Author Archives: weeklymaths

Summer Institute highlight: An amazing day on number

I’m posting a series on the highlights as I saw them from the Teach First Summer Institute at Warwick. One of these was the first day we devoted to studying how to teach number. Diana Spurr and Marcus Shepheard covered a wonderfully rich variety of content in impressive depth – it was a really valuable day. Highlights include:

More highlights to come in a few days…

The wonderful world of the empty number line

Screen Shot 2013-08-11 at 09.36.44

How interesting can an empty number line be? Not very, I assumed. I’d read before about teachers raving about the concept. I’d always thought they were a little funny in the head. I am now officially a convert.

It turns out the empty number line can be used in a whole range of ways. Most simply, it can be a great mental tool for students’ addition and subtraction, by using multiples of 10, counting on etc.

For example, 12+13 becomes:

Screen Shot 2013-08-11 at 09.36.51

25-12 becomes:

Screen Shot 2013-08-11 at 09.36.56

So far so good, but it was what Diana and Marcus did next that was so exciting…using empty number lines to visually represent linear equations. (I’m aware there are many other ways to represent linear equations – this just feels like a particularly powerful one)

For example, taking the equation 3x+8=23:

Screen Shot 2013-08-11 at 09.37.02

So:

Screen Shot 2013-08-11 at 09.37.11

so x=5

 

You can even use the empty number line to explore relationships between fractions, decimals and percentages:

Screen Shot 2013-08-11 at 09.37.18

What could A be?

Summer Institute highlight: IWBs and technology in the classroom

This is part of a series blogging the highlights (as I saw them) from the Teach First Summer Institute 2013.

Hannah Tuffnell and Joe Ambrose hosted a great session on IWBs and technology in the classroom. It was brilliant partly because of the content but also partly because, on the penultimate day of the Summer Institute, in a boiling hot room, at 7:30 they kept 20 or so exhausted participants engaged and learning for an hour.

The new technologies they promoted were:

  • Prezi: Most of us knew this one – a more engaging version of powerpoint. It’s time-consuming, though, so best for the occasional lesson e.g. introducing a new topic.
  • Powtoon: Use to easily create animations up to 5 minutes long – students can make them too.
  • Padlet: An online noticeboard where students can write on a wall (you can moderate comments!). Could be great for homework.
  • Edmodo: A safer version of facebook. You can use it to set up assignments, polls, resources etc.
    • Useful for homework setting
    • Marks multiple choice answers
    • Students can download an app that lets them do homework on their phone.
  • Google Forms: (find via Google Drive) Create a questionnaire to give to students. Useful for feedback on you as a teacher.
  • Poll everywhere: allows students to text into polls in real-time, and can embed within powerpoint.

In terms of IWBs themselves, some specific tricks:

  • Revealer tool: pull down a box to reveal specific parts of the board
  • Infinite cloner tool allows you to create duplicates of e.g. a coin
  • Layering can be used to allow some things into a box and not others
  • Using two colours can allow you to magically ‘reveal’ an answer
  • It is possible to lock things into place.
  • Shape recognition and text recognition tools are available
  • The magic pen allows you to:
    • Write in text that slowly fades
    • Circle (everything else goes dark)
    • Zoom in by drawing a square
  • You can create a random name generator with a hat (this allows you to differentiate by having different names in different areas of the hat)

SMART exchange/SMART world is the source of more information and training.

These IWB ideas are great, but have made me realise what I really need is a bit of time with the board to play around with creating and using things. I can already see how I could use these tools to sort shapes, or to reveal the correct answer to factorising problems.

Challenges in Leadership

Teach First event 24th July

Leadership is a slippery beast; I’ve spent years studying it and trying to put it into practice in various guises, but ask me to define what leadership is and I couldn’t tell you. Partly because of this, hearing inspirational people speak about leadership is always a good way to spend an hour and a half, and particularly so when the organisers manage to pull together such a diverse and interesting bunch of speakers as Teach First did on Wednesday night.

Thoughts on leadership from the session that have stuck with me:

  • Reuben’s advice to find what is brilliant even in the worst situations, and expand that. For me, this is most meaningful in relation to developing students’ self-esteem and engagement in learning. If I can find something that they are brilliant at/some nugget of brilliance in our relationship, I’ll try to use and expand this.
  • Elisa-Manningham Buller (via Hilary Spencer): “Laugh, say thank you and get enough sleep.” If I can achieve all three of those consistently next year, something will be going right!
  • Henry Kissinger (via Jo Owen): “Leadership is the art of taking people where they would not have got themselves.” This, for me, is what teaching is about. Keeping this in mind leads me to focus on promoting independent learning, constantly seeking to challenge my students, and creating a safe space to take risks in the classroom.
  • 5 top tips from Carly Mitchell
    • Get your rewards and recognition from the impact on students, not from adults and peers.
    • Don’t get swept into negativity.
    • Be solutions focused – respond to problems with 1 page: the need and the change it will lead to.
    • Sweat the small stuff
    • Never stop believing every young person can achieve.
  • Anna Dunne:
    • Leadership of business as usual scenarios can be much more challenging than project leadership.
    • Understand what your followers need and enable them.
  • Hilary Spencer, DfE: What’s usually a strength can spill over into being a weakness.
  • Lauren: You have to believe in yourself
  • Jo Owen:
    • You’re not going to succeed either by being yourself or by being someone else, but by being the best version of yourself that you can be.
    • Identify your weaknesses and collaborate with others to address them – but don’t spend all your energy trying to eliminate them.

