### Consolidation:

What do you notice about Scratch in terms of Geometry? Can it be used as a tool to spiral math? In what ways must students understand a coordinate system in order to move Sprites?

What do you notice about Scratch in terms of Geometry? Can it be used as a tool to spiral math? In what ways must students understand a coordinate system in order to move Sprites?

What do you notice about Scratch in terms of Geometry? Can it be used as a tool to spiral math? In what ways must students understand a coordinate system in order to move Sprites?

In terms of geometry I noticed that Scratch uses geometrical terms such as spin, move, turn and degrees. Sprites move on the grid based on the directions given to them by the programmer.

This means that it would be a great tool to spiral math because of all of the geometrical language and thinking needed and involved in programming the Sprite's movements.

Students must understand a coordinate system in order to move Sprites because of the set up and how the various block systems work, for example, when choosing scripts, costumes, and sounds. Students will also have to understand a coordinate system because they will need to move Sprites accordingly, for example, a positive or a negative amount of steps as seen in the Move Your Sprite Forward video.

I respectfully disagree that students must know co-ordinate systems going in. I think that at first, the concept of negative number isn't really necessary, since students can use the symbol to go "the other way" x many steps; they will need to be shown that it is an option, but from there they can experiment with it. In letting them experiment with this, it serves to introduce the concept in an informal but tangible way that later math instruction can build upon. Experimenting with the numbers to see what they do when they are changed can be a useful way to explore the concept. It would make for an interesting discussion--why do you think we put the - in front of the number? When do we need to do this? What if we don't, what happens?". In this way, it can form a part of the beginning of spiraling the concept of integers and the Cartesian plane. Later usage might include drawing a circle, or using integers as part of creating a game.

The use of angles may not be intuitive, even for students who have encountered angles in the past. Working with angles in Scratch can be a great tool for concrete exploration of this concept. Scratch also supports the development of spatial concepts such as the amount of turning needed to complete different polygons, as well as predicting the number of steps to complete a shape. Students can make predictions and then test them out immediately. Geometrical patterns are also easily explored. When we draw a triangle, then a square, what changes? Why and how? Can you use that to figure out how to draw a pentagon or hexagon? What if we wanted to draw a star?

Junior students might use the co-ordinates to create pictures that have one or more planes of symmetry. Older students might add to their understanding of angles by programming a pong-style game with reflexive angles.

I liked the concept of drawing a triangle and a square then moving onto a pentagon and hexagon. The great think about Scratch is that it allows for higher level thinking and easy next step activities that paper and pencil sheets do not provide as easily. Differentiated learning is such a big idea right now that you could have some students working on complex shapes while other might simply be working on drawing a line.

I agree with Laura that the kids don't need to know about coordinates (though you'd be surprised about how much they actually do know about them) or angles before they do geometry in Scratch. Since it is a exploratory environment, they will usually find the controls, play with them, and find out how to use them. They even find out from each other by looking at each others' work and remixing.

I found out that you sometimes have to unlearn a few things.

Try this Scratch code: https://scratch.mit.edu/projects/168224680/#editor It draws a square when you click the green flag. What do you need to change to have it draw an equilateral triangle? Let me know what happens and what you (un)learned. Now try making a pentagon, a hexagon, and so on.

Mitch Resnick, who is the current director of the MIT Media Lab talks about low floors, high ceilings, and wide walls. Everyone can start at some level, there's a lot that you can learn, and there's application to more than just what you are learning at the moment.

When we tried learning grade 7/8 motion geometry just using Scratch, it was amazing all the different ways the kids came up with solutions to make shapes and have them go through the motions. One kids in particular was looking at the coordinates before and after a quarter turn, and he noticed an easy pattern that he could physically type in to change the coordinates, but he was convinced there was a 'math way' to do it. Turns out he's right. I asked a mathematician friend who taught me how easy it is to do matrix multiplication on coordinates. Now we do that too, if they ask. The point is that without the high ceilings and wide walls to explore it in, motion geometry can be pretty dull and repetitive (I'm looking at you, Nelson math text). Instead, we wind up in a place of wonder where the possibilities are open to us rather than the final close of another text book unit test.

Hi,

Thanks for the challenge. I managed to made the triangle but it took a few tries. It is just trial and error and patience. I think my students would be able to see the next steps, way better than me. I think I will drop playing scrabble and will keep exploring Scratch as it is a bit addictive.

