Oracy in Maths

I looked at how to develop oracy strategies in Maths after some feedback from a colleague after a peer observation. I always thought that letting students discuss their work and careful questioning was enough oracy in my class, so I began to think how I could provide more opportunities for discussion. I tried a couple of things, like putting a question up on the board and asking them to think, pair, share their ideas on how to start the problem. This was a simple way to introduce opportunities for talking and worked relatively well. I got a bit stuck as to what else I could do, but then I went on a course specifically on oracy in Maths and Science by Voice 21 and now have several more tried and tested strategies that I have used in my classroom. Here are some of my favourites:

1. Discussion Points

Before starting a topic, make a statement for the students to decide whether they agree. If you carefully design the statement it can cause disagreements and bring out misconceptions. You must go round and listen to what the groups are saying during their discussion time. Assign groups and roles if you wish, my favourite role is a silent summariser who sits and listens to the discussion making notes and then feeds back to the class what their group thought. You can then go on to teach and practice a skill before coming back to the discussion point as a plenary to see whether they have changed their mind.

EXAMPLE: An example might be “angles in any polygon add to 360” which I would ask at the beginning of the lesson, give students no more than 5 minutes to discuss and get general feedback with a vote of who agrees before any teaching. I would then teach angle sums in polygons, investigate and generalise a formula which the students then practice. I would then come back to the discussion point at the end of the lesson to conclude the learning as a plenary.

2. Cartoon Concepts

Similar to discussion points, you can have a question or statement in the middle with several different opinions around the outside (including misconceptions). The students can then identify which opinions they disagree with quite easily. It is more difficult for them to pick out and justify who they agree with the most. You can provide a grid to help structure their discussion and help them develop their arguments by collecting evidence.

EXAMPLE: This is an example of a concept cartoon I created to introduce order of operations. The table was used to help guide and focus the students discussion and help them structure their feedback to the class. I gave one table per group and whoever had the table was the ‘silent summariser’ who made notes on the group discussion but was not allowed to contribute. The silent summariser was then the only student in the group allowed to feed back at the end.

3. Grouping Statements or Questions

Give students statements in groups to organise into three piles: always true, sometimes true and never true. This promotes discussion and encourages students to challenge each other’s thinking. Giving a range of different questions and asking them to group them without giving categories promotes discussion of what is similar and what is different, sometimes different groups will categorise them differently. Also asking students to rank statements or questions based on importance, difficulty, how many marks they think it is out of. Alternatively asking which is the odd one out, using questions, diagrams or graphs - https://nonexamples.com/ contains some examples of spotting the odd one out.

4. Non-questions

If you give students a diagram and ask them “what could the question be?” first, the students list as many different questions as they can based on the diagram ranging from obvious up to extremely challenging maybe even impossible questions. I'm always amazed by some of the questions the students ask, often asking some you would never have thought of yourself. Working in groups they can then explore whether their questions can be answered. If their question is impossible (or they don't yet have the knowledge or skills to answer it), they can explore what else they would need to know to be able to answer it. They can then feedback one of their questions (and potentially their answer to that question) to the rest of the class. There are lots of freely available resources, such as http://goalfreeproblems.blogspot.com/ the home of Goal Free Problems but any question can be adapted to be open ended for discussion by removing the question (usually the final line in an exam question) and instead writing “what other information can you tell me?”. I’ve done this as homework, where students have time in lesson to discuss the problem and make some notes. Then they independently write up on no more than one side of A4 what their group discussed and what conclusions they came to – this ensured everyone was part of the discussion and they had to listen to each other.

4 Top Tips on Hinge Questions

4 Top Tips on Hinge Questions

I studied hinge questions for my masters dissertation project. Most of my project was based on Dylan Wiliams work on hinge questions. A hinge question is asked before half way through a lesson, every student answers and the teacher responds within 30 seconds. As the name suggests, the response to the question determines the direction of the lesson, reteach, practice or move on. You can use them at several stages to determine understanding and you can layer them to separate students into various levels of understanding.

Here are my 4 top tips for an effective hinge question:

1.      Use multiple choice

You need to gather answers and process them quickly. The best way is to offer multiple choice. It also means that you can give students options with common misconceptions, which leads me on to…

2.      Plan carefully

Hinge questions shouldn’t just be flung into a lesson unplanned. You need to design them carefully to check student understanding. Think about what pitfalls students might fall into and incorporate that into your question. You need to see and process every students answer, mini whiteboards would be good if you want to see their working (remembering that responding quickly is important, so you might not want all their working). Multiple choice can be collected quickly using voting pads, raising hands, showing coloured cards (I get mine to use their planners as they have red, orange, green, purple and white pages meaning I can have up to five multiple choice answers).

