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Association of Teachers of Mathematics – Singapore Branch meeting

Last year we set up a branch of the Association of Teachers of Mathematics (ATM) in Singapore. The ATM is a UK professional organisation and I used to go to their meetings in the UK and in Hong Kong.

Last year, one of my colleagues in the Infant school decided to set up an ATM branch in Singapore. (Setting up a branch is free and astoundingly easy.) So far the ATM branch has met four times with about 50 teachers each time.

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We had a meeting this week and it was brilliant to meet both primary and secondary colleagues from around Singapore to talk about maths teaching ideas. And eat cakes and fruit drink wine!

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The theme for our meeting was shape and geometry teaching ideas. One good idea that was shared in the Secondary teachers chat was a gift-wrapped sphere with a note that said, “This Secret Santa present is yours if you can estimate its volume to within 50 cm2.” I made an estimate (without a calculator) but apparently I was 52 cm2 off the correct answer! Doh. I never did find out what was in that package.

I shared an idea for teaching about the surface area of a sphere using an orange that you unpeel. It’s described on this wonderful blog by William Emeny. (His blog’s name is eerily similar to my own!)

If you work in Singapore, please come along to our next meeting! We meet once a term (three times a year) and email invites are sent out.

If you don’t live in Singapore, consider joining a professional group near you. I highly recommend it for meeting new friends, hearing about other schools, and sharing ideas.

Reading and Writing in Maths Class

In light of the new report-style IAs in the IB classes, we are thinking of introducing more mathematical reading and writing in our courses. I am even thinking of having younger students do some reading and writing mathematically. For example, our IGCSE students regularly do investigations in class (from a book called New York Cop) and so I am thinking about developing some writing up lessons for them. Also I would like to help students read some mathematical material. For the younger (KS3, 11-14 year olds), I have been thinking about the Murderous Maths books (by Kjartan Poskitt). They are highly entertaining and very readable, yet also quite mathematical.

I have been reading a book called About the Size of It: The Common Sense Approach to Measuring Things (by Warwick Cairns) that I think I could use with 14 or 15 year olds. And a more advanced book is Math Through the Ages (by Berlinghoff and Gouvea), that older students could read, with short “sketches” of about 5 pages from various eras and areas. Now I have still to find some student-accessible mathematical articles of the kind that report on an investigation or problem. I suppose what I want to achieve is similar to the goals of teachers who show their students sample IAs.

Do you do mathematical reading or writing exercises with your students?

Tessellation

I learned something from the year 7 textbook recently! I was surprised that I had never thought about these two facts (as shown in questions 2 and 3 above.

And the answers were there, staring at me from the page. I would love make this into an activity where the questions build:

  • Draw a triangle that tessellates. And another. And another. Do all triangles tessellate? Prove it.
  • Draw a quadrilateral that tessellates. And another. And another. Do all quadrilaterals tessellate? Prove it.

What have you learned lately? Have you been surprised?

Glogging

I know it sounds as thought I am coughing on you, but no, glogging is a new technology that another teacher suggested to me today. Have a look at glogster.com for example. A glog is a poster page with graphics, sound, videos, and links. It looks pretty cool. And apparently some teachers use it too. More investigation will ensue. Have you ever heard of glogging? Or used it in school?

Marking–That Most Hated of Activities

I may have already mentioned that marking is something I find difficult, and that I also intensely dislike. As the school year ended and I was looking back on my marking especially I felt the same wistful longing as every year, “Maybe next year I’ll get it right.” I know how useful it can be to students and how important it is for them to know how they are doing and how to improve. So I feel that sooner or later I need to get out of my marking misery. So here’s an inventory of what went well this year and what could be improved.

What went well:

I made a lot of progress in terms of what I was recording in my (paper-based) mark book. I was more careful about writing in homework marks and I made more of an effort to collect these during class time when the students were on task with something. I was better at following up on students who didn’t do homework and applying the consequences I say that I will.

I was helped by a better way of recording missed homework in my mark book. I had a column on a separate page from the weekly homework columns where I recorded the dates of the first missing homework and any follow up offenses. Then I could more easily read these off, instead of trawling through the weekly columns. And I had a record there of detentions given as well. This made communicating with the Heads of Year or parents a lot easier.

I collected the books more regularly and more proactively. In some classes I collected them even when I thought I wouldn’t have any time to mark them, since on a few occasions this led to me spot checking and stamping a few books.

Still needs improving:

I have both paper-based and electronic mark books and this is confusing for me. My husband and I have talked about getting me some kind of hand-held device that I could use in my classroom tours when I am checking homework, but I don’t have one (yet?) and so paper still seems better. But electronic is the way of the future, and can provide data that is useful and searchable. It’s obvious to me that I need to move more electronically, but it just doesn’t seem convenient enough yet. I would love to survey other teachers about what they do electronically and how it is set up.

When I get busy, marking pretty much stops. I hate it and so I put it off and it is so easy to procrastinate from it completely. In my temporary job at the end of this term, I marked for the first half term, then didn’t bother. It was near the end of term and there were very few repercussions for me. I am ashamed of my dislike of marking and I want to know how to make it better!

I don’t always leave very useful comments for students. I am just moving to a school where the policy is that only comments are given in the lower school (years 7-9) and so I will need to improve my comment-making. Students deserve useful feedback.

I keep a lot of things in my head, especially those things I end up writing on reports. I wish I had a good way of recording them. My memory is out of space now and I am concerned that I won’t remember what I need. My students don’t have a great idea of how to improve because that’s not communicated to them very well. This could be done in lessons, not just through marking.

Ideas for next year:

I have a little stamper that says, “Lesson objective achieved” with my name and a smiley face and a thumbs up. I need to start using this at the end of lessons—work my way around the room checking work and seeing what I can praise.

I think it’s time to complete the transition to a fully electronic mark book. I hear a rumor that I might get a tablet laptop from the new school. That might make it all the more possible!

I have always talked about teaching students to peer assess. I know that this helps them gain an understanding of what makes good work. And, in the context of this discussion, it makes marking easier, and also more meaningful for me. It’s easier to comment on a peer’s assessment by saying what I agree with. And I can add comments that help a student assess better next time, as well as letting the student know what they can do to improve their homework.

The name of this blog reflects how much I value my own feedback loop, and so now I need to finally give the students the same positive feedback experience that I thrive on.

Dear Mrs A

This term I used Anne Schwartz‘s format for getting feedback from my students. I asked them to write me a letter. I’ve been teaching these students for ten weeks and I wanted to see what their impressions were.

Dear Mrs A,
1. The best thing you did was….
2. The worst thing you did was….
3. I am awesome because….
4. This summer I’m….
From, [name], your favourite student.

Here are some responses from top set year 7 students.

The best thing you did was let us play games.
The worst thing you did was giving us 3 exercises for HW.
I’m awesome because I did well on the fractions poster.
This summer I’m going to Taiwan, Beijing and San Francisco.

I’m awesome because I did well on the olympic stadium project and I learnt a lot about making sums simpler.

The best thing was you letting us choose our seats.
The worst thing you did was giving us a lot of homework.

The best thing you did was help me understand about shapes.

The best thing you did was let us work in pairs and groups.
The worst you did was give us quite a lot of homework.
I’m awesome because I improved my understanding in fractions, algebra and measurements.

The worst thing you did was give us lots of HW that was easy but long.
I’m awesome because I know year 13 stuff and beggining pre calculus and complex number and quadratic formulas.
This summer I’m doing an extra maths course and swimming class.

The best thing you did was giving us lots of practical tasks.
The worst thing you did was making us move the tables and chairs around.
I’m awesome because I went to every math competition, even purple comet and HKMO.

This summer I’m going to read a book of maths given to me as a present.

The best thing you did was to help me understand things when I am confused and made our lessons more interesting.
The worst thing you did was make us play a token game which was quite boring in my point of view.

The worst thing you did is… I really don’t know. You make your own mistakes, like every human.
I’m awesome because… I don’t think I am. I’m just a learner.
This summer I’m going to practise a bit of algebra.

The worst thing you did was give us far too easy work.

The best thing you did was talking for a minute about how people write.
The worst thing you did was not checking our homework.

The students quite rightly pointed out how much homework I gave and that after a while I stopped checking it. Marking is always my downfall. Sigh. I live in hope that one year I will get better at it.

Helping Students Work Together Better

Now that my surroundings have changed I find myself much more relaxed. It might be the change in my teaching classes (since some are shared) or the lack of exam classes, but I feel a lot less pressure these last few weeks. As a result I feel free to read more and try new things. I have been taking more risks in my teaching. We have weekly department meetings and in one of the first I attended, a colleague said, “You must make more time to think.” I have been making time, and there are so many good ideas to mull over. Increased motivation and inspiration has led to this blog. (I imported a few posts from years ago that I had about maths teaching but never published elsewhere.)

Students in my classes are learning maths and also learning to work together. I have one class that seems to struggle a bit with working together well; last week I happened to be reading about cooperative learning and I decided to teach my students to work together a bit better. I was reading about Kagan structures, which is where I got the activity called Sage and Scribe.

First I made up ten questions on the topic we are studying: percentages. (Actually, I borrowed them from an old worksheet.) Students work in pairs, each partner gets five questions. Student A gets the odd numbered questions, and Student B gets the even numbered questions. For the first question, Student A is the Sage (“a wise person”): they describe how to solve the question to their partner. Student B is the Scribe: they have to write down the solution as their partner describes it. Then A and B switch roles for question two. They keep taking turns; each time one person describes and the other records.

This is such an improvement on just practicing percentages from the textbook. I found that the activity helps the students explain what to do more fully and also helps them record better what needs to be done. And it’s cooperative, so they are learning about helping each other and working together. I tried this with my bottom set (“gentle set”) year 10s and my top set year 7s and both liked it.

things that worked

It really works to have all the next week’s worksheets copied up the Friday before. What a difference this makes to the ease of planning, especially homework. And what a difference it makes to my sanity. I pushed on Friday to get it all done and it really paid off today.

Better planned lessons are easier to manage. Behaviour was easier when I was calm and not flustered.

Organisation is everything. Mum said this summer, “Money spent on organising is never wasted.” To this I now add, “Time spent on organising is never wasted either.”

Reading something different (or different-ish) at lunch and directly after school relaxes my day. Funny how I have learned so many strategies for keeping my emotions and energy constant during the day and week. Sometimes (often?) a successful day is judged by whether I have survived. I wonder when/if I will move on to evaluate success by how much students learn.

marking: things i have learned

Get the students to do as much as you can.
Do some of it in class when moving about the room. Record all the homework marks.
Do it as quickly as possible. Write only the bare minimum. Do it as frequently as you can stand (every two weeks at the least). Take the books in every day there is not homework being assigned so that five or six books can be marked in an odd moment.
Keep track of homework religiously so that students know they can’t get away without doing it.
The key to this, as everything in teaching, is organisation. A well organised mark book makes marking easier. Classroom routines make marking easier.