In the holidays I attended the maths symposium, I was lucky to have quite a bit of PD around maths last year in my first year of teaching and this provided me with another boost and way to look at my maths programme. Two of the three workshops I attended were all for integration of maths. They talked about how many of us will teach addition subtraction for the first seven weeks then multiplication and division for the next seven, always beginning the year with statistics and so on. But why? Why do we have to start the year with statistics? Shouldn't it be brought in throughout the year when it actually fits, when kids can engage in a more powerful statstical investigation than how many people in the class have brown eyes etc. In my first workshop the teacher was all for fully integrating maths. She would select her big idea (often one driven by the kids interest, she would pose the question to the kids what do you want to learn about)? She would then brainstorm all of the maths that linked into that big idea (INCLUDING ALL STRANDS) to become more than just creating word problems around the big idea. Because "REAL LIFE IS A PROBLEM TO SOLVE."
She gave us one example to look at that she had used with a Year 5/6 class who were heading to camp. She asked them what they would have to prepare and get ready for going away. Naturally the kids came up with the maths they needed to use and highlighted areas that needed teaching. Questions like what will we have for dinner? Deciding to have burgers one night they had to do the costings (working with money) then the butcher might give them the price in kg's rather than a set price so they have to work out how many kg's of meat they have and how much it costs per kg to work out what their quantity will cost etc. The distance (measurement) from school to camp and how long the travel time is to book the bus etc. She would have what she called teaching clinics where if children had to learn a particular skill/strategy to work out their problem she would bring that group together for explicit teaching to happen. Meaning the teaching was relevant to what they were doing at the time. I can see how this would increase children's buy in particularly for students who often don't see the relevance of what we are teaching. Also if they are using the skills they are naturally getting the practice needed to consolidate a new skill.
I can see this idea of integration working really well. However I am a bit nervous about the fact that each group might be responsible for a different part and therefore if you are not on the dinner team you might not learn about weight and using kg/g for the burger patty pricing. How do you ensure that every child gets taught every strand in a fully integrated maths programme?
During the workshop she gave us a chance to brainstorm all the different ideas we had for a big idea with a lot of us looking at the Olympics we decided to run with this big idea. The ideas we came with were;
-MEASUREMENT-distance between NZ and London
-times recorded eg: in swimming, running etc with split seconds
-time zones (NZ being ahead of England)
-mapping-distance between one venue and the next
-money-cost to get to the Olympics
-STATISTICS-most popular sports watched
-most popular athletes
-probability with medal prospects
-RATIOS/PROPORTIONS-chlorine/water ratio for the pools
-decimals with the times eg: 1:12:45
-GEOMETRY-Olympic rings/shape (working with compasses)
These were the ideas that we came up with in a quick five minutes I am sure there would be more still but you can see very quickly just how much learning there is behind a big idea.
I still find it a scary thought that I am skimming over a number of areas and the children are not given time to master a skill or that particular strands or strategies are being taugh to some children but not others. So I am going to try and meet this idea of integration halfway until I become more confident in it. I have started a new thing called mailbox maths in my class where the class receives a letter from a book character that we are reading or have just read about. They pose a problem to the class to solve for them. I am going to make sure that I use a range of word problems across the various strands for these. (The idea for mailbox maths was taken from http://thefirstgradeparade.blogspot.co.nz/). I like the idea that it is teaching children to find the number problem in the word problem and share strategies being able to explain to the character who wrote the letter how we worked it out. As well as using reading skills to read the letter and writing in following the structure of a letter when replying.
I am going to use Olympic maths in my rotations. As a class we have found that the cheapest kids flight to London return is $2100. So as a reward for good behaviour I am giving out 'dollar points' to see who can reach the Olympic Games the fastest. Every second Wednesday Michelle comes into my room for BT and I usually get her to take a strand with me reinforcing it as well. This term we are looking at geometry to tie in with the Olympic ring shapes (I can see the kids doing some circle art work-praticing the skill of using a compass). To hold the interest in the Olympic games we will look at doing some statistics around our medal count and most popular athletes and sports. Some of these integrated ideas may end up beng more whole class but it still exposes children to the concepts while maintaining their numeracy projects maths.
