Things I Learned about Marking, Students Collaborating, Diagnostic Questions, and Students’ Reasoning (Notes from the Maths TeachMeet in Kuala Lumpur)

The maths TeachMeet in I attended today at Alice Smith School in Kuala Lumpur was inspiring. I attended sessions about marking (by Denise Benson from Beacon House School), a collaborative KS3 scheme of work (Phil Welch from Alice Smith School), things learned from Craig Barton (John Cartwright from Garden International School), and ways to deepen students’ reasoning  talk (Simone Dixon from Tanglin Trust School).

I also led a workshop about career progression for teachers (materials here). One of the tips I give is about reflective journaling. I recommend starting a blog, for instance. Someone asked me about my own blog and I realise I should probably practice what I preach and write some posts. A good first goal would be once a month since I’m currently writing a lot less than that.

Smart Marking (by Denise Benson from Beacon House School)

My main takeaways were twofold, one of which is not even about marking. First, exit tickets are the way Denise marks because it provides her with feedback for the planning and teaching of the next lesson and because it’s immediately useful to the student as well to see if they understood the lesson. I was struck that it would make them easier to have a little pre-printed form that they use and then the next lesson they could stick it in their book (if I deem that it would be useful for them to keep them). The scribbles below are a mock-up from my notes; hope you can read them!

Secondly, teachers complain about marking because they don’t have time. But actually teachers give up lots of time for lots of things, for example, reading teaching blogs, writing worksheets, or going to a TeachMeet on a Saturday. The problem with marking is that it’s not always a good use of time. Denise was saying that we should find a way to make it quicker and worth the time it takes.

She left us with a brilliant question.

A collaborative KS3 scheme of work (Phil Welch from Alice Smith School)

We had some good background discussion first about what KS3 looks like in each of our schools (using a Padlet). But I shall skip forward to the thing that struck me: Phil has capitalised on a timetabling quirk in that the whole of year 7 has maths at the same time. Thus they can have one week a term in which the students do a collaborative project in mixed groups. Also, the school has pairs of big classrooms with sliding doors between so they can squish a whole year group in for introduction or closing sessions. They also have a lot of breakout/corridor space for groups to work on projects. Really, this is such a great idea that works thanks in part to the brilliant facilities they have at Alice Smith School. Collaborative projects would still work in my school but would be a bit messier.

Highlights of the things learned from Craig Barton (John Cartwright from Garden International School)

Craig Barton was already one of my maths heroes but this feeling was intensified. John attended some CPD with Barton recently and in this 45 minute workshop he shared some of the highlights. It’s clear that I have to spend more time getting to know and using the Diagnostic Questions and Mr Barton Maths websites. John even said that all the classroom examples he uses on the board are now taken (via screenshot) from Diagnostic Questions. They are so good because the four multiple choice answers each stem from a common misconception.

Ways to deepen students’ reasoning  talk (Simone Dixon from Tanglin Trust School)

I was intrigued by the idea of multiple representations today – something I thought that I had considered before, but maybe I had not! Ha. Why do the triangles I draw on the board always look the same? Why are my fraction drawings always of 2D shapes? She showed this lovely example (poor picture alert) of fractions of a cuboid.

I’ve been lucky enough to go to a similar session by Simone in the past (we work at the same school). She mentioned both times an idea that I think would work for me. Put up questions around the room and ask for ‘silly answers’ to be written on them. For my students, who are older than hers, I might rephrase this to be ‘answers which look plausible but are actually not right’. This connected in my mind with what John said earlier in the day about having his students create diagnostic questions – complete with three wrong answers that each stem from a single misconception. Students have to really think hard about a concept to understand the misconceptions that others might have about it.


Besides these four sessions, I also enjoyed good chats with lots of thoughtful maths teachers. I always feel more energised and encouraged after a day like this one. What has encouraged you lately?

Test Champions

This idea was recently shared with me by Pietro Tozzi. He is a maths teacher at Gumley House Convent School in London but also works for Pearson (the Edexcel exam board) two days a week. We brought him out to our school in Singapore to do some training for the team about the new A-level in maths. (By the way, if you are looking for an A-level or (I)GCSE trainer, I would highly recommend him.)

During our time together, he shared this idea for returning a test. As it turns out I had a KS3 test to return and tried it out. As I marked I kept track of the best answers for each question. When I compiled this table, I made sure that every student was listed and students with lower scores were listed more frequently, if possible.

The class score represents the fact that among all the students, they have expertise to get full marks; someone scored perfectly on every question.

After passing back the tests, I asked students to get up and meet others who could help them correct their errors. They spent about half an hour up and about, talking over their questions, and making notations (using a coloured pen) on their tests. While they were doing this, I was able to work around the room and talk to those who had difficulties that their peers couldn’t solve.

