Category Archives: teaching

Seven Personal Highlights of 2016

Politically, 2016 was a terrible year, what with Brexit and Trump. I didn’t want to write a depressing, negative round up of the year so I am writing a more personal post about some of the high points  for me – things I’ve done and places I’ve been.

  1. Summer holiday in Majorca. We went on our usual all inclusive week in the sun, where the children can eat as much ice-cream as they like, and I can drink as many watered down cocktails in plastic cups, and nobody has to do any cooking or housework. The highlight of the week was a visit to the Caves of Drach which was memorable and spectacular and included a concert in a cave with the musicians floating on a boat. Well worth a visit if you’re in the area. 
  2. My mum’s 80th birthday. It’s not every day you turn 80 and my mum threw a great party for family and friends featuring a drumming workshop. My mum really knows how to live! I made a giant birthday cake which was intended to be covered with raspberries until I realised how much raspberries cost in October. 
  3. I asked a question on Question Time! This has to be my absolute highlight of the year. I was very lucky to be selected to be in the audience because about a thousand people applied and they only chose 150. Then I was even luckier to have my question selected as everyone submitted a question but only about four were used on the show. It was so exciting and for a long time afterwards people came up to me and said they saw me on the show. You can watch me ask my question here. Please do watch the whole of the clip as the ensuing discussion is very good, especially Ken Loach’s contribution. 
  4. Christmas in Italy. I managed to find cheap flights with Ryanair so that all four of us could fly to Italy for a week over Christmas for less than  £200. We stayed with my husband’s sister in Merano which is a pretty town near the Austrian border. We were hoping for snow but sadly we were disappointed. The boys got to spend time with their cousins and I got to drink plenty of the local vin brulé. The best  bit of the week was a visit to the thermal pools at the Hotel Terme. We sat in a hot, bubbly pool watching the sun set behind a mountain. A fantastic way to end the week. 
  5. Getting a grade one in my teaching observation. Just about every time I’ve had a graded observation, the observer awards me a grade 2 with aspects of grade one. I am always told that my lesson would have been a grade one if it hadn’t been for one little thing that they made up that means I am merely good and not outstanding. But in my latest observation I finally achieved that elusive grade 1 which I guess means I am officially an outstanding teacher.
  6. One of the most memorable family outings of the year has to be our trip to Birdland at Bourton on the Water. This is where my 9-year-old’s obsession with penguins began. 
  7. Association of Teachers and Lecturers Annual Conference. This is a fantastic event held every year in Liverpool. This year I was chosen to be on a panel of ten people to meet Nick Gibb, the minister for schools and ask him questions. We gave him a good grilling. 

Four Ways to Use Your Learners as Equipment in Maths Lessons

 

I cannot take the credit for these ideas; I got them from an excellent session run by John Suffolk at the Association of Teachers of Mathematics conference. John explained that it is a good idea to use your students as equipment because then you don’t have to carry the equipment around from one classroom to another. Another advantage of this kind of teaching method is that taking an active part in the lesson, rather than just listening passively, helps students to learn.

  1. Learning about multiplication tables, factors, and prime numbers. Ask ten students to stand up. Can they get into a solid rectangle shape? (5 x 2) Can they do it a different way? (A long rectangle 10 by 1). Now ask two more learners to stand up. Now how many different rectangles can they make? Now ask a thirteenth person to join in. What happens now? Why is this?

2. Sum of the angles in a polygon. Three students form a triangle. A fourth student moves around the inside of the triangle, being gently  guided by the three corners to make sure they turn through all the angles. When the student returns to where they started, they will be facing the other way because they will have turned through 180 degrees. Now try with a rectangle. What happens now? What about other polygons?

