Book Review - 1089 + All That by David Acheson

David Acheson has written an excellent little book about a journey into mathematics. This book is an ideal read for any teacher or student. It is an excellent holiday read to maintain and top up mathematical knowledge. 1089 is written in short passages, making it easy to read but doesn't shy away from some relatively complicated mathematics and contains some gems of mathematical insight. Amazingly, this small book deals with a whole range of topics from pi to chaos theory.

Online Markbook

Online Markbook

I have been developing my markbook online. See a blank version here. I prefer an online markbook to a paper copy because it allows me to edit and move things around easily. I have a separate markbook for each class.

The markbook has been divided into 11 sections: Seating Plan, Information, SEND, Marking, Homework, Mymaths/Sam Learning, Assessment, Intervention, Medium Term Plan, Postcards and Parents Evening. I don't record a register on the markbook because the data is collected elsewhere. Data is also collected separately centrally on a department tracking sheet. Therefore, the purpose of this markbook is to allow me to stay on top of classes by providing me with information needed to teach and most importantly to make notes so I can monitor individuals and classes as a whole.

Most of the sections are self explanatory. This year, I have added an Intervention section. In this section, I record all interventions for each of my classes. Examples of these include behaviour incidents, contact with parents or other members of staff, any concerns or worries I have about individuals, positive news/rewards. The outcomes is crucial to this intervention page. Here I record what has happened since the intervention eg has an individual students behaviour/attitude/performance improved? I have found this to be extremely useful, because it allows me to look back and see how individuals have responded and hopefully improved. Every half-term, I also write a quick class report. This allows me to reflect on the progress of the class and individuals. 

For the marking and homework, I use a very simple colour scheme. Green for good, Red for bad. Over time this provides a quick visual of class and individual performance.

My online Markbook is created on Google Sheets. Sharing this with other members of my department or SLT is easy. Google Drive has substantially improved in recent years. It is very easy and intuitive to create and save files. The filing system is now clear and structured, allowing you to find files quickly. The big advantage of Google Drive is I can access it anywhere. Files can be viewed and edited on my phone and tablet, aswell as any computer. Plus, I can't lose it! 

Next year, I want to develop my recording of assessment and progress. I'm looking to move towards analogue data per topic and using various sources to record data (e.g. quizzes, diagnostic questions, end of term tests, homework).

My markbook is designed to be simple to use and easily adapted to individual needs. It is not the markbook to end all markbooks and is a work in progress. Feel free to use or adapt if you want. (Press File, Make a copy...)

Reading List for New Maths Teacher

I was asked recently what I thought would be a suitable reading list for a new UK Maths teacher. Below is my list. Have I missed anything out?

General Teaching:

• "Teach Like a Champion", Doug Lemov 
• "Mindset", Carol Dweck 
• "Why Don’t Students Like School", Daniel T Willingham 
• "An Ethic of Excellence", Ron Berger 
• "The Hidden Lives of Learners", Graham Nuthall 
• "Visible Learning and the Science of How We Learn", John Hattie 
• "100 Ideas for Secondary Teachers", Ross Morrison-McGill 
• "Teacher’s Tookit", Paul Ginnis 
• "Trivium 21C", Martin Robinson 
• "Adapt", Tim Harford 
• "The Secret of Literacy", David Didau 
• "The Behaviour Guru", Tom Bennett 
• "How to Teach", Phil Beadle 
• "The Perfect (Ofsted) Lesson", Ian Gilbert 
• "Teacher Proof", Tom Bennett 
• "Getting the Buggers to Behave", Sue Cowley
• "The Lazy Teacher's Handbook", Jim Smith
• "How Children Learn", John Holt

Shaun Allison has created an excellent CPD video library


Mathematics:

