Drawing Kids into Mathematics

Drawing Kids into MathematicsTurtle Art & Scratch @peterskillenpeterskillen.org

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Here is the plan for today!!2

Seymour PapertThis is Seymour Papert the father of educational computing; the genius behind constructionism and the originator of the digital age maker movement. He, along with Cynthia Solomon and Wally Feurzig, created the Logo computer languagewhich is most famous for Turtle GraphicsAsk: Who knows of Logo and/or Seymour Paperts work? Show of hands?We are going to start with an advance organizer. A Minds on. CLICK slide

Ask: Ok, during this video Im going to show you, please think aboutWhat resonates with you? What surprises you? What do you find interesting?

3Early Seymour Papert Movie4Advance Organizer Minds On Crayons, glue, cardboard, blocksThese are the standard building materials from which children build their minds.love rather than logicEducation has very little to do with explanationsex than abstractionfalling in loveSeymour PapertComputers as mudpies!Ask: Ok, share with us your thoughts on these videos. What resonated with you? What surprised you? This is incredible history folks. A groundwork to never be forgotten and one to be built on. This pedagogical framework must be brought to our classrooms and our schools for any of this maker and coding stuff to have traction in developing intentional learners.Im Peter Skillenan elementary and secondary teacher since 1970and Ive been involved with this community since 1980 the maker movement the coding movement before there was such a term! But, I am not a programmernor am I a computer science teacher. My main interest has been in developing learners who are intentional or entrepreneurial about their learning. I want kids to be excited, passionate, to take charge, to set goals for their learning.to embrace mistakesand to have not just the permission to do sobut to develop the skill set to do so.

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Having said that.My first experiences with computers were with Grade ones in 1977.

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If you arent familiar with the Logo language, especially the turtle graphics aspect, dont worry, THAT is the focus of todays time together!!

The first workshop I ever gave to teachers in North York Schools was on how to use Logo and how to use it effectively to help kids think deeply. That was 1981. I then implemented Lego/Logo the precursor to Lego Robotics across North York schools. About 50 kits were made available. Youll see a little of something like that later today.It was also my good fortune to have spent time with Seymour Papert, MIT professor this co-creator of Logo who was a student and colleague of Jean Piagets. I spent time with him in Israel and at MIT.

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One time was just after they developed the intelligent brick - a Lego brick that had a programmable chip in it. This was in the mid 1990s. So about 20 years ago.

That brick made it possible to not have the turtle or other robot tethered with those wires you saw in the video!I have also been fortunate in a friendship with Brian Silverman since the early 80s. Brian is the creator of many of the worlds best logos. Brian and Seymour created Logo Computer Systems Incorporated in Montreal at the beginning of the 1980s. I was lucky to work there between 2000 and 2003.

Brian and his partner, Artemis Papert (Seymours daughter) and an artist in her own right developed Turtle Art our main tool for today!!

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I also ran this Logo conference when I was in charge of the Special Interest Group for Logo in Ontario LOOK TO THE LEARNER 1986

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During the 80s I also was privileged to study and work with Marlene Scardamalia and Carl Bereiter at OISE on their knowledge building initiative. We were involved in building CSILE a Computer Supported Intentional Learning Environmentit has grown into Knowledge Forum. My research was related to facilitating knowledge building in an online environment while kids were engaged in Logo projects. Journal Zone was a commercial online, scaffolded collaborative journal writing environment I developed as a result!

Ok. Thats a little about me!! How about you? Elementary? Secondary? Admin? Curriculum consultant? Other?

Okso now lets look at Turtle Art. I want to spend the bulk of the time on Turtle Artbecause, like Scratch, it is freebut has many fewer distractions than does Scratch. It is a less feature rich environment

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Introduce the basics of the interface for Turtle Art.

Explain each of the blocks on each of the tabs!

ForwardBackLeftRightRepeatArcSetxy

Show some basic commands from the Turtle tabPlay extensively with thisEnsuring people get what is going on!!

11Play Turtle

Because this is such a wonderful geometric activity based on relative movements playing turtle can be wonderful.

