Random glitch on an online weather map creates a vector field:

beautiful, no?

How to create enagaging, functional maths problems in 2 minutes *UPDATED

Step 1: Take a table of calculations that have already been done:

e.g. Bills, receipts, timetables, answer keys to textbook functional maths tasks.

or

Step 2: Progressively blank out more and more information:

Here the aim is to create questions that get harder as you work down the page. Often that means either blanking out more of the boxes or blanking out the initial boxes from which the calculations are made (creating a reverse, "here's the answer, what's the question?", problem).

or

Step 3: Profit?

For some reason, my pupils really seem to enjoy these. One possible reason for this is that it makes any random table in to a kind of logic puzzle. Mainly though, I think my functional maths groups get a bit sick of your standard functional maths problem, which looks like this:

Lots of good, and relevant, Maths here, but its terrifyingly wordy, there are so many constraints thrown at you at once, and you have to keep flipping between the question, your working and a data-sheet.

Blanking out a table can't replace these types of questions, as this is exactly the type of question that they will be tested on in their functional maths exams, but it is a good way to introduce a complicated set of calculations in a non-threatening way. The further constraints and wordy questions can be introduced later.

Optional extras:

• Before you show the table, get pupils to think about what its going to contain/what calculations will be done (e.g. "If you were trying to work out how much you'll be getting paid at the end of the month, what pieces of information are important? If you knew these things, what calculations would you do?").
• Use this as an intro, to get pupils accustomed to the table and calculations involved, then bring in the wordy questions as a follow-up.
• Get the pupils to come up with the constraints for the more complex problems (e.g. "Write a list of steps to take for getting up and taking the bus to school. How much does each one take (roughly)? When do you want to get in to school? Which bus should you take?")

  

  (instead of this question)

• Involve pupils in the process - I haven't tried this one yet, but it could be done when they have completed a more textbooky problem. Get them to tipex over some of the numbers in their calculations in order to create a problem set (as in steps 1 and 2 above), then swap books with their neighbour and try to fill in the tipexed blanks.

*UPDATE - Here's another pre-made  problem on probability and percentages:

Inspiring Mathematical Applications: Why Flamingos Stand on One Foot

Answer: Basic Thermodynamics

Just gonna link to the article where I read this, since he explains it so well.

Inspiring Mathematical Applications: Cheating at Pool

Apparently, this is a Portugese project which uses a camera above the pool table to detect the positions of the balls and cue.

And here is an explanation of how it works (us non-Portugese speakers can turn on English captions):

Inspiring Mathematical Applications: Cage-Fighting (which should really be called MMA).

The amount to which Mathematics can be applied to almost any real-world phenomena is simply astonishing (which is not exactly the same as saying is SHOULD be applied to everything). Most students don't ever see this. Most adults never see this. One of my favourite reactions when I do a #3Act lesson is "Why are we watching this, sir? This isn't Maths", because I know that they'll be happily modelling the situation in the next 5 minutes.

Anyway, I also like to bring in unexpected, interesting uses of Maths as a sort of show and tell in some of my classes and I thought that I'd share some of them on my blog.

To kick off, we're starting with my favourite sport: MMA, and one trainer in particular's use of basic game theory to plan out fights. Original Article.

Nodes
Every fight starts off with both fighters standing just out of striking range. We can call this the initial node. From there, a fighter can move in with a punch, a kick or by trying to grab hold of the other for a clinch or take-down. After each move you end up in a different position or node. Each of those moves lead to a different set of optional follow-up moves and fighters can chain together as many of these moves as possible, traveling from node to node. You can visualize this in a diagram. The nodes are circles with the edges being the moves to get there:

Greg Jackson uses these diagrams and adds success probabilities to each edge using data he collects by watching previous fights and sparring sessions. From there you can calculate the optimal nodes to aim at in order to allow for the highest probability of success later on. You can also block off the routes that lead to your opponent's strongest nodes to 'take them out of their A game'.

