Activity Based Mathematics, Exposure to Language, and Ideas Taken for Granted by Teachers (and myself!!)

I was tutoring two year 4 girls today, and reflecting on the experience now, I remembered something pertinent that my Maths education lecturer said this year - students can become 'dulled' or 'desensitised' from real maths learning, and want to sit down and fill in pages of 'maths' worksheets. This happened to me today! I had planned a rich hour-long session of activity based mathematics, using measurement activities, number patterns and counting exercises.... one of the girls said to me:<O:p</O:p

"Can we do homework now and write things down? I want to do sheets."

(I told her that she would learn more from activities than from 'writing things', because I knew her idea was to fill in a page of addition algorithms!)<O:p</O:p

The other thing that happened was a real life example of something that they keynote speaker (a mathematics education professor specialising in children) said in her address at a Primary (elementary) maths convention I went to in July.

Her theme on day 1 of the convention was about 'things we forget to say' in mathematics, or things we explain too haphazardly - perhaps because the ideas are taken for granted as adults.... I was trying..... to show the students the repeating pattern in the 'add 3' (from 0, onto 3, 6, 9...) sequence, showing that it does not repeat every 'ten' just like the 2, 4, 6, 8, 10 sequence.

One of the students looked at my carefully prepared 0 - 99 chart with every multiple of 3 coloured, and said "Well why does it only skip two each time? Shouldn't it skip three? When you count in twos you skip one!".

I thought about the language they had been exposed to, from early on when they were taught to count 'even numbers' or 'by twos' - to "skip" a number. The more I thought about the language of 'skipping' numbers, the less sense it made, and I told the students that what was really happening (and the only thing that was happening) is that 3 is added each time, and even made the point that if you count by 10's you don't "skip 9" you "add 10" (9 certainly are a lot of numbers to skip!).

I showed them with marbles and with counters, that the language 'skip' doesn't make sense, because numbers are to count things. I asked the girls how I could start with no marbles on the table, then 'skip' two and somehow end up with three marbles on the table!<O:p></O:p>
What I've realised is just how true the statement is about 'things we forget to say' - these children didn't realise that the ONLY thing that is happening when counting by 3s is that you "add 3", and to add to the complications, one of the students (for an unknown reason) seems not to understand 'face value' of coins, and will count 3 20c coins as 80c (calling the first coin '40' then counting on '20' for each other coin) - she needed to be told that 20c is 20c and it is only ever 20c (the same for all the other coins).

This all makes me wonder what I might do myself when teaching children, especially smaller children - do we simplify language so much that it actually impedes their understanding, because we think that young children cannot cope with language?
I wonder how deep the rabbit hole is, when dealing with children and mathematics!

<O:p</O:p

As a high school resource math teacher I'm often appalled at my students lack of math vocabulary. They often cannot tell me what a sum is. I think it's because we think they can't handle it and give them "easier" words, but there are times when there really aren't any other correct easy words. I spend a week with my students picking out and memorizing clue words for basic operations and then we apply them. I have a sheet where they use a word bank and then catagorize them under the appropriate opperation. By the end of the first semseter I have a 100% perfect paper rate for this exercise by giving incentives.

If we use the language to teach them as we go there is not a problem but we as teachers have to remember to use the mathematical language....sometimes that takes reprograming ourselves to do it...and yes we need to teach and model number theories so that they are not foriegn to the kids later.

Trust me when i say they rabbit whole is almost to China on my end.

Thanks for responding Jaycee.

I wonder why this thread has so many read results but only one reply? Maybe it's just too 'big' for people to think about right now? Sometimes we don't know what to "do" with things yet... This might be one of those things?