I am curious to know the research, if any schools have been using Scratch beginning in Kindergarten and moving up to the higher grades. Does this have an impact on consolidation of math concepts and the processing that is needed? I think it would have a positive effect. Our school board is so lagging behind in providing the tools (computer lab or frequent classroom access to computers etc) to really put a dent in providing consistent coding learning experiences.

Hi, Christy.

The research is being done right now in Ontario schools. One of the leads in the project is George Gadanidis who has a website at http://researchideas.ca. There are also videos somewhere here on TVO. TVO Kids, I think?

Iain

I've been playing with this task for most of the afternoon It did take trial and error, but the immediate feedback helped to keep it motivating and fun. I also recruited my little lab rat for some investigation. He has a general sense of coordinates because of games like Battleship, but it was amazing to see him keep at a task and try different numbers to see what would happen. My husband teaches grade 7 math and my sister teaches FDK. I'm pumped to have something to suggest to both of them.

Ian, what have you done with your students and coding thus far? I am looking for ideas. I also looked at the link you posted and see that the Faculty of Education Western University has Math + coding books for sale. Have you bought/tried them? I am just wondering if they are worth it. I will certainly explore that link more. Keep sharing your great ideas.

At least at the Junior division, I think it would be fairly straightforward to teach students about fundamental movement through the co-ordinate plane, even including negative numbers. And then, using Scratch, we can give students a very practical and interesting hands-on opportunity to move forward through their zone of proximal development. Or vice-versa: have students explore the concept in Scratch and then consolidate their learning in a mini-lesson. Overall, I can see Scratch being used as an excellent tool to bring geometry (especially transformational geometry) alive to students in a way that even the most well-intentioned foundational learning textbook resource cannot accomplish. To do so is the essence of inquiry learning, and at the level of my students (grade 4), I can see them really enjoying using Scratch as part of their protected daily mathematics block.

Reading your post, got me thinking about mapping out a large paper coordinate plane system on the classroom floor to introduce students to how we describe the movements of objects through space. You could do this before they begin to experiment with Scratch even in early primary classes. This will also help introduce potentially new language such as the geometrical terms spin, rotate, and also allows students to feel what turning a number of degrees is like.

The Computational Thinking article by Wing at first seemed to make everything more confusing for me and I began to get that panic feeling that I am way out of my league. But there were clear examples of what computational thinking and computer science is or means. The terminology was made clears as well: packing a back pack = caching, finding a lost mitten = back tracking, choosing when to buy instead of rent = algorithms, which line is best at the supermarket = main server systems, power outage but phone still works = redundancy design. It all seems a bit easier to understand now. I loved that statement that “having the confidence, we can safely use, modify and influence a large complex system without understanding its’ every detail. This gives me hope to use, modify and influence as well.

In school, I always had difficulty with that visual math piece: flips, turns and rotations. This needs to be a skill that is scaffolded over time and early negative experiences can have lasting effects. I had the scratch app since last year but didn’t use it much because I did not put in the time to see it’s value and how it could support our youngest learners. To me it was just a game. But now I am armed with new information how these early experiences with grids and coordinates and naming X and Y axis are important to developing competencies and making meaning. We recently purchased a math 100 carpet that our students have naturally organized and moved objects along the grid. In this unplugged coding activity, they began to use more math language in their work, move up/down, flip/turn/rotate. They composed and decomposed shapes and explained that the structure that they built was a rectangle shape but was made up of 8 squares. They used tape and string to create triangles and other 2 D shapes. The next steps in their learning would be to take this engagement and introduce the scratch program.

I don’t think that children will need to already understand the coordinate systems to use scratch. Through free exploration and trial and error they will gain this knowledge and it will be more meaningful to them because they are actively involved in the learning process. This experimentation will allow their projects to have more intention and details as they explore the different features of the game. They will be exposed to new math terms and concepts within this activity. I can see my children collaborating to create amazing videos that can be shared and open to feedback from their peers.

I too had difficulty with the visual math piece as a student and cringed as an occasional teacher when I had to teach flips, turns and slides! When we were first introduced to the Learning Carpet years ago, I had an epiphany! It made so much sense when I was able to play around with it. We use our carpet for unplugged coding activities as well. It is great to be able to roll it up and take it into the hallway if needed.