A great activity for the classroom, hallway, outside, or gym. Once the kids have the basic commands, they can team up and issue commands to each other to accomplish certain tasks:Making geometric shapes (squares, triangles, etc.)Following a preset pathObstacle course

Turtle could be blindfoldedTurtle could have an RT and an LT on their hands if need be

Now that youve seen the basics of turtle artI want to show you another piece of video related to how and why turtle geometry is so very relevant for kids in learning mathematics.

Well come back to Turtle Art shortly and delve much more deeply!

As you are watching this video, I want you to ask yourself: Which ideas really mean something for me and for my students? How might this be different, or similar, to other things I am doing in my classroom?12Seymour Movie 1983THOUGHTS??Which ideas really mean something for me and for my students? How might this be different, or similar, to other things I am doing in my classroom?

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Maria MontessoriCreation of artefacts publicly

Mediates conversationConstructionismPeople actively build their own schema.AssimilationAccommodationI wish to take a moment to describe the difference between constructivism and constructionism.

Constructivism is a theory which suggests that people actively construct their own understanding and knowledge of the world and are not merely passive recipients.

These understandings arise through experiencing events and then reflecting on those experiences. If we encounter something new, we either assimilate it into our previous ideas and knowledgeour schemaor we must accommodate it by changing what we believe, therefore modifying our schema. Or maybe we just discard the new information as irrelevant.

In neuroscience terms we are building neural pathways, cognitive routines, habits of mind, models with which to think, webs of ganglia, mental models

CLICK

So along comes Seymour Papert and in the mid-sixties begins to think very deeply about the role of kids making things>publicly.This is when he coined the term constructionism.

Constructionists believe that deep, substantive learning and enduring understandings occur when people are actively creating artifacts in the real world. Papert & Harel

Constructionism holds that children learn best when they are in the active role of the designer and constructor. This building of artefacts mediates conversation among kids.

14Constructionismrelies onvisible and discussablethinkingIn a constructionist approach, it is not merely the act of constructing that is essential.

OKback to the turtle!!15Total Turtle Trip Theorem

If a turtle takes a trip around the boundary of any area and ends up in the state in which it started, then the sum of all turns will be 360 degrees.

Mindstorms, 1980Total Turtle Trip Theorem

I created the Minds On activity the advance organizer - like this:

I asked the kids to write a story about a total turtle trip

Here is LeeAnnes story

So, as an advance organizer or a minds on as we might say today, I asked my grade twos, to write a story about a total turtle trip before we explored this powerful idea on the computer.Leeanne, aged 8 wrote

Once there lived a turtle. He was very curious. He wanted to take a trip. So he said to his mother, Im going on a trip. Oh, but what if you fall and land upon your back? his mother asked. I wont do that. And off he went. When he was walking along he met Father Bunny. Where are you off to on this fine spring morning, Father Bunny asked. Im going on a trip around the world. But what if you Turtle didnt hear. He was halfway down the road. He started down a big hill but he tripped and tumbled down, down, down the hill and landed on his back. And there he stayed. Meanwhile Turtles mother got worried and went to find him. She found him on his back. She helped him to his feet. And he said, I guess I took a total turtle trip!

DEMO: repeat 4 [ fd 100 rt 90]Repeat 3 [ fd 100 rt 120]Etc.16ProceduresOrStacks

So the turtle doesnt really know a lot of words just a few primitives like weve seen.

One of the most powerful aspects of Logo is that students can teach the turtle new vocabulary. This naming can be extremely powerful as students are building and structuring their own language.

Demo:square (talk about ttt)Triangle so for an equilateral triangle what is the angle we need to turn? (talk about ttt AND that this is turtle geometry a relative view of the world of geometry different from Cartesian geometry --- but complementing it

Youll remember that we can use the SETX SET Y or SETXY commands if we want to do coordinate or cartesian geometry.

What about a pentagon? Or Hexagon?

Tell Leeannes story about the the onzagon.

So in the previous story, did Leeanne understand the concept? Lets see. I asked the kids to make any polygon.

I was amazed at what LeeAnne did. Why? Because she not only understood the concept at hand, but realized that she could have the computer do the division (360/11). So her instruction to the turtle was repeat. This made the creation of any polygon really easy! A pentagon was 360/5. An octagon was 360/8.

