ADDitives

08-30-06, 09:20 AM

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

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