3.      Timing

Ask at the start of the lesson to determine what they already know, ask after teaching to see how much they have understood, ask at the end of the lesson to see if you can move on next lesson. When you ask your question, it must tell you something about where the students are and how you can get them to where you want them to be. The timing will depend on the purpose, and although initially research suggested before half way through the lesson, if your purpose is to determine prior learning why not ask before any teaching? Or if to summarise learning, why not at the end of the lesson? It goes back to tip #2.

4.      Have options to follow up the hinge question

So, my students understand. Do I waste time practicing the skills or do I move on to some problem solving? They don’t understand at all, do I reteach it or expect them to be able to practice? Or what if some get it, some sort of understand and some of them are totally stuck? You need to know how you are going to move forward with the lesson and prepare for every possible outcome. One thing I did was prepare a single resource based on every outcome, with a modelled solution followed by structured questions for those who are still struggling at the top of the worksheet, unstructured questions with scrambled answers at the side for those still a bit unsure, and problem-solving questions and rich open-ended tasks or investigations for those who have a good understanding of the topic. This meant students could move down the sheet as their confidence grew. You can also get a small group or individuals to work with you at the front if they are still really struggling.

Strategies to Develop a Growth Mindset

Strategies to Develop a Growth Mindset

Our school has had a strong focus on mindset for a while. We praise effort over achievement and champion the idea that those students who work hard will ultimately be more successful. Ana Castillo loaned me Carol Dweck’s Mindset book when I started at school, and I immediately identified the biggest barrier to learning in my classroom was students having a fixed mindset in Maths. I then started reading Jo Boaler’s work and based my CPD project on what I read, trying to develop a growth mindset in my classroom.

Here are 5 things I did:

1.      Focused on Effort

This is something school does well anyway, but when marking books I only ever made comments about effort rather than work (other than suggestions for improvements obviously). I would also shower the students showing excellent or improved effort with rewards, merits, postcards and phone calls home. I had a star of the fortnight too, where I would take picture of someone’s classwork who had put excellent effort into a lesson so other students could see what excellent effort looks like.

2.      Championed Mistakes

Mistakes in Maths are inevitable and probably what students are most frightened of. I created a culture that mistakes are brilliant if we learn from them. I would make mistakes myself to show it was human, I would give wrong answers and get students to analyse what was wrong and what the corrections should be, I would pick out students work who had made a mistake and show it under the visualiser to discuss with the class (then thank them for letting us all learn by sharing their work and give them a merit). I even started a display of “Our Favourite Mistakes Learning Opportunities”. A starter task I would use was “favourite no” where the students anonymously attempted a question, I’d sort them into “correct” and “wrong” piles, then look at some of the wrong answers under the visualiser comment on what was good but then highlight where students went wrong. This was great to see what students knew too.

3.      Taught them about Growth Mindset

I told them about how effort was fundamental to making progress. I discussed students I had taught previously who had been successful because of their effort (obviously not mentioning names). I did assemblies with examples of successful people, including staff, who had overcome difficulties to become successful at something. I used a lot of the information from Carol Dweck and Jo Boaler’s books to give reasoning behind some of the things we were doing. Unsurprisingly, if you explain the benefits students are more likely to get on board (although this was something I wasn’t very good at doing beforehand).

4.      Changed my Language

Again, linking back to #1 being careful to praise effort over attainment, so praising a student for working hard or improving rather than praising the one who always gets full marks without really trying. Moving away from talking about work being hard or easy, not labelling students or grouping them by ability. It was important to speak positively and challenge students showing a fixed mindset, when students said “I can’t do it” or “I don’t get it” remind them that effort is vital to be successful, I then would always say “ask me a question” and leave them to think. Then they would sit and carfefully think what the problem was and ask a specific question to move their understanding forward, having a ‘lightbulb moment’.

5.      Students Chose Mindset Posters

I selected a couple of different mindset posters and showed them all to the students, asked them which their favourites were, printed them and stuck on the wall to refer to them in lessons. As they chose them, it was powerful when a student said they couldn’t do something to point at the poster.

