use in classes, to go with its APL, Pascal, and others. >> Assuming that your students know no Python, you could use the Sugar Labs >> Turtle Art approach to math and programming to get started. Turtle Art >> was >> designed for children to use for math, programming, and art, and has >> natural ways to move to Logo, Python, or Etoys/Smalltalk. FORTH, too, >> but >> most people don't want to know that. ^_^ (FORTH love if honk then) > > I was a math teacher in a day school for humans of the female > persuasion, as one of the trusted male faculty (most were not male), > but this was long before the Free Software movement (GNU / GPL), > was still at the start of the first computer revolution. No Internet > yet, at least not for ordinary civilians like me. My father was using timesharing, and allowed me on at 300 bps. > I dreamed of hypertext (read Computer Lib / Dream Machines > by Ted Nelson) I met Ted when he gave an invited speech at the APL91 Conference at Stanford. > and joined IGC with a guest account at New > Jersey Institute of Technology. Proto-internet, pre-listserv. In > the meantime, snailmailers were proto-typing listservs via > Action Linkage. Anyone remember? You'd mail your post to > the anchor, who'd photocopy the lot and mail back out to > subscribers. The whole listserv phenomenon, happening > through snailmail. Pierre de Fermat operated as listserv for all of the top mathematicians of Europe before the journals got started. > Lots of ethnography as yet unwritten. > > Mid 1980s. > > 'A Network Nation' by Turoff and Starr Roxanne Hiltz. > http://web.njit.edu/~turoff/Vita/vita2005.html#a30 > > I lived behind Loew's Theater on Journal Square, the main > PATH station in Jersey City. By 1985, I was back in Portland, > having been raised there through 2nd grade. > >> >> The question is, which pre-algebra concepts? Do you have a curriculum >> standard or a particular textbook in mind? Are there other topics of >> interest? >> >> I can write TA or mixed TA/Python examples, and show students how to do >> the same, and we could work together on lesson plans to share in the >> Sugar >> Labs Replacing Textbooks program. There are others with an interest in >> doing this. >> > > Then I worked at McGraw-Hill (after some stuff in between), 28th floor, > Rockefeller Center, Manhattan, editing textbooks, testing educational > computer games, contributing curriculum writing (Logo, BASIC). We need you to do that again as we find out what children can learn with computer aid at earlier stages of development than we thought. > Back then, we thought computers were soon to take the math teaching > world by storm. Little did we suspect that the North Americans would be > conquered by Texas Instruments, leaving the innovation vista to > other cultures and/or subversive counter-cultures still operational > in some areas. Thousands of dollars for a computer, under $100 for a calculator. No contest. HP was content with the engineering market and didn't want to challenge TI to a retail war. > OLPC (One Laptop per Child) was one attempt to break the TI lock > on teacher imaginations. For the most part, it failed in North America. > The resistance was too great. No breakfast cereal boxes featured > the XO. Nothing on the backs of Kellogs or General Mills. No > donated G1G1 commercials during Saturday Morning cartoons. > http://www.youtube.com/watch?v=yFmQP3JimAE&feature=related > http://youtu.be/XSH_5YP0tU8 Ah, but what will happen when we have free digital textbook replacements, so that netbooks cost less than printed textbooks? Better education at lower cost. Can politicians resist that? > Few ever got a clue. Teachers fell further and further behind. > > The situation was so bad in Hillsboro (personal anecdote), home > of Intel in Oregon (Aloha plant) that the police got into the home > schooling business, tried to do outreach to tomorrow's gangland > by setting up a Linux Lab in West Precinct (where I came in, as > a contract instructor). I have an idea for going after homeschooling networks with OLPCs and Sugar, also. > The schools had proved incompetent to do their jobs (educating > for the future), so the Chief of Police was stepping in (he was > 2nd generation Chinese immigrant). > > I lectured about this Hillsboro experiment to the London Knowledge > Lab on my way to the Shuttleworth Foundation meeting with > Helen King et al, our benevolent dictator, Guido, another member > of our merry party (Scheme also represented). I met Guido at a BayPiggies meeting (Bay Area Python Interest Group) at Google, where I mentioned to the audience that both Guido and I were trying to compile sugar-jhbuild, and reporting to one of the mailing lists, and that I had not been able to do it. He chimed in from the audience that he had failed to build it also. > This was a meeting about South Africa, making long term plans even > then (government officials were part of Mark's entourage). The Shuttleworth Foundation funded development of a suite of digital learning resources for high school math and sciences for South Africa. >> > Are lesson plans and small programs available, for example, >> >> Probably. There are well over 100,000 digital learning resources on the >> Net. You can find some of them on pages linked from >> >> http://wiki.sugarlabs.org/go/Open_Education_Resources >> >> We will need a substantial number of teachers to review them, compare >> them, and select those that do the best job making concepts clear in >> ways that will stay with students. > > The South African model was shaping up to serve auto-didacts. > > Kids who could self teach would stand the best chance. I would like to see how much of that we can help children learn, given that they learn languages and