I can’t remember who said it, possibly Dan Meyer (edit: Ewan McIntosh), but it made a lot of sense.

Why is the central task in a lot of mathematical activities the computation of numbers? It’s important to get the basics, for sure, but are we spending too much time in the later years of primary school (and up) on computation? Is the computation of numbers by hand really a skill integral to living well in the 21st century?

A fascinating part of maths, an exploratory, playful, more authentic part of maths is when we don’t have the full story or all the data at hand – when we need to delve into the problem deeper, and ask the right questions to extract the right information. Then compute.

Problem Posing, THEN Problem Solving. Take one step back from the problem. Remove the numbers, the key data in a rich word problem, and leave the bones. The kids’ task is to read the supplied question, formulate their own questions they think will get them the information they need to solve the problem, get the data they require, then go and solve it.

Instead of:

“Martha’s Bakery makes three types of bread each day – 120 white, 80 multigrain and 90 Vienna.  How many loaves of bread are made each day?”

Why not:

“Martha’s Bakery makes three types of bread – white, multigrain and Vienna.  How many loaves of bread are made each day?”

It’s an interesting, engaging aspect of maths. It’s inquiry based, contextual, social and fun. In all my numerous three terms as a teacher, I’ve never seen such engagement – and to have that in maths! Awesome.

Problem Posing:

  • Encourages mathematical curiosity and investigation
  • Is highly engaging and fun
  • Is authentic – when are you given all the information you need to solve a problem from the get-go in real life?
  • Is collaborative and social – kids work with each other, discussing, building upon each others ideas
  • Is challenging at different levels
  • Can be reactive to student needs – if you notice kids have gaps in place value knowledge or strategies for example, make your session based on place value
  • Provides a forum to practice key mathematical skills, and develop number knowledge.

We’ve been doing this for a few terms now at Amesbury School, and have refined the process somewhat.

Planning and Implementing a Problem Posing Session

At our planning meetings, a mathematical focus is decided upon for next week’s Problem Posing (for example, place value). These typically change week-by-week depending on where we feel the kids’ needs are at.

The teacher tasked with planning Problem Posing (we rotate) decides upon a context – one which could be the “flavour of the week”, or related to our inquiry, a current event, or one which is just plain fun. Some which have cropped up are: One Direction, the Olympics, camp, Minecraft, medieval warfare etc.

The teacher plans four or five questions over the weekend. The complexity of the questions increase. The teacher also plans a hook – a photo or video or song which we quickly show and discuss at the start of a Problem Posing session to get things cranking. The teacher also plans the groups (usually of three or four kids each, multi-leveled Year 4 – 6) or plans a cool way in which to put the kids into groups randomly.

The teacher writes two documents: one for the students, containing the core questions (which we cut up into strips), and the other for the teachers containing the core questions, the particular questions the kids should be asking you, and the right information – the answers, which we supply them with if they have asked the right question.

On the day (excitement is building!), the teacher prints out copies of the core questions, cuts them up, and puts them in four or five numbered envelopes. The teacher copies are handed out to teachers so they know what questions they will expect and the answers they should be giving.

We hook them in with some exciting or thought provoking media, they get into groups, we hand them the first question, then step back and watch the magic happen. Kids are constantly mobbing teachers with questions, discussing between themselves, scratching down numbers and strategies furiously, all coming at it from different angles.

Expect frustration, persistence, thinking deeply and widely, Aha! moments, excitement. It’ll get louder and more chaotic in the room.

Once a group has come to a final answer to their core question, they proceed to the next question up. I like to announce the step up as a loud “LEVEL THREE, UNLOCKED” or another kind of ridiculous announcement. The kids utter whoops of joy and satisfaction, then speed off to open the next envelope and reveal their next problem.

Problem Posing Plans

I’m going to post all of our Problem Posing lesson plans eventually, but for now, here are a few links to some of our more successful sessions over the last couple of terms.

Farmerama PP (Mult, with a little Div) by Matt (me! @hunch_box)
Olympic PP (measurement) by Urs (@urscunningham)
Minecraft PP (subtraction) by Tara (@taratj)
Feel free to use these, or adapt them to your own needs / contexts. They could also give you ideas to come up with your own.
Go forth and Problem Pose!
tl:dr Take the data out of rich mathematical tasks. As Dan Meyer says: “Be less helpful”. Have the kids pose questions to ask you – if they are right, they reveal the data needed to solve the problem. Give them a hook and an interesting context to spice things up.

Ahh! What better way than starting a blog with a post titled with an overused, clichéd internet meme. Fortuitous beginnings.

Anyway. I got sick of being stuck with the 140 character limit on Twitter – and being a naturally rambly fellow, decided to get a blog up and cranking.
Hi! I’m Matt, and I’m an edu-holic tech-aholic.
My micro-CV:
B.A + Hons @ Vic
1 year in Korea teaching English (안녕하세요!)
3 years in Taiwan teaching English (你好!)
Teacher trained in Palmerston North @ Massey (Wassup dawg!)
It’s my very first brand-spanking-new year as a teacher. I was lucky enough to land a gig at Amesbury School in Churton Park, Wellington. It’s also brand-spanking new, so we get along together pretty well.
We do some amazing stuff out at Amesbury School. We have flexible learning spaces, we run two hubs (Year 1 – 2: Koru Hub, and Year 3 – 6: Harakeke Hub), we team-teach, we ground our curriculum in Inquiry, we learn Mandarin, Te Reo, and music. Heaps more stuff too! I’ll catch you guys up with it in upcoming blog posts.
Flexible, open learning spaces at Amesbury School
So why did I start a blog? Well, it’s a fairly interesting mundane story really. I’ve just been initiated into the demographic of ‘smartphone user’ (to be specific, a Samsung Galaxy S3 – love!) and I was going to hit up my fellow teachers about some sweet apps I’d been investigating and how they could be of use in the classroom / for teacherly organisation / for playing grumpy birds. I thought, if I’m going to be writing some mini app reviews, I may as well make them available to any other teacher people lurking about the internets. Hence, these humble beginnings.
Here’s what I was hoping this blog could also be:
A place for reflection, thought and critical analysis.
A place to share – ideas, resources, tidbits, and stuff we’ve been up to.
A place to celebrate.
A place to not take things too seriously.
I’m particularly interested in:
Holistic assessment, meaningful usage of tech, enhancing parental and community involvement, teacher training and PRT, passion-based-learning, and authentic, purposeful, engaging learning. Techy-interests include Google Apps, Android, open-source. Also, rocking it out on the guitar (and making a fool of myself).
That’s a little bit of a look into what will follow on this blog.
So.. yeah, nice to meet you!
tl;dr Name’s Matt. I’m a primary school teacher in NZ. This is my blog. Going to post education-related bits and pieces.