Basic facts, to teach or not to teach, that is the question.
But to that question there are always a range of answers, ranging from absolutely yes, children need to rote learn these, to at the other end of the scale, no children will have calculators there is no point.
Many of us sit in the middle.
This blog post offers my opinion on basic facts and some of my discoveries that have pleasantly surprised me over the last two years.
I was one of those teachers that did believe in the importance of explicitly teaching basic facts...don't get me wrong, I also strongly believed that children need to understand what the facts actually meant, but I can put my hand up and say I valued the correct answer and speed just a little to much.
As I have gone deeper into Number Agency I have noticed something that has really intrigued me, the less I paid attention to explicitly teaching or 'testing' the 'facts' the more it became clear to me that I didn't really need to waste my time doing this.
Because despite me no longer referring to basic facts (and when I say that, I mean referring to them as something we need to rote learn) the more capable my agents started to become with working out such problems in their head.
Now when I say this, I am of course referring to agents that are ready for this knowledge, I would never expect a child only beginning to develop their number sense to be able to solve problems in their head. In this post, I am thinking of children that have had at least six months in agency.
The fact that they were becoming so good at this intrigued me, I started to think back to when I had noticed this and what maybe I had changed or added in agency to provoke this new awareness.
I have always used songs, to me learning new knowledge through song is very powerful, however when it boils down to it, this is just good old rote learning again, just tied up with a different and much more appealing and kid friendly bow.
So it wasn't the songs.
This increased ability to solve basic problems in their head (and when I talk problems I mean addition and subtraction, however there are a few already starting to solve basic multiplication and fraction based problems in their head) directly coincided with my increased use of dot talks and other visual problems alongside the Three Headed Dragon problems that involved materials and thinking about shapes.
It intrigued me to see how the agents started to think of shapes as numbers, quite naturally, instead of being a square it was four, instead of being a triangle, it was three...etc. I thought I was being mean only allowing three seconds to see a visual problem like a dot talk, but in fact, many of my older agents could quickly lock onto a strategy that saw them close, or right on the answer. However they also knew it was the strategy I valued, not the right answer, so they started looking deeply for patterns that could help them. Many found strategies that I would never have seen.
The songs, the dot talks/visual problems, and daily problem solving using materials seem to have combined to create the perfect storm...because they need the knowledge in order to solve the problems and given the urgency of solving the problems to defeat the villains they appear to develop this knowledge a lot quicker than before, and not only that, they understand exactly what they are doing, meaning they can solve new facts they may not have encountered, using the ones they know.
Jo Boaler is probably a better example of how this is done :)
This guy presents us with problems, which many use materials to solve, they are great problems because they are accessible for all. Some use popsicle sticks to make the shapes, some draw them, some have learned to represent the shape with a number for repeated addition and some have started solving the problem with other strategies, sometimes in their head.
We use visual images in a similar way to dot talks. However these are more complicated than the dots and there can be a range of different questions that can be asked. Sometimes a visual image may take up half of an agency session, and that is ok.
|This is an example of an 'open' image, basically any photo taken of anything, these images are used to explore what we notice and may or may not lead to any deeper discussions than that. We use these images to really train our 'agent eyes.' The idea for this came from this site http://www.haveyougotmathseyes.com/|
What surprised me when I started doing this was how much the children actually noticed that I did not expect. Photos don't have to be elaborate and there can be a lot of fun had in discussing where that photo may have been taken, where that object belongs, who may use that object...etc.
|In this image there can be a range of questions asked...how many green stars, how many red? How many altogether? Or how many blue shapes? Etc...|
|We got a lot of great discussion out of this one, and some fabulous maths.|
|This visual image leads children into a strategy as I am wanting them to use what they know.|
|This is an example of a dot talk.|
The use of visual images, in a range of different ways seems to have boosted what we call 'basic facts' for want of a better term. Not only that, it has increased independence with number and more agents seem to be able to image now.
Imaging was something we were told in the numeracy project that children had to go through, golly gosh, how many of us held children back because the couldn't image. Then we were told that that was a false understanding, not all children would image, and we should not be using this as an assessment point.
I know myself I never imaged...probably due to lack of number sense more than anything. But for want of a better word, this is what these visual images are gifting my agents, an ability to image in order to solve problems, but whats more an ability to use the known, to solve the unknown, in their heads. Funnily enough my own abilities to image have increased, just because we are doing it over and over again...so maybe all of us do have the ability to image, we just haven't been exposed to the right activities to help us do so?
So where am I going with this? Well I think what I am saying is there is no need to 'teach' basic facts in terms of a stand alone compartment of knowledge, because I think this is how many children are seeing them...they memorise them, know them, but are not able to use them to solve problems. I know I did this, I always believed myself to be 'bad' at maths, but I was the fastest in every one of my basic facts tests. Go figure!
Why then would we use basic fact speed tests when we can teach through visual images, use song to reinforce this, provide beautiful authentic problems, add a bit of tension through the role of the villains and low and behold actually see a child's ability with basic facts in action, explained through the talk moves.
Does this mean I am against teaching facts as children progress into the senior school...no it does not, because by then, they should have an absolute understanding of why they need them and how they can be used. By this stage, there will be a lot of learning that they seek to do themselves because it is a portion of knowledge that they absolutely need. Not the answer to a single problem, but just part of the puzzle.
Does it mean I am against speed learning of basic facts, yes, yes it does. If a child is able to whizz through a basic facts test, but unable to solve an open authentic problem and explain how they have solved it, what have we achieved? In my opinion, we have achieved this...we have told children that maths is about being right, being fast, and that there is always one answer and one way to solve it. We have defined to them, that in order to be good at maths you need to be right the first time and you need to be fast.
We have closed the beauty of maths off to them and made work for those they go to in the future.
Below are three of my favourite quotes about maths. In my opinion they are words to live by when teaching maths.