December means Advent Calendars and Nrich have published two Advent Calendars, one for Primary and one for Secondary each containing twenty-four problem-solving activities, one for each day in the run-up to Christmas. The primary Calendar tasks focus on encouraging mathematical habits of mind and the Secondary tasks have been chosen to encourage mathematical creativity.
Alex Pett created his advent calendar complete with history and problems for each day. Alex has provided a pdf versionor use as aGoogle document. For an Activeinspire resource this versionalso has sound.
Completing the question by question mark entry for each of the three papers as mentioned in the previous post has shown some clear trends as to facts students have recalled incorrectly. I plan to check that students can accurately recall facts, terminology and definitions (A01) as a regular part of lessons, even for a few minutes. Clearly to achieve highly on questions requiring students to reason, interpret and communicate mathematically (A02) and Solve problems within mathematics and in other contexts (A03) students do need easy recall of all these facts.
mathscard – Loughborough University
Resources to help with this aim include Flashcardson Tanner Maths, A4 or A5 size cards are available. For use in lessons I intend to project flashcards of my choice. Also useful here is Mathscard from Loughborough University; whilst written for A Level, several parts are useful for GCSE. The online version can easily be projected.
If we look at Trigonometry for example you will see that the graphs are included as are the standard triangles used to find exact values of angles.
mathscard – Loughborough University
I plan to ask the questions of students in the form of a mini test, so I will ask students the question and they just write down the answer, I can then display that answer. For trigonometry for example I will ask them to draw sketches of the standard triangles illustrated here. Appropriate flashcards can be displayed whilst asking the questions. An alternative would be the syllabus itself or a document such as AQA’s Teaching Guidance illustrated below. For example, from AQA we have:
As Howard has pointed out in his comment below – note the structure of the values for sine and cosine!
For this first post – just some initial notes having marked the mock examination papers for my Year 11 class (UK age 15-16). This class is studying for AQA GCSE Mathematics and also the AQA Level 2 Further Mathematics qualification; they have completed the AQA specification and have taken a complete set of Practice Papers (Set 3) for their mock examination. (Teachers who offer, or are considering offering AQA maths qualifications can register for AQA’s All About Maths). AQA recommend the use of these papers as mock exams as they reflect the balance and expected standard of their new assessment. The papers have been trialled with over 6000 students. Detailed mark schemes and further marker training materialis available to support teachers. Many of the points here apply for any specification.
It is time consuming but provides a really valuable analysis and I feel time well spent on this new specification – For each paper, I am entering the marks for each question or part of a question into an Excel spreadsheet. I have used AQA’s Higher Papers AO grid so I and my students can see a breakdown of marks for AO1, AO2 and AO3. The grid is available with the Practice Papers.
AQA Higher Papers AO Grid
This type of analysis clearly shows which topics and/or question types were more problematic for individual students as well as for the class as a whole. Using Excel with conditional formatting makes the information easy to interpret.
Some AO1 marks have been lost simply because students have forgotten material or misread a question, perhaps reading too quickly and not noticing key words. Continuing to use mini-testsshould help with this. It also strikes me that we can sometimes display some flashcards as a starter. We can also use starters for GCSE revision. Links to Flashcards from Tanner Maths and other high quality GCSE revision questions are in this post on Mathematics for Students. Last time I taught a year 11 class having done a similar analysis I made sure that questions on the most problematic areas from their mock examination featured regularly in our mini tests. We used Corbettmaths 5-a-day regularly which they found very helpful.
An understanding of graphs is crucial, it seems to me we should take every opportunity to provide a graphical representation where possible for all year groups. Multiple choice questions where students have to identify a graph could be used in KS3; students simply need a common sense approach: for example “if x is 0 what is y?” They need us to help them be confident that they can work it out – work it out, not everything is a memory test. Many students who were successful in identifying an exponential graph simply took a moment to work out a small number of coordinates. Encourage graph sketching in Key Stage 3.
On notation – something I have often seen before – students confuse notation for inverse functions with a reciprocal.
Naming angles and sides, it is so much clearer when students use what use what is given in the question – if an unknown side is BD then call it BD – certainly don’t call it c when there is a C elsewhere in the diagram! Encourage students to mark angles on diagrams – it provides very clear evidence.
Whilst the laws of indices may be understood, students can be thrown with algebraic examples, (32x)3 for example.
Constructions – one of my favourite quotes from a Principal Examiner, “No arcs, no marks!”
Some facts turn up so often, for example: 2 is the only even prime number, if you square a number it’s always a positive result – watch out for these – they turn up is so many different questions!
The value of a sketch: eg reflect a quadratic with a negative coefficient of x2 in the y axis and you’ll get another quadratic – also with a negative coefficient of x2.
I train my students in the ways of marking! They all understand isw – ignore subsequent working. So a harmless extra bit on the end of their answer may not matter. However there are times when extra information will lose you marks – for a question specifically asking about the spread of marks – don’t mention the median!
On my To Do list for my Year 11s and I’ll comment further on these in blog posts to come:
What are the most common things they have struggled to remember?
Plan the flashcards to display
Providing some model answers – annotating the questions, highlighting key words, clear explanations
Using the analysis of the papers, with other assessments to write helpful reports for Year 11 this term
Cambridge University’s Underground Mathematics is an outstanding resource for teachers of students age 16-19 and I believe will be an important source of ideas for teaching the new Advanced Level specifications.
To use the links in this post you will need to be logged in to the brilliant Diagnostic Questions site. Create an account if you have not already done so as this site with thousands of high quality diagnostic questions and additional analytical features is free. If you scroll down the page you’ll see that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.”
Diagnostic Questions provide a way of assessing your students’ knowledge and understanding, they are excellent for identifying misconceptions. Try for example the collections of GCSE 2017 examination questions from AQA, OCR and Pearson Edexcel.(scroll down each of the pages linked to for numerous quizzes on different topics on the GCSE syllabus).
Diagnostic Questions GCSE 2017 Collections
Diagnostic Questions – GCSE examples
You will find excellent coverage of topics new to the GCSE specification. You can also search all questions for a topic of your choice, for example a search on iteration will lead you to the whole collection of Trial and Improvement and Iterative Methods questions.
When you are logged in to Diagnostic Questions, you can easily return to the menu using the icon on the left.
Returning to the collections, there are many – scroll down the page and you will see collections such as GCSE Maths Takeaway – 111 mini topic-specific quizzes covering all the content on Higher and Foundation GCSE (keep scrolling down the page for all the quizzes). These quizzes are ideal to use as baseline assessment before revising a topic, or as a measure of progress following the teaching of a topic.
For schools teaching AQA’s Level 2 Further Maths specification, the AQA Level 2 in Further Maths collection has 12 sections of very useful questions for this specification.
You will see choices for each quiz including the very useful option to download the questions as a pdf.
For example I created a quiz on Circles and Tangents, downloading this as a pdf creates this file. See the guide mentioned below for instructions on creating quizzes.