How do we empower students to solve problems in maths?
(A.K.A. Exploring newman's Process skills)
Activity 1:
Review the blog and lessons undertaken using Newman's Error Analysis.
At what stage were students typically having problems? What are you doing to support them?
Review the blog and lessons undertaken using Newman's Error Analysis.
At what stage were students typically having problems? What are you doing to support them?
Responses:
Hollie's class drew their own visuals for each of the steps and the kids responded well to them.
Most difficulties are in step 3 - transformation and then moving into the process skills.
Some are having difficulties articulating/explaining what they are doing or what they did or why they did it. Maybe because of tradition of more closed questions/expectations of maths being one right answer rather than choices and judgements.
Continue working through problems, justifying strategies.
Hollie's class drew their own visuals for each of the steps and the kids responded well to them.
Most difficulties are in step 3 - transformation and then moving into the process skills.
Some are having difficulties articulating/explaining what they are doing or what they did or why they did it. Maybe because of tradition of more closed questions/expectations of maths being one right answer rather than choices and judgements.
Continue working through problems, justifying strategies.
Activity 2:
Read article by Jones, C. 2003 'Problem solving - what is it?' Australian Primary Mathematics Classroom, vol. 8, no. 3, pp 25-28
Identify the different strategies students can use. Discuss what helps them to choose a strategy, develop a list of clues.
Read article by Jones, C. 2003 'Problem solving - what is it?' Australian Primary Mathematics Classroom, vol. 8, no. 3, pp 25-28
Identify the different strategies students can use. Discuss what helps them to choose a strategy, develop a list of clues.
Responses:
What strategies are we not using so much -
* using a table/chart
* working systematically
* guess and check
Younger years always go back to drawing a picture
Asking students to share if they have done it a different way.
What strategies are we not using so much -
* using a table/chart
* working systematically
* guess and check
Younger years always go back to drawing a picture
Asking students to share if they have done it a different way.
Activity 3:
Given different problems. Work with a partner to identify what strategy you would use to solve it and why.
Given different problems. Work with a partner to identify what strategy you would use to solve it and why.
Responses:
Process of elimination - what definitely won't work.
Simplify the numbers and then work out method and then apply to the more complex problem.
Language - eg straight line could use number line or picture
If using knowledge of multiples often a table will help to match up.
Acting out or using concrete materials if it's an unknown quantity.
Process of elimination - what definitely won't work.
Simplify the numbers and then work out method and then apply to the more complex problem.
Language - eg straight line could use number line or picture
If using knowledge of multiples often a table will help to match up.
Acting out or using concrete materials if it's an unknown quantity.
Activity 4: Reflection and planning
How can we include explicit teaching of strategies in our maths program? What other wasy can we support students in developing these skills? Look at a class blog from a yr 3/4 class in Victoria - http://kidsspeak.global2.vic.edu.au/2013/06/11/addition-and-subtraction-in-real-life/. Work with partner to plan a real world problem that the students could solve. Share and add to the blog. Discuss each other's problems and identify the strategy that you would be encouraging students to use/explicitly teaching to help them solve it.
How can we include explicit teaching of strategies in our maths program? What other wasy can we support students in developing these skills? Look at a class blog from a yr 3/4 class in Victoria - http://kidsspeak.global2.vic.edu.au/2013/06/11/addition-and-subtraction-in-real-life/. Work with partner to plan a real world problem that the students could solve. Share and add to the blog. Discuss each other's problems and identify the strategy that you would be encouraging students to use/explicitly teaching to help them solve it.
Responses:
I'm baking for the school cake sale next week. I want to sell $100 worth of cakes. I'm going to price my chocolate cupcakes at $1.75, my gingerbread people at $1.25 and my vanilla slice at $2. What are the different combinations of cakes I could make?
I recently recieved my mobile phone bill for the sum of $235.15. My usual bill is around $215. My itemised charges I could see were: data $16, SMS $35.20, international calls $17.15. The remainder of my bill is for local calls. How much did I spend on local calls this month? working backwards, recording calculations
I had $28 to spend on the weekend. At my local shopping centre, movies cost $9.20, lunch special is $6.50, drinks cost $3.40, a pack of pokemon cards is $6.10, a pack of new oil pastels costs $11.30 and a treat from the bakery costs $4.70. How could I spend my money so that I have less than $3.00 change? Is there more than one way I could spend my money? estimation, guess and check
If ten children brought in bananas, 3 less brought in apples and three more children brought in oranges than bananas how many children brought in fruit that day? Does this mean that there is only that many children in the class? Two children forgot their crunch and sip, how many are there in the class? diagram, friends of ten, guess and check, previous knowledge of how many children in a class.
At the school canteen there are iceblocks (100% fruit juice) at 60c and popcorn for $1.50. I have $20. How many friends can I buy an iceblock and popcorn for, not forgetting myself? multiplication, subtraction, working backwards, calculations, estimation
I'm baking for the school cake sale next week. I want to sell $100 worth of cakes. I'm going to price my chocolate cupcakes at $1.75, my gingerbread people at $1.25 and my vanilla slice at $2. What are the different combinations of cakes I could make?
I recently recieved my mobile phone bill for the sum of $235.15. My usual bill is around $215. My itemised charges I could see were: data $16, SMS $35.20, international calls $17.15. The remainder of my bill is for local calls. How much did I spend on local calls this month? working backwards, recording calculations
I had $28 to spend on the weekend. At my local shopping centre, movies cost $9.20, lunch special is $6.50, drinks cost $3.40, a pack of pokemon cards is $6.10, a pack of new oil pastels costs $11.30 and a treat from the bakery costs $4.70. How could I spend my money so that I have less than $3.00 change? Is there more than one way I could spend my money? estimation, guess and check
If ten children brought in bananas, 3 less brought in apples and three more children brought in oranges than bananas how many children brought in fruit that day? Does this mean that there is only that many children in the class? Two children forgot their crunch and sip, how many are there in the class? diagram, friends of ten, guess and check, previous knowledge of how many children in a class.
At the school canteen there are iceblocks (100% fruit juice) at 60c and popcorn for $1.50. I have $20. How many friends can I buy an iceblock and popcorn for, not forgetting myself? multiplication, subtraction, working backwards, calculations, estimation
