Secondary Maths - introducing probability

Asking a question ‘What is the probability of rolling two fair dice and obtaining two sixes’ can generate all kinds of misconceptions and incorrect answers;  this question reflects the underlying challenges associated with teaching probability theory effectively.
I first observed the brilliance of ZILCH attending a Masterclass for Gifted and Talented pupils based at Bath University.    A unique feature of the game is the ability to generate interest and enthusiasm across the age and attainment range;  a top set year 7 group can be just as engaged as a foundation year 10 group.  The game is played using packs of six dice and ideally the game is played in pairs.  A scoring system is clearly explained as follows:

Scoring 3 Two’s all in one go  =   200 points
Scoring 3 Three’s all in one go = 300 points
Scoring 3 Four’s all in one go =  400 points
Scoring 3 Five’s all in one go  =  500 points
Scoring 3 Sixes all in one go = 600 points
Scoring 3 One’s all in one go = 1000 points
Scoring  1,2,3,4,5,6  all in one go  =  1500 points  
Scoring 1 One  =  100 points
Scoring 1 Five = 50 points

Each player rolls one dice and the highest score takes the first turn.  All six dice are rolled and the scoring dice are placed to one side.  If there are no scoring opportunities consistent with the above scoreboard the player scores nothing – ZILCH – and it is the turn of the next player.  If some of the dice are scoring dice, the player uses intuition and skill to determine whether to ‘stick’ or to ‘gamble’ to improve their score.   For example, the first roll of the dice might yield: 4, 4, 4, 4, 2, and 6

Three fours together score 400 and the player decides to roll the three non scoring dice again with the hope of improving a score of 400 points.   The 4, 2 and 6 are picked up and rolled again in the hope of scoring three of the same number or at least rolling one five or one 1.  If nothing is scored the gamble has not paid off and the player ‘ZILCHES’ thereby losing their score for that turn.
The first player to score 2000 (or more) points is the winner.  

Following a few games of Zilch, the introduction of a Zilch World Cup has generated great interest and it is intriguing to witness that ‘lady luck’ seems to follow certain individuals around, especially in a World Cup Final.  Introducing the ‘Zilch Dilemma’ further enhances the conceptual understanding of probability;  if you have a good score of say 350 points in your first throw, is it best to ‘gamble’ or to ‘stick’ with two dice remaining?  Representing the possibilities on a 6 by 6 sample space diagram illustrates that the chances of a gamble increasing a score is higher than we may intuitively think – 20/36 or 5/9.   The sample space diagram also makes our initial question crystal clear to students;  the probability of rolling two fair dice and both dice landing on a 6 is 1 chance in 36.   Gifted and Talented groups may wish to find the probability of scoring 1,2,3,4,5 and 6 in one throw or the probability of winning in their first throw with an extraordinary throw of six one’s!

Chris Curtis
Curriculum Team Leader for Mathematics

Secondary English - questioning techniques

I’ve been reading about ways of multiplying the learning in the classroom, i.e.making small changes which can have a significant impact on students. Now ‘small changes’ sounds good to me, as at this point in the year I am running out of time to breath, never mind find time to plan more complex lessons. One of these small changes is strangely called ‘Basketball not ping-pong’. This seems at first glance far too sporty for me but actually it requires very little effort- phew!

The idea behind ‘Basketball not ping-pong’ is that some questioning techniques can help learners to explore and develop their ideas in more depth. One of these techniques is for teachers to stop themselves from intervening in question and answer sessions and instead to ask learners to comment on a peer’s answer, so that each learner can build on the ideas of the previous student, maybe exploring what they found useful in the previous answer or adding a new idea to the one just offered. This is called the ‘basketball’ effect and should stop the ‘ping-pong’ effect of teachers asking questions, receiving an answer, commenting on the answer then asking another question. In the ‘ping-pong’ approach it is felt that teachers are doing more work than students and in the ‘basketball’ approach the class will be more engaged and ‘on the ball’ as they are expecting to be included in the feedback.

I thought it was worth a try. I combined it with a ‘no hands up’ approach and after giving my year 10 class time to look at a magazine article on fast food, I started them off with one question, ‘How do the headline and image contribute to the effectiveness of the text?’ Each student then had to add to the last student’s comments, by either developing the previous point, adding another idea which answered the question or commenting on what was good about the previous point. I have to admit that I was surprised by how well it worked. I was expecting it to peter out after about two students but we managed to get through ten students in the class before the run broke down. And if I can get my year 10s to play ball then this can work with any class!

