The Best Compliment I’ve Received this Year

I was in my year 13 A-level lesson. Students were working away on some integration questions that use partial fractions. One student called me over, asked for a hint, and after my explanation he nodded. “Lit,” he said. And went back to work.

That’s the best compliment I’ve had in ages. And, gosh, lingo changes so frequently, doesn’t it?

Learning Names at the Beginning of the New School Year

I am a slow but persistent learner when it comes to names. This year I asked my students to use a sticky note and put it on their desk with their name. When I’m walking around I use their names as often as I can. Then at the end of the lesson, I asked them to put their sticky note on the wall near the door.

Then the next lesson they take down their name to use again on their desk.

wall of names

In between lessons, I’ve been using the wall of names as a self-test. I ask myself which class someone is from, or interrogate myself to say something about them. So far, so good.

I teach one pair of siblings and the older sister found her brother’s name and decided to put it really high up the wall where she thought he couldn’t reach it. Ha!

Do you find learning names easy? Do you have some tricks to share?


Stereotypes of Mathematicians

I was reading on the NCETM website about films that have mathematicians as main characters. Four films are mentioned:

  1. A Beautiful Mind
  2. Pi
  3. Good Will Hunting
  4. Enigma

One commentator says that these films contribute to stereotypes about maths since they are all about men, men who are unsociable, and that they are uncomfortable in their roles. Films are not helping maths break away from a “nerdy” stereotype.

Then another commentator goes on to lambaste this idea by saying:

the first three films are about mental illness, not mathematics: the characters happen to be mathematicians, their profession is incidental to the drama that arises from their malfunctioning brain chemistry. The negative, frightening “nutter” stereotype they perpetrate is far more reprehensible, and dangerous, than any “nerd” stereotype.”

The article ends by asking what schools are doing to counteract these stereotypes. For our part, we have named ten of our classrooms after mathematicians. Nine are men and one is a woman: Sophie Germain. They are not all dysfunctional; though Georg Cantor did go insane.

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My classroom is named after Paul Erdös but I have yet to capitalise on this with my students. There are so many good stories about Uncle Paul and his love of maths. He was a bit nutty though, so I am not sure he refutes any stereotypes. The truth is, a lot of mathematicians are men and a lot of them are a little odd. (I say this as a proud nerd.) I think this is especially true among academics, and perhaps less so among mathematicians in industry.

Does your school do anything to counter stereotypes of mathematicians?

Is Your Email Signature as Nerdy as This?

I was reading blogs and came across this wonderful idea for an email signature.

Even if you think you don’t love mathematics, mathematics loves you.
Don’t believe me? Solve for “i”.
9x – 7i > 3(3x – 7u)

How marvellously nerdy! This is from the blog Math = Love.

Is your email signature as nerdy as this?

Using Exit Slips: an #eduread post

My grade 11 class (Mathematics SL year 1) are getting ready for an exam in a week and a half. I was reading this week’s #eduread article about exit slips while they were doing a quiz. I got to the end of the article a few minutes before they finished and I was pondering the last two sentences of the article:

Exit slips are easy to use and take little time away from instruction. Many teachers use them routinely—even daily—and attest to their positive influence on student achievement.

It’s been a while since I used exit slips so I thought, well, there is no time like the present! And I wrote these three questions on the board to use immediately with my grade 11s.


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I passed out some small pieces of scrap paper, and voila!, exit slips.

The article mentions four main uses for exit slips. First, to get formative assessment data. My first two questions are of this type. Students give feedback on what they have learned. I now know that my students feel somewhat prepared; the median and modal level was 3. I need to plan more review about trigonometric functions and applications of differentiation.

Secondly, exit slips can be used to have students reflect on their learning strategies or effort. An example question would be “How hard did you work today?” I am planning to use this question soon–it could be illuminating.

Thirdly, the slips can be used to get feedback about my teaching. In the past I have often asked how my pace was during that lesson. My third question today is also of this type. Some students asked for more exam-style questions, several others want me to do tricky stuff on the board.

Last, exit slips can be a place for open communication with the teacher. In the past, I have frequently asked, “What is your foremost question or concern?” This prompt allows students to say whatever it is they want to about mathematics, our class, or anything else. The responses have ranged from useful to hilarious.