More data is used from an MMA data collection website: FightMetric

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

How computer games can teach complex skills AND make you feel like a bad-ass

Below is a short video playlist showing how a new game mechanic, Rope Arrows, is introduced and then used in Tomb Raider:

Video 1 - You first get rope arrows and the game shows you an example of how to use them.

• Notice how the gameplay does not stop.
• There is good reason for introducing the mechanic now; you just found the rope and there are several immediate (and fun) uses for it.
• At no point is this dull; you are learning a new skill, but using it makes your character feel instantly more powerful. See how excited the guy is, first when he realises that he has a new tool to play with, then when he discovers another place he could use it: "Oh, this is awesome!"

Video 2 - Over the next hour or so of gameplay there are multiple basic puzzles using solely rope arrows (but in different ways)

• No step-by-step tutorials here, you just try things out in a low-risk setting and see what happens.
• The puzzles very slowly rack up in difficulty and introduce new ways to use the rope arrows.
• Many of the puzzles are optional and for extra rewards (makes you feel like you are a good player).

Video 3 - A later puzzle involving rope arrows and earlier learned skills

• This is a fairly complex puzzle with multiple steps and multiple pre-introduced skills used in combination (although still a pretty early puzzle).
• Throughout the rest of the game you use rope arrows along with other learned skills. Many other skills are then added and introduced in a similar way.
• Each puzzle requires you to think about how you can use your learned skills in the environment, what the effects will be, and how you can combine these effects.
• The pay-off for solving the puzzle is fully satisfying, excellent cinamatography - you feel like a bad-ass!

Conclusions

This is not how maths games (currently) work: either they focus solely on practicing a pre-learned skill or include a dry written explanation of the concept (probably copied from some revision website). This is because maths games are not made by people who understand much about computer games (and not always much about teaching), and their budgets are miniscule in comparison to the blockbuster franchise of Tomb Raider.

Focusing of practice does serve a purpose to a certain extent, but there are some problems:

• As you focus on one skill, all the problems become exactly the same (and easily gameable)
• It is difficult to incorporate any feeling of progression or mastery (one of the main rewards all computer games use)

So can maths games teach maths in this way? As a gamer who now possesses a wealth of completely useless knowledge of moves and button combinations and tactics, I am inclined to say yes. There are obviously big differences between what a game will teach and what is included in the standard maths curriculum, and taking the steps to understand how to intuitively introduce these topics will not be easy. However, there is an online company who seems to have solved at least part of this puzzle. More on that company and my thoughts next week. Stay tuned!


Bonus - See how the gravity gun is introduced in Half-Life:

16% Time Revised: Scaling it back

Hi there. Been a while hasn't it? Well I'm back baby!

I'm now on my second term of the 16% time experiment, and I've made a few minor changes. There were two big problems with my first attempt; we didn't have time (only 3 or 4 hours per term) to really get in to some of the more impressive sounding projects I (or they) suggested and many pupils had no idea how to start answering some of the questions posed. This is a top-set group and yet I repeatedly had to suggest googling a maths word they didn't yet know!

I still think that these big projects are within their grasp, but I think we started too big and students who have not done anything like this before just got lost.

Scaling it back

• Project suggestions are now reasonably 'completable' in 1-2 hours.
• They come with minor prompts and questions, to scaffold the directions they could take.
• There is a difficulty rating on each project.
• If they want to do a different project, I have a form for them to work through that gets them to write their own criteria for success and scaffold the project themselves.

We've had one lesson in this style and it was a lot more purposeful an environment and more accessible to the lower end of the class. I'm not sure if this will be quite as inspiring as before though. I'll let you know how it goes.

Here are my new suggested projects so far:
Revision  Complex Numbers  Arithmetic Proofs  Euclid  Different bases  Estimation and Large Numbers  Magic

16.6666666666% Time

I have some very bright and very highly motivated pupils in my top-set year 10 class this year and I feel like my classes are a bit wasted on them. The topics we go through need to be practiced and there is always extension material for them, but they just breeze through it. Last week I completely failed at tried to create a 3D-Graph, following this excellent post by Ashli. Basically I botched the explanation and expected too much to get done in a single lesson. Anyway, it was motivating to some, but others just felt it was another standard maths lesson.