cultures, among other things, with no formal instruction. > The teachers were proving hopeless. Adult teachers could not be > expected adapt to these technologies in sufficient time in sufficient > number. Those were the facts on the ground. I don't think that that is necessarily so, and I intend to have our Replacing Textbooks project create a sufficient set of teacher training materials also. On some points, however, we might have to wait until some of our XO students enter teachers colleges. > It's not like anyone wanted it to be this way. One had to make the > best of a bad situation. > >> >> > where students could write and >> > "drop in" a script that includes integers and the output would not >> only >> > calculate it, but see the relevance of it in a real world situation? >> >> There are many ways to do that. One of the weirder ones is my Turtle Art >> Turing Machine for addition. ^_^ >> >> http://wiki.sugarlabs.org/go/Activities/TurtleArt/Tutorials/Turtle_Art_Turing_Machine >> >> More directly to your needs, Pippy is a Sugar activity that shows a >> number of Python examples that students can edit. For example, >> >> Fibonacci >> a, b = 0, 1 >> while b< 1001: >> print b, >> a, b = b, a+b >> >> Changing the 0, 1 in the first line changes this from a generator of >> Fibonacci numbers to a generator of the related Lucas numbers. There is >> a Pascal's Triangle program. Plotted mod 2, it reveals a Sierpinski >> fractal. > > "Generator" also has a technical meaning in Python, such that one > might actually write a Fibonacci generator (of the GeneratorType). > >> >> Relevant Python resources include NumPy and PyGame. >> >> > Or, perhaps, the program controls a "wheelchair" robot and students >> would >> > write scripts to drive the robot at a certain speed considering the >> slope >> > of a ramp? >> >> See the Etoys tutorial challenge for programming a "car", and the robot >> program in Uruguay with robots controlled by Sugar software. > > Alan Kay was at that Shuttleworth meeting in Kensington. I'm sure > there've been many follow-up meetings which I've not been privy to, plus > I've continued to meet with Oregon-based colleagues. I met Alan Kay at the 40th anniversary of Doug Engelbart's Mother of All Demos at Stanford. I had met Doug previously, and was apparently the first to show him an XO. > I also work with an outfit in Sonoma County, where Python is concerned. > >> >> http://www.flickr.com/photos/christophd/4827926508/ >> XO turned into a robot thanks to the Butiá project >> >> > As you can see, I am a novice, but I see great potential and am >> > willing to learn. >> >> Delighted to meet you. >> > > Ed writes a lot of good posts on many a math-related list. I recommend > paying attention to his thinking (I know I do). Thanks, Kirby. > Kirby > _______________________________________________ > Edu-sig mailing list > [hidden email] > http://mail.python.org/mailman/listinfo/edu-sig > -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://wiki.sugarlabs.org/go/Replacing_Textbooks _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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Mary,
I think elements of Python programming would fit very nicely with fractions, probability and all the number sense topics you listed (as well as problem solving strategies). Gary Litvin www.skylit.com At 09:43 AM 7/1/2011, [hidden email] wrote: Thank you to everyone who has responded to my inquiry. I truly appreciate your willingness to help. _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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In reply to this post by mary.dooms
@David: thanks for the autobio, starting in Hillsboro where I was talking
about the police jumping into Linux to improve their relations with youth culture. It was an experiment. Saturday Academy was where the police turned for instructors, which I where I came into that story, via George Heuston (formerly FBI and NORAD). Last year I taught Martian Math for Saturday Academy. This summer it's about math as a globally social activity or something like that. I'm inspired by Maria Droujkova's work on math as a social networking tool. We'll practice doing show & tell is my plan (aka Lightning Talks in Python world). On Fri, Jul 1, 2011 at 6:43 AM, <[hidden email]> wrote: > Thank you to everyone who has responded to my inquiry. I truly appreciate > your willingness to help. > Gary Litvin just chimed in. He's got an upper level math textbook written around Python. > Our math curriculum addresses the Illinois state standards, however within > the next 3 years we will be moving to the Common Core. > > A breakdown of the curriculum is below: > > Advanced math (1 section) supported by McDougal-Littel Course 2 textbook > > http://www.classzone.com/cz/books/msmath_2_na/book_home.htm?state=IL > > Integers (order of operations) > > Fractions/Decimals/Percents > One successful format is for a classroom to have a projector and an Internet connection. Better if the classroom may darken some. That's already a big problem in many settings, as many school rooms are designed to have as much light flooding in as possible at all times. The teacher is the anchor and guide and does quite a bit of role modeling and presenting, but the students also take turns, speaking to the entire group, sharing content. This is akin to inviting a student to the front of the room to use a chalk board. With a Python interpreter window showing, the teacher can engage in conversation, show this as a kind of "chat window" where the interpreter "talks back". Turning to this window from time to time, not exclusively nor excessively, and interleaved with time in other exhibits, with other languages, would be my idea of a productive math