• "The Elephant in the Classroom", Jo Boaler 
• "Alex’s Adventures in Numberland", Alex Bellos 
• "Taming the Infinite", Ian Stewart 
• "Murderous Maths" series by Kjartan Poskitt
• "The Perfect Maths Lesson", Ian Loynd
• "Adapting and Extending Secondary Mathematics Activites", Stephanie Prestage & Pat Perks 
• Collection of Professional Development Materials for Maths Teachers by Mark McCourt at Emaths
• Cockcroft Report 1982 
• "Getting the Buggers to Add Up", Mike Ollerton
• "Key Ideas in Teaching Maths - Research-based Guidelines for ages 9-19", Anne Watson, Keith Jones, Dave Pratt
• "Nix the Tricks", Tina Cardone and MTBoS
• "How Children Learn Mathematics", Pamela Liebeck
• Collection of Publications by Professor Malcolm Swan
• "Children Discover Arithmetic", Catherine Stern
• "Understanding Mathematics for Young Children", Derek Haylock
• "1089 and All That", David Acheson
• Debates in Mathematics Education, edited by Dawn Leslie and Heather Mendick, for the more reflective practitioner

Collaborative/Cooperative Learning

"Collaborative or cooperative learning can be defined as learning tasks or activities where students work together in a group small enough for everyone to participate on a collective task that has been clearly assigned. This can be either a joint task where group members do different aspects of the task but contribute to a common overall outcome, or a shared task where group members work together throughout the activity. Some collaborative learning approaches also get mixed ability teams or groups to work in competition with each other, in order to drive more effective collaboration."
(Education Endowment Foundation)

My Practice

This year, I have begun to develop my practice specifically towards cooperative learning. In my classroom, students work together in small 'pods' (3 or 4 students) where the goal is to help and support each other to develop their learning and understanding.

(source: National Wildlife Federation)

Within each pod, I try to mix gender, ability and other factors. When needed, students have changed pods during the year. For a small minority students, it has been more of a challenge to settle them to work collaboratively within a pod and to find the most effective pod for them to work in. I have found older students are more likely to create a stable and effective pod which stays in tact for the whole year. I would suggest this is probably because their friendships with other students is more secure. Younger students are generally happy to work within pods, but these have to be altered more frequently throughout the year to achieve balance and harmony within the class.

I have not imposed a competitive element into my system yet. I am considering it carefully for next year and I'm thinking of trialing it with my KS3 classes (11-14). I am aware of the importance of getting this right so will need to do more research over the next couple of months.

I actively encourage students to work closely within their pods. Specific tasks are created to encourage discussion within the pod. When an individual seeks help from me, I tend to talk and involve the pod as a group, thus encouraging them to work and think as a team. This often ensures quieter members of the pod also get support. On this note, both introvert and extrovert students seem to work well within this system and neither type dominates. I encourage higher ability members to support their pod with explicit praise, both verbal and written.

Evidence

"Evidence about the benefits of collaborative learning has been found consistently for over 40 years and a number of research studies have been completed. In addition to direct evidence from research into collaborative learning approaches, there is also indirect evidence where collaboration has been shown to the effectiveness of other approaches such as mastery learning or digital technology. It appears to work well for all ages if activities are suitably structured for learners’ capabilities and positive evidence has been found across the curriculum."
(Education Endowment Foundation)

Reflections

Collaborative/Cooperative learning has helped to develop a positive atmosphere within my classroom. I have found the vast majority of students work well within the pods and this has helped to develop independent learning skills as they tend to ask each other first and only ask me if confusion or uncertainty remains. To help students, I move between pods, rather than individuals, which is more time-effective. This strategy seems to work very naturally with Mathematics.

For more information:

• Concept to Classroom
• Education Scotland
• Behaviour Advisor
• Carlton University
• Collaborative Learning Project

Alan Turing

Today, 23rd June, is Alan Turing's birthday.