Inspired by Shawn Cornally's Inquiry style of teaching and the idea I first heard from Google of 20% Time for employees, I decided to try out our own version of 20% Time in class:

In a recent survey I did with the pupils, most were happy with the pace of our classes, about 6 felt it was too slow and a couple felt it was too fast. I didn't want to leave that majority out of this, which is why I give them the option to revise topics. I will provide materials for this and it should hopefully help those less confident students.
To start with, my guess is that pupils will not have any idea where to go with this, so I have a few suggested project ideas:

Though I'm dangling these in front of them in the hope that someone will bite, I made it clear that they can really choose any topic they want. There are only two constraints:

• It must be mathematical and include maths which is currently beyond their knowledge/ability.
• Success or failure in the project is not so important, but you must aim for the project to be awesome (no powerpoints based heavily on wikipedia, etc. I want outrageous 6ft models and flashing, dancing lights!)

When they have picked a project and started working on it, I will drop a few words like 'game theory' as hints to the directions they could go, and vet their projects for mathematical content and awesomeness. Apart from that though, I hope to sit back and let them explore.

What do you reckon? Do you have any other intriguing/inspiring project ideas I could offer up as bait?

Thoughts on 3Act Maths - FOLLOWUP

Last week I posted about a great TED talk on effective story telling and decided to analyse it from the perspective of 3Act maths, so here it is.

The first act:

"It's making a promise to you that this story will lead somewhere that's worth your time."

This is probably what I first liked about the 3Act idea. The first act hooks the students in and it can be extremely effective for engaging them to the end. 101 questions is a really good place to make sure your first act poses the questions you want it to or for finding good first acts.

"A well told promise is like a pebble being pulled back in a slingshot and propels you forward through the story to the end."

This is still something I am trying to master. My 1st acts are still pretty hit and miss at the moment.
To me the perplexity score on 101 questions is a more a measure of how obvious the questions are rather than how intriguing is that first act. I believe the website could be improved by having some sort of way to rate how much you want to know the answer to the question.

"That's your job as a storyteller, is to hide the fact that you're making them work for their meal."

This is particularly true of lower ability sets; pupils' engagement and confidence seems to inversely correlate with the amount of maths you can see in the first act (measurements, formulae, grids, etc.).

The second act:

"It's this well-organised absence of information that draws us in...We can't stop ourselves from wanting to complete the sentence and fill it in."

"The elements you provide and the order you place them in is crucial to whether you succeed or fail at engaging the audience."

This is a really interesting idea to me because it fits in very well with the idea of building up layers of abstraction on to the initial hook. For example, in Act 1 you might start with this image and ask whether pupils think it will go in:

In Act 2 you give them the information and tools they need to work it out mathematically (angles, tangents, power, etc.). My gut instinct says that I should hand out the information as pupils realise they need it, as it feels organic and you're rewarding that pupil for their thought process. There are definitely some questions though, where giving out certain information straight away would turn a rich problem in to a series of calculations, so its definitely something to watch out for.

Here are some tentative thoughts on giving out information:

• Try to keep pupils at that perfect difficulty level so that pupils feel empowered.
• Hold off the point where pupils are doing trivial calculations as much as possible.
• Give pupils the opportunity to work out what they need, even if that doesn't change how the information is given out.
• Make sure pupils fully understand the problems they've completed before giving out extension tasks.

On the central theme:

"A strong theme is always running through a well-told story."

"Al Pacino's character in "The Godfather,"...his spine was to please his father. And it's something that always drove all his choices."

This is something that I feel is more of a problem in the English system than the U.S. system. In the U.S. (as far as I know) maths is split in to geometry, algebra, pre-calc, etc. classes. In England we just have 'Maths' and when you're jumping from topic to topic I think that students often get lost. I think trying to keep a constant theme, at least for the length of a term, that underlies everything done in class could really help anchor pupils in the point of each lesson.

