Yes, I think that it is important practice for students to have to memorize information. Students who know information "by heart" can then flexibly use that information for problem solving and critical thinking that we all aspire for our students. I have seen 8th graders who are taking honors Geometry (a 10th grade class) ask me how many points each question is worth on a 20 question test. When I tell them to figure it out, they ask me for a calculator!
Hello Theresa. Yes, repetition learning is a basic style of learning and can be very boring. However, used at appropriate times it is an essential method of learning, as long as the underpinning information is understood. Yes I remember chanting the times tables ... and I still know them. This is beneficial for students who learn more effectively using auditory methods. Looking back, it wasn't very inclusive as some learners required more or less repetition than others, and it didn't always accommodate for students who learn visually or kinesthetically.
Regarding the use of calculators I do agree people can rely on them too much and then don't know if the answer is right, maybe it goes back to the point that people can be more concerned about the answer than the process and not trusting that they can get to the answer and trust technology more.
A math professor at Berkeley in the US Alan Schoenfeld videotaped some of his students working on math problems and one of them he found illustrated what he considered to be the secret to learning maths. That is, that it took a student 22 minutes to solve a maths problem, she didn't give up trying to solve it just after few attempts, but was persistent and experimented and then got the answer. So he considered the secret to learning maths (and I think it goes for everything) is attitude and not natural ability, he gave students more time than usual to solve problems, he wasn't expecting students to do it quickly, he could wait for 22 minutes for a student to get the answer and was happy to wait, as they learnt and really understood the answer in the end. There's schools in the US called KIPP and they have a longer school day and less holidays so the students get time to think and solve problems without feeling it must be done straight away, they're big on maths as well. (This information is taken from the book Outliers by Malcolm Gladwell).
So I think students may use the calculators as its quick and gets them an answer, as I can remember there was always that time pressure to get the answer quickly at school, it was one question after another and a limited amount of time, so you just wanted to answer as many questions as possible. I know in previous discussions you have said there's a lot of marks for working out now, which I think is good, but students may still be in a different frame of mind and it'll take time for them to readjust. If maybe they've not been given the time previously to explore and learn how to do the basics I can see how this will be detrimental to their future learning and they go to the calculator as a quick fix.
I've seen it with students I teach, they say they're no good at maths and when incorporating maths into a lesson, a wall goes up and if they can't get the answer very quickly they get very down about it and just want to use a calculator. I'm trying to teach students it's ok to be wrong, but its something, which I myself am always trying to learn as well.
Hi Theresa, I'm dyslexic and my memory is really bad, so having to memorise anything was and is difficult, so just simply having to remember things by heart was very difficult and when it seems everyone else can remember it makes you feel quite stupid. Songs, rhymes, having something more visual when learning can help to trigger memories and I think would be more valuable to some students, also showing students patterns with the numbers and any tricks to help them get to the answer, I think this could make it more accessible for learners to remember. As we've said before there's more paths than one to get to the answer.
Thanks for your input - I will look the school and Malcolm Gladwell up! Sounds like an interesting read! I think maths does take practice as many skills do. The more a student can use basic skills, the easier and more automatic these 'truths' become. This should mean that the mind is able to work on the more complex skills such as problem solving and developing logical and analytic skills. I agree that some people do find it incredibly difficult to learn times tables so any memory aid that works for the student can be a useful tool. I say to my students that they can work out any multiplication from a fact they know - eg most students are comfortable with the 5 times table so they can use this as a staring point. Grabbing the calculator can be all too tempting but it's not going to help if the units are not the same and the student hasn't converted. (Sorry, I'm rambling onto maths speak now.....).
It's really easy to tell students it's okay to be wrong, in fact, it's a very important step when learning. However, I appreciate the importance of getting the 'right' answer as we all do!!! I have met so many students who have said they are no good at maths. It can be very challenging to bring those barriers down!
I have always been useless at maths! And remember being taught the times tables in this way. For me it did work because I had it droned into me so often, I think for people like myself who struggle with maths it does help you remember them. But I am only speaking for the people who didn't "get" maths, I remember the people who were mathematically minded who would soon tire of this style of teaching.
we did this a lot at my school. I wouldn't have said so at the time but it was very effective. We had a teacher who would walk slow-ly down the aisles between desks as we recited and then he would point to one girl and she would have to carry on on her own. Not a technique that I would ever propose but here's why it worked:- 1) Yes, you did concentrate. 2) The cadence and rhythm helped me to remember the patterns 3) It would drive him nuts if we got too "sing song" when we did it (a later discovery) 4) It was a tangible achievement that could be repeated to impress relatives who asked.
Memorizing works because it stretches all the muscles in the mind that need to remember stuff and it makes it easier to remember more stuff accurately. Memory training is itself a skill and a very useful one at that.
And finally it worked and I am grateful for it because, I still do it when waiting in a boring queue or staving off dentistry fear!
Hi Theresa, I think the rules are less rigid for literacy learning, especially spelling. It seems for every rule there is an exception. There is something deeper though. That feeling that it doesn't look/sound right becomes very embedded. That is what makes it so hard to explain to learners. I definitely think there is an advantage in getting the automatic responses bedded down in the memory in order to allow for the higher order problem solving.