Assessment and Feedback in Mathematics

Some further notes and additional resources on Assessment and Feedback…

The first few slides (slides 1-15) introduce Assessment and Feedback, looking at definitions. To summarise:

Assessment and feedback is something we do every day in our classrooms. It’s a two way process, students and teachers working together. The feedback needs to be helpful to the students in that they can do something with it to improve their learning.

Some further useful reading:

The next section of the presentation (slides 16-23) concerns teacher – student relationships, so important and something which comes up continually in my own conversations with students, note section 3 on Classroom Climate and also these comments from younger (age 11-12) students. This is all about knowing our students well and creating a climate where it is OK to be stuck, there is trust between teacher and students and the students know that their teacher has their best interests at heart. To quote Dylan Wiliam:

Without that relationship, all the research in the world won’t matter.

Continuing with the theme of knowing our students well, it is so useful to ask them what works. Slides 24-31 show quotes from students about what helps them learn. Included in this section – Corbettmaths 5-a-day.

5-a-day
Continuing with the theme of knowing our students well, it is so useful to ask them what works. Slides 24-31 show quotes from students about what helps them learn. Included in this section – Corbettmaths 5-a-day.

Slides 32-38 illustrate some learning activities such as matching exercises which have built in feedback. For some useful resources for this type of activity try the following:

Teachit Maths KS3 Percentages code breaker

Teachit Maths though a subscription site offers its entire collection of activities as pdfs free.
I have found many high quality resources here for all ages. Look at this activity on quadratic functionsfor example – this should really help understanding.

questionsThe next section (slides 39-45) is on questioning. Used wisely, well planned for questions can help us work out just what our students know.
Recommended reading and resources:

Retrieval Practice (Slides 46-49) looks at low stakes testing to help students recall information. Something I have found valuable throughout my teaching career and an area I am currently working on and will write further on in the near future. See:

Homework ideas are given on slides 50 to 53.

The next section is on marking (slides 54 to 63). See:
Test Analysis

  • Consider a question by question analysis on tests; this can be very revealing as to which topics a class has found harder.
  • Look at examiners’ reports to give advice to students about what examiners are looking for.
  • A very interesting read from the University of Oxford and the Education Endowment Foundation is A marked improvement? (April 2016)
  • Plan for marking, what are you looking for in a particular piece of work. Consider Ross Morrison McGill’s (@teachertoolkit) 5 Minute Marking Plan
  • For simple day to day marking, ask your students to assess themselves using RAG123.

Further Resources

Feedback

I have read some great posts on feedback, see Alex Quigley’s Improving Written Feedback  and Verbal Feedback Given….. on Shaun Allison’s ‘Class Teaching’. Such a good idea, I couldn’t resist – so I bought myself the stamper and decided to try this with Year 7 – early days yet, but I love the idea so far..

Nought & CrossesA student in my Year 7 class was determined to find the number of winning lines in a game of 3D noughts and crosses which she did successfully. She drew some clear sketches of the different groups of winning lines and after a discussion with me was the recipient of my first stamp! I was very enthusiastic about her written work on this as you can see from her response! I had explained to the class that if I discuss their work with them, then give them a stamp – they have to write down that feedback as Shaun suggests in his post.

verbal feedback v3

It is important for students to make a note of verbal feedback and I have asked students to do this more often recently, so for example if I am giving any verbal feedback to the class after a test or homework I expect them to make a note of any verbal feedback they believe applies to them.

Something we must do of course is allow students time to respond to feedback, ideally I want a conversation in their books! I acknowledge where a student has responded to feedback by awarding a Feedback Response point (see ClassCharts for recording learning behaviours). We need to allow time in class for students to act on any feedback given; another possibility is to give freedom of choice for homework. My notes for my Year 7 class on our homework blog includes the following:

Note that the independent homework gives you the chance to respond to feedback; for example you might want to try to solve some equations and present your solutions very logically and show that you are checking your work. It may be a response to my feedback or your ‘self-feedback’. When you reflect on something we study in class, sometimes you might think ‘I’d like to practise some more examples’. Your independent homework provides that chance. Remember you could choose any topic, your homework offers you the chance to revise work.
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Staying with the use of homework, it may be appropriate to give a follow up homework allowing students the opportunity to act on feedback received from the first attempt.
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See also: Dollops of Feedback which includes some useful resources on feedback.
The most powerful single modification that enhances achievement is feedback. The simplest prescription for improving education must be “dollops of feedback”.
Hattie, J.A. (1992). Measuring the effects of schooling. Australian Journal of Education (see page 9).

