As seasoned readers may know, I have always been intrigued by the beauty of math. (See here, here, or here for some examples.) Now that my job title is S.T.E.A.M. Master Teacher, I have been looking even more for ideas on how to integrate math and art.
Math Craft is a great place to start. From mathematical knitting to Sierpinski Christmas trees, there is no shortage of inspiration on this site (though it is a bit heavy on polyhedrons). Not every post gives you instructions, as some of them feature work by professional artists – but you could always pose the question to your students, “How do you think they made this?” They may end up making something completely different, but equally as beautiful, along the way.
I have students in various grade levels working on design projects this year, and it only seemed right that they would give each other feedback. The 4th and 5th graders were working on designing video games, and the 8th-12th grade engineering students were more than happy to play the games and critique them. My two periods of engineering students are designing a playground for the 4/5 students, so it seemed only fair that the younger students give the older ones input on something that would ultimately impact them. Finally, I had the engineering students give feedback to their contemporaries (in opposite classes).
In the past I’ve used graphic organizers like, “Two Stars and a Wish,” or Glows and Grows, or deBono’s Thinking Hats. The most success I’ve had is using Thinking Hats, but even then the feedback is often vague.
Sonya Terborg recently did a post on a tool called, “The Ladder of Feedback,” and I decided to try it with my older students. It has been, by far, the most successful peer feedback tool that I have seen in the classroom. The steps on the ladder help students to consider a project more deeply, and the sentence stems were perfect prompts for the students to consider at each stage.
Sonya also mentions some other resources in her post, including a Mind/Shift post that has practical suggestions on how to guide your students through the process of crafting meaningful feedback.
If you ever wondered the age that students need to be in order to give constructive feedback to each other, Austin’s Butterfly will show you how even young children, once they have had some practice, can positively influence the outcome of a peer’s project.
One piece of advice from this article on TeachThought that I intend to use the next time we do peer reviews is to give feedback on the feedback. This may also encourage the students to be thoughtful on future critiques – a valuable skill in a school that focuses on Project Based Learning.
Colleen Graves (@gravescolleen) shared some pictures on Twitter a few days ago that showed prototypes she was making of a library data tracker and a classroom exit ticket tracker. Both use the Makey Makey along with some minimal Scratch programming. I begged for some more details, and she has released the instructions here. (That sentence makes it sound like she only published the directions because I asked, but I’m pretty sure the two events just happened in chronological order because Colleen planned it that way – not because I have the power to demand anyone to explain things in detail just so I can copy their ideas.)
I’m hesitating to recommend any more games because it was recently brought to my attention that a card game I reviewed in January now costs $899 on Amazon. I know I don’t have a degree in Economics, but I only paid $20 for it 6 months ago, and unless this game is somehow disguising a Bitcoin laundering scheme, I’m not sure why it climbed in price by 4500%.
The game in question, Mockups, is good for practicing Design Thinking. If that is what you are looking for, you may want to go a less pricier route by checking out Disruptus, also good for Design Thinking practice – and about $874 less than Mockups at the moment.
Or, you could download Dialogo for free. It’s not really a Design Thinking game, but at least you don’t have to pawn your motorcycle to acquire it.
Dialogo is a product from the KAICIID Center. According to its website, the organization “is an intergovernmental organization whose mandate is to promote the use of dialogue globally to prevent and resolve conflict to enhance understanding and cooperation.” The free download is available in 5 different languages, and includes a printable gameboard, instructions, and cards.
Dialogo is meant to be used for encouraging discussion of a particular topic. The game offers creative, probing questions that can be used for just about any subject. There are also suggestions for reflecting on and facilitating the conversation. Though the age suggestion is for 10 and up, I think it could be used with younger students with a bit of practice.
So, download Dialogo now, whether you think you can use it or not, before it gets listed for $1000 or something ridiculous. Good group conversations are priceless – and should stay that way.
First of all, this is the best book title I’ve ever seen. It is intriguing when you see the cover, and totally makes sense on a variety of levels once you read the book. Even the author’s name, Dusti Bowling, seems perfect for a story set in a theme park in Arizona.
I think I first learned that Insignificant Events in the Life of a Cactus existed from @TechNinjaTodd on Twitter months ago. Before I even had a chance to read the book, I followed @Dusti_Bowling on Twitter and she almost immediately followed me – which I took as a sign that I am a Very Important Person. After reading her tweets for a few month, I realized that Dusti Bowling is just a down-to-earth author who responds quickly to her readers. She also supports her fellow authors by recommending other great books, and Skypes with students on a regular basis. So, it turns out that, to Dusti Bowling, everyone is an important person – a theme she models in this book.
I finally got some time to read Insignificant Events in the Life of a Cactus a few days ago, and I was not disappointed. The main character, Aven, is a young girl who was born without arms. Her adopted parents have raised her to be a confident problem-solver instead of a helpless complainer. She can do pretty much anything with her feet, and the friends she has grown up with don’t even notice her unconventional methods anymore. However, Aven becomes much more self-conscious about her uniqueness when the family moves from Kansas to Arizona. Starting a new school with students who have never seen a person eat with her feet, Aven realizes the one problem she can’t solve is that some people fear those who are different. Just when she seems to have reached her lowest point, Aven meets a few friends who have also been mistreated due to their differences. Throw in some tarantulas, a tantalizing mystery, and the declining Wild West theme park her parents manage, and Aven must summon up all of her will-power to ensure the family’s move to Arizona doesn’t end up as a disaster.