3. Algebraic Graphs. This requires a big space. A playground would be ideal. Mark out the x and y axes, either with chalk or with cards. To start with, each student stands on the x axis and they are told their x value according to where they are standing (x = -2, x = -1, x = 0, x = 1 etc.) and they all hold onto a long piece of string. You can give the more able students the negative numbers for differentiation. Then you give the students an equation such as y = 2x – 1. Each student has to move to the correct position. They should note what shape they make – a straight line for a linear equation and a curve for a quadratic. You can even solve simultaneous equations in this way – use two groups of students and two pieces of string. The point where the two strings cross over is the solution to the equations.

4. Loci. This is best done outside where there is plenty of room, but can be adapted for the classroom. Ask the students to stand approximately two metres from you. Ask them to note what shape they are making. (They should be roughly standing in a circle.) Now if you have two trees nearby, ask them to stand so that the trees are equidistant from them. You could also use two chairs, two students, or any other objects. What shape are you making now? The students should be in a straight line. This activity can also be used to show the loci of all points a certain distance from a straight line (just draw a line on the floor), the bisector of an angle (stand so that two walls are the same distance from you). Perhaps you can think of others.

Seven Reasons Why I Hate Graded Observations

This week is the dreaded observations week in the English and Maths department. Everyone hates observation week. Here’s why.

1. It’s so stressful! We find out on Monday morning that we will be observed at some point during the following week. This means we are in a state of anxiety for at least a week and possibly two weeks. I teach about twenty lessons a week and I could be observed in any of them. My anxiety levels rise just before the start of each lesson and then I relax again when it becomes clear that it won’t be this lesson.

2. It literally gives me nightmares; a few nights ago I dreamt I was in a huge open plan classroom with teachers and students all over the room, tucked away in corners and behind curtains, and I didn’t know who I was supposed to be teaching or what I was supposed to be teaching them.

3. It’s so subjective. We don’t know who is going to observe us until they turn up at the classroom door. It could be a subject leader or head of department from any department in the college. Although in theory they are all using the same criteria, there is bound to be subjectivity. Will they even know what an outstanding maths lesson looks like?

4. The outcome affects our pay. If I don’t get a grade 1 or 2, I won’t go up a point on the pay scale this year. That seems unfair when I might be observed with a lovely, compliant, enthusiastic class or it might be a group of unruly reluctant learners. (Thankfully I taught my big group of boisterous rugby boys today and I wasn’t observed!)

5. It wastes so much paper. Normally my lesson plans are kept digitally, but in observation week they must be printed out to give to the observer along with a scheme of work, class profiles and other paperwork.

6. It wastes so much time. Teachers spend hours writing lesson plans in minute detail, remembering to indicate where they have embedded English, maths, Equality & Diversity and now also British Values.

7. It does nothing to improve learning or teaching. Even a bad teacher can pull it out of the bag for one week and then go back to teaching badly the following week. And good teachers teach well whether or not they are observed once a year. There are better ways of improving teaching than stressing teachers out for a week.

So wish me luck. It is Tuesday evening now and I haven’t been observed yet but it will happen at some point over the next three days.

Four Christmas Maths Activities

Here are some Christmas maths ideas for all of you who are maths teachers or who just like doing maths.

  1. This picture shows two Christmas tree shapes. The first shape has eleven corners. How many corners does the second shape have? How many corners would the 11th shape have? Can you write an expression for the number of corners on the nth shape? Would there be a shape with 100 corners?P1090213
  2. Santa is buying clothes for his elves. He has trousers, jackets and hats in red, blue and green. He wants all the elves to be different. How many combinations of the three items of clothing can he make with the three colours? (They can have two or three items the same colour.) What about if he had some yellow clothes too? Elf Clip Art
  3. There are approximately two billion children in the world. If Santa has to give each child a present in 24 hours, how many presents does he need to deliver each second?
  4. My friend collects toy cars. They come in cube shaped boxes with length y cm. I have bought her 32 of them for Christmas and I want to wrap them. What will the surface area be, in terms of y, if I wrap them individually? I could wrap them all together in a cuboid shape to save wrapping paper. How many different ways can I put 32 cubes together to make a cuboid? Which way would give me the smallest surface area? What would the surface area be?

