Saturday, 7 October 2017

Mental Addition Strategy Experiment

One of our pre-assessment questions was to show the strategy we would use to mentally add the following:

                                   13 + 6 + 7 + 8 + 4

The question was designed to see which of us look for number bonds that add to 10 as an easier strategy.

Not many of us employed that strategy, so I used that for the following investigation into this strategy.

I explained we were going to do an experiment to help us understand our central idea.

We discuss regularly that doing maths quickly does not mean you are good at maths and we often discuss how it is more important to think deeply about the maths we are doing.  However, for this experiment  we will time to see how long it takes us to answer these 3 questions. We shouldn't feel stressed or pressed for time though; we are doing an experiment into strategies. 

Partner A was given the following 3 questions to solve.

The only strategy they could use though was to add each number in sequence.

Just add each number in the order that they are like so:

Partner B monitored to make sure they only used this strategy and they timed how long it took to answer them using a stopwatch.

Experiment result sample:

We discussed our thoughts and feelings about adding the numbers like this. 

We then looked with our partners at the numbers to see if there was an easier strategy to use to solve them.  

One pair shared how they could see some numbers added to 10. If we add those numbers first, it could make make adding them easier and probably faster:

We thought that was an interesting approach.

So, we continued with our experiment.

The same partner answered the same questions, but this time by first finding number bonds to 10.

Partner B had the same role- monitoring they used the strategy and timing them with a stopwatch.

A few felt it wasn't fair that the same person added again.

But, others pointed out in for the experiment to have a fair result, it needs to be the same person.

We then compared how long it took us with this strategy.

Most of us were surprised to see that it took a lot less time to answer them with this strategy.

They shared how they could see this strategy makes adding easier for us.

Some of us though found it took longer to solve using this strategy.

I asked if we thought scientists doing experiments might also be surprised by the results.  We thought they probably were.  I shared how my hypothesis was that all of us would have done this faster with this strategy, but that didn't happen.  Why do we think it took some of us longer with this strategy and for others it was much faster?

One theory shared was that it might take some of us a longer time to look for the numbers that add to 10, but others could find those more easily.

We thought that was a plausible theory.  

(It also told me how some us need some extra help in reviewing number bonds that add to 10, 100, 1 000 etc.) 

Experiment result 2 sample:

We then spent some time reflecting in our Maths Reflection Diaries and were encouraged to think about our central idea.

After writing our reflections, we shared our thoughts with our table.

Quite a lot of us reflected how we need to look for connections and relationships between numbers first so we can then decide which would be the easiest strategy to mentally add.  

We wondered if we could apply this strategy to subtracting numbers and others wondered if it would work with decimal numbers too. Others wondered what other strategies exist for mentally adding and subtracting.

So we partnered up with others and experimented with numbers to find out and then we shared our discoveries with the whole class. 

I think this was a pretty successful way for us to inquire into our central idea. It reminded us of a key mental strategy that most of us had forgotten over the years and it sparked good wonderings to help make the learning student-led.

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