class, with students piloting alongside the teacher, time sharing the projected content. Of course one need not project all the time, just saying that's a configuration I look for (and had at the police station). Then of course one wishes each student had a computer too. That's not a requirement though. I think it should be required that students get to co-pilot the shared / projected classroom computer. I like to see teachers sharing the floor, not hogging the limelight. But this isn't a hardware / tool issue, it's a formatting issue. The ideal at Saturday Academy and of One Laptop Per Child is a sense of having one's own computer, no need to share. That's a useful mode to be in, productive sometimes, but if there's only one computer, then projecting it may be the solution. Then more of a round robin format. I use this with adults as well. I like the public speaking angle. Math gets too isolating and solipsistic, to the detriment of everyone involved. > Algebra (1 and 2 step equations, simplifying, distributive property, > inequalities) > > Geometry (polygons, angles, surface area, volume) > A weakness in contemporary geometry is this belief that it's best to start in the abstract / ethereal realm of the infinite this and the dimensionless that. Anti-experiential. Wow 'em with less than self evident axioms and definitions and pretend that's elite and superior (a kind of snobism). Regular old objects of everyday space are more polyhedrons than polygons. The Earth is an oblate sphere. Keeping geodesy in the picture, ala Google Earth, Google Mars etc., ... so easy to pull ahead of the rank and file. One needs to be free of district strictures though, straitjacketing "standards". At Saturday Academy, we are not bound and gagged the way they do in some other schools I won't name in this post. > Ratios and Proportions > > Probability > > > > Standard Math (3 sections) Supported by McDougal-Littel Course 1 textbook > > http://www.classzone.com/cz/books/msmath_1_na/book_home.htm?state=IL > > Problem Solving Strategies > > Fraction operations > > Decimal operations > > Geometry > Maybe get some polyhedrons in here. I was just visiting with Father Magnus Wenninger in Minnesota. He's one of the premier polyhedronists. I met a young guy recently (he was waiting our table) who saw the polyhedrons we had (lunch meeting) and correctly named them. I was amazed and asked him which school system he'd attended. Minneapolis Public Schools. > Number Sense (Prime factorization, GCF, LCM, Divisibility Rules) > > Our district is generally supportive to adding new software to the school > computers, however requests are only honored during school breaks (winter, > spring, summer) as they want to keep the computers available for student use > and MAPS testing. (http://www.nwea.org/) :-( > Typically, they'll teach GCF using prime factorizations and bleep over Euclid's Algorithm. That's a fork in the road. What I call "digital math" includes Euclid's. Here's Guido's version: def gcf(a, b): while b: a, b = b, a % b # modulo arithmetic return a Milo on mathfuture thinks number theory was expunged from Lower48 curricula during the anti-German backlash of Woodrow Wilson and WW1. Planar Euclidean geometry became the new pavement. More like the Russian curriculum in some ways. We could use a lot more ethnography of math education. Many full time anthropologists should be tasked to this important work, observing and reporting. One thing you can exhibit using the Python window (one of many) is this idea of types. We all know that objects (like dogs and shoes) come in types. "What type of thing is that?" So then in Python we have this "type" function that spits back the type of a thing. >>> type(1) <class 'int'> >>> type(1.0) <class 'float'> >>> import decimal >>> type(decimal.Decimal('10')) <class 'decimal.Decimal'> >>> type({'pig','dog','monkey','bat','snake','hamster'}) <class 'set'> This is rather generic language, almost like basic English (which it is, translates to other languages pretty easily). Weaving together an "object oriented" patter with everyday ordinary speaking is a goal of my math classes. It's a language class. Nomenclature matters. Dot notation: noun.verb( ). results = thing.action( inputs ). noun.adjective. More grammar. Lights go on when students realize how much computers deal with alphanumeric data, not just numbers. There's this stereotype from the outside that it's all "number crunching" meaning glorified arithmetic. It's as much about text, about parsing, about markup. I like to dive in with some ideas about tcp/ip and shared infrastructure. To this end, I project 'Warriors of the Net', admittedly pretty basic: http://video.google.com/videoplay?docid=4523214973725842000 > My plan is to begin with my advanced math students. > > On a side note, I have enjoyed reading the personal stories you have been > sharing. Mine is that my first job out of college was working for the now > defunct Teletype Corporation, a part of the now defunct Western Electric, a > part of the now defunct Bell System, a part of the perhaps soon to be > defunct AT&T?! I spent ten years in public relations, took time off to raise > children, then returned to the workforce to teach middle school. > > Again, I appreciate your support, and I look forward to collaborating with > you. > The Baby Bells are striving to get back together they say. Sounds like one of those summer science fiction movies where the alien Globs are seeking to rejoin and form the Mother Glob. Anyway, I should get back to the day job (teaching Python as it happens). Great chatting, Kirby _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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In reply to this post by david-2
