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.)


,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!


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.

Diagnostic Questions revisited

questionsIt was a couple of  weeks ago I wrote about Craig Barton’s and Simon Woodhead’s brilliant Diagnostic Questions site. At the beginning of November I wrote that there were in excess of 1300 questions, just a short time later there are over 1600 questions (September 2014 update – more than 2500) – brilliant! There are some fantastic new questions – do explore all the recent additions.

I have been using this in class, with Year 7 we used some algebra questions; this led to some excellent discussions, not only did we discuss the right answers but all the wrong ones as well. We even decided on some alternative responses that could have been used. I feel a homework coming on here – we’ll write our own questions. Watch this space!
Update: Diagnostic Questions by Year 7.

It is now possible to download a quiz you have created and easily create a PowerPoint slideshow for offline use. I have created a slideshow with instructions:

Diagnostic questions download and create PowerPoint slideshow from Colleen Young

Craig has created this video giving a tour and commentary on the site:

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.
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.
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.

  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.
  • 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.
  • 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.
  • Learn to use WolframAlpha to check your work.
  • Learn to use the Desmos Graphing Calculator
  • 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?
  • 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 8

This week in class…
  • In my first lesson with each class I have been talking to my students about being gritty and green!  The green refers to our engagement with learning assessments where we traffic light students green / amber / red for their engagement with their learning. They certainly all listened and understood the message and clearly want to do well.
  • I have used the name cards I described here; I printed the address of my homework blog on one side for them to see and note and they wrote their name on the other. I find these really helpful, seeing the name beside the student means you can use their name when you talk to them and I already know many names. I collect them in at the end of the class, providing another opportunity to use their name thanking them for returning the card. (The ‘cards’ are actually folded A4 paper.)
  • Diagram - T SherringtonI read Tom Sherrington’s post “Empowing students to own their learning solves maths problems“; a great idea to start with a diagram with no labels at all as a way into a problem. I tried this with Year 10 (very able students) in their first lesson, presenting them with only Tom’s diagram and was very pleased indeed with the outcome. I didn’t even give them the question – just the diagram (a small copy each) and we started by deciding what the question might be. We quickly got onto areas as a possibility so then answered Tom’s original question ‘what fraction of the shape is shaded?’. The class happily discussed how to solve the problem and a student asked ‘can we write on the diagram?’ which of course was perfect – absolutely they could write on it. We solved the problem, revising some basics and had the discussion about what to do when you don’t know what to do! I will certainly use diagrams with no labels again.
New Discoveries
  • Numbers AndroidNrich now have modules for STEP preparation which look excellent. Note also their related resources such as preparing for university.
  • The wonderful Desmos graphing calculator keeps getting better and better and now has animations.
  • I tried an Android app I rather like, Numbers which is similar to Countdown. Use the given numbers to achieve the target. There are over 200 levels. I’m not sure the levels have a lot to do with increasing difficulty – look at level 61 here for example – this is much easier than some of the earlier problems. When I first started playing I didn’t realise you could click on intermediate results as you see in the illustration here and actually managed several levels without doing do! Dave Gale has written a post on the app here. I think I’ll try some of the problems this week with my Year 7 class when we discuss order of operations because we could write out the solution on several lines as in the app but then discuss how we could write the solution with brackets. I really want this on my interactive whiteboard (as well as my tablet and my phone!)
  •  Maths News
  • I have written before on Jane Hart’s Top 100 Tools for Learning, the 2013 list is now published.
Blog Updates 
….and finally 
Thank you Doug Belshaw, I enjoy your Thought Schrapnel every week.

Highlighting is a Waste of Time

Highlighting is a waste of time according to a comprehensive report released on Jan 9th 2013 by the Association for Psychological Science. The authors, led by Kent State University professor John Dunlosky, looked at various learning tactics and rated each from high to low utility. You can read the full report by clicking on the above link or for a summary have a look at this article in Time.

The authors conclude that the most effective learning techniques are distributed study sessions (last minute cramming is not effective) and more practice testing, the use of flash cards can be very helpful with this, as the conclusion to the Time article states ‘ditch your highlighter and get busy with your flash cards’.

A TES user has uploaded an excellent resource: Effective learning/study techniques which summarizes the work well and provides some great ideas for the classroom. I really like the ‘Cup of questions’ idea – I’ll be trying that! In fact the ideas given are very much in line with my own thinking, I have said before that I have become convinced of the need for frequent recall, perhaps even more true in the UK now that students are assessed with linear exams. Something I do regularly and certainly plan to do in this coming academic year for all my classes from age 11 to 18 is ask them some questions at the beginning or end of a lesson to see if they can recall recent (or not so recent!) work. See this file for an example: Mini-test example. The questions are short and can just be read out for students to write responses in their exercise books (making this a great starter – no IT or resources required). The questions in my example here are just recall type questions on a variety of topics but could of course be a series of questions on just one topic. Questions requiring higher order thinking skills could also be used (see Rich Questions for ideas). I have added a new page to which I will add any mini-test resources.

I think this type of exercise is valuable at any time, not just at examination time and we should spend time regularly helping our students recall current or earlier work. If they have a basic ‘toolkit’ with which they are comfortable and secure they have a foundation to which they can link new learning to.

 A really useful source of questions which can be used this way are the mental tests from CIMT; these are included with their resources for Years 7, 8 and 9 and also for GCSE. For Key Stage 3 (ages 11-14) scroll down this page for the Year 7, Year 8 and Year 9 course material, the resources include mental tests as part of the teacher support material. On the GCSE page scroll down to the teacher support material and note the mental tests available for most units, see this on Formulae for example.

Be imaginative with homework, it does’t have to be on the current topic – it could be on last week’s topic…or last month’s…or something you have not done yet!

The Collective Memory resources on TES are ideal in helping students understand and recall information and link ideas together. These can be used in a variety of ways which are fully described in the article. (A further set of resources is available here). Last year my GCSE students created several posters of their own which they found a very useful revision activity.

Bubbl'us diagram

Some students find mind maps helpful to recall information, I have seen students create some excellent diagrams with Bubbl’us for example. For some more online revision tools including some to make flashcards the resources mentioned here may be helpful

As I write I am reminded of a favourite quote from John von Neumann who said “Young man, in mathematics you don’t understand things. You just get used to them.” I know that for me, when I am more used to ideas I feel I understand them better. If we help our students recall all the basics – perhaps they will feel more secure – and confident.