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.
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.
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.
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.
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