In class this week ….

Year 7 (age 11-12)
…had an Independent homework this week and I was really pleased with the variety of choices made. Some chose to use online resources / their text to practise a topic tested recently, others worked further on some investigations we have looked at in class, some chose to do a Junior Maths Challenge. A couple of students used the Diagnostic Questions site to practice their chosen topic. One of the investigations we have looked at recently was on the number of winning lines in a noughts and crosses game – the 2 dimensional  game was fairly quickly sorted out – so moving to 3 dimensions is the natural extension.

Nought & Crosses

Some were fascinated by this and determined to find the number of winning lines in a game of 3D noughts and crosses – two students so keen that they made a model of their own to help them answer the question successfully! They made some counters as well!

I have read some great posts on feedback recently, see Alex Quigley’s Improving Written Feedback  and Verbal Feedback Given….. on Shaun Allison’s ‘Class Teaching’. Such a good idea, I couldn’t resist – so I bought myself the stamper and decided to try this with Year 7 – early days yet, but I love the idea so far..

Another student in the same Year 7 class mentioned above was determined to find the number of winning lines in a game of 3D noughts and crosses which she did successfully. She drew some clear sketches of the different groups of winning lines and after a discussion with me was the recipient of my first stamp! I was very enthusiastic about her written work on this as you can see from her response! I had explained to the class that if I discuss their work with them, then give them a stamp – they have to write down that feedback as Shaun suggests in his post. 

verbal feedback v3

Year 10 (age 14-15)
desmos-gradients1Year 10 and I have been looking at inequalities – using algebra and graphs. After a ‘self-check’ (somehow that sounds so much better than test and the emphasis is very much that it is useful to see what they can recall) in class, the feedback from the students was that most of the questions were fine but any problems seemed to be on working out the equation of a line when trying to describe a given region. The wonderful Desmos graphing calculator to the rescue – this page allows students to experiment with several variables. (Post for students here.)

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,Update – since writing this post, along came Desmos

Desmos tweet
and created a superior version! This shows many of the awesome Desmos features. I really must explore these further – note that where a folder is used selecting the arrow shows or hides the contents. This is a brilliant feature for creating pages to share with students.

Gradient of a straight line by Desmos

I mentioned feedback from the students – a simple feedback idea – I asked this class as the first part of a homework to email me with any outstanding queries from the mini test, having looked at the worked solutions on our homework blog. I have been impressed by their understanding and articulation of what they initially found tricky.

Year 12 (age 16-17)

zweigmedia – numerical integration utility

In Year 12 we have been studying integration. Teaching the trapezium rule I remembered some applets I used last year which demonstrate this well. 

Graphs images - WolframAlpha

Graphs on WolframAlpha

The Year 12 Further Maths class are currently studying Decision Mathematics and a student asked what WolframAlpha can do?! Looking at the examples we can see that describing connections between nodes will generate images of a graph. I must explore further!

normal2

Normal Trainer – Mike Hadden


Year 13 (age 17-18)
Studying the Normal Distribution I showed students Mike Hadden’s excellent normal trainer which generates an endless supply of examples. I really like the step by step approach and the very clear page on the backwards problems.

With the Year 13 Further Mathematicians I was reminded of the huge variety of Tarsia puzzles around and that these are not just for younger classes. In Year 13 we use a Tarsia on De Moivre’s theorem.

Smarty Pants and other badges!

7 Badges

Near the beginning of this academic year I wrote that Year 7 (UK age 11-12) and I decided we would use Class Dojo this year to record learning behaviours. We have since adopted the term badges to describe our system which I rather like; it reminds me of the excellent work by the Mozilla Foundation on their Open Badges and I wonder if at some point in the future I can somehow link our system to an open badge.

See also – the later post on ClassCharts which can also be used to record learning behaviours and additionally offers the facility for students to view their own complete online record.