This is a great book to use for teaching empathy, perseverance, and the power of a growth mindset. (For another great story that has those themes, I also recommend Fish in a Tree.) I could see using it as a class read-aloud in grades 3 and up. To learn more about the inside story of Insignificant Events in the Life of a Cactus, you can visit the StoryMamas website for an interview with the author. If your class wants to ask the author more questions, be sure to fill out the form on Dusti Bowling’s home page to request a Skype with her.
I think I’ve finally come to terms with my Kickstarter addiction. Basically, I choose an item to “back”, and wait until that product arrives on my doorstep before I find something else to invest in. Most of the items I fund take around a year to get manufactured, so this seems to be a compromise that my bank account can handle.
Last summer, I wrote about my latest Kickstarter purchase, the Turing Tumble. I expected to receive it in January, but a few obstacles were encountered during production that delayed it to the summer. Sadly, this meant that only the few students that attended my robot camp got a chance to test it out, but I think I got a pretty good idea of its impact from them and my 15 year old daughter.
Paul and Alyssa Boswell, who invented this unique game, kept their Kickstarter backers very well-informed during the production process. Packaging is a huge part of getting products like this into the hands of consumers, and there were a lot of bumps along the way. However, I think they got it right in the end. Turing Tumble arrived in a substantial box that has a customized insert for all of the pieces. It will definitely make it easy to store.
Speaking of pieces, there are a lot, including tiny red and blue marbles that are “tumbled” in the games. The quantity of small pieces is a definite reason you should not ignore the age rating of 8 to Adult. I would caution anyone with young children or pets (like mine) who are living vacuum cleaners to set up this game in an area where accidental flying marbles won’t be immediately ingested .
The Turing Tumble is basically a mechanical computer. The different pieces represent what happens in a computer when a program runs. The set comes with a puzzle book that is written in the form of a graphic novel. Players are given 60 different objectives (challenges) throughout the story to complete using the pieces. (You can see an excellent description of the game, along with pics and video, on their Kickstarter page.)
A few of my students, ages 8-10, got to try out the game. Despite the beautiful images by Jiaoyang Li that accompany the story in the puzzle book, the students skipped straight to the challenges. Once they understood the basic structure of the book (each challenge has an objective, a picture of the starting setup, and the available parts you should add), they began to cruise through the scaffolded puzzles. A small crowd gathered around whenever they “started a program” by pressing the lever to release the first marble, and everyone watched in fascination as red and blue marbles fell in patterns determined by the placement of pieces.
My daughter was equally interested in the game. We sat at the dining room table working our way through the puzzles, and I ended up being the gatherer of pieces as she mentally visualized where to place them in order to accomplish each new objective. I was the one who finally stopped that night – mainly because I was feeling a bit grumpy about her solving the puzzles much more quickly than I ever could.
The good news is that anyone can now buy the Turing Tumble – and you don’t have to wait a year to receive it. It is available directly through their website, from Amazon, or Gameology (for New Zealanders and Australians).
Turing Tumble also has an education portion on their website, which includes a practice guide. You can submit your email address if you want to hear from the company when they release their Educator Guide.
I think that the deepest discussions I ever hear in my classroom happen when we do Hexagonal Thinking. If you haven’t heard of this strategy, I explain how I use it with my 4th graders in this blog post. Last year, I did a post on using Hexagonal Thinking to reflect on the school year. In the past, my 3rd-5th graders have used Hexagonal Thinking. This year, on a whim, I decided to try it with my 2nd graders.
My 2nd graders have never done an activity like this before. It was our last day of class together, and I wanted to help them sum up the things they have learned in our Gifted and Talented class this year. Because they were new to Hexagonal Thinking, I conducted the activity in a slightly different way.
First, I went to this awesome Hexagon Generator, and asked the class to help me brainstorm words that represented things they have learned in GT. Here is what they came up with:
I did this right before their recess time, so I could make some quick copies for everyone while they played.
When we got back to the classroom, I paired up the students and gave them the paper. Now this is where I really departed from my traditional lesson. Instead of asking them to cut up the hexagons and place them where they wanted on a new sheet of paper, I asked them to make connections between words that were already sharing sides. We went over a couple of examples so they could understand that I didn’t want them to say things that used the words in the explanation, (such as creativity goes with problem solving because you need to be creative to problem solve) but to think about the qualities that each word shared.
You know how you sometimes come up with an idea right before class and you start executing the idea and realize about 3/4 of the way through explaining it that it was the dumbest idea ever and now you need to figure out how to get through the next 45-minutes without anyone crying – including you?
That’s how I felt as I started monitoring the partner discussions. Expecting 2nd graders to “go deep” on the last day of class was not a brilliant decision on my part. There were comments like, “Well, bridges goes with stability because they need to stay up or they will fall down.” True, but not what I was going for.
And then something kind of magical happened. I heard partners saying, “No, no, that’s not what she wants.” And I started reading some of their notes. And I realized that these kids can think deeper than I can when given the opportunity.
A few of their comments:
Stability and Support – “You have to be strong and stand up for your friends.”
Creativity and Perspective – “You have to think the way others think to make them happy.”
Perseverance and Adaptations – “They both don’t give up trying to survive.”
Perseverance and Adaptations – “Sometimes you need to change to work together.”
Ethics and Perspectives – “When you don’t look at different points of view, sometimes you get in a fight.”
You can see the working drafts one pair used below.
The great thing about this activity was hearing the students use the vocabulary, like “ethics” and “perspectives” correctly, and being able to tell from their comments if they really understood these topics.
If you still have some time with your students before closing out the year, I definitely recommend this activity!