On Fri, July 1, 2011 9:28 am, David Handy wrote: > I've written a beginning Python > programming book (an updated attempt at the "BASIC from the Ground Up" > that got me started), I've taught short, free seminars here in North > Carolina and Virginia, and am doing what I can in my "spare time" to > tutor youth, including my own children. > > Best wishes to all you fellow travelers! > > David H Where can we find your book? -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://wiki.sugarlabs.org/go/Replacing_Textbooks _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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In reply to this post by mary.dooms
On Fri, July 1, 2011 9:43 am, [hidden email] wrote:
> Thank you to everyone who has responded to my inquiry. I truly appreciate > your willingness to help. > > Our math curriculum addresses the Illinois state standards, however within > the next 3 years we will be moving to the Common Core. > > A breakdown of the curriculum is below : > > > Advanced math (1 section) supported by McDougal-Littel Course 2 textbook > > http://www.classzone.com/cz/books/msmath_2_na/book_home.htm?state=IL > > > Integers (order of operations) I take it that they mean function precedence, with multiplications done before additions and subtractions. Students can write programs to tell the computer how to evaluate expressions. > Fractions/Decimals/Percents > > Algebra (1 and 2 step equations, I don't know this terminology. > simplifying, distributive property, > inequalities) > > Geometry (polygons, angles, surface area, volume) > > Ratios and Proportions None of the above present problems for using Python. > Probability There are two tricky ideas here. The first is equiprobability. Suppose you have two cards, red on one side and black on the other. How many ways can they land if you toss them all at once? All black 1 black, 1 red All red Are these cases equally probable? No. (Try it.) What are the equally probable cases? The second, conditional probability, takes that thought further. Suppose you toss one card first, and it comes up red. What are the cases and probabilities for tossing the second card? This is easy, and nobody should have real trouble with it. Now suppose you are a contestant on Let's Make a Deal, and you have to choose among three doors, one with the grand prize, and two with nothing or useless prizes. You pick one, but don't get to open it. Then the host opens a different door that does not have the grand prize behind it. Should you stick with the door you first chose, or switch to the other one? This simple problem, which has a simple method of solution, has caused huge arguments among supposedly bright adults, many of whom get it flatly wrong. There are many other simple problems that most people get wrong, but that is a topic for another time. > Standard Math (3 sections) Supported by McDougal-Littel Course 1 textbook > > http://www.classzone.com/cz/books/msmath_1_na/book_home.htm?state=IL > > Problem Solving Strategies There are several useful approaches. In the long run, nothing beats practice on a wide range of problems and puzzles. > Fraction operations > > Decimal operations > > Geometry > > Number Sense (Prime factorization, GCF, LCM, Divisibility Rules) All readily programmed in Python. Thank you. Some of us will check them out. All of these except the problem solving strategies are within the range of elementary Python programming. Programming and debugging are excellent ways to teach problem solving strategies hands on. Which topics have your students had the greatest difficulties with? We need to make a list of topics and subtopics to Pythonize, then a list of Python features required to do that, then a sequence of lessons and challenges to teach all of that Python and math together. Simple functions and expressions, elementary program logic (branch and loop), and very simple graphics commands will cover most of it. We can discuss the use of data arrays and more advanced vector and matrix math for solving simultaneous equations. OT: I would like to see a larger unit on algebraic rules, not just the distributive law, emphasizing that different systems obey different sets of rules, and that certain sets of rules, or axioms, come up over and over again, and are worth understanding. However, that is called Modern Algebra, and anything Modern is nearly verboten in schools. ^_^ The result is that we are not permitted to explain that clock time is an algebraic ring, and to talk about other rings; nor can we talk about arithmetic on remainders, modulo some number N, as generating rings when N is composite and fields when N is prime. Not Boolean algebra unless we are specifically teaching computers; not vector spaces and their linear transformations, a concept that is trivial visually, and that makes trigonometry trivial to explain. We do not talk of groups of symmetries or permutations. We cannot even mention that each of these sets of rules, and many others, defines a category. Especially we cannot explain how to add apples and oranges in a graded ring of Laurent polynomials, even though we expect children to add 2x and 3y without explanation. You can look up graded rings and Laurent polynomials, but the point is that these are just names for the stuff of algebra itself, where you can use an arbitrary number of variables to make expressions by adding, subtracting, and multiplying, and sometimes, but not always, you can divide. And it's OK to use negative numbers, but not complex numbers or hyperreal numbers, (including infinitesimals and infinities), which have endless applications to topics that interest children, such as secret codes and games, and become essential later on in calculus, physics, and other