Friday, 15 August 2014

Playing homeschool mum. Helping a child gain understanding in maths.

I'm playing homeschool mum today. Yesterday I thought Isabel was getting better, then by lunch time her temperature was sky high again. With sport up first today, I thought it would be best to keep her home. But this is the fourth day off in a row. Time for me to use some of those teaching skills that usually remain unused for much of the week at home. Great excuse to take my focus off cleaning and food preparation.

So where to begin? I decided to ask Isabel.

Unfortunately by the time children are in year three they often have already decided what they are 'good' or 'bad' at. The difficulty with this is that they tend to put less effort into the areas in which they have decided they are 'bad' at because they don't see the point in trying. I try to remind my children that their brains are not set at good/bad. 

Recently I have come across some research by Dr. Lisa Blackwell (whilst reading the book Nurtureshock: why everything we thought about children was wrong) that was really interesting. Her research focused on attempting to halt the decline of maths scores in a group of students, using only two short lessons on how the brain actually works, challenging the students notions of smart/dumb. A total of 50 minutes was spent focusing on one idea: that the brain is a muscle, give it a harder workout and you will be smarter. By the end of the semester the control group had seen a further decline in maths scores, but the intervention group had not only ceased the decline, the scores had improved. 

As a result of reading this, along with other various books, research and watching the earlier 'Life at' episodes, I have begun to speak to my own children about how their brains work. I tell them that our brains are a set of connections. It takes time, work and effort to make these connections to start with, and then continued use of the skill to stop the connections from being cut (because the brain determines which connections to be unnecessary, strengthing only the ones that are used.) So for the things that they say they are 'bad' at, I reply with: all that is missing is the firm connections in their brains. I'm constantly reminding them, "your brain is like a muscle- strong muscles don't just magicically appear and you need to use them or lose them!"

Isabel was instantly able to tell me that she still did not really understand multiplication or division, so would like to work on this area of maths. As it turned out she knew about turn around facts and some of her times tables, yet still didn't have an understanding of the relationship between addition, multiplication, subtraction and division. This is like having part of a spiral staircase, with nothing at the bottom to hold it up. There were gaps to be filled and understanding that was needed. 


She already had play doh out so I decided to start with this as a tool. I find it is almost always best to go with the things they naturally gravitate towards, as a positive attitude to start with can make all the difference. I deliberately didn't get out a single pencil or piece of paper. I got out our small whiteboards for her to use to practice representing what she had discovered with the concrete items, in an abstract way. Again this was a deliberate choice. Children who know they are struggling in an area are less willing to take risks. Whiteboards and chalkboards (we have both to use with homework) are a great way to encourage kids to take a risk and try, as it is not a big deal to quickly rub out and have another go, or even write over the top of an answer. I also got out buttons because she loves them, and Henry does too. He wanted to do some 'work' like Izzy, so I had him doing some different activities (at his level) using similar materials. Daisy played with Play Doh and then a puzzle on the floor while we worked.



I started by asking her to cut out lots of berries from Play Doh. While she did that I found a few items that could work as plates. We counted how many berries she had made, then I asked her to make 2 more so she would have 24, a number divisible by 4 (to match the plates.) I explained her that these plates belonged to the older kids in our family and I was too busy to sort out how many berries to give to each child, so could she do it. Smiling, she got right too it, commenting that it was too easy (always a great start.) I then helped guide her through the process of representing what she had before her, using subtraction, addition, multiplication and then division. She even gave herself a smiley face on each algorithm because she was so pleased with herself!





She went through the process again, changing the number of berries and plates. I continued to focus on understanding with each of the questions she asked me, by asking her questions in return like "why does 6 groups of 4 make 24?" She would then use her props to explain her answer. Once she started getting bored, it was time to move on. I asked her what we could do with the buttons, then repeated the process Isabel imagined 4 dresses, deciding how many buttons would end up on each dress. She did this twice. Then I asked her to show me how she could arrange the buttons to give the same information, without taking them off the tray. This encouraged her to make an array. We then discussed how it would be possible to draw this. We left it there for the morning.




While eating her lunch I noticed that she was working on the whiteboard. She had transferred this new understanding to a picture she had drawn of people swimming. She was very proud to show everyone that she could write algorithms to explain her picture.

After lunch I gave her some loom bands and asked her to have a play around with grouping into different amounts and numbers people sharing. She had fun doing this. She is now at the point where we will work on remainders and also introducing numbers of a higher value (using bundles of 10.)


Meanwhile, with Henry I began discussions based around tens and ones, eg. 83 is 8 tens and 3 ones. He will see 8 rocks and a group of 3 rocks and say "that makes 83." I started by writing single digits, teens and twenties numbers, with whiteboard marker on plates. He then counted out the number written and put the buttons on the plate.

After a while he put two plates together. One said 8, the other 1, to which he exclaimed "it's 81!" I then made a joke out of it saying "is there 80 buttons on that plate?!" He thought this was hilarious (easy to please a 4 yr old.) We then talked about what 80 buttons would look like and decided together that we could put them into bags of ten to make it easier to count. He really enjoyed this. And after putting the bags onto the plate decided that 8 isn't the same as 80. Great. He then went off to play, saying he had done enough work for the day. I haven't really sat down much with Henry before, because he prefers to have Jack or Isabel show him things instead of me. This was a nice change.


Overall it was a really nice morning. I rarely spend time teaching my own children, as I figure the whole being at school for 6 hours is enough. I also have a few other things occupying my time. But as they have all been asking for "interesting learning" lately, I might consider doing this a bit more. Now that Isabel has excitedly told the others how much she learnt today, I may not really have much of a choice! 

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