"Alan Turing was a British Mathematician, logician, cryptanalyst, philosopher, computer scientist, mathematical biologist, and marathon and ultra-distance runner. He was highly influential in the development of computer science, providing the formalisation of the concepts of "algorithm" and "computation" with the Turing Machine, which can be considered a model of general purpose computer. Turing is widely considered the Father of Theoretical Computer Science and Artificial Intelligence." (Wikipedia)

Turing is famous for his work during World War II at Bletchley Park decoding the German Enigma machine. Bletchley Park has recently been revamped and reopened by the Duchess of Cambridge (see BBC article)

Below are some of my photos of Bletchley Park from a couple of years ago.

German Enigma Machine

Turing's Office at Bletchley Park

Colossus Computer

Alan Turing - Celebrating the life of a genius by Cambridge University (Dr James Grime)

SciShow - Hank introduces us to that great mathematical mind, Alan Turing.

Dr James Grime explains the Enigma Machine

The Mathematics of Alan Turing - Professor Angus MacIntyre (Gresham College)

For more information about Alan Turing's life see:
BBC - History - Alan Turing page
Alan Turing: The Enigma
Alan Mathison Turing - MacTutor
Royal Pardon for Codebreaking Turing

Visit Bletchley Park

La Salle's National Mathematics Conference

La Salle's National Mathematics Conference for Secondary and Primary Teachers, Kettering Saturday 14/6/14 - Sponsored by AQA 
#mathsconf2014

My Notes and Reflections

Mark McCourt - Chief Executive, La Salle Education

Mark introduced La Salle's new mathematics product, Complete Mathematics. This provides complete support for mathematics teachers by providing them with help with planning and assessment. I look forward to investigating this in more detail in the next couple of weeks.

Keynote speaker, Dr Vanessa Pittard, Assistant Director, Curriculum and Standards, DFE

Dr Pittard began her talk with an analysis of the PISA results for Mathematics in the UK. (Key findings for the UK). English students are good at data and number, but need to focus on shape and space, and problem solving. Not sure why then, the weighting of Geometry in the New GCSE is reduced? 

Dr Pittard moved on to discussing the new Maths Curriculum and how it is benchmarked against high-performing jurisdictions like Singapore and Massachusetts. The new A-level Mathematics will be introduced in 2016, along with the Core Mathematics qualification for post-16.

The New GCSE - Andrew Taylor AQA

Andrew Taylor provided a comprehensive introduction to the new Maths GCSE and gave an overview not just from AQA but all the exam boards.

The GCSE will be writtten papers only. Exams will be linear and summer exams for all. November entry is only available for post-16.

The papers will be 4 1/2 hours long and split 1/3 to 1/2 between calculator and non-calculator papers. Foundation Tier and Higher Tier remain (no return to the intermediate tier). Grades are from 1-9 (9 being the highest). Foundation Tier 1-5 and Higher Tier 4-9 (there is a safety net grade 3 on the higher-tier).

The Mathematics GCSE will carry a double weighting in the new accountability measures. (See Factsheet on Progress 8). Andrew described the new GCSE as a "Maths GCSE on steroids".

AQA have split the time allocation into 3 papers each 90 minutes long. The first paper in a non-calculator and the other two are calculator exams.

The big news about content is there is a large shift towards Ratio, Proportion and Change (largely at the expense of Geometry and Measure), which a number of people in the audience felt aggrieved about. Both the Higher Tier and the Foundation Tier will be skewed more towards the top grades than currently.

More information see Craig Barton's blog

Assessing Without Levels - David Thomas and Alan Gothard (both from Westminster Academy)

Westminster Academy's mathematics curriculum has beed designed around three principles:

1. Break the curriculum down
2. Define it with questions
3. Use Analogue Data

The curriculum is split into discrete topics e.g. adding and subtracting decimals. Per year, there are 15-20 topics and each one is assessed individually. For clarity, the topics are defined with questions from three categories: Use & Apply, Reason, Interpret and Communicate, and Solve Problems.

