Category Archives: General

143. Jumping the gap

The transition from GCSE to A-level Maths is as smooth as can be for some students. Others need the London Underground sign:

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This time last year the biggest issue (amongst many others) was the lack of logic and rigour in their algebraic solutions and graphs. I tried giving model answers (‘Thank you, Miss’, then file it in the recycling …. Grrr!). I tried explaining why it was important (you could almost hear the shutters slide down in most of their heads). I tried sharing the best student’s work on the board using the visualiser (type of document camera), but all to no avail. The majority of students thought they knew best and ignored all advice.

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Now rather than go all Professor Umbridge on them*, I switched things around. They critiqued each other’s work.

Activity

1. You will need an exam (style) question, paper and post-it notes.

2. Ask students to complete the question on a sheet of paper – do not write names on it.

3. Put all the solutions out at the front or stick them to the board.

4. Give each student three post-its. They should write something good and something to improve and stick it on the work. Do this three times.

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5. Each student reclaims their work and reads the notes. They then discuss the feedback and draw up a list of keypoints for improvement.

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That could be the end of it, but I wanted to remind them of the task so:

6. Collect in the work and notes and mount them on half a noticeboard.

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7. In the middle of the board put the question, the model solution and their list of key points for improvement.

8. For the next week or so keep referring to the wall display in lesson.

9. Set another question and repeat steps 2-5. Discuss how their work has (hopefully) improved.

10. Fill the remainder of the wall display with the work and comments.

This could be a useful activity to do at the start and end of a topic. It would also be a good BLP (Building Learning Power) activity.

* Professor Umbridge had a particularly sadistic detention task in Harry Potter, where whatever you wrote on the paper was etched into the detainee’s skin. Vile woman, odd ideas on education.

141. Book(s) of the week 3

If you remember ‘The Wonder Years’ you are probably old enough to remember grunge the first time around and television programmes that didn’t involve so called ‘Reality TV’.

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So what happens to female child stars?

Some have a rocky youth, work really hard and become hugely successful (Drew Barrymore). Some have a rocky youth and become hugely notorious (Lindsay Lohan). Some work really hard, do research, writing and acting, have a theorem named after them and become advocates for women and maths education!

Step forward Danica McKellar!

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Apart from playing ‘Winnie Cooper’ in ‘The Wonder Years’, Danica is also a successful mathematician. She has written four books aimed at promoting maths to high school students, in particular girls. I strongly suggest you have a look at them or get your school library to purchase them as they are full of inspirational ideas and new ways to think about ‘dusty’ topics.

Her books to date are:

Girls Get Curves: Geometry Takes Shape (2013)

Hot X: Algebra Exposed! (2011)

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Maths Doesn’t Suck: How to survive year 6 through year 9 maths without losing your mind or breaking a nail (2010)

Kiss my Math: Showing Pre-Algebra who’s boss (2009)

138. Kandinsky Combinations!

This week I gave a talk to a group of PGCE/Schools Direct associates about innovation and ‘keeping it fresh’. One of my points was you should ‘Keep the good ideas and bin the rubbish/pointless ones’. This is one of my ideas I kept – first used in the late 1990s!

Background
Wassily Kandinsky was an artist, born in Russia in 1866. He died in France in 1944. He is credited with being the first artist to explore purely abstract work. Researching him is a nice homework task which can add to the final work.

Farbstudie quadrate mit konzentrischen ringen

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This work has been reproduced thousands of times -you can see it everywhere from student bedrooms to upmarket coffee shops. The original was completed in 1913. It roughly translates as colour study squares with concentric circles.

Investigation

You will need:
Squared paper (or plain)
Coloured pencils or pens

1. Show the class the painting and discuss how the colours are arranged.

2. How many ways can you colour in one square with one colour? 1

3. How many ways can you colour in two concentric squares with two colours? 2

4. Repeat for three colours and ask for predictions. The usual prediction is 3, the answer is 6.

5. Repeat the process and ask them if they can see a pattern forming. Encourage them to be methodical.

The colour patterns form a set of factorial numbers. Finding out about factorials could be a good extension task.

After the work is completed you’ve potentially got a great wall display, a cross-curricular link to art and an understanding of combinations/factorials.

Variation
This also looks rather cool done with concentric equilateral triangles or hexagons on isometric paper.

136. Quiz-Its

Here’s a simple starter/revision activity. All you need is Post-it notes.

Hand out Post-its as the class arrive.

Once they have got their things out they each write four questions on a topic of your choice. Encourage them to make the questions challenging. Once that’s done tell them they need to write the answer lightly in pencil on the back.

Stick all the Post-its on a table or wall.
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Everyone then collects a Post-it (or Qwiz-it) to answer (not their own).

Once they’ve answered, they can check their answer. If the answers don’t match, who is correct? Why?

This can lead to discussions about question-style, methods, misconceptions and understanding.

135. Book (& Website) of the week 2

If you are on Twitter, you may have heard of the perfectly titled @MathsBookClub. If not, let me explain.

People were asked to nominate their favourite Maths related book (Fiction or Fact).

People voted and the most popular was chosen.

The winner was: ‘Alex’s Adventures in Numberland’ (‘Here’s looking at Euclid’ USA) by Alex Bellos.

Just like a “meet down the pub bookclub” there will be an online discussion on Wednesday 23rd October. Except with this bookclub, the author has offered to join in! Very cool!

To join in the mathematical literary fun either follow @MathsBookClub on twitter, visit the mathsbookclub website or do both!

(Support your local Library. If that’s not possible then click on the book for a link to the paper version on Amazon.co.uk; ebook also available)

133. Smart Research

Teachers often get students to do research homework for one of two reasons: to increase independent learning and develop an inquiry mindset or as an easy homework to set/mark.

Pupils often see research homework in one of two ways: as an opportunity for independent study and to find out cool facts that no-one else will find or as ‘None set’ – the teacher won’t check it and if they do there is the excuse that the computer wasn’t working, the printer had run out of ink, the internet went down or it wasn’t their classes day to use the school library.

How can you change this mindset?

Over the years I’ve set this type of task with varying degrees of success. Conscientious pupils write/type a short essay, with diagrams if appropriate – you could put it straight on the wall to be admired. Others print out webpages or copy a couple of lines from the internet/textbook/friend. Then there is the woeful list of excuses brigade …

This time I changed one thing in the task and I was frankly amazed: 100% successful completion. The change was so simple – how it could be done.

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I asked them to research letter frequency analysis. Some wrote a page in their book, some took a photo of a page from a book, some did a printscreen and others bookmarked a website. Three of these four formats involve the use of smartphones. Unless your school has draconian rules on mobile phone use in the classroom, this is a good way to engage pupils. It promotes responsible use of technology and prompted discussions on how they’d searched to get their result.

All I had to do was walk around the room and let them show me their homework while they did the follow up task. Cynics might say that they could quickly do their homework before I got to them – this is a valid comment, except the ‘Usual Suspects’ came into the room waving their phones, desperate to show me their work!

BTW I was rather amused when one of the pupils showed me a screengrab of this blog – he didn’t have a clue that I’d written it.