5 Live Marking Strategies

5 Live Marking Strategies

We were given freedom to choose our topic for our triad work this year, I picked immediate feedback which to me meant questioning and assessment for learning. However, my triad interpreted the topic differently, and thus my journey with live marking started. I researched what it was, it was surprisingly difficult to find anything outlining the actual process, but I understood it to be marking students work in lessons rather than afterwards. The triad set out with ambitions of a line of students like at Primary school and you mark their work and get to speak to every student every lesson. We soon realised that wasn’t feasible, nor is it beneficial for teacher or students. There was lots of reading about the benefits of live marking, but here are five things I tried and found useful:

1. I marked every student’s book every lesson

I only managed this with my small year 10 class. At most I have 11 students in the group. They can lack motivation, and they all lack confidence. Going around with a red pen and sitting marking with them boosts their confidence and keeps them motivated, as I visit them numerous times during the lesson I can monitor the effort they are putting in and spot misconceptions early. I can set work targets and make my expectations clear. Students were asking me to come mark their work, and when we go through work altogether on the board students in that class wouldn’t be focused or mark their own work, so me going around with a red pen really was beneficial for the students. It works well for that group and I wish all groups were that small so that more classes could benefit. I tried it with bigger groups, but it didn’t work the same. It became more difficult to monitor students behaviour and effort as I was distracted and there were too many students to manage them in this way.


2.  I marked under the visualiser

I did this before our triad work, but normally I would write out answers on worksheets or on the whiteboard as we went through them, questioning different students. This year I tried marking students work under the visualiser instead. I worried about getting students to volunteer their work as I know some students worry about getting the correct answers. Last year I spent a lot of time working on Mindsets in Maths, and I developed a lot of strategies to help overcome this kind of issue. Championing making mistakes as you learn from them, making mistakes myself to show them it is human, discussing mistakes to see why they were made and having a good conversation as a result. Also students who volunteer their work get merits for being brave, and most students want to be brave and get merits! Looking at their work did wonders in terms of discussing what is good about it and reading through, checking their working. It also gives me a chance to praise good presentation and for students to see what good presentation looks like. The student whose work is being marked benefits from direct feedback, but the students in the room also benefit marking their work from me marking their peers. There are still some students who are reluctant to get involved, I’m yet to pick their books but I think I will keep an eye out for a task they have done well on first. Younger students tend to be more outgoing, older students tend to be more private with their work. One of my colleagues had done research on disengaged boys and found live marking boys work engaged boys in lessons. I am looking forward to developing this further in the next half term.

 
3.  Favourite no

This is something I used before, I think it falls into the category of live marking. I found I was doing a fair bit of live marking anyway, it was just nice to focus on developing aspects further. I would normally ask a question and get students to answer anonymously on a piece of paper. I would collect all the answers in and sort them into piles under the visualiser. One pile of correct answers and a pile of incorrect answers. Then I would look at some of the incorrect answers to discuss the misconceptions. I always start with “what is good about this one?” before then going on to discuss where the student had gone wrong. I would then pick out a correct answer to show how it should be done. I love this technique because even with my class of 32 I can collect their answers and sort them in 2 minutes, I know how many students know how to do it, I can see how far away the rest are. Students are happy to do it because it is anonymous, I encourage them to start the question and get as far as they can even if they can’t finish it- there is no pressure because the paper goes in the recycling.


4. Early finishers become markers

When a student finishes the task early, I sometimes ask them to go around with a “Numeracy Leaders” badge and help anyone who puts up their hand. This works well for students who for some reason don’t like bothering the teacher and the obvious benefits of peers explaining to peers. However, I recently tried marking an early finishers work and then sending them round with a red pen and a numeracy leader badge to mark others work. Another student finished not long after so I had two students marking the rest of the student's work and giving feedback – a bit like I do with my small class but making in more manageable by creating more markers!


5. Put the answers on the wall

Another suggestion by a wonderful colleague (thanks Maddie!). If you put the answers on the wall and let the students know, then they can go check their work at any time. Students who aren’t confident can go check they got the first answer correct, and every other if they really need to, immediately after doing it. It means they spend more time practicing and less time panicking if they are wrong or waiting for me to check after every question. It also means students who finish can go check their work as soon as they finish, they can identify if they got any wrong and check their work, then ask you for help if they can’t see where they are going wrong. It gives students independence and frees you up. I’ve done similar in the past by putting answers on the back of worksheets or muddling up answers and putting them in a box so they can see if their answer is there (immediate confidence boost if it is, hand up to ask for help if it isn’t). Students are more willing to try. I find Mathsbox settlers are really good for this too.