They enjoyed this way of reviewing and correcting their tests. Having them out of their seats was good for their concentration (for the most part!) and also allowed me to be less conspicuous in my help of a few key students.

I completed this lesson with a fill-in sheet for students to list strengths and targets based on the test. We spent the following lesson with students doing individual work on their targets before we moved on to our next topics of study.

Which is More Valuable: Getting or Giving Feedback?

Students can get feedback from me, their teacher, when I mark their work or talk to them in class.

Students can give feedback to me when I ask them about their learning.

Which is more valuable for student learning? According to an article I was reading today, getting feedback from students is more powerful than giving students feedback. Cris Tovani argues that when teachers obtain feedback from students they can make changes easily to subsequent lessons, and this leads readily to improvement in the students’ performance. Tovani is a reading teacher, so here are a few ideas from me to help get feedback from students.

Three Minute Feedback

I do love this strategy and it’s the only thing I’ve continued doing since the very first teaching I did at university. (Sometimes I forget to use it, though, for months at a time. Does anyone else have this problem, even with great ideas?!) See here for an example when my IB SL students were preparing for a test; see here for an example when students were learning to expand brackets. Here’s one I prepared for my year 9s for tomorrow; they are revising for a test. Tovani says that after she spots the patterns in her exit tickets, she throws them out – it was freeing to read that.

3 minute feedback revision

Looking for Themes in Book Marking

When I take in a set of books (or tests), I jot notes to myself about commonalities among the students’ work to see on which topics they need help. If it’s just a small group of students who need help with factorising, for example, I might invite them all around one table when the class are working on something.

Quick Quizzes

Short quizzes with only a few questions that can be done at the end of class let me know if a concept from earlier is still secure. For example, I gave a four question trigonometry quiz to my year 10s a few weeks ago (and discovered that I need to refresh their memories about the difference between trigonometry and Pythagoras). I would like to get into the habit of using more mini quizzes.


Giving and Getting Feedback

Each of these examples allow students to give me feedback about their learning but they are also a means of the students getting feedback from me. In the case of the Three Minute Feedback, they have the chance to reflect on their learning and identify what they need to do next. With book marking, I have been challenging myself to only write questions to prompt thinking that will help students improve. In the case of quick quizzes, I provide detailed exemplar solutions afterwards for them to see and analyse. Thus students know where they are now and how to improve.

Which do you find easier in the classroom: giving students feedback or getting it? Tweet me (@mathsfeedback) or comment below.

Reflection Time

Last week we had a professional development session with Andy Hind (@andyhind_es4s) about deep learning. One thing that stuck out to me was the value of reflection time in order to deepen learning.

  1. Reflection time for students.
  2. Reflection time for me.

Students need time to reflect on their learning in order to embed it and connect it to their existing knowledge. One strategy Andy used which I will use in lessons was a small picture of a nutshell that popped up about twenty minutes into a session. Andy said, “Tell your partner everything that has happened so far, in a nutshell.”

He said that students should reflect at four points in a one hour lesson. At the beginning (thinking back to the last lesson), after twenty minutes, after forty minutes, and at the end. I scribbled down this time line.

reflection times

Tomorrow I’m incorporating reflection time into my lessons twice. At the beginning of one of my lessons we are going to recap the last session with the instructions on this slide.

recap last lesson

In another lesson I want to ask students to reflect at the end of the lesson, and I’m using the slide below. It’s a feedback structure I have used since even before I was a school teacher. I learned about it from my colleague Richard Hoshino while I was a lecturer at university.

3 min feedback

The “3 Minute Feedback” questions always follow the same pattern. The first question is related to today’s lesson and allows me to see if students have succeeded with the objective of the lesson. The second question relates to my teaching. The third one is always worded exactly as above and gives students a chance to share anything on their minds. I like to respond to these via Edmodo after the lesson by giving the class an idea of the proportion of responses of each type and by answering the questions.

I need reflection time in order to become a better teacher. I used to blog more regularly and this was a good method of reflection for me. But Andy also suggested a private reflection journal and I’ve started one this week. I set an alarm for half an hour before I want to go home. I use 15 minutes for writing reflection and 15 minutes for tidying up my desk. I haven’t managed to do it every day this week, but I’m pleased that I have done it three out of the last six workdays. I’m going to either write in my journal or on this blog during my afternoon reflection times this year.

How do you include student reflection into your lessons?

Famous Mathematicians Choice Board (Differentiation Idea)

A few years ago I made a project that I used with my year 7 (eleven year old) students. I introduced it by talking for about two minutes about Blaise Pascal, a mathematician I find personally interesting.

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Then I told my students they were going to choose a mathematician to learn about and it would be their choice how to show their learning. There are nine options for them to produce, and they needed to do three of them which form a vertical, horizontal, or diagonal line from the choice board. (Here is the choice board file.)

