### Archive

Posts Tagged ‘Textbooks’

## A lovely trigonometry question

This post is cross – published and can be seen on Betterqs here.

I’ve written before about textbooks,  they can be troublesome if used incorrectly but they can also provide a good amount of questions to allow students to get their teeth into without having a ridiculously high photocopying budget. A good textbook, in my opinion, is one with great questions covering a range of difficulties to allow stretch and differentiation when used properly.

Currently I have been struggling to find good textbooks for the A level syllabus,  I think the majority of the textbooks out there for the current syllabus are a little rubbish and I hope that the ones being produced for the new board are better. (If anyone wants to pay me a load of money I’ll write you a belter….)

The ones we use are produced by our exam board and are one of the better ones out there but are still lacking.  The questions tend to be straightforward, testing skills and not understanding and not really differing in difficultly. Imagine my surprise, then, when I came across this little beauty:

It was in an exercise on addition formulae and it really threw a number of my students. I loved the question and in the end we worked through it together on the board:

Once I’d railed at them about the importance of sketching they agreed that would be the best place to start. I made them sketch the triangle on mini whiteboards first to ensure they could then I sketched it in the board. They worked out the angle to be 60 minus theta and came up with the sine rule the selves, and then it was just a case of simplifying with the addition formulae.

This question doesn’t involve any overly taxing mathematics, but it does mix the skill being learned in with prior knowledge and as such serves to enhance the relational understanding of the students. They can see where the links are and they can build those links themselves. I think that this is a superb question and we need to be using questions like this regularly to build that relational understanding, helping our learners become mathematicians, and not just maths exam taking machines.

Categories: #MTBoS, A Level, Pedagogy, Teaching

## A surprising find

The other day I my timehop showed me this lovely little post from last year. It includes “Heron’s Formula” for calculating the area of a triangle, as I read it I remembered thinking it was a little strange that not many people had heard of it before.

Today I was looking through a number of textbooks trying to find a decent set of questions on area, perimeter and volume for my year nines as I wanted to consolidate their learning at the start then move onto surface area. I’m not a fan of textbook misuse- ie “copy the example and try the questions” but I do sometimes use them for exercises as we have a very limited printing budget and some of them have superb exercises. For a fuller picture on.my view of textbooks, read this.

I was looking in one of my favourite textbooks:

And I happened across this:

There it is! Plain as day! Heron’s Formula! In a KS3 textbook!

I was disappointed that its function was described and its name wasn’t and there was no mention of why this worked. It basically reduces the question down from a geometry one to a purely algebraic substitution task and I would question the appropriateness of including it in an exercise on area, but still, I was incredibly exciting to find it there!

Are you a fan of Heron’s Formula? Had you even heard of it? Do you have a favourite textbook? I’d love to hear your views.

Categories: KS3, Maths, SSM, Teaching

## Textbooks

A lot has been said recently on textbooks, the benefits they have and the bad press they get. This has had me thinking a lot about them, and their use in lessons. I rarely use them, certainly not the way they were used in my own schooling, but this doesn’t mean that I don’t think they have their uses.

Why do they have such a bad press?

I think they bad press comes from bad use of textbooks. I remember when I was at school lugging a ridiculously heavy bag around all day every day because there was a huge textbook for each lessons. I remember many lessons which began “Turn to page 6, Stephen (or whoever) can you begin reading.” then after the page was read the class would attempt the exercise. I remember a biology teacher who read the book to us, she’d fire questions off if she thought you weren’t listening. I sat next to Liam, and we’d sussed that you could answer the questions if you had the textbook on the correct page. One time the lesson was on organs, and the question was thrown at Anthony, who sat on the next table along. Liam and I often gave him answers. This time the question was “what’s the largest organ in the body”, I whispered “pipe organ”, which he then shouted out. It was hilarious.

I could go on, but I’m sure you all had your share of uninspiring textbook lessons. I’ve seen them as a professional. I witnessed an A Level lesson where the teacher sat at the front and read the textbook to the class verbatim. It struck me as rather pointless, as they all could have read it themselves. I’ve seen a KS4 teacher, when I was an Nqt, hand out textbooks with the instruction “look at the example on page ten, then attempt the questions”.

All these examples are uninspiring, and not conducive to good learning. But I think it’s unfair to lay the blame on the textbooks themselves.

How can textbooks be used then?

During lessons, there will be a point when you want the students to do some work. Practicing a skill or solving a problem. Using textbook exercises isn’t necessarily worse than a worksheet or questions on the board. In fact, it could be argued it’s better. It’s a greener and cheaper long term alternative to a ton of printed worksheets. The right textbooks have extension work built in, or offer a selection of exercises of differing difficulties. They also usually have plenty of examples, so learners can use them if they’re struggling, then can request help if they still need it.

I’ve seen a large variety of maths textbooks, I own a fair few. Here are some of them:

My favourites of the ones I have are probably these for KS3/4:

And these for KS5:

Within all these books there are some great things, but none of them are what I would call ideal. Each has plenty of flaws. I find that having access to all these, and many more, textbooks allows me to use ideas, examples and exercises from them as and when required. I sometimes think I should write one, it would be great!

So you think the right textbook would be fine?

Not on their own, no. The recent Sutton Trust report showed that a teacher with strong pedagogical subject knowledge is extremely important to the learning of a class. The right textbooks could aid these teachers, not become a band aid to cover for poor teaching or teachers with shallow subject knowledge. I also wouldn’t like to see them used in isolation. There are many other activities that can aid learning. Things that are quick and easy to check pupils have correct without the need to check each bit, resources such as Mathsloops and Tarzia or activities on mini-whiteboards. All these have a place in lessons, and all would be complimentary to the perfect textbook, which would aid, not replace, good teaching. Examples would be additional to the lesson and offer help learners who are still struggling.