This post is for a group of mathematics teachers who read an article and chat about it each week using the hashtag #eduread. You are welcome to join in; our chat about exit slips is on Wednesday night at 8pm in North America/Thursday morning at 9am in Singapore (and the time where you are).

What questions would you ask on exit slips?

The Most Popular Spot in My Classroom: Who Tall Are You?

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At the back of the room, near the back door, is this brilliant height chart, titled “Who Tall are You?” It’s the most popular place for students in my room. Sometimes when I go out for tea at break times, I’ll return to see some young people have slipped in and are crowding around it. Here’s a link to a good quality image of it. “I’m as tall as Beyonce!” one person squeals.

Every once in a while students will be as tall as someone they don’t know: some of the celebrities now seem a little dated (singer Charles Barkley, for instance) and others are just people my students haven’t heard of yet (such as Alexander Pope).

Since I bought it about five years ago I’m having trouble finding somewhere to buy another copy. But I was thinking today that students could make one of these for display. They could have one featuring their classmates (and teachers?) and heroes of their choice. I reckon my current classes would include more sports people than the original chart.

I’m as tall as George Clooney. If I was making a new chart I would be sure to include Jensen Button, since I am also the same height as him. If you know your height in centimetres, please leave a comment telling us “who-tall” you are!

Building Collaboration Using Changing Partners Activities

A few classes needed to revise at the end of teaching units and I wanted them to collaborate while they did so. I printed off a class set of these small checklists with the first names of everyone in the class.

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I also printed some review questions onto colourful card. I separated my tables and spread the questions out over the tables, with two or three on each table. I put some tables facing the wall or the windows so that pairs of students would hopefully focus better on just their partner and the question at hand.

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I gave each student a name checklist to glue into their notes and displayed these instructions.

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From time to time there were not two students looking for new partners at the same time. As a result, sometimes they would have to work in a group of three. Other times there was one person who had to wait a minute to start their next problem. However, this didn’t happen too much and overall I would say that the students did a lot of work. Sometimes in a revision lesson such as this one, students get bored and lose momentum. Not so during this lesson. They stayed on task until the end (80 minutes later) and completed loads of questions. In the last few minutes of class we checked their work as I displayed the answers on the board.


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I have tried this with a few classes now and it has worked well every time. It goes most smoothly when the class size is 20 or more. Though I did try it one day when lots of students were at a field trip and I only had seven learners. That still worked but it was a little harder for students to begin and end questions at the same time as others. it devolved into mixed group work instead.

One time I tried this in my class that has a wheelchair student. This also worked smoothy. I positioned her in a place where she wouldn’t be bumped by others walking by. From time to time I prompted students to go over to her since she can’t come to them.

Some tips for myself and others to make this work well:

  1. A class size of 20 or more works best.
  2. It works best if you have enough tables to have at least two empty tables at the start for the first students who finish and find new partners to move to.
  3. Having three questions on each table means students can sit down at the same table a second or third time with different partners and solve different questions.
  4. Make sure the questions are numbered (or lettered) and students write these down as they solve. Then sharing the answers becomes easy.
  5. Mixed revision from several units of study can be done this way. Just mix up the questions around the room.

Do you have ideas about helping students collaborate in math(s) class?


Collaborative Talking in Math Class

For the next eight weeks I am participating in Exploring the MathTwitterBlogosphere, a project designed to help math teachers meet others in the cyber community we call home. (It is still a good time to join in, if you haven’t yet.)

Mission 1 is to write about what makes my classroom my very own. One thing I prize and make sure I develop in my students is their ability to communicate with each other about their math. I have been doing more and more discussion-based activities in lessons. I want them to talk about their conjectures and developing ideas. It is rare that my students are sitting in silence. They are usually discussing with the person next to them. Often they are moving around the room, talking to others. Even when we are doing “boring” practice questions they are talking.

umar remi probability never sometimes always true

Here two grade 12 students are discussing probability statements that may be never true, sometimes true, or always true. They had to go meet as many others as they can, discussing the statements on their cards, and each time trading cards. Then they go off and meet another person. (This is a quiz-quiz-trade activity.)