I am so thankful that the article gave some everyday examples, because I was bit boggled by the time I got to that part! Participating in this course is helping "to spread the joy, awe, and power of computer science" the author spoke of. This article referred to the fact that we are limited only by our curiosity and our imagination - the same thing was mentioned in the video "What most schools don't teach".

We are having a dandy thunderstorm here and I rode it out by watching the Scratch tutorials. I am amazed by this and the thinking that is behind it. In terms of geometry and spatial sense, the language is rich - up, down, turn, flip, vertical, horizontal. It is rich with concepts of sequencing, if/then, magnitude of number. I do not think that the students need to know about coordinates in order to play. I think playing around with it first and then talking about coordinates would be a better idea.

The entire program relies on knowing where a centre point is and evolving from there. Allowing the use to tell the "sprite" what they want it to do, watching it, making changes if necessary provides that great immediate and constructive feedback that is essential to learning and making mistakes. What a great tool...wish our iPads had flash! Ability wise, you could create one solid quadrant, ask students to move positive or negative, follow a path, endless possibilities.

I think that as long as students understand the spatial awareness and positional concepts of

**up, down, backwards and forwards**they can do Scratch (or Scratch Jr. for younger students). They "learn by doing", experimenting with rotating**(turning)**the Sprite in different directions - I have definitely seen students doing this when programming Dash and Dot to move in a variety of ways. The visual cues given provide immediate feedback as students experiment and create.I see that Scratch is oriented around geometry and spatial sense:

- As your mouse moves around on the screen the coordinates are tracked along the x and y axis - coordinate plane
- Introduces positive and negative values and the impact on direction the sprite moves on the stage as a result
- Transformations (turn, flips, slides)
- Utilizes degrees to spin the sprite
- Scaling images up or down (grow or shrink images)
- Spatial sense on the stage

Scratch serves as a great way to introduce, practice, reinforce, assess many math concepts and skills. In many ways students are utilizing math skills without really feeling like they are doing math, since it’s embedded in play/making.

As students play and move their sprites, they must have some concept of moving forward and backward, up and down, and diagonally. They will have to have at least a rudimentary understanding that positive values are associated with up and right, while negative numbers are related to down and left. Depending on the task, students may have to be aware of the quadrants on the grid, and the relationship of coordinates to the plane.

Scratch is a great tool to introduce Cartesian Plane geometry, transformations, positive and negative integers (grade 7/9).

Students learn about the 4 quadrants and the corresponding numerical value of the integers. By moving the sprites in different directions, the students are actually learning transformations. Glides for translation, Rotate and reflect when the sprite spins, etc.

After exploring each video activity, consolidation, reflection, practice/re-teach will follow to guide students to develop a deeper understanding of the concepts.

Scratch would be a great interactive “game” that integrates math concepts throughout. As I was watching the tutorials and tinkering around playing the games I noticed how scratch is very much math oriented. I agree that many geometry terms and criteria are present within the design of the game. This would be a great tool to learn coordinates, x/horizontal axis, y/vertical axis, negative and positive integers and how to plot specific points. To get the sprite to jump or glide entails different transformations (translations, rotations). When coding students also have the opportunity to experiment with numbers to see what happens to the sprite when applying different commands. I had a great afternoon learning how to code a game using different sprites. While I was creating, I thought of how this could be used in geometry when looking at different polygons on the same grid and applying different transformations to see what happens to these shapes. Learning math through experimenting, tinkering, debugging, reflecting and then applying new concepts is a great way to get mental constructions built. I felt a sense of accomplishment!! Students will definitely be motivated to become deeply involved in their learning through this coding program.

Looking at the tutorial videos I can see a number of connections for students between creating in Scratch and the Geometry and Spatial Sense strand. As others have mentioned the location and movement big idea is pervasive in the programming part of activities. As well, the relationships of two dimensional shapes along with geometric properties are explored. In watching creating a simple game tutorial, students are forced to this about orientations, relationship and movement of the various figures.

I have played around with basic scratch. But I am always amazed at how many different options of blocks there are in coding in Scratch as well as how much problem solving and debugging is required to ensure that the blocks are put together in the correct nesting order.

WOW! Watching these introductory videos about scratch I feel like I could really impress someone with my mad coding skills by coding a game for them! Who knew you could create such complex games so simply. Everything surrounding coding seems some complex and complicated… Clearly once you have an understanding of what it is, it is totally possible.