topics. > Our district is generally supportive to adding new software to the school > computers, however requests are only honored during school breaks (winter, > spring, summer) as they want to keep the computers available for student > use and MAPS testing. (http://www.nwea.org/) :-( Do you mean that new software can be put on during the breaks only to be removed at the beginning of the next term, or that it can be installed and left there for future use? What software do you have now? Windows, Mac OS, or Linux? Commercial programming language products or Free Software? It appears that this might be a good case for Sugar on a Stick, a bootable USB drive, so that nothing is installed on the computer. This also means that each student who has one can carry any work done from one computer to another. > My plan is to begin with my advanced math students. > > On a side note, I have enjoyed reading the personal stories you have been > sharing. Mine is that my first job out of college was working for the now > defunct Teletype Corporation, a part of the now defunct Western Electric, > a part of the now defunct Bell System, a part of the perhaps soon to be > defunct AT&T?! Great pioneers in the computer industry, all, whose management thought that they understood the computer business better than the companies that dominated it. :( > I spent ten years in public relations, That could be helpful later on, when we try to sell our program to other teachers and to administrations. > took time off to > raise children, then returned to the workforce to teach middle school. > > Again, I appreciate your support, and I look forward to collaborating with > you. Likewise. > ----- Original Message ----- > From: [hidden email] > To: "kirby urner" <[hidden email]> > Cc: [hidden email] > Sent: Friday, July 1, 2011 1:32:45 AM > Subject: Re: [Edu-sig] Python and pre-algebra > > On Fri, July 1, 2011 1:41 am, kirby urner wrote: >> On Thu, Jun 30, 2011 at 8:03 PM, <[hidden email]> wrote: >>> >>> On Wed, June 29, 2011 7:15 pm, [hidden email] wrote: >>> > >>> > I teach 6th grade math and Python was suggested as a way to apply >>> > pre-algebra concepts in a programming context. My programming >>> background >>> > consists of one C++ programming class. How do I begin? >>> >>> Python is one of several excellent options. Others are Logo, Smalltalk, >>> and APL, all of which are available at no cost. I worked on a free APL >>> for >>> 8-bit computers before the Free Software movement got started, and I >>> have >>> friends working on APLs for current computers to put under the GPL. >>> >> >> APL was my first love at Princeton, back when most people (including >> me) had to use punch cards. > > You and jazz guitarist Stanley Jordan. He wants to create an APL-based > computer music education program. > > At Yale in 1963 we only had octal and FORTRAN. Later on, Yale hired Alan > Perlis away from Carnegie-Mellon to be Chairman of the Computer Science > Department. He made APL the first language for all CS students. > >> It was the interactivity I loved, among >> other aspects. Logo the same way. Grew into dBase later, always >> interactive, a dialog. Languages divide into those which respond, >> conversationally, and those which must be looked at as >> non-conversational. >> Python joined the ranks of the conversationals. > > LISP was the first. On the other hand, Waterloo University in Canada > created a FORTRAN interpreter for use in classes, to go with its APL, > Pascal, and others. > >>> Assuming that your students know no Python, you could use the Sugar >>> Labs >>> Turtle Art approach to math and programming to get started. Turtle Art >>> was >>> designed for children to use for math, programming, and art, and has >>> natural ways to move to Logo, Python, or Etoys/Smalltalk. FORTH, too, >>> but >>> most people don't want to know that. ^_^ (FORTH love if honk then) >> >> I was a math teacher in a day school for humans of the female >> persuasion, as one of the trusted male faculty (most were not male), >> but this was long before the Free Software movement (GNU / GPL), >> was still at the start of the first computer revolution. No Internet >> yet, at least not for ordinary civilians like me. > > My father was using timesharing, and allowed me on at 300 bps. > >> I dreamed of hypertext (read Computer Lib / Dream Machines >> by Ted Nelson) > > I met Ted when he gave an invited speech at the APL91 Conference at > Stanford. > >> and joined IGC with a guest account at New >> Jersey Institute of Technology. Proto-internet, pre-listserv. In >> the meantime, snailmailers were proto-typing listservs via >> Action Linkage. Anyone remember? You'd mail your post to >> the anchor, who'd photocopy the lot and mail back out to >> subscribers. The whole listserv phenomenon, happening >> through snailmail. > > Pierre de Fermat operated as listserv for all of the top mathematicians of > Europe before the journals got started. > >> Lots of ethnography as yet unwritten. >> >> Mid 1980s. >> >> 'A Network Nation' by Turoff and Starr Roxanne Hiltz. >> http://web.njit.edu/~turoff/Vita/vita2005.html#a30 >> >> I lived behind Loew's Theater on Journal Square, the main >> PATH station in Jersey City. By 1985, I was back in Portland, >> having been raised there through 2nd grade. >> >>> >>> The question is, which pre-algebra concepts? Do you have a curriculum >>> standard or a particular textbook in mind? Are there other topics of >>> interest? >>> >>> I can write TA or mixed TA/Python examples, and show students how to do >>> the same, and we could work together on lesson plans to share in the >>> Sugar >>> Labs Replacing Textbooks program. There are others with an interest in >>> doing this. >>> >> >> Then I worked