This might be a little bit of a rant, but I'm going to try to keep it calm.
My bugbear is division algorithms. It's not that I can't do them - I'm very good at them - but I'm constantly frustrated by the fixation people have with teaching them to students waaaaaay before they're ready for them.
I know that sometimes it is in response to parents showing up on the classroom doorstep wanting to know when or how you're going to teach them (or why you're not doing so at the moment), and sometimes it is because we think it's going to show our colleagues how clever our class is and what a great maths teacher we are.
But division algorithms really must wait until students have a good grounding in multiplicative number sense, and plenty of experience of sharing and dividing objects, amounts and numbers in concrete ways. Otherwise our students will leave our classrooms carrying a maths mental block and the feeling that they are no good at it because they can't do "guzinters" properly.
Leave the algorithms until your students are securely at stage 6, ladies and gentlemen, please. If you try to teach them before the students are ready the best you can hope for is a child who can perform the algorithm but does not understand what they're doing or why. The more common occurrence is a child who is completely baffled and feels that they're somehow at fault for not being able to do it.
Thursday, February 23, 2017
Wednesday, February 8, 2017
Grown up maths
The children in my classes (and sometimes the parents too) have often commented that they don't know why they need maths because "you don't use it when you grow up."
I don't know how to counter that, because to me it's so blindingly obvious how we all use maths. I normally manage to blather something about working out budgets for shopping or saving for a holiday, about measuring garden fences or cooking ingredients, about laying tiles in hypothetical bathrooms. And all of these things are true, but these are just the tip of the iceberg.
I've just spent an entire evening using maths. And maths that's more complex than just adding money values or reading a measuring tape. This is because I've been assessing reading all day.
Those of you who are familiar with running records will understand that seemingly tenuous connection - I've been working out percentages - often from some rather odd numbers. I must also add that I've been using a calculator to help me, just for the speed.... but I do still need to know what order to put the numbers in and what operations to use. I also created graphs to show the progress children had made - again on a computer programme, but I still had to know what terms like axis, horizontal, vertical and scale mean, and how to input the data in order to achieve the desired result.
I used my concepts of time to put together a timetable fitting in a range of tests (all of different durations) around a complex variety of swimming lessons (30 minutes), soccer training (1hour 10 minutes) and cycle safety training (45 minutes), a basic facts test (6 minutes 30 seconds), assembly (20 minute) and a whole raft of other events.
And I also used scale to make a rice pudding..... because my ravenous teenage boys have such enormous appetites the standard recipe is just not enough, so I double all the measurements - or maybe even, like today, multiply them all by 2.5!
The third thing I did using maths was to make the name labels for some books and folders. This was an exercise in geometry, as I tried to find the most efficient way to arrange the labels on the page without making them too close to cut out easily or so far apart that there's a lot of wasted paper. I needed my estimation skills, and also an idea about tessellation, rotation, translation (but no reflections as I don't want the words the wrong way round!
So next time one of the children in my class asks me what the point of maths is, I might just direct them to this blog post for a start! I'm certainly going to make sure that there are a huge range of authentic contexts for maths in my classroom this year.
I don't know how to counter that, because to me it's so blindingly obvious how we all use maths. I normally manage to blather something about working out budgets for shopping or saving for a holiday, about measuring garden fences or cooking ingredients, about laying tiles in hypothetical bathrooms. And all of these things are true, but these are just the tip of the iceberg.
I've just spent an entire evening using maths. And maths that's more complex than just adding money values or reading a measuring tape. This is because I've been assessing reading all day.
Those of you who are familiar with running records will understand that seemingly tenuous connection - I've been working out percentages - often from some rather odd numbers. I must also add that I've been using a calculator to help me, just for the speed.... but I do still need to know what order to put the numbers in and what operations to use. I also created graphs to show the progress children had made - again on a computer programme, but I still had to know what terms like axis, horizontal, vertical and scale mean, and how to input the data in order to achieve the desired result.
I used my concepts of time to put together a timetable fitting in a range of tests (all of different durations) around a complex variety of swimming lessons (30 minutes), soccer training (1hour 10 minutes) and cycle safety training (45 minutes), a basic facts test (6 minutes 30 seconds), assembly (20 minute) and a whole raft of other events.
