Taking observation into practice

On Monday I observed our Maths PLD lady, Sue Pine, taking a group of students for instructional maths. 

She focused on teaching the group decimals - only the tenths and hundredths place values.

It was a great lesson, and I learnt a lot, particularly how to use decimats to reinforce the conversion of part-whole thinking when discussing decimal numbers. 

During our discussions afterwards, Sue reminded myself and the other teacher observing about the importance of teaching students how to be good mathematicians. The fastest person to get an answer is not the best mathematician, nor is the person who does the problem in their head. Good mathematicians share their thinking, take their time and think deeply about their problem. 

She posed the problem 7x8 to us - 

I said I would solve it by going 7x9=63 then taking away one group of 7. 

The other teacher said she would have gone 7x6 then added one. 

Sue said she would have solved it drawing an array. 

Her point was, that we need to SHOW students how to be good mathematicians. We need to remind them all the time about what that looks like.

I felt inspired! I thought to myself - my kids do this!

When I went back to my own class, I put this problem on the board. 4x6. 

Then I asked students, not "what is the answer?", but, "what are different ways we could solve this problem?"

Here is what we came up with - 

One student used repeated addition, one skip counted in 4's, another skip counted in 2's (which was actually doubling and halving), another used 4 groups of 6 as an array, another did 2x6 twice, and then I showed them how to split the array to use multiplication facts they might actually know at this age (2x3=6). 

I reminded the class what good mathematicians do 

-take their time

-think deeply about the problem

-share their ideas

-ask for help