at McGraw-Hill (after some stuff in between), 28th floor, >> Rockefeller Center, Manhattan, editing textbooks, testing educational >> computer games, contributing curriculum writing (Logo, BASIC). > > We need you to do that again as we find out what children can learn with > computer aid at earlier stages of development than we thought. > >> Back then, we thought computers were soon to take the math teaching >> world by storm. Little did we suspect that the North Americans would be >> conquered by Texas Instruments, leaving the innovation vista to >> other cultures and/or subversive counter-cultures still operational >> in some areas. > > Thousands of dollars for a computer, under $100 for a calculator. No > contest. HP was content with the engineering market and didn't want to > challenge TI to a retail war. > >> OLPC (One Laptop per Child) was one attempt to break the TI lock >> on teacher imaginations. For the most part, it failed in North America. >> The resistance was too great. No breakfast cereal boxes featured >> the XO. Nothing on the backs of Kellogs or General Mills. No >> donated G1G1 commercials during Saturday Morning cartoons. >> http://www.youtube.com/watch?v=yFmQP3JimAE&feature=related >> http://youtu.be/XSH_5YP0tU8 > > Ah, but what will happen when we have free digital textbook replacements, > so that netbooks cost less than printed textbooks? Better education at > lower cost. Can politicians resist that? > >> Few ever got a clue. Teachers fell further and further behind. >> >> The situation was so bad in Hillsboro (personal anecdote), home >> of Intel in Oregon (Aloha plant) that the police got into the home >> schooling business, tried to do outreach to tomorrow's gangland >> by setting up a Linux Lab in West Precinct (where I came in, as >> a contract instructor). > > I have an idea for going after homeschooling networks with OLPCs and > Sugar, also. > >> The schools had proved incompetent to do their jobs (educating >> for the future), so the Chief of Police was stepping in (he was >> 2nd generation Chinese immigrant). >> >> I lectured about this Hillsboro experiment to the London Knowledge >> Lab on my way to the Shuttleworth Foundation meeting with >> Helen King et al, our benevolent dictator, Guido, another member >> of our merry party (Scheme also represented). > > I met Guido at a BayPiggies meeting (Bay Area Python Interest Group) at > Google, where I mentioned to the audience that both Guido and I were > trying to compile sugar-jhbuild, and reporting to one of the mailing > lists, and that I had not been able to do it. He chimed in from the > audience that he had failed to build it also. > >> This was a meeting about South Africa, making long term plans even >> then (government officials were part of Mark's entourage). > > The Shuttleworth Foundation funded development of a suite of digital > learning resources for high school math and sciences for South Africa. > >>> > Are lesson plans and small programs available, for example, >>> >>> Probably. There are well over 100,000 digital learning resources on the >>> Net. You can find some of them on pages linked from >>> >>> http://wiki.sugarlabs.org/go/Open_Education_Resources >>> >>> We will need a substantial number of teachers to review them, compare >>> them, and select those that do the best job making concepts clear in >>> ways that will stay with students. >> >> The South African model was shaping up to serve auto-didacts. >> >> Kids who could self teach would stand the best chance. > > I would like to see how much of that we can help children learn, given > that they learn languages and cultures, among other things, with no formal > instruction. > >> The teachers were proving hopeless. Adult teachers could not be >> expected adapt to these technologies in sufficient time in sufficient >> number. Those were the facts on the ground. > > I don't think that that is necessarily so, and I intend to have our > Replacing Textbooks project create a sufficient set of teacher training > materials also. On some points, however, we might have to wait until some > of our XO students enter teachers colleges. > >> It's not like anyone wanted it to be this way. One had to make the >> best of a bad situation. >> >>> >>> > where students could write and >>> > "drop in" a script that includes integers and the output would not >>> only >>> > calculate it, but see the relevance of it in a real world situation? >>> >>> There are many ways to do that. One of the weirder ones is my Turtle >>> Art >>> Turing Machine for addition. ^_^ >>> >>> http://wiki.sugarlabs.org/go/Activities/TurtleArt/Tutorials/Turtle_Art_Turing_Machine >>> >>> More directly to your needs, Pippy is a Sugar activity that shows a >>> number of Python examples that students can edit. For example, >>> >>> Fibonacci >>> a, b = 0, 1 >>> while b< 1001: >>> print b, >>> a, b = b, a+b >>> >>> Changing the 0, 1 in the first line changes this from a generator of >>> Fibonacci numbers to a generator of the related Lucas numbers. There is >>> a Pascal's Triangle program. Plotted mod 2, it reveals a Sierpinski >>> fractal. >> >> "Generator" also has a technical meaning in Python, such that one >> might actually write a Fibonacci generator (of the GeneratorType). >> >>> >>> Relevant Python resources include NumPy and PyGame. >>> >>> > Or, perhaps, the program controls a "wheelchair" robot and students >>> would >>> > write scripts to drive the robot at a certain speed considering the >>> slope >>> > of a ramp? >>> >>> See the Etoys tutorial challenge for programming a "car", and the robot >>> program in Uruguay with robots controlled by Sugar software. >> >> Alan Kay was at that Shuttleworth meeting in Kensington. I'm sure >> there've been many