There is still work to do- ideally I would like to get the whole class involved but I guess that, as with basketball, the more we practise this the better the students will get at commenting on and developing each other’s answers.
The most successful part of this strategy is that it forces the students to really listen to each others’ answers. But best of all is didn’t require any time or effort in planning- that has to be good!

Naomi Hursthouse
Advance Skills Teacher
Steyning Grammar School

Primary reading - How will the book end?

My favourite author of all time is Michael Morpurgo and I was fortunate enough to meet him when he opened the new KS1 building in our school.  Last year we did a week of work on Morpurgo.  This was one of our favourite activities (but it could probably work for any author).

Ask the class to select a Michael Morpurgo book and read up to halfway through it. Can they predict how the book will continue and how it will end? This helps children to see the structure in stories, the complications and the resolutions of them. It also enables them to consider other scenarios and endings and many are pleased when on completing the book they find they were correct.

I would also ask older children to consider a change in the chain of events and how that could affect the main character of the book. Some will be able to arrive and their own alternatives but others may need you to say ‘What would have happened if…..?’

Dave Lewis
Portsmouth High School Junior Dept

Secondary Science - Literacy skills in science

The written text for many pupils in science is a challenge.  Science is a process of learning a new language of complex terminology. Problems in coping with this new terminology can greatly hinder progress and enjoyment of the subject.

It is therefore important that science lessons provide the opportunity to develop ‘science and communication’ skills.

Here are some ideas of things that we use within my own department to provide further opportunities for the development of language skills such as:

• Identification of key scientific words in a passage.
• Using different colours on a worksheet to identify scientific words and definitions.
• Using ‘Postits’ to match words and definitions as part of a developmental wall display.
• Describing the scientific content of a paragraph in one sentence and the reasoning behind the whole article in a short paragraph.
• Describing a set of apparatus - use the white board drawing scientific apparatus tool to draw a variety of equipment. 
• Writing an experimental plan using key words.
• Describing the conclusion of an experiment using key words, phrases and conjunctives.
• Making a drawing from a description or vice versa e.g. a specialised human cell. 
• Displays of key words for each year group.
• Viewing a generic video where pupils will be called upon to identify the key scientific words provides an opportunity for pupils to develop literacy skills researching definitions to formulate a dictionary of terms. The activity may also be used to foster class discussion and debate.

Graham Farrall
Cleeve Park School

Secondary Maths - A new approach to homework

Does homework necessarily mean more work?

One of the greatest challenges facing the present generation of students is to find ways of completing all class work and homework on time in the context of the many potential distractions along the way.  In an ideal world, there might be general agreement that a world without homework would be a less stressful world where school work was completed at school and home was a place to spend quality time with family and friends.  However, with the multitude of demands from an enriched curriculum and the pressure to succeed at every level, homework is generally considered essential for consolidation of key concepts and to keep on track in the pursuit of excellence.

Following a strategic meeting with Sue Briggs, former County Mathematics Adviser in Somerset, I have been piloting a new look at the homework issue which takes a more radical view in terms of the purpose, place and procedure for success in the  homework debate.  In the context of promoting Assessment for learning (AfL), my students are regularly given a homework assignment in the form of an A3 sheet of paper or large index card – together with multicoloured gel pens – and asked to create a poster on key learning moments in the understanding of a topic.   Each poster begins with “My poster on....fractions” or “My poster on simultaneous equations”.  Students are asked to make up their own examples and to explain, in their own words, the strategies they use to make progress in this topic area. 

A recent fractions poster full of colour had the following ‘clouds of knowledge’ -  If we add 50 pounds to 30 dollars, we need a common exchange rate, - the same is true when adding and subtracting fractions.   We look at the two denominators and write down the times tables for each one.  The smallest common denominator is used to write fractions so that they can be added or subtracted.  Another part of the poster is adorned with vivid mathematical images, key language and colour;  To multiply fractions is easy – cross cancel diagonal where necessary and then multiply the numerators and multiply the denominators.  To divide fractions – we don’t!  We simply flip or invert the second fraction and multiply – very straightforward!    Each AfL statement is backed up with a colourful example created by the student.

Recent results from this approach have been hugely encouraging, especially from groups where the homework hand in rates were not 100% and, in particular, from students who find mathematical concepts difficult to grasp.  The key aspect has been for students to ‘own’ their homework tasks and to feel that if they did not complete their learning poster or index card then a learning opportunity has been lost.  Students using their own semantic interpretations of the language of mathematics has helped enormous progress to be made in this area.

Chris Curtis
Curriculum Team Leader for Mathematics

KS3 & GCSE English - cover sports commentary in spoken language

If you're looking for opportunities to give your Key Stage 3 classes an accessible and relevant taste of what’s to come in the spoken language element of the GCSE, what better way to do that than to tap into the verbal dexterities (and gaffes) of our sports commentators.

Sports commentary is a mine of verbal treasures: passionate rhetoric; over-the-top exaltations; apt and often extraordinary analogies; sensitive (and insensitive) litotes; dramatic repetitions. And then there are the biased jibes and jokes. Analysing how commentators comment on the action, which unfolds in front of them, could prove to be as unpredictable as the events themselves!

As we come up to summer there's a few games left of the football season to examine, or you could look to spot commentator bias in Champions League games containing English teams and then there's the prospect of Wimbledon and the chance to compare McEnroe’s style of commentary with Becker’s. I will be investigating the ladies’ and men’s matches to find out if gender-bias still exists. The possibilities are endless.

All of these plans rely upon me having to have no specialist sports’ knowledge at all. But hopefully I can play swapsies with my students: they educate me about sport; I educate them about English Language. That seems like fair play to me.

Naomi Hursthouse
Advance Skills Teacher
Steyning Grammar School

Primary Maths - Pizza fractions

Pizzas are great for learning about fractions in mathematics.

Using basic pizzas, cut them up into halves, quarters etc depending on the fractions being taught. You can use them very effectively to do simple fractions or to do mixed or improper fractions. Visually the children can easily identify that seven quarters make one whole and three quarters. They are also very good for doing addition and subtraction of fractions too and if you’re feeling really brave division of fractions where you might have four pizzas divided into sixths so twenty four sixths and share these between six people they’d have four sixths (or maybe visually two thirds) of a pizza each. This makes maths (and the tricky and potentially dull topic of fractions) exciting and motivational for the children and will guarantee that the lesson, and hopefully its objectives, will stay in their minds.

They can also be used in a shape and data extension by asking the children to consider why pizzas are round.


Dave Lewis
Portsmouth High School Junior Dept

All subjects - Making it easy to use technology in the classroom

Would you like to use more technology in your classroom but you're not sure how?  I've just found this great site containing videos showing you how to use different software and online resources in your teaching - and quickly!  Undertenminutes.com gives you simple short video clips explaining how to use tools like Google Pres, Gmail, Corkboard and more in the classroom.

This one shows how a teacher has been using Google Apps Edu Presentations with their students for AFL activities:

How to Google Pres 

This one shows using ToonDo to create a simple, content-rich comic strips with your pupils:

How to ToonDo

Have a look at www.undertenminutes.com for other ideas from teachers using technology in the classroom.  You can do it too!

Julia
The Collins Education blog

GCSE Science - Bad Science is good for schools

What is Bad Science? Well, bad science is when people have misused scientific procedure, such as by cherry picking evidence to prove their case or assuming a causal link by ignoring other factors. However, Bad Science is more than that.

Ben Goldacre is both a doctor and a journalist; he has written a book (Bad Science, published by Fourth Estate. ISBN 978-0-00-728487-0), writes a regular column in The Guardian and runs a website. His mission is to track down and expose, amongst others, “credulous journalists misrepresenting good science for the sake of a headline, advertisers, with their wily ways, and good scientists who have passed to the dark side.”

Now this represents a real opportunity for science teachers. A lot of bad science can be exposed by applying concepts that are covered in secondary school science. Despite what some people might say, you don’t absorb water into your body by holding it in your mouth, you can’t stimulate your carotid arteries by gently massaging your chest and the interlocking of the fingers of both hands doesn’t set up a circuit around which positive energy may flow. There is, however, real opportunity in science lessons by getting pupils to sort out the good science from the bad. It gives them a chance to use their understanding to evaluate assertions and to suggest why some ideas are better founded than others.

Eight of the ideas from the Bad Science book have been turned into lessons for pupils in secondary schools.  Download some of them and turn your students into "Science Detectives"!

Ed Walsh
Science Advisor with Cornwall Learning