Iterative Methods

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”.

Teaching the new specification this year I needed to work on this and wrote this post;
GCSE New Content – Iterative Methods for Numerical Solution of Equations.

I see from my blog Statistics that this is a very popular post so have made it my first summer holiday job to update it.

Note the additional section on Further Resources / Questions (scroll down the post).
Eq solved by iterative method

 

Low Stakes Testing in the Mathematics Classroom

To download:
Low Stakes Testing in the Mathematics Classroom (PowerPoint File, takes a few moments to download)

Low Stakes Testing in the Mathematics Classroom (pdf)

Slides from the BERA Conference, Learning from the classroom – Practitioner research in mathematics education – July 2016

There are many hyperlinks provided in the presentation, for ease of access these are also provided below:

Further Reading

End of term…

Relay from Chris Smith

Relay from Chris Smith

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.

For more end of term activities, see the End of Term Activities page under the I’m Looking for  … menu.

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

BERABefore 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).

 

The Standards Unit – Mathematics

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.

Start by reading Improving Learning in Mathematics – Malcolm SwanThe following links give you access to the resources, also some IWB resources.

Home pageThe resources are hosted by Nottingham University, including all the pdf files very clearly indexed. Note that this sites includes the complete set of resources including the software; (though some software is too old to work!) Note that Tom Button has rewritten the Traffic Simulations in GeoGebra for A5: Interpreting Distance-Time Graphs with a Computer. The Professional Development resources are excellent. Look at PD1 ‘Getting Started’ for example, note PD1.4 on page 9 – 8 Principles for Effective Teaching.

Alternatively:

All materials – hosted by National STEM Centre. Including:
Mostly Algebra   Mostly Number  Mostly Statistics   Mostly Shape and Space   Mostly Calculus   Others   

…or Craig Braton has the pdf files on mrbartonmaths

IWB Materials This 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.

PowerPoint Files

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.

Standards Unit MMT Files

Standards Unit A1:Expressions – MMT PowerPoint

Stretch & Challenge – Mathematics

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:

Colourful Chi Squared!

Updating a presentation –  Colour in Mathematics led to a happy find!
Chi Squared examplw

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!

From Social Science Statistics this Chi Squared Calculator is 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.
Chi Squared Calculator 1
Chi Squared Calculator 2

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.

The calculator is included on the Statistics 16+ page of Calculators & Tools.

Note the many other calculators  for statistical tests  available on Social Science Statistics.

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 here including vey clear videos such as this on the Statistics strand. For further information on A Level Mathematics reform see A Level Reform and Resources.

Review Questions – Underground Mathematics

Underground Mathematics - QuadraticsI wrote earlier on the wonderful resources on Underground Mathematics from the University of Cambridge. Thinking about the new A level specifications  I believe this site 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.

Alternatively you can browse all the Review questions.

Review Questions - types
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.
Review Questions - search

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.

Review Question - Gemetry

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.
Desmos illustration

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.

Mathematical Miscellany #4

A compilation post this week…
(More collections of mathematical goodies.)

White Rose Maths Hub problemsFor 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.


AQA Problem Solving Questions

AQA 90 ProblemsFrom AQA comes an outstanding resource, ‘Problem Solving Questions‘.
The Teacher’s Guide includes indices by topic and also by strategy.
AQA Problems – updated version.

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

AQA


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.


And finally, 28th June is a Perfect Day to enjoy some Mathematics!
28 is also a happy number!
It’s also National Tau Day! Pi is wrong…..
This video provides a short version of the Tau Manifesto (14 minutes)

A Level – Draft Specifications & a Statistics Qualification

The A Level Draft Specifications have now been published, including specimen papers.

For the specifications use the following links.


Further resources:
AQA Resources including a very useful Specification Summary. AQA have several very clear resources, see: Planning  Teaching and Assessment which includes the Specimen Papers and mark schemes.

Edexcel Sample Assessment Materials

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:

MEI have helpfully compared Further Mathematics Specifications so you can compare the content and structure from each board.

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.
MEI Sample Resources

OCR A Level Check In Test

OCR A Level Check In Test

I do like OCR’s check in tests for GCSE and 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).


Royal Statistical Society Problem SolvingEduqas will not be offering AS / A Level Mathematics specifications, but note their Level 3 Statistical Problem Solving Using Software. See also  the International Centre for Statistical Education (ICSE) with Plymouth University and you can follow @IntCSE on Twitter. It may be that some of the resources here will be useful for our teaching of Statistics.

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!

Assessment and Feedback in Mathematics

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.

Some further useful reading:

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.

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:

Teachit Maths KS3 Percentages code breaker

Teachit Maths KS3 Percentages code breaker

Teachit Maths though a subscription site offers its entire collection of activities as pdfs free.
I have found many high quality resources here for all ages. Look at this activity on quadratic functionsfor example – this should really help understanding.

questionsThe 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:

Homework ideas are given on slides 50 to 53.

The next section is on marking (slides 54 to 63). See:
Test Analysis

  • Consider a question by question analysis on tests; this can be very revealing as to which topics a class has found harder.
  • Look at examiners’ reports to give advice to students about what examiners are looking for.
  • A very interesting read from the University of Oxford and the Education Endowment Foundation is A marked improvement? (April 2016)
  • Plan for marking, what are you looking for in a particular piece of work. Consider Ross Morrison McGill’s (@teachertoolkit) 5 Minute Marking Plan
  • For simple day to day marking, ask your students to assess themselves using RAG123.

Further Resources