And I also used scale to make a rice pudding..... because my ravenous teenage boys have such enormous appetites the standard recipe is just not enough, so I double all the measurements - or maybe even, like today, multiply them all by 2.5!
The third thing I did using maths was to make the name labels for some books and folders. This was an exercise in geometry, as I tried to find the most efficient way to arrange the labels on the page without making them too close to cut out easily or so far apart that there's a lot of wasted paper. I needed my estimation skills, and also an idea about tessellation, rotation, translation (but no reflections as I don't want the words the wrong way round!
So next time one of the children in my class asks me what the point of maths is, I might just direct them to this blog post for a start! I'm certainly going to make sure that there are a huge range of authentic contexts for maths in my classroom this year.
Wednesday, February 1, 2017
Back to basics
So I've met my class for this year, and it has reinforced that I really will have to take two steps back in order to move forwards again.
I know that basic facts are not the be-all and end-all of maths, but by the time children are at the top end of primary school they should have a reasonable degree of automaticity with their basic facts. This is so the cognitive load is reduced during problem solving, allowing them to pay more attention to the strategies that would be helpful to them.
Automaticity is something we will be working on this term, and this is how I plan on doing it:
Some of these things seem counter-intuitive. I have been asked why I send home the answers before the test ("isn't that cheating if they know the answers in advance?") but there is a good reason for doing this.
On Thursday, I want children to score the best possible score on the test. They've had a chance to practise the facts on Monday and Tuesday, but they don't actually know if they got them right or not - and experience has shown me that some will spend a long time learning a 'fact' that is actually incorrect. Sending the answers home allows them to check that they do know the right answer to the basic facts problem.
And when they check the answers, they're seeing the whole equation written out again, so they're sub-consciously doing the problem once again while they're looking for confirmation that they got it right. If they find a mistake then they're more likely to remember the correct answer one they've been shown it, because it scratches the itch of cognitive dissonance that is generated when they see the right equation and an incorrect equation side by side.
And on Thursday when we swap papers and take it in turns to call out the answers and mark them, they're having to read the whole equation again, and they're using their memory of the fact to see if the person reading it out is right or wrong.
So over the week they experience each basic fact a number of times (pardon the pun!) and in a variety of ways. And that repeated exposure and the multiple modes of accessing it (seeing it, completing it, hearing, reading it aloud) all help to develop that automaticity that is so important.
Watch this space for updates in how they do with Maths Cafe, which is being introduced next week.....
I know that basic facts are not the be-all and end-all of maths, but by the time children are at the top end of primary school they should have a reasonable degree of automaticity with their basic facts. This is so the cognitive load is reduced during problem solving, allowing them to pay more attention to the strategies that would be helpful to them.
Automaticity is something we will be working on this term, and this is how I plan on doing it:
- Monday - 50 basic facts get sent home for homework.
- Tuesday - 50 more basic facts get sent home for homework.
- Wednesday - the answers to the 100 basic facts get sent home so that the children can check their homework.
- Thursday - the same 100 facts are given in class as a timed test. Children swap papers and take it in turns to read out the answers, marking correct answers and incorrect attempts.
Some of these things seem counter-intuitive. I have been asked why I send home the answers before the test ("isn't that cheating if they know the answers in advance?") but there is a good reason for doing this.
On Thursday, I want children to score the best possible score on the test. They've had a chance to practise the facts on Monday and Tuesday, but they don't actually know if they got them right or not - and experience has shown me that some will spend a long time learning a 'fact' that is actually incorrect. Sending the answers home allows them to check that they do know the right answer to the basic facts problem.
And when they check the answers, they're seeing the whole equation written out again, so they're sub-consciously doing the problem once again while they're looking for confirmation that they got it right. If they find a mistake then they're more likely to remember the correct answer one they've been shown it, because it scratches the itch of cognitive dissonance that is generated when they see the right equation and an incorrect equation side by side.
And on Thursday when we swap papers and take it in turns to call out the answers and mark them, they're having to read the whole equation again, and they're using their memory of the fact to see if the person reading it out is right or wrong.
So over the week they experience each basic fact a number of times (pardon the pun!) and in a variety of ways. And that repeated exposure and the multiple modes of accessing it (seeing it, completing it, hearing, reading it aloud) all help to develop that automaticity that is so important.
Watch this space for updates in how they do with Maths Cafe, which is being introduced next week.....
Subscribe to:
Posts (Atom)