Learning Creative Learning: Reading List for Week 3

Seymour Papert (1994): The Children’s Machine (Chapter 7: Instructionism versus Constructionism)

    "If a man is hungry you can give him a fish, but it is better to give him a line and teach him to catch fish himself." Traditional education codifies what it thinks citizens need to know and sets out to feed children this "fish". Constructionism is built on the assumption that children will do best by finding ("fishing") for themselves the specific knowledge they need.
    "The kind of knowledge children most need is the knowledge that will help them get more knowledge."

    (on learning 'kitchen maths') "The natural context for learning would be through participation in other activities than the math itself...it is precisely this continuation of the familiar into the new that brings her breakthrough to connecting fractions with "everything"."

    "[There is] a need to offer children a more modern image of the nature of science...[partially] for the mundane reason that the image traditionally presented repels students who would be attracted to the life of science if they only knew what it was really like."

    The constructionist point of view says that nonabstract (or concrete) reasoning is equally valid and prevalent in society (including scientific reasoning). "While formal thinking may be able to do much that is beyond the scope of concrete methods, the concrete processes have their own power."

    "Rather that pushing children to think like adults, we might do better to remember that they are great learners and to try harder to be more like them."

Dale Dougherty: The Maker Mindset

    The JPL (Jet Propulsion Laboratory) managers went back to look at their own retiring engineers and . . . found that in their youth, their older, problem-solving employees had taken apart clocks to see how they worked, or made soapbox derby racers, or built hi-fi stereos, or fixed appliances. The young engineering school graduates who had also done these things, who had played with their hands, were adept at the kinds of problem solving that management sought. Those who hadn’t, generally were not.

Dale Dougherty: Learning by Making

     “Making creates evidence of learning.” The thing you make — whether it be a robot, rocket, or blinking LED — is evidence that you did something, and there is also an entire process behind making that can be talked about and shared with others

This statement reminds me very much of Shawn Cornally, his inspiring foray in to Inquiry/interest/project based learning and Blue Harvest competencies.


Mitchel Resnick et al. (2009): Scratch: Programming for All.

    We know that people learn best, and enjoy most, when working on personally meaningful projects. So in developing Scratch, we put a high priority on two design criteria: Diversity (creating as many entry points as possible)...[and] Personalisation.

    (on Scratch having a 'low-floor' and encouraging 'tinkering') we have always been intrigued and inspired by the way children play and build with Lego bricks. Given a box full of them, they immediately start tinkering, snapping together a few bricks, and the emerging structure then gives them new ideas. As they play and build, plans and goals evolve organically, along with the structures and stories.
We wanted the process of programming in Scratch to have a similar feel. 

Seymour Papert (1980). Mindstorms - Chapter 2: Mathophobia: The Fear of Learning

    (On mathophobia) Imagine that children were forced to spend an hour a day drawing dance steps on squared paper and had to pass tests in these "dance facts" before they were allowed to dance physically. Would we not expect the world to be full of "dancophobes"?

Learning Creative Learning: Embracing Multiple Motivations

This is a post inspired by the Week 2 Lecture for Learning Creative Learning, the MIT Course I'm doing.

The emphasis of this course is clearly to promote creativity and play as an important motivation for learning. However, Mimi states in this video:

"So, its not that one is better than the other but I think that different people, different young people have different kinds of affective registers, different things that drive and motivate them."

 Making clear that this technique is not for everyone, and that it should not necessarily supplant some of the more traditional motivators (grades, etc.), but can be added in order to reach people for who are left disengaged by traditional motivators.

"I think the point of what we've been trying to pursue at least with our idea of connected learning and interest based learning is to really broaden the kinds of entry points, pathways, motivations and the ways we recognize learning so that it can accomodate more diversity of styles."

That inspired me to think about the different types of motivation I currently use and could use in my classroom to encourage learning. Hopefully this will help me to keep them in mind whilst lesson planning. I also found it interesting to categorise them in a way other than on the Extrinsic/Intrinsic scale discussed by Dan Pink and others. Then I made a pretty poster about it:

Let me know if I missed any.