Other things I gained from the key note speakers was the idea of letting kids wonder and then focus them n on what you want them to look at. Learning from our mistakes is a common saying but often kids are too scared to give things a go because they know it will be wrong. We need to encourage kids to put commit an idea to paper because doing something even if you know it is wrong and then working out why it is wrong may bring you to the right way of doing it and therefore the answer.
One key note speaker who was also a classroom teacher and DP talked about how he would often pose an open ended rich word story problem with three levels of the same sort of question. Children could then choose which one they wanted to tackle or may choose to do all three. I found this an interesting point as it is simliar to three level guide questions in reading. We get children to do all three in that case but they are scaffolded up to the tricker questions. I like the idea of giving children the choice as I think the more reluctant mathematicans might be more willing when they have choosen which problem they which to solve. This teacher encouraged students to have a go at solving a problem and then sharing back to the group but he gave students the opportunity to rehearse their explanation in two's or three's. When it was shared back to the group he encouraged the rest of the group to question the student sharing. He initially gave students a copy of these maths questions to train them in probing each other for more information and understanding.
-What does that number mean?
-What do you mean by...?
-Can you show us what you mean by...?
-Can you convince me...?
-Why did you...?
-How do you know it works?
-What about if you say...does that still work?
Use these words 'so,' 'if,' 'because,' and 'then' in your questions.
And lastly I really liked one problem a keynote speaker posed around fairness.
The question was 'Who is the most generous?'
KIM-Had 10 fish and give up 2 fish
KELLY-Had 10 fish and give up 3 fish (so Kelly is more generous she gave up more)
KIM-Had 8 fish and gives up 2 fish
KELLY-Had 20 fish and gives away 2 fish (so proportion wise Kelly had more to give away so Kim was more generous even though they both gave up 2 fish)
KIM-Had 20 fish and gives up 4 fish
KELLY-Had 10 fish and gives up 2 fish (so they were both as generous as each other)
KIM-Had 20 fish and gives up 5 fish
KELLY-Had 25 fish and gives up 5 fish (again despite the number of fish given up being the same Kelly had more to give away so Kim is more generous)
KIM-Had 20 fish and gives up 5 fish
KELLY-Had 25 fish and gives up 6 fish (Kelly had more to give away and gave one extra away then Kim so she is slightly more generous)
I liked this problem as it would challenge children's thinking having to justify their reasoning and understand that while some of the time they were giving up just as much as each other it wasn't always equal.
She gave us one example to look at that she had used with a Year 5/6 class who were heading to camp. She asked them what they would have to prepare and get ready for going away. Naturally the kids came up with the maths they needed to use and highlighted areas that needed teaching. Questions like what will we have for dinner? Deciding to have burgers one night they had to do the costings (working with money) then the butcher might give them the price in kg's rather than a set price so they have to work out how many kg's of meat they have and how much it costs per kg to work out what their quantity will cost etc. The distance (measurement) from school to camp and how long the travel time is to book the bus etc. She would have what she called teaching clinics where if children had to learn a particular skill/strategy to work out their problem she would bring that group together for explicit teaching to happen. Meaning the teaching was relevant to what they were doing at the time. I can see how this would increase children's buy in particularly for students who often don't see the relevance of what we are teaching. Also if they are using the skills they are naturally getting the practice needed to consolidate a new skill.
I can see this idea of integration working really well. However I am a bit nervous about the fact that each group might be responsible for a different part and therefore if you are not on the dinner team you might not learn about weight and using kg/g for the burger patty pricing. How do you ensure that every child gets taught every strand in a fully integrated maths programme?
During the workshop she gave us a chance to brainstorm all the different ideas we had for a big idea with a lot of us looking at the Olympics we decided to run with this big idea. The ideas we came with were;
-MEASUREMENT-distance between NZ and London
-times recorded eg: in swimming, running etc with split seconds
-time zones (NZ being ahead of England)
-mapping-distance between one venue and the next
-money-cost to get to the Olympics
-STATISTICS-most popular sports watched
-most popular athletes
-probability with medal prospects
-RATIOS/PROPORTIONS-chlorine/water ratio for the pools
-decimals with the times eg: 1:12:45
-GEOMETRY-Olympic rings/shape (working with compasses)
These were the ideas that we came up with in a quick five minutes I am sure there would be more still but you can see very quickly just how much learning there is behind a big idea.
