Looking at the new content for UK GCSE Mathematics a completely new entry on the specification is “find approximate solutions to equations numerically using iteration”.

The end of term approaches. I will certainly be using this great Summer Relay; students can have a more informal lesson but still do some useful maths! See Relays from Chris Smith.Note there is a complete set; I used his Valentine relay very successfully this year! Featured in Mathematical Miscellany#2.

This holiday I’ll be doing my usual tidying up and also updating my Results apges with any UK Statistics.

Before that I am very much looking forward to this Saturday’s BERA (@BERANews) Event, Learning from the classroom – Practitioner research in mathematics education where I will be speaking myself on the value of Lows Stakes Testing in the Mathematics Classroom and enjoying presentations from other speakers including the Keynote speaker, Dr Alison Clark-Wilson (@AliClarkWilson Institute of Education, University of London @IOE_London). The event has been convened by Dr Alf Coles (@AlfColes University of Bristol) and Dr d’Reen Struthers (Institute of Education, University of London).

This is an outstanding resource – many excellent activities here for the secondary classroom.

This page has a permanent home under Resources and has been recently updated.
There are flipcharts available for each lesson and note the excellent Professional Development materials.

IWB MaterialsThis website has come about as a result of the NCETM research project: Enabling enhanced mathematics teaching with some interactive whiteboards (September 2006- September 2008) and is supported by the IWB research team at Keele University and s supported by the IWB research team at Keele University and the Spire Maths team.

MMT has written a set of PowerPoint files for almost all of these excellent resources, he has made them – in his own words ‘classroom ready’. MMT has provided the resources in an editable format so that they can be tweaked to your own requirements. Thank you MMT! These files are available directly from Dropbox; note they are also hosted on Craig Barton’s site.

A really quick post this week, I see the Twitter #mathschat today is on Stretch & Challenge so I thought I would check some bookmarks I have saved; I will add some more references to this post in the next day or two and return to these later but in the meantime – some very useful links:

When teaching the Chi Squared test I have often found that students sre not always clear on ttheir interpretation of the contributions to the test statistic. A worked example with a little colour to help where we look at the observed data. the expected probabilities and the chi squared contributions seems to work well . This exercise made me realise that a chi squared calculator I had previously recommended did not seem to be working, so fortunately I found a better one!

FromSocial Science StatisticsthisChi Squared Calculatoris for a contingency table with up to 5 rows and columns. It is very simple to use, enter the group and category names, then the data, choose the significance level and calculate.

A clear conclusion is then given:
The chi-square statistic is 10.2061. The p-value is .037096.
The result is significant at p < .05.

Looking at the new A Level Specifications – I can see that on the OCR MEI course the Chi Squared test for association is an option in the Further Mathematics A Level. The Chi Squared goodness of fit test has also been introduced. MEI have comprehensive information on the Mathematics specifications hereincluding vey clear videos such as this on the Statistics strand. For further information on A Level Mathematics reform see A Level Reform and Resources.

I wrote earlier on the wonderful resources on Underground Mathematics from the University of Cambridge. Thinking about the new A level specifications I believe thissite will provide us with rich resources for these new specifications.

Each section includes Review Questions, look at Thinking about Algebra for example; scroll down the different resource types for the Review questions for this station.

An excellent feature of Underground Mathematics is the excellent search facility; we could look at the Review questions by type. One can also search by line ( Number, Geometry, Algebra, Functions or Calcuus) and by Station.

See the example question below, for each review question you will find the question, a suggestion, the solution and sometimes suggestions for taking it further with for example GeoGebra resources.

Note the star by the title – if you choose to log on to the site (you don’t have to but it’s a very good idea!) you can save any favourite resources to your collection.

I can never resist a quick illustration on Desmos! I think I’ll start an Underground Maths Desmos collection! Note the use of the hyperlink on Desmos to link to the question.
Select the image for the Desmos page.