follow-up meetings which I've not been privy to, plus >> I've continued to meet with Oregon-based colleagues. > > I met Alan Kay at the 40th anniversary of Doug Engelbart's Mother of All > Demos at Stanford. I had met Doug previously, and was apparently the first > to show him an XO. > >> I also work with an outfit in Sonoma County, where Python is concerned. >> >>> >>> http://www.flickr.com/photos/christophd/4827926508/ >>> XO turned into a robot thanks to the Butiá project >>> >>> > As you can see, I am a novice, but I see great potential and am >>> > willing to learn. >>> >>> Delighted to meet you. >>> >> >> Ed writes a lot of good posts on many a math-related list. I recommend >> paying attention to his thinking (I know I do). > > Thanks, Kirby. > >> Kirby >> _______________________________________________ >> Edu-sig mailing list >> [hidden email] >> http://mail.python.org/mailman/listinfo/edu-sig >> > > > -- > Edward Mokurai > (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر > ج) Cherlin > Silent Thunder is my name, and Children are my nation. > The Cosmos is my dwelling place, the Truth my destination. > http://wiki.sugarlabs.org/go/Replacing_Textbooks > > > _______________________________________________ > Edu-sig mailing list > [hidden email] > http://mail.python.org/mailman/listinfo/edu-sig > -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://wiki.sugarlabs.org/go/Replacing_Textbooks _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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In reply to this post by mokurai-2
On Fri, Jul 01, 2011 at 10:33:35PM -0400, [hidden email] wrote:
> > On Fri, July 1, 2011 9:28 am, David Handy wrote: > > I've written a beginning Python > > programming book (an updated attempt at the "BASIC from the Ground Up" > > that got me started), I've taught short, free seminars here in North > > Carolina and Virginia, and am doing what I can in my "spare time" to > > tutor youth, including my own children. > > > > Best wishes to all you fellow travelers! > > > > David H > > Where can we find your book? I sell my book in e-book format, or in batches of 20+, at: http://www.handysoftware.com/cpif/ Thanks, David H > -- > Edward Mokurai > (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر > ج) Cherlin > Silent Thunder is my name, and Children are my nation. > The Cosmos is my dwelling place, the Truth my destination. > http://wiki.sugarlabs.org/go/Replacing_Textbooks > > _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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In reply to this post by kirby urner-4
On Fri, July 1, 2011 2:06 pm, kirby urner wrote: > A weakness in contemporary geometry is this belief that it's best to start > in the abstract / ethereal realm of the infinite this and the > dimensionless that. The real origin of geometry was the necessity of resurveying all agricultural land in Egypt after the annual Nile floods. > Anti-experiential. Wow 'em with less than self evident axioms and > definitions and pretend that's elite and superior (a kind of snobbism). See Thorstein Veblen, The Theory of the Leisure Class. > Regular old objects of everyday space are more polyhedrons than > polygons. The Earth is an oblate sphere. Oblate spheroid, approximately. The Earth-Moon orbital equations currently have several hundred terms, to do with their figures and their mass distributions. Many of those terms have been worked out using the retroreflector placed on the moon by astronauts, allowing us to measure its distance with an accuracy of a few inches. Kirby likes to focus on certain aspects of polyhedra, like his Martian Math. But polyhedra are endlessly fascinating in a multitude of ways, in crystallography, in topology (the Euler formula V-F+E), in error-correcting codes, in the proof of Fermat's Last Theorem (the relationship between elliptic functions and modular forms), and many other areas. The Bit in the original Tron movie had two forms, both stellated polyhedra (and both rendered for the movie in APL by Judson Rosebush). Then there are the much wider range of non-Euclidean polyhedra and the higher-dimensional polyhedragons, starting with the well-known tesseract. > Keeping geodesy in the picture, ala Google Earth, Google Mars etc., > > ... so easy to pull ahead of the rank and file. One needs to be free > of district strictures though, straitjacketing "standards". and the tyranny of the Right Answer, which prevented the recognition of negative numbers, non-Euclidean geometry, and complex numbers for centuries in each case, and is now holding back non-standard analysis, which allows us to use infinitesimals correctly in calculus. H. Jerome Keisler, Elementary Calculus: An Infinitesimal Approach http://www.clrn.org/search/details.cfm?elrid=8124 > At Saturday > Academy, we are not bound and gagged the way they do in some > other schools I won't name in this post. > >> Ratios and Proportions >> >> Probability >> >> >> >> Standard Math (3 sections) Supported by McDougal-Littel Course 1 >> textbook >> >> http://www.classzone.com/cz/books/msmath_1_na/book_home.htm?state=IL >> >> Problem Solving Strategies >> >> Fraction operations >> >> Decimal operations >> >> Geometry >> > > Maybe get some polyhedrons in here. > > I was just visiting with Father Magnus Wenninger in Minnesota. > He's one of the premier polyhedronists. > > I met a young guy recently (he was waiting our table) who > saw the polyhedrons we had (lunch meeting) and correctly > named them. I was amazed and asked him which school > system he'd attended. Minneapolis Public Schools. > >> Number Sense (Prime factorization, GCF, LCM, Divisibility Rules) >> >> Our district is generally supportive to adding new software to the >> school >> computers, however requests are only honored during school breaks >> (winter, >> spring, summer) as they want to keep the computers available for student >> use >> and MAPS testing. (http://www.nwea.org/) :-( >> > > Typically, they'll teach GCF using prime factorizations and bleep > over Euclid's Algorithm. That's a fork in the road. What I call > "digital math" includes Euclid's. Here's Guido's version: > > def gcf(a, b): > while b: > a, b = b, a % b # modulo arithmetic > return a This is a variation of the general pattern for recurrence relationships def fn(a, b): while True: a, b = b, f(a, b) print a which actually works better if written as a Generator. If f is + and a, b = 0, 1 we get Fibonacci numbers. > Milo on mathfuture thinks number theory was expunged from > Lower48 curricula during the anti-German backlash of > Woodrow Wilson and WW1. Planar Euclidean geometry > became the new pavement. More like the Russian curriculum > in some ways. We could use a lot more ethnography of math > education. Many full time anthropologists should be tasked > to this important work, observing and reporting. > > One thing you can exhibit using the Python window (one of many) > is this idea of types. We all know that objects (like dogs and shoes) > come in types. "What type of thing is that?" So then in Python we > have this "type" function that spits back the type of a thing. > >>>> type(1) > <class 'int'> >>>> type(1.0) > <class 'float'> >>>> import decimal >>>> type(decimal.Decimal('10')) > <class 'decimal.Decimal'> >>>> type({'pig','dog','monkey','bat','snake','hamster'}) > <class 'set'> Understanding types makes it possible to form a correct notion of adding apples and oranges. Ordinary addition doesn't work on most combinations of types, but one can define addition and the other basic arithmetic functions for anything. As I said the other day, this is called a graded ring of Laurent polynomials, which is a fancy way of saying "algebraic expressions" like 2/x + 3y. It is important to understand that there is not just one kind of addition, but a vast multitude of kinds, operating under different algebraic rules and forming a multitude of categories of algebraic structures with all sorts of mappings between them. Shopping cart arithmetic is but one of them, and in shopping cart arithmetic, you *can* add apples and oranges. > This is rather generic language, almost like basic English (which > it is, translates to other languages pretty easily). Weaving together > an "object oriented" patter with everyday ordinary speaking is a > goal of my math classes. It's a language class. Nomenclature > matters. Dot notation: noun.verb( ). results = thing.action( inputs ). > noun.adjective. More grammar. > > Lights go on when students realize how much computers deal with > alphanumeric data, not just numbers. There's this stereotype from > the outside that it's all "number crunching" meaning glorified > arithmetic. It's as much about text, about parsing, about markup. > > I like to dive in with some ideas about tcp/ip and shared infrastructure. > To this end, I project 'Warriors of the Net', admittedly pretty basic: > http://video.google.com/videoplay?docid=4523214973725842000 > >> My plan is to begin with my advanced math students. >> >> On a side note, I have enjoyed reading the personal stories you have >> been >> sharing. Mine is that my first job out of college was working for the >> now >> defunct Teletype Corporation, a part of the now defunct Western >> Electric, a >> part of the now defunct Bell System, a part of the perhaps soon to be >> defunct AT&T?! I spent ten years in public relations, took time off to >> raise >> children, then returned to the workforce to teach middle school. >> >> Again, I appreciate your support, and I look forward to collaborating >> with >> you. >> > > The Baby Bells are striving to get back together they say. Yes, one of them bought AT&T and assumed its name, and I get TV and Internet from them. > Sounds > like one of those summer science fiction movies where the alien > Globs are seeking to rejoin and form the Mother Glob. Terminator 2. > Anyway, I should get back to the day job (teaching Python as it happens). > > Great chatting, > > Kirby > _______________________________________________ > Edu-sig mailing list > [hidden email] > http://mail.python.org/mailman/listinfo/edu-sig > -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://wiki.sugarlabs.org/go/Replacing_Textbooks _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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In reply to this post by david-2
On Sat, July 2, 2011 2:10 pm, David Handy wrote:
> On Fri, Jul 01, 2011 at 10:33:35PM -0400, [hidden email] wrote: >> >> On Fri, July 1, 2011 9:28 am, David Handy wrote: >> > I've written a beginning Python >> > programming book (an updated attempt at the "BASIC from the Ground Up" >> > that got me started), I've taught short, free seminars here in North >> > Carolina and Virginia, and am doing what I can in my "spare time" to >> > tutor youth, including my own children. >> > >> > Best wishes to all you fellow travelers! >> > >> > David H >> >> Where can we find your book? > > I sell my book in e-book format, or in batches of 20+, at: > > http://www.handysoftware.com/cpif/ I see. I was going to ask whether Sugar Labs could distribute it in other languages under a Creative Commons license, but our booki software is not set up to host a commercial product for translation. Well, doubtless there are other ways. > Thanks, > David H -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://wiki.sugarlabs.org/go/Replacing_Textbooks _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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