My observation of Archana's observation

This morning Sue Pine came in for Archana' observation/co-teaching session. As I her co-teacher and always in the class, I was just helping out with the lesson whilst Archana ran it and was discussing everything with Sue.

This was our problem - 

Our students are very used to solving open-ended maths problems by now, as we have been doing them for most of this term. 

While Archana was introducing the problem, I noticed that she

-asked the students to read it themselves first in their heads

-then read it aloud herself

-then ask students "is there anything you don't understand?"

-after discussing, asked "what do we know? (e.g. we know that there is only 60 kids)

The students spent 30 minutes working out different answers in their mixed-ability groups of three.

We came back together and the students gave their different answers (in the middle of this photo).

Archana wrote on the board the way the first student said their answers '10 kids in 6 cars'. Sue quickly pointed out that that would later translate to 10 kids in 6 groups, whereas the 'groups of' should come first, as 'groups of' leads into multiplication, and this will cause problems there.. 

So this is something we as teachers should be careful of..

Archana and Sue talked the students through how to re-word their answers, from written ''6 vehicles and 10 kids in each', then changing it to 'groups of', for example "6 groups of 10 kids equals 60", finally to an equation '6x10=60'.

Sue also spent five-ten minutes trying to get students to understand the difference between 5x12 and 12x5. The students are very new to the concept of reversibility, so only some of them understood the difference here.

Sue then wrote these onto the teaching station (copied from the students answers on the whiteboard).

She asked the students 'what do you notice'? An open-ended question, it encourages students to look for any possible thing they might see, and it lets them know there may be more than one answer as well. 

The students noticed that 6 was double of 3, and 12 was double of 6. Sue then took it further, and pointed out how as one doubled (3, 6, 12), the other 'factor' halved (20, 10, 5). 

Some students did not really understand this concept, however some did which was awesome. 

Sue then drew this diagram - another visual representation of the concept she had extracted from the students responses. 

As she was talking to Archana about how drawing it in a diagram might hook in other students who previously didn't get it (visual learning preferences), one student almost screamed I GET IT NOW!

She didn't understand how they all equaled 60, but once this diagram was drawn, her understandings clicked into place and she got it. (and was delighted about it too!)

Afterwards, Sue and Archana discussed how some of the students approached the problem. One pair of boys, who are below the National Standards tried to find factors of 60 using an array diagram (shown above). We were all quite impressed with these particular boys using this strategy, and highlighted it to the class to remind them there are lots of different ways to solve problems.

Thoughts and Reflections

I liked the way Sue used many different ways to try to explain the mathematical thinking at different levels/points in time, and how each way obviously worked for some learners and not others. Archana and I talked about making this a goal for ourselves in term 3 - trying to use a variety of ways (multiple visual, multiple oral) to explain the mathematical concept. 

I also found the questions Archana asked the students BEFORE they went and solved the problems very helpful. 

-asked the students to read it themselves first in their heads

-then read it aloud herself

-then ask students "is there anything you don't understand?"

-after discussing, asked "what do we know? (e.g. we know that there is only 60 kids)

It took only a few minutes, but gave the opportunity for students to think, ask, answer, pull apart the question before they actually went away to try and solve it. I will be using these in my future practice.