Celebrating National Numeracy Day

Big Numeracy Day Plans:

I asked the leadership team at school if I could get involved in the first ever National Numeracy Day (see https://www.numeracyday.com/) and they were very supportive in giving me the go ahead. My aim was to raise the profile of numeracy around school and enable students to see how they use numeracy skills in other subjects as well as trying to make links with real life. So with a couple of weeks planning, here’s what I did:

1.       Daily Puzzles in our Student Bulletin in the lead up: To get students curious and generate a buzz, for two weeks leading up I had a daily puzzle for forms to have a go at. I was bombarded with questions and comments from both students and staff from the first entry (see below) – success! A buzz was generated. Also I managed to sneak a Star Wars themed puzzle on May the 4^th (be with you).

2.       Form Time Quiz: The day before Numeracy Day, the students took part in a form time quiz with some information about what would be happening on National Numeracy Day. All the solutions were provided, it started easy and got tougher so was suitable for all year groups (year 7 could do the first ten and then stop, year 10 could go all the way through).

3.       National Numeracy Day itself: I asked my wonderful colleagues to get involved by doing some numeracy in their lessons that day, and to entice participation I ran a staff raffle, so the more often they managed to do numeracy tasks with their students the more entries they had in the raffle. To encourage students to participate, I held a student raffle. Staff were given tickets to fill in for their nominated students who were most engaged in their numeracy tasks. I had some numeracy leaders with badges just like staff or visitor badges specially made for the occasion. The numeracy leaders were given instructions to be my eyes and ears (unfortunately I was teaching most of the day!) and I gave them forms to fill in (see below), they visited classrooms, interviewed students and filled in the information so I could gather information about what had gone on around school. They pretty much ran the event for me, and I wouldn’t have been able to do it without them!

How did it Go?

Numeracy in Other Lessons:

I suggested some ideas beforehand in our staff bulletin, and I spoke to several departments when I couldn’t think of anything myself. All departments seemed to have some ideas of how they could support National Numeracy day in their subject, but I wanted to make sure I had ideas up my sleeve just in case they needed any suggestions.

Here are some of the amazing things our staff did (what I have managed to find out so far at least!) you will have to forgive if I have missed details or over simplified what actually happened, I couldn’t be there as I was teaching so this is all based on my Numeracy Leaders accounts:

·         Maths

I really do have to talk about Maths first, I was initially split in two about whether I needed to do something special or not. Surely in Maths we develop numeracy skills every day? But then surely also as someone who is asking people to adapt their teaching for the day I should lead by example? So I did think of what I could do to make a deal out of it in my lessons. I decided to do several long multiplication and division questions. I find I rarely spend time on these basics as we are looking at several other areas of Maths and have so much to get through, it was nice to go back to basics. To add a twist when going through the answers, the students timed me using a big stopwatch on the board as I raced through the questions as quickly as possible, while the students cheered me on/tried to put me off! It was great fun and I made a point about discussing how I wasn’t that quick and accurate when I was their age, but it has taken lots of practice. I also emphasised the importance of confidence in these skills given there is a whole paper at GCSE they must do without a calculator.

·         Science

Science naturally lends itself to Maths anyway, so our Science department had plenty of ways to get involved. Year 9s were measuring their pulses and plotting some graphs with the data they had collected, as well as practicing substituting into energy

equations and calculating proton, neutron and electron numbers. They were also doing practical work collecting their own data, including sampling populations with daisies outside (which students always love!).

·         Technology

A fantastic department supporting National Numeracy day in plenty of different ways. Food tech were looking at recipes and measuring ingredients, electronics were looking at  potential dividers and calculations involving watts and volts, studying ergonomics. IT were looking at statistics involving social media. Again I was pleasantly surprised to see how much numeracy happens in all the different technologies!

·         MFL

The wonderful colleagues in MFL had the students enjoying performing calculations in French and Spanish! The students were really positive and had loads of fun!

·         Drama

Drama were looking at designing sets and how they can make scale designs of their sets to later design and build, as well as role playing different scenarios in which numeracy skills are used such as an exchange of money when someone is buying and selling in a shop.