Data is used to create an Assessment for Learning rather than an Assessment of Learning model. Rather than an approach of can they do this? Yes or No, analogue data is used (a percentage score) so it is easier to define the students level of mastery. Data is collected and weighted from small quizzes (40%), homework (20%) and end of term tests (40%). This leads to clear reporting to parents of what their child's strengths and weaknesses are topic by topic. 

The main advantages of this system is that it can highlight when an individual student's performance drops or when a member of staff might need support with teaching a particular topic.

What I liked about this system is the simplicity and clarity it provides to students, parents and teachers. It is far more practical to report on how a students is progressing in particular topics though out the year, rather than focusing on meaningless sub-levels.

For more information, read "Assessing Without Levels" blog by David Thomas including presentation given at Conference.

Blindingly Obvious - Bruno Reddy, King Solomon Academy

Bruno's work is highly influenced by the Cognitive Scientist, Daniel T. Willingham (author of "Why Don't Students Like School?"). Why do pupils get stuck? Their working memory runs out of space. On average, people can have 7 working memory slots. However, some students may only have 4 and three of these might be taken up with listening/speaking, writing and remembering.. It is therefore important to reduce the amount of pressure on the brain.

King Solomon Academy focuses on mathematics. Students receive between 6 and 7 1/2 hours per week of lessons on mathematics. Classes are taught as mixed ability form groups and it is the teacher which moves classroom rather than students, to reduce transition time.

The curriculum focuses on longer studying fewer things. In year 7 in particular, a lot of time is focused on the foundations of maths, number and place value. Some of the more complex areas of the KS3 curriculum and left until KS4. Similar, but confusing, concepts are separated e.g. area and perimeter or median, mean and mode. 

Blindingly Obvious refers to how they approach lesson planning. The pitfalls of modern day maths textbooks and worksheets are highlighted. 

1. Minimally Different Examples - questions where just one variable changes. 
2. Trickle Feeding - a little bit of the same every day.
3. Building Automaticity - practising the basics until perfect.
4. Splitting the Steps - and practice each in turn
5. Take the first step last

Bruno introduced his product, Times Tables Rock Stars

A challenge was also laid down to beat the KSA's World Record for the largest number of people rolling numbers

For more information see Mathematics Mastery.

La Salle Education Conference materials - presentations and handouts.

My personal reflections - this was a fantastic day. Managed to get up to speed in latest developments in the Mathematics Curriculum. Listened to inspirational Maths teachers, Bruno Reddy, David Thomas and Alan Gothard. Finally, got to meet some amazing people and put names to twitter handles - El_Timbre, MakeMathsMatter, Just_Maths, Ms_Kmp and missradders. My only regret is I couldn't see the other speakers. Wow. What a fantastic day. 

Thank you Mark, La Salle and AQA.

PS Cakes were amazing!!!!

Maths isn't *just* beautiful... #mathsconf2014 pic.twitter.com/bVdj7YiEtf
— Em (@El_Timbre) June 14, 2014

Logical Fallacies

I regularly see arguments on Twitter and straw men get mentioned. Initially, I thought it was something to do with the Wizard of Oz and lacking a brain. However, after a little research found it to be a little more sophisticated.

A fallacy is an argument which uses poor reasoning. An argument can be fallacious whether or not its conclusion is true. An error that forms from a poor logical form is sometimes called a formal fallacy or simply an invalid argument. An informal fallacy is an error in reasoning that does not originate  in improper logical form. Arguments containing informal fallacies may be formally valid, but still be fallacious. (wikipedia)

A straw man, also known in the UK as an Aunt Sally, is a common type of argument and is an informal fallacy based on the misrepresentation of an opponent's argument. To be successful, a straw man requires that the audience be ignorant or uninformed of the original argument. (see more here on wikipedia)

The image below outlines the main logical fallacies:

(source: Sheffield Company - can also download bigger version on this site)

For more on this, read "An Illustrated Book of Bad Arguments" by Ali Almossawi (thank you to Tim Taylor for providing me the link).