Our system seems to be working well, particularly as it is very much ours not mine and it’s all about being the best you can be, which is quite different from being the best in the class. Year 7 have come up with many suggestions, I quote some of them here:

  • Some of my ideas for a badges are: Well prepared, Contributes in class, Good Marking.
  • I have an idea that maybe there could be a good effort/trying your hardest badge, so this doesn’t necessarily mean that someone has got 10/10 but when you know they are struggling in a particular topic and then they might get a just above average mark in it , you will still know they tried there hardest because they were struggling with it before.
  • There could be a badge for a great badge idea! Also neatness. A tidy page is easier to read and mark.
  • I think we should have an organisation badge because it’s important to have everything you need for a lesson.
  • You could also include a gritty child badge.
  • I think we should add a presentation badge, a best effort badge and a badge called Smarty Pants so if we get full marks for quite and few times in a row we can get a smarty pants badge!
  • I think there should be a ‘happy to do my homework’ badge. Where we ask ourselves, are we ok to do our homework because I only really get my homework correct if I am motivated enough to do it! Also none of us want to feel like we ‘hate’ homework!
  • Mrs Young, do we have an enthusiasm badge on classdojo? Because I think that that would be quite useful ;)

…and the suggestions are still coming. We have discussed how these badges will be awarded, for example when I asked how will I know that you are happy to do homework, we decided that their homework would show care, would always be done on time and if they had any problems they would ask before it is due in. What has been so pleasing about all these discussions is all the talk about what it means to be a good learner.

JDI!I do like to get a class working immediately, I have written on Bell Work before; Year 7 are aware of this and just recently a student suggested a JDI! badge for those students who come into class and without fuss get straight on with their work. The student who suggested that was obviously listening to me at the beginning of the year when I mentioned that there were times when you just have to get on with things – just do it!

In our discussions on homework we have decided that sometimes it would be a good idea to have an independent homework where each student decides for herself what she will spend time on. This offers the chance to practise more examples of any topic a student feels she needs or perhaps try some extension work; there are many possibilities. I have reproduced below the instructions I have written for students (on our homework blog) on how this will work. I will report back in a later post on how this is working.

Independent Homework

Independent Learner DojoWe decided it would be a good idea to have an independent homework sometimes, giving you the freedom to work on something of your own choice. This will enable you to demonstrate your independent learning skills. There are several suggestions here but you may choose any activity that will support your learning in Mathematics. Your activity should usually include trying some problems.

When we have an independent homework you should include in your work an introduction to say what you have chosen and why you chose it. You should also evaluate your chosen activity when you complete it. Was it useful? Have you achieved what you hoped? If you have used any particular resources would you recommend them to others?
Feedback responseNote that the independent homework gives you the chance to respond to feedback; for example you might want to try to solve some equations and present your solutions very logically and show that you are checking your work. It may be a response to your ‘self-feedback’. When you reflect on something we study in class, sometimes you might think ‘I’d like to practise some more examples’. Your independent homework provides the chance. Remember you could choose any topic, your homework offers you the chance to revise work.
Suggestions
A chance to practise a topic you feel needs extra work. You could use any of the following resources:
Your textbook: the Test Yourself exercises at the end of each chapter have the answers at the back so you can check your solutions as you work. You could also work through examples in the Yellow boxes or try some of the puzzles. If you do use worked examples – never just read them, work them out yourself.
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Online activities: if you choose any online activities you should show some working in your book.

  1. MyMaths –  remember to use your second level password if you try any of the homeworks.
  2. MangaHigh – the quizzes – not just games!
  3. CIMT Tutorials Year 7 or Year 8
  4. The Maths Teacher
    The Maths Teacher Number

    The Maths Teacher – David Smith

    David Smith’s site, The Maths Teacher has an extensive collection of videos to help you study Mathematics. Many of the foundation GCSE topics are also ideal for KS3 (age 11-14). For each topic not only is a video available but also a transcript and exercises with solutions. This makes the site ideal for revision – you have the choice of perhaps just trying the exercises or if you feel you need more help you can watch the video – whatever is right for you.
    the-maths-teacher