The problem is that I'm not sure what theme I want to drive my classes forward. I want it to be some central facet of maths or mathematical thinking, rather than 'this term we will look at the maths relating to sport', and I want it to be something that we can refer back to in lessons.

Here are some ideas so far:

• Practical problem solving/Applications of mathematical tools
• Mathematical habits of mind
• Developing Fast, Efficient and Accurate Methods

"An example would be in "Finding Nemo," in the short tension, you were always worried, would Dory's short-term memory make her forget whatever she was being told by Marlin. But under that was this global tension of will we ever find Nemo in this huge, vast ocean?"

 This idea of having a central theme (I hope) may help keep interest from previous lessons so that pupils come to class ready to be engaged again. At this point its only a theory though.

Other thoughts:

 "And that's what I think the magic ingredient is, the secret sauce, is can you invoke wonder."

 To me, this is the difference between this:

and this:

Its the same question of scale, but the possibility of a 'big' cat spotting in England trumps (for me) working out the size of sombody's shoe (although it can be sold as a CSI technique).

TED talk: The Clues to a Great Story

Just watched this great talk on TED about storytelling:

Here are some of the main points transcribed:

• The children's television host Mr. Rogers always carried in his wallet a quote from a social worker that said, "Frankly, there isn't anyone you couldn't learn to love once you've heard their story."

 

• It's making a promise to you that this story will lead somewhere that's worth your time. And that's what all good stories should do at the beginning, is they should give you a promise.
• A well told promise is like a pebble being pulled back in a slingshot and propels you forward through the story to the end.

 

• ...the audience actually wants to work for their meal. They just don't want to know that they're doing that. That's your job as a storyteller, is to hide the fact that you're making them work for their meal. We're born problem solvers. We're compelled to deduce and to deduct, because that's what we do in real life. It's this well-organized absence of information that draws us in...it's like a magnet. We can't stop ourselves from wanting to complete the sentence and fill it in.
• Make the audience put things together. Don't give them four, give them two plus two. The elements you provide and the order you place them in is crucial to whether you succeed or fail at engaging the audience.
  Stories are inevitable, if they're good, but they're not predictable.

 

• ...all well-drawn characters have a spine. And the idea is that the character has an inner motor, a dominant, unconscious goal that they're striving for, an itch that they can't scratch. She gave a wonderful example of Michael Corleone, Al Pacino's character in "The Godfather," and that probably his spine was to please his father. And it's something that always drove all his choices. Even after his father died, he was still trying to scratch that itch.

 

• When you're telling a story, have you constructed anticipation? In the short-term, have you made me want to know what will happen next? But more importantly, have you made me want to know how it will all conclude in the long-term? Have you constructed honest conflicts with truth that creates doubt in what the outcome might be? An example would be in "Finding Nemo," in the short tension, you were always worried, would Dory's short-term memory make her forget whatever she was being told by Marlin. But under that was this global tension of will we ever find Nemo in this huge, vast ocean?
• [On Lawrence of Arabia] That was the theme: Who are you? Here were all these seemingly disparate events and dialogues that just were chronologically telling the history of him, but underneath it was a constant, a guideline, a road map. Everything Lawrence did in that movie was an attempt for him to figure out where his place was in the world. A strong theme is always running through a well-told story.

 

• I walked out of there wide-eyed with wonder. And that's what I think the magic ingredient is, the secret sauce, is can you invoke wonder. Wonder is honest, it's completely innocent. 

I think a lot of these ideas can apply directly to 3-Act-Math #3Acts. I will write a follow-up soon with my thoughts.