I still find it a scary thought that I am skimming over a number of areas and the children are not given time to master a skill or that particular strands or strategies are being taugh to some children but not others. So I am going to try and meet this idea of integration halfway until I become more confident in it. I have started a new thing called mailbox maths in my class where the class receives a letter from a book character that we are reading or have just read about. They pose a problem to the class to solve for them. I am going to make sure that I use a range of word problems across the various strands for these. (The idea for mailbox maths was taken from http://thefirstgradeparade.blogspot.co.nz/). I like the idea that it is teaching children to find the number problem in the word problem and share strategies being able to explain to the character who wrote the letter how we worked it out. As well as using reading skills to read the letter and writing in following the structure of a letter when replying.
I am going to use Olympic maths in my rotations. As a class we have found that the cheapest kids flight to London return is $2100. So as a reward for good behaviour I am giving out 'dollar points' to see who can reach the Olympic Games the fastest. Every second Wednesday Michelle comes into my room for BT and I usually get her to take a strand with me reinforcing it as well. This term we are looking at geometry to tie in with the Olympic ring shapes (I can see the kids doing some circle art work-praticing the skill of using a compass). To hold the interest in the Olympic games we will look at doing some statistics around our medal count and most popular athletes and sports. Some of these integrated ideas may end up beng more whole class but it still exposes children to the concepts while maintaining their numeracy projects maths.
Other things I gained from the key note speakers was the idea of letting kids wonder and then focus them n on what you want them to look at. Learning from our mistakes is a common saying but often kids are too scared to give things a go because they know it will be wrong. We need to encourage kids to put commit an idea to paper because doing something even if you know it is wrong and then working out why it is wrong may bring you to the right way of doing it and therefore the answer.
One key note speaker who was also a classroom teacher and DP talked about how he would often pose an open ended rich word story problem with three levels of the same sort of question. Children could then choose which one they wanted to tackle or may choose to do all three. I found this an interesting point as it is simliar to three level guide questions in reading. We get children to do all three in that case but they are scaffolded up to the tricker questions. I like the idea of giving children the choice as I think the more reluctant mathematicans might be more willing when they have choosen which problem they which to solve. This teacher encouraged students to have a go at solving a problem and then sharing back to the group but he gave students the opportunity to rehearse their explanation in two's or three's. When it was shared back to the group he encouraged the rest of the group to question the student sharing. He initially gave students a copy of these maths questions to train them in probing each other for more information and understanding.
-What does that number mean?
-What do you mean by...?
-Can you show us what you mean by...?
-Can you convince me...?
-Why did you...?
-How do you know it works?
-What about if you say...does that still work?
Use these words 'so,' 'if,' 'because,' and 'then' in your questions.
And lastly I really liked one problem a keynote speaker posed around fairness.
The question was 'Who is the most generous?'
KIM-Had 10 fish and give up 2 fish
KELLY-Had 10 fish and give up 3 fish (so Kelly is more generous she gave up more)
KIM-Had 8 fish and gives up 2 fish
KELLY-Had 20 fish and gives away 2 fish (so proportion wise Kelly had more to give away so Kim was more generous even though they both gave up 2 fish)
KIM-Had 20 fish and gives up 4 fish
KELLY-Had 10 fish and gives up 2 fish (so they were both as generous as each other)
KIM-Had 20 fish and gives up 5 fish
KELLY-Had 25 fish and gives up 5 fish (again despite the number of fish given up being the same Kelly had more to give away so Kim is more generous)
KIM-Had 20 fish and gives up 5 fish
KELLY-Had 25 fish and gives up 6 fish (Kelly had more to give away and gave one extra away then Kim so she is slightly more generous)
I liked this problem as it would challenge children's thinking having to justify their reasoning and understand that while some of the time they were giving up just as much as each other it wasn't always equal.