To help students communicate with each other, I have mini whiteboards (MWBs) and pens on each group of tables. Students love using them because they can quickly explain their thinking. They feel more free to make mistakes on the MWBs and to help and comment on each other’s work. Since having them always available, I have noticed a big increase in how much students help each other and talk about their thinking.

With the MWBs it is also easy to share the thinking of one or two students with the rest of the class. In another probability lesson, I asked students to visualize and then draw what they thought a certain probability distribution would look like. Then I brought six of the MWBs up to the front to discuss with the class their common and distinctive features. In the end, our discussion focused on just two of the graphs made by students.

fibber's game probability distributions

All this constant discussion helps my students clarify and solidify their developing ideas. This makes my classroom unmistakably mine.

What makes your classroom unique?

Better Group Work

I just finished reading an article called “When Smart Groups Fail” (Barron, 2003). It’s a study of groups of three sixth graders solving maths problems. Barron divides the groups into less successful and more successful at solving the problems and then analyses what features of their group work were significant.

Surprisingly to me, the success of a group of students was not influenced by:

  • the amount of talk
  • the average achievement level of the students
  • whether anyone in the group had a correct idea

Instead, Barron found that group success was marked by:

  • accepting or discussing correct ideas rather than dismissing them
  • correct ideas were brought up when they related to ideas that were being discussed at the moment
  • group members paid attention to each other and if the others were paying attention to them
  • group members physically showed their togetherness by eye contact and standing around or pointing to a common workbook

This article’s findings indicate to me that my classroom culture can lead to better group work. I can help students learn to discuss a mathematical idea by building on each other’s thoughts. A well-managed whole group discussion can lead to more cooperative group work sessions. I want my students to learn to listen carefully to what is said and then agree or disagree or ask questions. I can request these responses in whole class time. Then students will see they are the norms that also should guide their group work.

Furthermore, the groups in Barron’s study were of mixed ability and their previous achievement levels did not correlate with their success as a group. This adds to my feelings about the benefits of mixed ability teaching. If students of differing abilities can be helped to communicate well, they can all achieve well.

The study also found that students in successful group went on to be more successful in individual tasks. Interestingly, students in less successful groups did as well as if they had worked on their own. Thus poor group work neither helped nor hindered their achievement. However, good group work improved the success of individual students in to a significant degree.

The school year is just about to start and I am looking forward to inculcating a culture of social, mathematically focused talk.

Barron, Brigid. “When Smart Groups Fail.” The Journal of Learning Sciences 12.3 (2003): 307-359.

Teaching to the Test

While reading today, I discovered an unexpected side effect of the practise of teaching to the test. (At least it was unexpected to me; perhaps you will not find it so surprising?)

First, the “usual” problems with extended coaching[1] for exams:

  • the exam is no longer a good indicator of what students understand since they have only been narrowly trained to do specific question types
  • the exam is no longer a useful way of selecting students for further courses since we don’t know if they really understood the mathematics they have “learned”
  • the possible ranking of schools (for example, league tables in the UK) by student grades is not accurate since some schools have used extensive coaching while others have not
  • employers can not be sure that students’ ability matches their test score

All these arguments are ones I have heard before about coaching students to pass an exam. But one undesirable side effect of exam coaching stood out to me:

  • younger children see older ones being coached to success and they learn that at just they right time, they, too, will be spoon-fed what they need to know

As a result students learn that they do not need to take responsibility for their own learning, they do not need to study seriously or make an effort to understand and connect what they are learning.

Wow! I was shocked by this. One of my main goals is to make sure students understand what they are learning and can connect their mathematical ideas. I don’t want younger ones to learn that they don’t really need to work hard until the exam coaching begins.

My school only partly subscribes to the idea of coaching for exams. But I fully subscribe to the idea that students need to take responsibility for their own learning.

What exam preparation strategies do you use?

[1] I am talking about the repetitious, algorithmic coaching that happens in the lead up to standardised tests. Students, especially those who are near a grade level borderline, are taken (forcibly, at times) though many, many revision resources.