The 5 most common misconceptions about gamification of the classroom

1. Gamification means rewards and rewards means achievement medals

Though many educators talk big about gamification, their ideas on implementation often boil down to feedback through rewards; you do something well, you get an achievement medal. They often look something like this:

Khanacademy.org reward system

Feedback and rewards are used often in computer games and I believe that there is a lot that can be taken from them, but medals are the lowest form of reward used in games. When you achieve something in a game, you go up a level making some of the more mundane tasks easier, you get in-game money, you get a new weapon to play with, a new area to explore, an action-packed cutscene, you get a new level of challenge. You get to stand on the corpse of your vanquished foe and watch your friends run to safety. Complete a level and you get to fly around the world on an indestructable dragon. Learn how to use the gravity gun in Half-Life 2 and you can rip the world apart and use the pieces to impale your enemies. The game is the reward.

So how can this be applied in the classroom? Maths can be exciting and engaging in its own right. An interesting and rich problem can be used as the reward for learning a new skill: Know how calculate surface areas? Design your perfect house using exactly one million bricks!

2. Gamification is about making boring tasks fun

The standard thought goes like this: 'Kids are bored in class. I want kids to find class engaging and fun. Kids find computer games engaging and fun. I should copy computer games!' The problem is that games don't have a syllabus to work around. They are not trying to teach you anything. If something is boring in a game, you just take it out. Games start with fun activities and build a story around them. If you took away all the reward systems, feedback, pacing, graphics, exploration, etc. away from a modern game, it would end up looking something like this:

 

Or this:

 

The point is that it would still be fun. If you want to gamify your classroom, start by making the tasks fun, not by hiding the tedium behind flashing lights:

3. Game mechanics are directly transferable to classrooms

As hinted at above, the central goals of teaching and game design are different; games are there to entertain, teaching is there to encourage learning. Games designers target an individual's attention span, not a class of 30, they have high production values and they do not try to make people do antyhing widely disliked such as maths. Therefore, many of the tools games designers use are just not applicable to teaching. Games can not be blindly copied, but each element should be looked at, adapted or thrown away, depending on its usefulness. Much like Dan Meyer attempts to do, taking elements of good filmmaking, in his 3act math.

4. Gamification means following a set of rules

People often talk about the science of game making; getting the perfect amount and timing of feedback, analysing user interfaces to make them as intuitive as possible, recording millions of data points every second to make a game as addictive as possible, etc. I am currently playing Skyrim. It looks like this:

...See what I mean? Computer games design is just as much an art form as film-making or composing. So while these rules and analysis may be useful, that is certainly not all there is to it and following them would not necessarily make a good game.

5. Classrooms need gamification

This is probably the biggest mistake people have about classroom gamification. The thing is, classrooms are already gamified. In any decent class pupils will:

• Get timely feedback to know what they have done well and how to improve.
• Have their achievements recorded.
• Are rewarded in a variety of ways.
• Do fun activities which promote engagement.
• Have the difficulty of tasks adjusted to suit their abilities.
• Have concrete objectives and rules.
• Feel no pressure to succeed on the first attempt, but try to learn from any failures.

Now tell me that that is not what gamification tries to achieve!

By the way, Skyrim is completely awesome.

Gamification of the Classroom?

It seems that lately I'm hearing about gamification (applying the mechanics of gaming) of everything, including education. My initial reaction was wary, since gaming and education have different core objectives (entertainment and learning respectively). However, reading this article on 'Cognitive Flow: The Psychology of Great Game Design', I couldn't help but think of the similarities between its discussion of feedback and my ideas of what makes good assessment.

This has inspired me to think about gamification and what features of game design it may be useful to apply to teaching. This is just an open thought experiment, so if you have anything to add, or disagree with, please let me know. Note that as well as the article mentioned above, I will also reference "Creating Flow, Motivation & Fun in Learning Games".

Characteristic 1: Games should have concrete goals with manageable rules.