I think we have a wonderful supply of excellent questions here to challenge our students and help them see connections between the various areas of the subject. These are ideal to use with A Level students; some are also useful for higher level GCSE students aiming at those top grades or Level 2 Further Maths students. Any student who wants to study Mathematics at university should certainly be using this site.

For Problem Solving – a wonderful find, GCSE Problem Solving Questions of the Day – Compilation from The White Rose Maths Hub Team @WRMathsHub available on TES Resources. The booklet contains over 50 problem solving questions suitable for KS3 and GCSE classes, answers are also provided. Also from the team, their mastery schemes of learning now includes Year 7 material (UK age 11-12); an assessment is also available.

Em @EJmathshas a brilliant PowerPoint with all the questions and answers – see it here.

The Subtangent resources from Duncan Keith are available from the National Stem Centre (the original site is no longer available). This is a great collection including various worksheets, starters, investigations and revision activities. Some files are also available on Mathisfun. A personal favourite of mine has always been the linear equation calculator.

From OCR, specifications, specimen papers and other resources can all be downloaded here.
Note the option to download a zip file with the specifications and sample assessment materials.

OCR have individual subject pages with further resources:

OCR have also linked to some new sample MEI resources. These include some very nice “problem shorts” and also the use of technology to analyse large data sets.

OCR A Level Check In Test

I do like OCR’s check in tests for GCSEand I see a small number check in tests and lesson elements on the A Level subject pages; I assume this collection will grow.

From MEI, see this short video presentation on the new specification including the new work on large data sets.

For further reference documents and some suggested resources see A Level Reform.

For easy access to announcements regarding Maths from the examination boards, use this twitter list. (You do not have to use Twitter to access the list).

Educas state: “The objective of this qualification is to assist the understanding of the problem-solving cycle of planning, collecting, processing and discussing in meaningful contexts and to use statistical software to process real data sets. It has been specifically designed to be taught in schools and colleges to equip learners aged 16-19 with a broad range of skills empowering them to successfully negotiate statistical problems in Higher Education or the world of work.”

This discovery led me to a treasure trove of resources from Educas for Mathematics at all levels, including GCSE – this definitely needs further exploration!

Some further notes and additional resources on Assessment and Feedback…

The first few slides (slides 1-15) introduce Assessment and Feedback, looking at definitions. To summarise:

Assessment and feedback is something we do every day in our classrooms. It’s a two way process, students and teachers working together. The feedback needs to be helpful to the students in that they can do something with it to improve their learning.

What makes great teaching?Review of the underpinning research.
Robert Coe, Cesare Aloisi, Steve Higgins and Lee Elliot Major

The next section of the presentation (slides 16-23) concerns teacher – student relationships, so important and something which comes up continually in my own conversations with students, note section 3 on Classroom Climate and also these comments from younger (age 11-12) students. This is all about knowing our students well and creating a climate where it is OK to be stuck, there is trust between teacher and students and the students know that their teacher has their best interests at heart. To quote Dylan Wiliam:

Without that relationship, all the research in the world won’t matter.

Continuing with the theme of knowing our students well, it is so useful to ask them what works. Slides 24-31 show quotes from students about what helps them learn. Included in this section – Corbettmaths 5-a-day.

Continuing with the theme of knowing our students well, it is so useful to ask them what works. Slides 24-31 show quotes from students about what helps them learn. Included in this section – Corbettmaths 5-a-day.

Slides 32-38 illustrate some learning activities such as matching exercises which have built in feedback. For some useful resources for this type of activity try the following:

Tarsiafor making your own matching activities – or you can find many Tarsia resources on TES Resources for example.

Spot the Mistakethese activities can be a good alternative to peer marking

The next section (slides 39-45) is on questioning. Used wisely, well planned for questions can help us work out just what our students know.
Recommended reading and resources:

Retrieval Practice (Slides 46-49) looks at low stakes testing to help students recall information. Something I have found valuable throughout my teaching career and an area I am currently working on and will write further on in the near future. See: