Aug 11 2013

Expectations – Gritty Students!

Direct link to TED video

Traditionally at the beginning of a school year teachers discuss their expectations of their students, I am going to completely change my emphasis this year and talk to my students about being gritty! It seems to me that for gritty students the often quoted expectations about listening carefully, always bringing a calculator, handing in homework on time,……the list goes on (and on ..) become statements of the obvious!

You can hear Angela Duckworth’s definition of grit in her TED talk, to quote her:
Grit is passion and perseverance for very long-term goals. Grit is having stamina. Grit is sticking with your future, day in, day out, not just for the week, not just for the month, but for years, and working really hard to make that future a reality. Grit is living life like it’s a marathon, not a sprint.

How gritty are you?!

How do we develop gritty students? Certainly the answer to that is not obvious. Angela Duckworth refers to Carol Dweck’s work, something we take very seriously at our school. We need to develop a “growth mindset” in our students; they need to understand that their ability to learn is not fixed but something they can change through their attitude and effort.You can hear Carol Dweck talking about teachers and coaches developing a growth mindset in their students in this interview with Basketball School. Some points she made struck a chord with me: for teachers to develop a growth mindset in their students they need to develop their own growth mindset; do we ever judge our students too quickly? Also, such a useful reminder that we may sometimes worry too much about ‘teaching to the test’ when we just need to remember that ‘The outcomes are natural byproducts of engaging in good practice’.

For more on a growth mindset see this very clear article by Michael Graham Richard using excellent illustrations by Nigel Holmes which he worked with Carol Dweck on (look at that website – there’s a man who knows about design!) and Vickie Schafer’s presentation:

Angela Duckworth’s closing remarks seems the perfect ending to this post!

“In other words we need to be gritty about getting our kids grittier”

Gritty Students

Jan 19 2013

Misconceptions in Mathematics

Post updated: January 2022

I must start this post with something Dan Meyer said at the MEI Conference 2021 that really struck a chord with me, he said “There are no mistakes or misconceptions, just takes and conceptions.” Dan Meyer mentioned WW Sayer who said:

Most remarks made by children consist of correct ideas very badly expressed. A good teacher will be very wary of saying ‘No, that’s wrong’. Rather he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole art of teaching.
WW Sayer

classic mistakes 2 — Nevil Hopley’s excellent Classic Mistakes site.

For a starter addressing common misconceptions try the excellent Classic Mistakes resources by Nigel Hopley.

A superb resource to use in class (or for students to use at home) to address misconceptions is of course Craig Barton’s and Simon Woodhead’s Diagnostic Questions site. The site has many thousands of questions with carefully designed multiple-choice responses to address common misconceptions.

The Insights feature is so helpful for learning about misconceptions, suppose we look at a White Rose Quiz on Algebraic Notation, for example, looking at the Insights we can see for any question the number of responses for each option from the many students who answered this question.

….

NCETM – resources for supporting KS3 Maths Topics

From NCETM, these videos and resources for teaching Key Stage 3 maths topics include common misconceptions and pitfalls; looking at Directed Numbers for example we find slides and a pdf support document including as illustrated here, “What things typically go wrong?”

Some years ago a website, counton.org which is now no longer available published a very useful document on misconceptions. In 22 sections, in each section misconceptions are given along with the correct version. Further explanations are also provided and also follow up exercises with answers.

misconceptions122 Download

The above pdf document includes all 22 sections. The first 8 of these documents, by Ilan Samson & David Burghes, are on the CIMT website.

Malcolm Swan’s excellent ‘Improving Learning in Mathematics‘, includes a section (5.3) on exposing errors and misconceptions. An activity suggested there is to let your students become examiners and mark the work of others, this works very well, I have highlighted some excellent resources for this on the ‘Spot the mistake!‘ page.

See for example from Andy Lutwyche, his excellent Erica’s Errors series for Spot the Mistake activities or, also, on TES, Andy’s Clumsy Clive series. Andy’s many Spot the Mistakes resources.

Many of the outstanding resources from the Standards Unit address common misconceptions; see PD2, learning from mistakes and misconceptions.

On the SERP website before see MathByExample and AlgebraByExample which is a set of Algebra 1 assignments that incorporate worked examples and prompt students to analyze and explain. These resources can provide prompts for discussing common misconceptions.

From this page you can access all the resources.

From Michael Pershan, see his Math Mistakes site, to quote the Author:

The purpose of this site is to collect, organize and make sense of the mistakes that students make while doing math. I’m also increasingly interested in using mistakes to help us create worked examples that students can learn from.
Michael Pershan

Steve Blades’ site www.m4ths.com has many excellent resources; on the GCSE page we see under ‘Miscellaneous Worksheets‘, several documents including 18 Common Misconceptions.

All the examination boards publish helpful material which addresses common misconceptions, such resources can promote very useful class discussion as can examiners’ reports.

From Cambridge University, see Common Errors in Mathematics.

Jan 13 2013

Here’s the diagram….

What’s the question?

Updated post: August 2018

August 2018

Here's the answer...

Sep 16 2012

‘Bell’ Work

(Image courtesy of chrisroll /: FreeDigitalPhotos.net)

For an updated post – see Bell Work, published in 2020.

At the beginning of a lesson I like to get everybody busy straight away, making a calm start to the lesson and very much like the idea of so called ‘bell’ work. Give students a task that is simple to understand and requires no more than a simple instruction on the board (no technology required – unless you are in the room ahead of your students which offers more possibilities). This is a particularly useful idea if students arrive at different times. Students are expected to get to work as soon as they enter the room.

Some ideas:

Some short questions on a topic studied recently.
Ask students to write down all they can remember on any topic. They could perhaps draw a mind map or a picture to represent their ideas.
Ask for some specific facts, eg write down the names of all the quadrilaterals they can with a quick sketch for each.
Students make up some short questions to review a topic – they could then put their questions to the class.
Provide students with a diagram, they write a question, (See ‘Here’s the diagram ….’)
Questions from Dynamic Maths by David Watlins
A good starter that is easy to explain is asking students to find numbers with exactly 2 factors, 3 factors ….
Countdown type problems or ‘Make 24‘. Print out some Make a number puzzles with solutions from Brain Food. Note the other problems available on Brain Food, a Logi-Number puzzle could be written up quickly for example. Many such problems are available, see for example As Easy As 1234 from MathsChallenge.net. For further information on Make 24 see the Number page of my Starters and Plenaries blog.
UK Maths Challenge questions can make excellent starters and you don’t even have to provide the multiple choice answers!
Some of the problems on sites like Starter of the Day or A+ Click Maths are simple enough to easily write up on the board, for example see this problem on adding fractions.
A book I like very much is ‘Thinkers’ from ATM, many questions here would be very simple to put to students at the beginning of a lesson.
At the end of a lesson – tell them what you expect them to do the minute they walk into the next lesson, so they know what there bell work is before thy even get to the lesson!

Why not start a collection of such ideas? Many of these ideas could also be used for those odd moments in a lesson when you find you have some extra time.

Jul 14 2012

Spot the mistake!

A great way to get students thinking about mistakes and misconceptions and hence deepen their understanding of topics is to have them mark the work of others. There are some great resources hosted on TES that will allow your students to do just that.

Particularly excellent resources come from Andy Lutwyche, look at his excellent Erica’s Errors seriesfor Spot the Mistake activities. See also, on TES – further Spot the Mistakes resources from Andy Lutwyche.

Edexcel’s A Level Teaching and Learning Materials, a growing library of resources offer excellent support for teachers.
The exemplar answers with examiner comments provide a particularly valuable resource. These booklets look at questions from the AS and A level Sample Assessment Materials, which was used in the trial undertaken in summer 2017. Real student responses are shown together with commentary showing how the examining team apply the mark schemes. The commentary includes always useful notes on common
errors. These could be used in class and students asked to find errors.

TES resources I have come across include:

R Barnard’s Bob’s Ratio Homework

Craig Barton’s lovely little starter on Algebraic Misconceptions (this one is truly tried and tested – I used it as a starter for a lesson observation and followed it up with a class discussion on what advice students would give to students making the kind of errors here – it went down rather well with the observers!)

Kaszal’s Fractions Mistakes

and Damian Watson’s

Transformations AfL Spot the Mistakes

Enlargement Spot the Mistake Booklet

Fractions AfL Plenary Spot the Mistake Booklet

Thank you to all the great authors of these resources.

On the subject of mistakes, the Classic Mistakes website has a gallery of posters of classic errors made in Mathematics. These could be a prompt for a useful discussion starter activity. Note that an audio file is also available for each poster.