I will also start a series of more in-depth posts about different ways to incorporate these motivators in lessons. Watch this space.

Interactive: Polyrhthmic fractions

I've been coding again! See my latest maths game below...

I was inspired by how some of favourite musicians (Joanna Newsom)
overlap simple rhythms containing quarter, sixth and eighth notes and make something that is subtly complex and interesting. The above version is a much more advanced version of these polyrhythms.

I thought that this was an interesting way to look at how fractions add up. I also wanted the game to be a little more informal and sand-boxy than the last, so it allows you to try things out and see what works. Have a play:

 

Direct students to a fullscreen version with this memorable address: thedrummer.rocks.it

Its not perfect. Some of the problems are solvable, others aren't (because my original file has corrupted!!!)

• there's no way to tell which achievements you've done (i was implementing this when the file corrupted)
• you can't save and share your beats, which would have given an incentive to make a good one.
• the tradeoff with it being informal and intuitive is that its gamable and you can get away with using little fraction knowledge - I would solve this by having a worksheet of questions to answer (but only once people have already got in to playing the game). It feels like a cheap cop-out though. What could I have done to make it organically more challenging/rigorous? I would love your thoughts on this.

Great Posts of March

• Inquirist's Cookbook by Think Thank Thunk: Shawn's rough and ready guide to creating inquiry based learning.
• What value Khan? by Angles of Reflection: A look at why khanacademy is still useful and powerful (even though its a bit rubbish).
• Coding IS a super(edu)power by Gealgerobophysiculus: Another edu-blogger takes to coding to create the exact tools they need.
• Being an SBG teacher in a non-SBG world by Continuous Everywhere But Differentiable Nowhere.
• If you like learning, could I recommend analytics? by e-Literate: Great read which explains clearly why you cannot apply similar analytics systems in education as are applied in online shopping.
• Foil Prank by Yummy Math: Lovely little lesson about surface area.

Teaching Maths Without Words

These are bold statements from http://www.mindresearch.net for what is essentially another raft of online games, and we all know online games are abominable.  They have not made many of their applets available to try for free, but what's there is definitely interesting (to check them out click here and here).

**UPDATE - Before posting this I decided to contact MINDResearch to give them a chance to comment. Not only did they reply, answering many of my fears about the shortfalls of these applets, but also included a much better demonstration (here) of the way that progression between levels is handled.



Players must guess how far along the number line the fractions (here two thirds) will take them.

Positives

• The emphasis here is definitely on making the maths intuitive using the information on the screen. This is a great first-step in comparison to the majority of online learning, where repetitive maths is tacked on to an existing (not very) fun game. The maths feels natural and even vital in this game world, whereas usually it is a chore to get through before you get to 'the fun bit'.
• The feeling of progression is the main/only motivating factor. In fact, the way that more difficult questions are linked to earlier questions is outstanding (It gave me huge pleasure to see the aliens start zapping some of your fractions to force you to find an equivalent)! Progression and 'acquiring new skills are intrinsic motivation and means your reward is the feeling that your maths is improving. Many studies have shown that intrinsic motivators such as this are more effective AND have fewer side-affects than the usual extrinsic (badges, etc.) motivators. (See 'Drive' by Dan Pink).
• Teaching is happening. There is a feedback loop on your initial guesses, showing what your guess means in this world. This is a great way to give pupils an idea of what the maths problem is really asking.
• It is a low-risk environment (no stigma for failure), so you feel free to try things out and lose a couple times. Allowing students to guess and try again can cause the problem of pupils gaming the system by spamming guesses until its right. These games get past that in two ways: you only have a few lives on each level, and the teacher is alerted to any student making too many mistakes so they can help with the misconception.
• This alert system, along with an 'ask for help' button, implicitly admits that this software will not be able to teach everyone and other interventions will be necessary. This is something that few other sites (in my experience) admit to.
• The fact that there are very few words will be a great boost to a huge range of pupils with EAL, dyslexia, etc.
• The game environment and interface is clean and doesn't include unnecessary distractions.



