Teaching the properties of equality through problem solving- repost from Keeping Mathematics Simple


linear equations

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I’ve found getting some pupils to understand the concept of equality to be surprisingly difficult. The problem seems to limit pupils’ ability in many other topics such as equivalent fractions, solving equations and changing the subject of a formula. I stumbled upon an article the other day that gave me some insight into why pupils struggle with it. When you do a calculation on a calculator, what button do you press to get the answer? The equals button. The article argued that kids think of the equals sign as an operator. Kids see the equals sign as something you press to get an answer.

Enlightened with this possible explanation for kids’ misconceptions, by fortune I then came across an interesting blog post by the excellent Keeping Mathematics Simple blog called “How to teach the properties of equality through problems solving“. The author puts forward a way of teaching the topic of solving linear equations. Her method, of focussing on developing the concept of equality first, before moving on to solving the equations later is logical and well thought through, ensuring there is no misconception about the properties of equality before teaching how to solve the equations.

When teaching solving linear equations (or similar) in the future I think I’ll experiment first with giving them something like 2x = 10 and ask them to come up with 5 equations based manipulating the first one (do the same to both sides etc…) e.g. 4x = 20, 2x + 2 = 12 and so on. They could produce a spider diagram with the starting equation in the middle and alternatives off on legs. Once they solve for x they can then subsitute it back into all of their equations and they’ll see that the statements of equality still hold true. Hopefully this will help develop an understanding of the properties of equality which is so important if their learning of solving equations is going to be anything less than procedural.

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Probably the best blogs by maths teachers around the world


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There are some really great blogs out there written by maths teachers who really care about their practice. I enjoy reading their posts as they share their insight and ideas and think about how it could improve my own teaching.

There is wheat and there is chaff out there. To save you time in separating the two, I have compiled this list of the best blogs I have found so far: Read more of this post

Idea for ICT based homeworks; your thoughts and suggestions welcomed…


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Why do we set homeworks?

What is the point of homework? What are we trying to achieve by setting the kids homework?

Consolidation and practice of what was learnt in class? Promoting self-study skills and independent thought? Learning of new concepts?

I’d like to think we set homework for all these reasons. It is well known that getting the kids doing homework improves their attainment in maths. Colleagues I have discussed the topic of homework with have commented that they find that lagging the topic of the homework approximately one week behind when the topic was studied in class leads to better attainment. This is perhaps unsurprising as it promotes the revisiting of previous learning to secure long-term memory retention. If you haven’t seen the Ebbinghaus Forgetting Curve before then you really must look at it now!  It doesn’t tell a good teacher anything new or surprising, but does answer the question that perpetuates through every staff room: “why can’t the kids remember what they learned last week?”. Revisiting concepts is the key to long-term memory rentention. Repetition, repetition, repetition.

A typical representation of the forgetting cur...

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We use the brilliant MyMaths software for some of our homeworks. Student voice surveys we have conducted suggest that on the whole, pupils enjoy doing the online homeworks more than conventional book-based ones. This isn’t surprising since most modern pupils feel more comfortable infront of a computer than a textbook. The big bug-bare we have as teachers about the online MyMaths homeworks is that the kids type their answers into the software and don’t have to record their workings. As teachers we are more interested in their route taken to the solution rather than the final destination itself as this shows up misconceptions in understanding.

Our pupils must never lose the skills of putting pen to paper to show workings through maths problems. I do wonder sometimes how we can combine the engaging ICT format that seems to motivate kids so well with the traditional skills learned through textbook homeworks. In short, I haven’t any perfect answers, only ideas. I’m not sure whether the ideas have value and are worth trying so would really appreciate your thoughts in the comments section below!!! Here are a couple of ideas I have been pondering on recently: Read more of this post

Thoughts on why kids struggle to understand fractions and proportion


Division (mathematics)

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I’m at the very beginning of my teaching career. Amongst the day-to-day business of teaching, whilst on my PGCE I spent quite a lot of time thinking about how to break down mathematical ideas into key concepts that the kids could understand and thought about how best to communicate them. I found this time valuable and illuminating as it challenged my own deep understanding of concepts that I’d taken for granted. The area of maths that I have so far found most interesting to think through in this way has been proportion and the link with fractions.

Why do so many kids really struggle to understand the idea of proportion and also how you can represent it as a fraction? I’m not sure for certain but I think one explanation is that they don’t understand division. Read more of this post

New ‘Pedagogy’ topic- sharing thoughts, ideas and good practice


First of all let me say a HUGE thanks to everyone who has been following this website in the short two weeks that it has been running. As of today we have had 179 different visitors to the site from 14 different countries including 1 visitor from Brunei! People have been downloading the resources non-stop. In the first fortnight it seems as though the site is already helping maths teachers improve their practice and save time by sharing ideas and resources which was the mission from the start.

To build on the great early success of the site I’ve introduced a new topic of blog posts called ‘Pedagogy’. You’ll see it in the menu at the top of the page. The idea is to blog about pedagogy: the method and practice of teaching sharing things that I have learned, experimented with or good practice other people have written about. Will it be subjective? Of course. Will I change my mind about things as I become more experienced? Undoubtedly. Is it still worth blogging about? Definitely because healthy debate and reflection is always a good thing, for beginners just as much as for experienced pros.

This area of the blog will be much more interesting if people get involved in the debate, sharing their thoughts and experiences. You can do this by simply submiting them in the ‘comments’ section at the end of blog posts. Let me know what you think of my first pedagogy blog post Going through the praise withdrawal.

Thanks again and I hope you keep finding the site useful and thought-provoking.

Going through the praise withdrawal


Is giving lots of praise counter-productive?

It seems as though recent research is suggesting so. Too much praise apparently can send the message that you are surprised the kids can solve the problems you set them and actually leads to them becoming demotivated. Read more of this post

Keeping the work ethic


Thanks to Lewis H for this great idea to keep the pupils on task:

To monitor pupils learning, write the time in the margins of a pupil’s book, and then come back 15 mins later to write the new time. No need to say anything! Pupils then have to answer to the evidence (or lack of) in their books!

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