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I arranged the nine items so that the lines require some diversity of products. The two times I have used this project my students have responded very positively to the choices. The second time I did it, after they had made their three items, I made larger groups of those who had chosen the same mathematicians to put together a display board of their work. It’s a bonus for me that this project makes for a lot of good display work if you need/want to change your classroom displays.

I think if I did this project again, I might allow more choice on the person as well, perhaps by adding the option, “Choose another mathematician of your choice and have it approved by Mrs A”.

I am posting about this today because I was reading Mr Bigger’s post about differentiation using choice boards. It also makes me think that I should try to use a choice board for a more “meaty” mathematical topic. Has anyone done this before and have an example to share?


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?

Giving More Useful Feedback to Students: an #eduread post

How to give better feedback is always a goal of mine. I sometimes (maybe frequently) find it hard to keep up with the pace of teaching, assessing, giving feedback, and reflecting on it. What about you?

Today I was reading a short article titled “How Am I Doing?” with some pointers for effective feedback. Five very useful ideas were presented; have a look at the article to see them all.

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The item that struck me the most was that students need a clear view of where they are heading with their learning and what their learning target is. Phrased in this way, it is a very simple idea and one I have been familiar with for years. However, I have found that at times students think their job in my classroom is to complete the activities I give them. They think that completion of activities is the success criteria. Instead I need to get across to them that their job in my class is to reach desired learning outcomes.

This relates to feedback in that there is no use giving feedback when students think they have successfully completed the task of “learning”. Feedback may seem like giving them more work to do, rather than helping them learn. But if students know their job is to achieve a learning goal. Feedback about progress towards learning goals helps students know how their efforts are leading to success.

In my classroom I am not the best (yet! growth mindset!) at giving indicators of where learning is heading and how we will get there. I was marking student work today and saw this comment (pictured above): “This is confusing because you have not explained what you are trying to do.” As it turns out, that is exactly what I need to hear myself! I appreciated this article as a reminder to expose the learning goals more frequently. And to provide personalised, specific feedback to students about how they are going towards meeting those goals.

#eduread is a group of mathematics teachers that read an article each week and discuss it on Twitter. Here is the blog that organises it. The chat is on Wednesday evenings in the US, which is Thursday morning for me. I can’t always participate in the Twitter chats but I can usually follow along later thanks to the hashtag. Would you like to join us?

Do you find it easy to give useful feedback to students?

Peer Assessment: The “Production Line”

My grade 9 students did an individual investigation last week and I wanted to involve them in the process of marking it. I heard about a peer assessment structure called the production line from a colleague last year. In brief, the students mark each other’s work in groups, and each group concentrates on one aspect of feedback. The assignments travel around the group, gaining lots of detailed feedback.

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The investigation task already had an assessment rubric. It is based on the MYP year 4 criteria. The rubric focused on Investigating Patterns (MYP criterion B) and Communication in Mathematics (MYP criterion C). I divided the task specific criteria into themes – five in total:

  • B1: Finding and stating patterns
  • B2: Problem-solving techniques
  • B3: General rules
  • C1: Language and representation
  • C2: Reasoning

The Lesson

I rearranged the tables in my room and assigned groups of three students to sit together. I gave each group the details of one of the criteria. An example is shown below (and you can get them all in the investigation file).

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I had some instructions on the board (shown below) and we talked about what we were going to do. I had students help me staple an extra sheet of paper to the back of each task so that we could use it give feedback.

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I gave each group three tasks and asked them to read them, as a group, one at a time. Then they were to discuss the criterion and give some feedback. When they were finished with a task, I passed it on to another group.

Reflection on the Lesson

Since the rubric was already set up for this task, the preparation was quite easy for me. Making a task-specific rubric is a job that can take some time! Thankfully it only needs to be done once.

The number of criteria I wanted to mark didn’t match the number of groups I made in the class. I opted to have three criteria marked by two groups each and two criteria marked by one group each. This turned out to not work very well. The repeated criteria groups finished all the class tasks much more quickly (obviously!) and the other groups had much more to do. When I realised this, I asked two groups to take on a different criterion so take up slack from the inundated groups. Next time, I need to think more carefully about this. I didn’t want to make bigger groups because I felt like they would not work together well. In that case, I should have more criteria so that each criterion is only assessed by a single group.

I just managed (in 80 minutes) to get all the tasks marked by all the criteria groups. Next time I will not need to explain the production line in as much detail and I expect it will be more comfortable in terms of time.

The feedback that was given was extensive, though, I think I need to talk with the students about what the criteria is looking for. I can see the value of a class discussion about what constitutes good reasoning or communication or pattern stating.

The students gained a much more clear view of what criteria they are marked against. (The same criteria are in use throughout MYP maths.)

How do you use peer assessment in your classroom?