This seems a fairly obvious statement when applied to the classroom. Pupils are generally happier when they know what is expected of them and its why there is so much emphasis from OFSTED about making learning objectives (L.O.s) and outcomes clear throughout the lesson. Ways to achieve this:

• Make the goals plainly comprehensible in every part of the lesson. This could include linking explanations, questions and assessments to the L.O.s. Particularly useful may be the questions, so that 'if you can do these questions then you have met this L.O.'.
• Goals and new skills need to be introduced with a minimum of distractions.
• Time should be taken to train the pupil on new skills in a low risk environment (e.g. when you get the Gravity Gun in Half-Life you first use it to play fetch with dog). Traditionally this is achieved by examples and practice questions. You could also use group activities where pupils can confirm each other's correct answers.
• 'The completion of small goals (e.g., clearing a field of boars) links to larger goals (e.g., getting enough XP to level up), which in turn link to even larger goals (e.g., getting access to level-specific gear). This linkage creates a series of rewarding experiences that can hook gamers to a game and create the goal-achievement-reward cycle.' This link is certainly present in education; learning skills, connecting with other skills, enabling a higher test score etc., which all links to your final exams. I do think though that this link is not always clear. Sharing standards achieved and how it links to termly reports etc. (see SBG) would be one way of doing this. Another link which I will talk about more below is the link between classwork and 'maths in the real world'.

Characteristic 2: Games should only demand actions that fit within a player's capabilities.

This is obviously desirable, particularly with pupils who lack confidence, but is not always easy to acheive in a class of 30+. Use of optional support and extension tasks can help to find the right difficulty, as can rich tasks, which allow for multiple entry points and investigation. This is similar to the game design idea of Dynamic Difficulty Adjustment.

Other things mentioned are how games should 'avoid introducing a lot of skills at the same time', 'avoid the tendency to over-specify', sticking only to the most important parts, and 'start out simple, with minimal information, and add in new data as needed'.

Characteristic 3: Games should give clear and timely feedback on player performance.

This is what initially caught my attention as a lot of SBG is about creating the opportunity for timely and useful feedback, and in fact people have already discussed its similarities to game systems. Its also what I like about Kate Nowak's Row games, because pupils get almost instant feedback on each question. Its also something that computer apps, such as this excellent algebraic equations app, are capable of achieving.

This section also mentions setting up feedback systems from the start and maintaining them. This is something I've had trouble with in the past and am currently trying to focus on being more consistent with merits, etc.

Characteristic 4: Games should remove any extraneous information that inhibits concentration.

This links to Dan Meyer's discussion of pseudocontext, where he invites you to ask whether the context adds anything to the problem or just disguises it.

Getting people to repeat tasks.

Repetition is obviously conducive to learning, but its sometimes hard to get pupils to perservere when they don't immediately understand. Here are some ways that games can do it:

• Most games simply let players 'try again' without any stigma attached. This is harder to achieve in a classroom, but it probably starts with encouraging a "growth mindset" culture that embraces initial difficulties, like this 'favourite no' idea.
• 'Give the player enough feedback so they can figure out how to improve their performance the next time.' This can be achieved through direct instruction and questioning or group/peer work. Its also another stated aim of SBG.
• 'Allow players to skip excessive and meaningless repetition of the same skill. Focus on skills related to the learning objectives, let the player know when they succeeded, and move on.' Having a harder task that pupils can move on to when they feel they've mastered the basics. Dan's version of SBG has pupils skip problems they already have evidence of mastery with. This is something that I really feel needs improvement in schools. For example, a popular answer to the question 'When Will I Ever Use This????' seems to be that pupils should treat math class like brain training, like how a footballer does weights. However, where is the motivation if you never actually get them to play football? The gaming equivalent would be a computer game that was just one long tutorial. Functional maths tasks and Dan Meyer's 3Acts/WCYDWT problems are a couple of ways to address this. Here, you are applying maths in unmistakably real-world situations. They may be hand picked to be simple enough for pupils to understand, but they do not feel contrived and because they have multiple entry points and solution strategies, they allow pupils to 'play' with the skills they have learned.
  
• 'Make the repeated task feel different each time around. This means providing choices, actions, and control so that the player can become engaged in a similar but slightly different experience. Alternately, the next time around, the process should go much faster. This allows them to enjoy the experience of mastery over previously challenging content.' This one has stumped me. Though it sounds entirely applicable to education, I can't really think of ways to do it. Any help on this?

Loving SMBC's newest comic

http://www.smbc-comics.com/