17Sub-Procedures

Discuss and demonstrate procedures and sub-procedures

Then speak about TRANSFER ---

If you ever wonder at the end of a day just what your kids learned while working at the computers and you are dissatisfied with your thoughts, consider the following simple model. Gavriel Salomon has posed an analysis of the difference between effects with and effects of computers.

Effects with are the changes that take place while one is engaged in intellectual partnership with peers or with a computer tool, as, for example, is the case with the changed quality of problem solving that takes place when individuals work together in a team. On the other hand, effects of are those more lasting changes that take place as a consequence of the intellectual partnership, as when computer-enhanced collaboration teaches students to ask more exact and explicit questions even when not using that system.

In other words, the effects with are the enhanced ability one gets from the use of technology. Salomon elaborates: The combined product of human-plus-machine yields a higher level of performance. The effects of are the lasting individual changes resulting from the computer-supported collaboration, the cognitive residue, one might say, the transferable knowledge or skills.So, just how might you go about helping your students experience the effects of coding?

And tell Jeffreys story!!

Jeffrey (a Grade 2 rascal!) made a most interesting leap from Logo to a completely different domain one day.We were having a discussion inspired by the flight of the space shuttle piggybacked on a jumbo jet. Our Grades 2/3 class had the opportunity to watch the flight. When we return- ed to the classroom, a discussion of space naturally arose. One child asked if Earth was in space, and in asking the question, she determined it must be, because it wasnt sitting on anything. The discussion continued until Jeffrey piped up.You know . . . its sort of like Logo. We stopped and looked at him curiously. What do you mean? I asked him studiously. He replied, Well, Earth is like a procedure. Its like a subprocedure inside the solar system. The solar system is the superprocedure. And the solar system is like a subprocedure inside the universe. The universe is like the superprocedure. Fascinating, I said, then asked, Whats the biggest superprocedure? After a moment he replied, I dont know. I guess the universe. Well, I was truly amazed at the generalization across domains that Jeffrey had made. He clearly demonstrated significant transfer of a concept from his experiences with Logo to an authentic event. Although Jeffreys illumination happened spontaneously, I learned that I could play an important role in helping students to acquire Salomons effects of by providing opportunities for them to look for these comparisons across subject areas.

MetaphoriaI started playing a game with students that I called Metaphoria. I gave them sentence starters such as:Programming in Logo is like or,Finding a bug in a program is like .Students have answered: Programming in Logo is like playing tennis. First, I take a turn, then the computer takes a turn. Finding a bug in a program is like looking for a needle in a haystack.

18Getting Started Tutorial

Other Commands

Step through GETTING STARTED with themrepeating and reinforcing19

SamplesDo SAMPLES from FOLDER on computer

Deconstruct as we go!!

And do some modifications for fun!20

BUG HUNTING!Tell bug hunting story

This is but one example that provides students with a mental modela model that is durable and independent of coding. It is what Salomon would call a residual effect.One example of this residual effect became evident after the students experience with bug collecting during their time with Logo. They had learned that identifying problems in their Logo code meant that they had mistakes, or bugs, in their thinking.

Of course, actively seeking bugs was a necessary component to getting the program to do what they wanted. Bug seeking naturally evolved into bug collecting. Every time a bug was solved, the kids squished itmetaphorically, of course!

The class had built a large papier mach turtle, and one of the students suggested that perhaps when a bug was solved it could be fed to the turtle instead. This was delightful and useful in and of itself, but the transfer of this model became clear as I overheard two students working on a traditional paper math task. They knew their answer wasnt right.

One student said to the other:

Theres a bug in here somewhere. Wed better find it!

I believe it is important to maximize the opportunity for the acquisition of these skills as your students are coding. Do not leave it solely to the use of the computer. Be explicit in building the bridgein making the connection of this skill to other domains. Discuss them in class. Have students describe other situations where these skills might be used.In fact, take it one step further. Ask your students to think of particular aspects of that give them generalizable skills. In this way, you are empowering them to take more responsibility for their own learning..21

SCRATCH22BeeBots and Probots

BeeBots and Probots23Resources drawingkidsintomathematics.wikispaces.comResources

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