 

One Hundred and Twenty Reports to Write

i-love-mathsI have committed myself to writing a blog post a day for the whole of November for National Blog Posting Month. Today is my 29th blog of NaBloPoMo but I really have other things to do that need my time. I have to write a report for each of my 120 students.

I am  a maths teacher. I teach GCSE maths in a Further Education college to students who failed their GCSE maths when they were at school. I love mathematics and I love my students but I sometimes find my job disheartening because my students do not love mathematics, no matter what I do to share the love with them. I spend hours looking for new ways to teach maths that are different  from the ways they were taught at school, because the ways they were taught at school didn’t work for them. I enthuse about the beauty of mathematics. I show them awesome visualisations like this one.  I tie them to the table leg and make them walk round the table to teach them about loci.

But they moan and say that this won’t be on the exam paper. They just want to do past papers.

What they really want to do is go out on their horses or their tractors, or go and play rugby or football. They went to college to study agriculture, equine or sport, not maths. They already feel like failures because they failed their maths. Now they have to sit in a classroom and do maths while their friends who passed their GCSEs are out on the football pitch. They hate my subject and they are not too keen on me either since I am the one making them study it.

And now I have to write a report with a positive comment for each of my students. It’s going to take up a lot of my blogging time!

Here is an excellent article explaining why my job is so hard.

 

 

 

Six Things that Maths Teachers in Shanghai Do

Teaching for Mastery

I was privileged today to observe a maths teacher from Shanghai teach a maths lesson to a year 7 class in Cheltenham. This was organised by the GLOW Maths Hub for teachers from Gloucestershire, Oxfordshire and Worcestershire. After the lesson we talked about some of the differences and similarities between maths teaching in Shanghai and the UK.

  1. The answer is only the beginning. In Shanghai, maths teachers put more emphasis on how a student arrived at the answer, rather than the answer itself. Students are encouraged to discuss and explain their reasoning and their methods, thus deepening their understanding and clarifying their ideas.
  2. Variation in examples and representations are used – pictures, numbers, diagrams, and symbols.
  3. Mistakes are encouraged. “Mistakes are good for us,” says the teacher, “because we can notice something and avoid doing it again.”
  4. Homework is set every day to practise and consolidate learning. Because this is done every day at home, it means that all the time in the lesson is used to introduce, discuss and explore the ideas rather than for mechanical repetition.
  5. Teachers introduce “wrinkles and confusion” into their lessons – deliberate mistakes which address common misconceptions and explore the students’ understanding.
  6. Key ideas and rules are repeated and recited by the whole class. “Keep the denominators the same and add the numerators,” they chant.

For more information about the work of maths hubs click here.

 

Three Maths Problems to Tease Your Brain

After work yesterday afternoon I went to a Teach Meet – an event organised by the local Maths Hub for maths teachers to meet and chat and exchange ideas. This meet was on the theme of problem solving – a topic which is gaining importance in the curriculum. People who know me know that I love a good Professional Development event – a chance to meet other maths teachers, talk about maths and eat cake. Yesterday afternoon’s event did not disappoint – and neither did the cake. I also love a good maths problem, so here are three problems from the event.

  1. There are five single digit numbers. Their mean, median, mode and range are all the same. What are the five numbers?
  2. ABCDE x4 = EDCBA (where ABCDE is a 5 digit number) what digits do the letters represent?
  3. The 24 Game. Using all four numbers 4, 6, 6 and 8, but using each number only once, there are over 60 different ways of getting the answer 24 by adding, subtracting, multiplying and dividing. How many can you and your friends find? You can try it with different numbers – some websites will randomly generate four numbers for you, time you, give you a score, and cool stuff like that.

Here are 3 websites where you can find lots more challenging maths problems. These websites are great for parents, teachers, home educators, or for maths geeks who just enjoy spending their spare time doing this stuff.

  1. Transum
  2. Nrich
  3. Mathsticks