  5. Any website of your own choice, many students like BBC Bitesize for example. There are other suggestions on this page.
  • A chance to study any new area of Mathematics that we have not studied in class yet that interests you, you could use any of the above resources or perhaps you could try a problem from the Nrich website. Note that you can search NrichSuppose you want to work on Algebra for example, you will find lots of activities here.
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  • Try some Maths challenge questions – see this page. Note the challenges from the University of Mississippi, the Middle School Madness and Elementary Brain Teaser problems are for school age children, Middle School Madness for grade 8 (age 14 and under), the Elementary Brain Teaser for grade 6 (age12 and under). If you submit a correct solution by the deadline that week your name will be published on the website.
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  • Work on your mathematical vocabulary, you will find the dictionaries here helpful. You may want to look at some other reference material, many students find these notes from Craig Barton very helpful.
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  • Learn to use WolframAlpha to check your work.
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  • Learn to use the Desmos Graphing Calculator
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  • If you want to practise (and assess yourself) at a particular level then try Convinced from Kangaroo Maths. Also from Kangaroo Maths see the Levelopaedia and Level LaddersEmily Hughes has a clear and attractively presented guide for both KS3 and KS4.
  • Are you guilty of making any of the Classic Mistakes here?
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  • All the above are suggestions if you are not sure what to try. You are of course free to make any choice of your own as long as it supports your learning of Mathematics!

Remember that getting stuck helps you learn. Gritty students persevere and work things out when they get stuck, asking for help is fine too! Try and ask specific questions.

Do you have any observations / suggestions for independent homework? Please add your comments below.

Things I Learned This Week: Sep 14th

This week in class…

ClassDojoYear 7 – ClassDojo
Year 7 and I have decided to try ClassDojo this year. ClassDojo is a classroom tool that helps teachers record student behavior quickly and easily. Feedback points for specific behaviors can be awarded. (This is completely free). The class were very keen and this is our class decision not mine. The beauty of ClassDojo is the ease with which you can customise it. We discussed all the various categories we could have for points and have some great suggestions, points for marking and correcting work clearly for example and for asking great questions. We can also link this with our engagement with learning criteria used in school. We discussed the negative behaviours and decided that we should have anything which stops them learning either in or out of class, ‘off task’, or ‘no homework’ for example. We have far more positive behaviours than negative. Students can log in and see their own records and I do like the fact that they have a chance to reflect and add a comment themselves. Part of their homework this week is to think about the points system we will use, in fact whilst writing this post two students left comments on our homework blog with suggestions for points which I have duly added! I then used my phone to award the two of them a participation point! A computer can of course be used to award points but it is also possible to use a tablet or phone, apps are available for android and iPhone.
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I regard this as a good way to document their learning behaviours, it is absolutely not a traditional ‘reward’ system which I think can be a minefield! I want something accessible to all and is clear to us all that it is about each student being the best they can be. Writing that statement has made me realise we need points for being gritty (and the value of writing things down)!
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There are many leaflets and handouts with clear instructions and ClassDojo’s YouTube channel has a collection of tutorials showing you how to use ClassDojo, see this introduction for students for example:
Sixth Form – WolframAlpha and Desmos
Select the image for the Desmos graph.

Select the image for the Desmos graph.

As I always do I have been showing all my classes how helpful WolframAlpha is for checking working, so I was very pleased that when two of my Sixth Form students (UK age 16-18) came independently to see me about some homework they had both been using WolframAlpha to check answers. One student also asked about modulus inequalities and I showed her how simple it is to use the Desmos graphing calculator to illustrate the problem.

New Discoveries

Maths News
The National curriculum in England, Mathematics programmes of study for key stages 1, 2 and 3 were published on September 11th. (Link added to the News page).

Miscellaneous
I mentioned Jane Hart’s Top 100 Tools for Learning last week, this is the last chance to vote for the 2013 list as Jane will publish the latest list on September 30th. Jane Hart’s definition of a learning tool:  “A learning tool is a tool for your own personal or professional learning or one you use for teaching, training or e-learning.” Voting closes at midnight GMT on Friday 27 September 2013.
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….and finally 
For your amusement (thank you to my daughter Sophie for the link), can you figure out these movie titles? from Spiked Math.