Some of this isn’t new, but amongst other things keeping the Kissinger and Manningham-Buller quotes in my head will be really useful for me next year.

Putting place value in its place

ATM article putting place value in its place by Ian Thompson. Also the first I’ve really read on developing students’ understanding of place value in the classroom. Thompson uses a research study to argue that:

…children are able to add two-digit numbers successfully using partitioning without needing to have an understanding of place value.

Which is interesting for me, because up until now I hadn’t appreciated that there might be four properties of place value: positional, base-ten, multiplicative and additive.

Thompson’s central idea: moving digits to the left requires very sophisticated understanding of place value – it may be better for teachers to accept and teach the ‘rule’ ‘add a nought’ whilst later recognising (and discussing) the misconceptions this idea creates.

Tips from behaviour for learning session

We had a behaviour for learning session as part of our Teach First training last week. The points that came out of it that struck a chord with me were:

  • When taking the register, be human! Ask how each person is/something about them and listen to the answer.
  • For a tricky class/to assert my authority early on, consider telling students to line up at the back and tell them individually where to sit.
  • Get students to repeat instructions back to you to ensure they’ve heard, listened and understood.
  • You can set/maintain expectations when meeting students at the door (e.g. uniform, chewing gum) which reduces the amount you have to talk about things as a whole class.
  • If I take any classes with a reputation, I can make clear that as I’ve come from another school the class gets a fresh start with me, and that I’m really looking forward to teaching them.
  • Consider writing extra minutes on the board for late students.
  • Be very clear and specific with your instructions – often poor behaviour comes from students not understanding what they’re supposed to do.
  • Put classroom rules on the inside cover of students’ books.
  • At the end of the lesson, give students jobs, and act quite authoritatively to counteract the end-of-lesson excitement.

 

Boaler: What is maths? And why do we all need it?

Another recommended reading from Teach First. Selected quotes below:

Mathematics is a performance, a living act, a way of interpreting the world. Imagine music
lessons in which students worked through hundreds of hours of sheet music, adjusting the notes
on the page, receiving ticks and crosses from the teachers, but never playing the music. Students
would not continue with the subject because they would never experience what music was. Yet
this is the situation that continues in mathematics classes, seemingly unabated.
Those who use mathematics engage in mathematical performances, they use language in all its
forms, in the subtle and precise ways that have been described, in order to do something with
mathematics. Students should not just be memorizing past methods; they need to engage, do, act,
perform, problem solve, for if they don’t use mathematics as they learn it they will find it very
difficult to do so in other situations, including examinations.

We cannot keep pursuing an educational model that leaves the best and the only real taste
of the subject to the end, for the rare few who make it through the grueling eleven years that
precede it. If students were able to work in the ways mathematicians do, for at least some of the
time – posing problems, making guesses and conjectures, exploring with and refining ideas, and
discussing ideas with others, then they would not only be given a sense of true mathematical
work, which is an important goal in its own right, they would also be given the opportunities to
enjoy mathematics and learn it in the most productive way.

Boaler’s vision is an inspiring but ambitious one. Like Swan, Boaler discusses the end goal of a maths classroom without always making explicit the precursors necessary to allow students to work like mathematicians. Working like a mathematician is hard and, amongst other things, requires grit, persistence and a willingness to be wrong before being right. None of these things will come naturally to a mathematics student.

On the other hand, each of these things can be encouraged. The challenge is that it will take time, persistence and agility on my (the teacher’s) part to encourage students to work like mathematicians. It isn’t easy, but if Boaler is to be believed it’s worth the effort.

Boaler: What is Maths? And why do we all need it?

Swan: Collaborative Learning in Mathematics

From Swan’s paper (available below):

Teaching is more effective when it …

  • builds on the knowledge students already have;

  • exposes and discusses common misconceptions

  • uses higher-order questions

  • uses cooperative small group work

  • encourages reasoning rather than ‘answer getting’

  • uses rich, collaborative tasks

  • creates connections between topics

  • uses technology in appropriate ways.

Types of teaching activities that can achieve these principles:

  • Classifying mathematical objects
  • Interpreting multiple representations
  • Evaluating mathematical statements
  • Creating problems
  • Analysing reasoning and solutions

But what are the precursors to this? Swan talks about the challenge of ensuring all group members participate, and some ways to encourage this, but reflecting on what I’ve heard from other teachers in the past few weeks, I think we need to take another step back first.

The challenge that I’ve seen and heard from several teachers is to create the conditions within their classroom that allow productive collaborative work, rather than students spending group work time chatting about something other than maths.

Those classes that have used group work time productively have all had some common features:

  • The level of challenge is just right – students want to do the work because they want to find a solution to the problem the teacher poses.
  • There is a balance between letting students spend quality time on a difficult problem, but not letting activities run for so long that attention wanders.
  • Most importantly, the teacher has a good, professional, mutually respectful relationship with the class.

These points are hard as a teacher to achieve, but worth working on when I get to school in September. The last one, particularly, is what I keep coming back to – mutual respect and a professional relationship with the class are absolutely central to good teaching.

Another reflection is that the stuff Swan is suggesting is tough for students too. That’s part of the point of his activities. But if my classes are to have success with strategies like this, I need to scaffold them through Friday skills lessons or similar. Asking students to undertake activities like this when they’re not used to them will take time and effort on both our parts.

Swan: Collaborative Learning