1. Choose how to split the square (for the denominator)
2. Choose the numerator visually
3. Compare it to how much the aliens remove from the bridge



Negatives

• The trade off with having a clean, uncluttered game environment (and sticking to progression as the only motivator) is that the puzzles can feel a little dry and samey. My guess is that this is not much of an issue for their core, primary school audience, but would have more of an effect with older pupils.
• Only one motivator; I like the fact that progression is the core motivator, but there are other intrinsic motivators that could have been employed as background motivation. I feel that this would help give a more rounded gaming experience. These could include feelings of mastery (on optional, extension levels or mixed question levels) and feelings of exploration (of the mathematical concepts, e.g. through sandbox style environments).

Conclusion

After trialling the fractions demo, I am very excited about this project, as I am in total agreement with a lot of their core principles. Unfortunately it is not yet available outside the U.S. and is more appropriate for a primary school.

Quotes from a MINDResearch representative

Indeed, our aim is to present math concepts in a simple, uncluttered way, so that students aren’t faced with distractions and they are able to purely focus on solving the puzzle. The feedback they receive is informative; the approach stems from neuroscience research involving the perception-action cycle, or rather learning by trial-and-error.

...our focus is to create intrinsic motivation instead of extrinsic motivation. The former compels students to challenge themselves because they enjoy the challenge, not because they will be rewarded with a badge, or prize (extrinsic motivation). Intrinsic motivation is much more powerful in the learning process...JiJi is the centerpiece of the puzzles, and you probably wouldn’t be surprised that students want to help JiJi get across the screen, so much so that they continue to persevere until they do

...Class-level and student-level [live] reports allow teachers to see which students are struggling (the report highlights a student who is “stuck,” and has tried a game/level a number of times) and thus intervene to help the student using questioning strategies or other intervention. The software also allows teachers to freeze the student’s screen, go back to the puzzle the student answered incorrectly, so that the teacher can pinpoint the exact issue that was causing the student to struggle.

Motivation in computer games

Here is an article at Gamasutra outlining (some of the) motivational techniques computer games use to keep players hooked. Try to ignore the horrendous use of algebra. Some of these include:

• Exploration and mastery of the game world (and set of rules)
• Rewards (Better equipment, experience points)
• Setting up a need (New equipment, resources, skill) then giving it
• Challenge (Tournaments, etc)
• Player state (levelling up etc)

Achievement badges do not get a mention.

Also of note is the mention of negative motivation:

However, there are opposite motivations based on negative characteristics as well, such as addiction, alienation, anger, frustration, etc. It can be interesting to exploit these feelings sometimes, for deeper needs, but to build a complete system based on this would be destructive. At the end, the player would be left feeling bitter and would be repelled by the game.

Many online math learning tools rely heavily on repetition and the human desire for collection and completion, which falls easily in to this category.

Here is another article arguing that acheivement badges are very much negative motivators, stating: "I think that any system that is based on endless collection, or any system where there is collection without a larger purpose is exploitative and uninteresting (and therefore unfulfilling)."

Related posts

Lesson Sketch: Introducing Infinity at year 8

I recently gave a cross-school lecture to Gifted and Talented year 8 and 9 students on the subject of infinity. I got great feedback from it, with most of the kids hungry for more (after a one-hour, after-school lecture no less!), so I thought I'd share it in case anyone else wanted to use/adapt it.


Powerpoint file                     Worksheet

It contains:

• Prompt to discussions about the difference between large numbers and infinity
• A proof that 1=0 using infinity
• Modified Zeno's paradox
• Fractals
• Fractal-like behaviour in nature and its uses
• Puzzles using infinitely nested shapes
• Introduction to the concept of calculus and some of its uses
• Links to (excellent) videos about infinity

P.S. There are notes inserted in the slide-comment section of the powerpoint that explain how I presented it.

P.P.S. The speed slide refers to this distance-time graph creator, which I used to briefly introduce the concept of Calculus.

P.P.P.S. There are so many links at the end because there were so many topics I didn't have time for (Different types of infinity, Infinite/fractal dimensional space, etc.)