·         English

I struggled with English when I was in the initial stages of planning and talked to our not so secret amazing Mathematician who also happens to be the head of English. He came up with the idea of discussing the Monty Hall problem after reading an exert from The Curious Incident of The Dog in the Night Time with his classes who then did the experimental probability to test the theory. Also several of the teachers were using Venn Diagrams and other graphs to compare and contrast different poems and stories. Some even managed to wedge some numeracy in by designing storyboards, where students had to measure the page, divide into even boxes and accurately draw the structure before they did their storyboards – amazing!

·         History

There were comparisons between dates and looking at differences between different times, including looking at pricing from Victorian times compared to current. Some comparisons of how populations have changed over time, discussing the capacity of Olympic stadiums. I was impressed the different angles teachers had come from in introducing their numeracy element!

·         Geography

Having studied Human Geography myself at university, I knew Geography was yet another subject which lends itself well to Maths. The wonderful Geography teachers were taking averages from climate graphs and using them to compare the weather over various months. This involves so many skills, reading information from tables, finding averages involves lots of arranging, adding and dividing, them using the information to compare shows why finding averages is useful in the first place and how it can be used in real life.

What would I do differently?

I am thinking next year to run things fairly similarly as I think it went pretty well. Staff will have ideas from this year and maybe more for next year. I think I need to get more information about National Numeracy across to both students and parents, as parents may well benefit from some of their fantastic resources. I am thinking maybe putting something on the school website and giving some information in assemblies- one of my colleagues did an assembly on National Numeracy Day the day before which helped raise the profile of the event for that year group. This is definitely something I would consider for next year, maybe see if the numeracy leaders want to be involved.

Also I would try to incorporate more fun ideas at break or lunch, for example I could have times tables against the clock or beat the teacher at break or lunch time. More ways to create buzz and maybe give the day a more fun tone.

Speed Exam Questions

You will have to excuse my poorly constructed example question, but I’ve noticed a lot of speed, distance, time questions of this nature:

“Sophie travels 90 miles from Manchester to Birmingham. Altogether the journey takes her 1 hour 40 minutes.

Aside from 20 miles of roadworks on the route, her average speed was 70mph.

What was her average speed through the roadworks?”

Initially my current year 11s wouldn’t attempt a question like this, too many different numbers and not the expected (more straight forward) “a train travels 120km in 4 hours, calculate the speed”.

In one question I saw a diagram which helped break the question down, and now I encourage all my classes to draw a simple diagram to model the problem:

It is basically a straight line split up into different ‘legs’ of the journey (in this case two different parts of the journey roadworks and no roadworks) and then write out “s=“ “d=“ and “t=“ for each leg of the journey.

They fill out the bits they know and then it is clear the bits they need to find out. In my example, the distance with no roadworks can be found by total distance subtract 20 miles of roadworks, then the time can be found using speed and distance:

Then they can find time taken through roadworks to find the average speed:

I find this can be applied to most speed, distance, time questions and as soon as my students get a more complex question like this adding the structure highlights what needs to be calculated in a student friendly way.

Any other suggestions on how to tackle some of the heavier, more complex exam questions the students are now facing?

“I Don’t Know How To Revise!”

“I Don’t Know How to Revise!”

With GCSE’s looming (19 lessons left before paper one!) Easter is the perfect time for students to get some serious revision done. Regularly I hear students comment “I don’t know how to revise” or worse “I don’t revise!” and simply suggesting and showing them some ideas and giving them freedom often results in no revision being done whatsoever. When you are asking a student to “go and revise” it is a massively daunting task and often students don’t know where to start!

So this Easter (as well as three papers!) I’ve handed out a revision checklist. It’s very simple to create and they are not exactly ground breaking, but the impact of using them should never be underestimated.

I selected topics I knew my students needed to work on and inserted them in the first column of an excel spreadsheet. This in itself is powerful, cutting down the mass of topics to a smaller, more manageable and focused chunk. You can even make personal lists for individual students or for groups of students with different targets.

Then along the rows I suggested different tasks they could do to revise each topic, for example our school subscribes to several online resources so each resource had tasks within it on their own row.

The students can then check off topics they have looked at by completing the different tasks. As there are several suggestions of tasks for each topic they can even interleave their revision and make sure they come back to topics again using a different resource.

It is one of the simplest and quickest resources I have created as a teacher, yet it powerfully enables students to focus their precious time on to the type of revision you want them to be doing. As they tick off various tasks it will help them feel productive and build positive and productive revision habits.

I have even given my year 9s the list in a hope that they have more time to improve their revision habits so when they reach year 11 it won’t feel like such a daunting task!

Let me know if you have any tips for Maths revision strategies for students!