I can absolutely see the math in the program scratch. Having the x and y axis, as well as the rotational turns (degrees) and move forward x number of steps. The grid coordinates are also a great math connection. I think the students may need an idea of what ‘degrees’ means, as well as what the x and y axis are, however, beyond that – I see students doing some trial and error and with the immediate feedback that the program gives once you run it, the students are able to try again and eventually conceptualize their own understanding. I think kids can do this even at a young age, however, reading the blocks may be the only setback. Great program, awesome math connections!

I don't teach math and have not used geometry terms in several decades so in some respects this question simply advances the notion that one must teach math to CODE. Fortunately I don't think Coding can only occur in math and sciences. I can easily see this program being used without any math background as the tutorials I viewed simply follow "rules". If you want to do A then do this. Likewise if you want to do B then do that.

Personally, I can see this being a great tool in my ASD resource room. Yes, special education and Autism. Often my students are frustrated and exasperated when they come into the resource room and simply want to "chill" (as they say) or play on the computer. I can well imagine Scratch grabbing their interest and giving them something to do other than rehash their day in their mind. I am really looking forward to trying this out next fall.

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Geometry: shape, size, position, space

You can change the size of the sprite, you can make it move in different directions, turn at multiple degrees, make it move anywhere amongst the space, etc. You can even use the x and y coordinate (Cartesian plane) when you program the actions of your sprite.

Number sense: positive and negative integers Students can work with positive and negative integers.

In all this programming, students will communicate by using proper vocabulary and can share with classmates. They will also learn by trial and error (experimenting). They will be able to question and try to answer them themselves or ask a classmate (enquiry). At

first, for some students it will be more a trial and error work. However, the more they try, the more they should learn the reasoning behind why this worked and that didn’t. This should bring an easier time for the next programming session. They also get

immediate feedback.I see all the connections, but once again, I am at a loss on what activities to give to students so it’s not just PLAYING with scratch. My problem is that I lack creativity.

In exploring Scratch I can see direct links to degrees, rotations, coordinate grids, ordered pairs, positive and negative numbers. The concept of spiralled math is a new one to me as I am teaching math again for the first time in 9 years but I think this concept is very important as it is a more realistic representation of how math presents itself in real life. I work with a group of fairly reluctant learners so Scratch certainly presents an interactive and interesting way of students to learn and practice math without even realizing they are doing it. Anytime this can happen that is extremely appealing to me. Does anyone have any experience with students using Scratch? I expect giving students time to simply explore would work well and then begin giving small challenges or tasks that practice some of these math skills. The intro videos I thought were great because they showed a skill and then posed a question that would encourage students to try something out. Building that very natural curiosity!

Having used Scratch in my classroom for a few years, I believe that there is a great deal of learning that can take place in this environment. When students work in Scratch it gives them a real world application where they have to understand and manipulate items on the Cartesian plane. Students have to have a thorough understanding of flips, rotations, and slides in order to manipulate the sprites in the program so that they arrive at the end result they envisioned when they began.

Scratch allows students to manipulate a variety of elements in which they can create programs that have a geometric pattern, create geometric shapes, especially three-dimensional ones that are difficult to recreate in a classroom environment.

One of the first learning tasks we gave our students was to use Scratch to create a math machine. The expectation was that they would create an algorithm which could compute addition math facts. ONce the students completed the task they were then challenged to take on a different math calculation and see if they could create a program to demonstrate that fact. Using a program such as Scratch allows the students to play in a safe environment where they can make errors and learn from them without worrying about ridicule. I think it is a great platform for students to explore and internalize the math facts they are learning.

I love the idea of making the connection to the grid for students from the get-go. But this means negative grid locations, too. So why not, I am all for it. Grade 4, sure. And have other fun, physical games available like a Twister kind of thing using grid locations, always with both negative and positive. Do-able, right? Hopscotch brought to a new degree!

Statistics have shown that more of our students typically struggle with the Geometry and Spatial Sense strand than any other strand. For schools and teachers who are reluctant to introduce coding into their classrooms, the connection between Scratch and G & SS makes learning to code a more relevant and necessary introductory experience.

Scratch provides an introduction to x and y coordinates. It also allows early discussions about negative and positive numbers within the x and y grids. The motion scripts teach students about degrees as they turn the sprite around. Students can have conversations about errors with coding as some students confuse turning and moving. I also know that Code Studio provides similar opportunities to connect coding with G & SS through some of its activities.