Good Maths Teachers…

equationYou will see from my post on Dec 1st I asked someone else for his thoughts on Mathematics education – Simon Singh, whose book ‘The Simpsons and Their Mathematical Secrets’ was published in paperback recently answered some questions I put to him.

I thought I’d also ask Year 9 about good Maths teachers…

I asked my wonderful Year 9 class about their ideal Maths teacher – this was not about personal comments about any individual teacher – but the qualities of their ideal Maths teacher. Their comments are in blue:

A Maths teacher should be optimistic, enthusiastic (but not overboard), have a good knowledge of the subject and be helpful, engaging, practical and organised.

So many of their comments seemed to me to fit with the key components of this extremely worthwhile read: What makes great teaching? Review of the underpinning research.
Robert Coe, Cesare Aloisi, Steve Higgins and Lee Elliot Major
October 2014

The report lists six common components suggested by research that teachers should consider when assessing teaching quality. The authors state that “This should be seen as offering a ‘starter kit’ for thinking about effective pedagogy. Good quality teaching will likely involve a combination of these attributes manifested at different times; the very best teachers are those that demonstrate all of these features.”

I thought I would list the students comments’ under what I feel are the most appropriate components from the review. Their comments I felt fell into the first four components.

  1. (Pedagogical) content knowledge (Strong evidence of impact on student outcomes)

“The most effective teachers have deep knowledge of the subjects they teach, and when teachers’ knowledge falls below a certain level it is a significant impediment to students’ learning. As well as a strong understanding of the material being taught, teachers must also understand the ways students think about the content, be able to evaluate the thinking behind students’ own methods, and identify students’ common misconceptions.”

Good at explanations and lecturing.
Someone who can explain in different ways.
Someone who won’t just tell you how to do something, but will explain how and why it works.
Helpful Maths websites for students.
Lets us be independent.
Provokes your mind to think beyond the syllabus.

  1. Quality of instruction (Strong evidence of impact on student outcomes)

“Includes elements such as effective questioning and use of assessment by teachers. Specific practices, like reviewing previous learning, providing model responses for students, giving adequate time for practice to embed skills securely 3 and progressively introducing new learning (scaffolding) are also elements of high quality instruction.”

Hard working.
A teacher who provides the student with the opportunity to see what they need to revise. Regular tests and quizzes do this.
Puts a lot of time into lesson planning.
Doesn’t mind repeating things.
Speaks at a suitable pace.
Gives us notes which are helpful like worked examples.
Make sure we can write good notes.
Go through examples together.
The right amount of homework.
Someone who is willing to answer any question.
Pushes you to work on harder questions to extend your abilities.
Helpful individually AND generally.
Does practical work.
Gives detailed and constructive feedback.
Someone willing to help outside class

  1. Classroom climate (Moderate evidence of impact on student outcomes)

“Covers quality of interactions between teachers and students, and teacher expectations: the need to create a classroom that is constantly demanding more, but still recognising students’ self-worth. It also involves attributing student success to effort rather than ability and valuing resilience to failure (grit).”

Should be passionate and enthusiastic.

Firm but kind.
Someone you can feel comfortable with.
Recognises achievements.
Genuinely caring about the students.
Someone who knows who you are.
Someone who you know won’t judge you. 
Expect the best out of your students, but don’t be angry if they don’t always achieve it.
Check with students individually if they are stuck.
They should be able to cater to all abilities.
Lets you talk about the work in class.
Praises students.

  1. Classroom management (Moderate evidence of impact on student outcomes)

“A teacher’s abilities to make efficient use of lesson time, to coordinate classroom resources and space, and to manage students’ behaviour with clear rules that are consistently enforced, are all relevant to maximising the learning that can take place. These environmental factors are necessary for good learning rather than its direct components.”

Someone who can still keep control in the classroom.
Is organised and creative.
Use different media, it’s really important – the ordinary board, the whiteboard, worksheets, jigsaws, cut and stick (matching up exercises), drawing, walk around the classroom problems (treasure hunts), computers.

A few more comments to finish…

Have readable handwriting.
Someone who knows how to use the Smart board.

Here’s a comment to make you smile!
Maths teachers are different from other teachers, because Maths can be very different to other subjects. 

…and an appropriate final comment:

What makes a good Maths teacher is someone who is passionate about Maths and explains everything REALLY well. I think being passionate is really important as we students can tell if a teacher is enjoying a subject and sometimes the explanations of topics are better when a teacher loves a subject.

I think it is also important that the teacher can challenge the most able students whilst making sure that the least able are keeping up.

Thank you so much to my amazing Year 9 students!

See also ‘More on good teachers’ where Year 7 (UK age 11-12) have plenty to say!

Diagnostic Questions – new features (select image for site)

I have written several posts on this excellent site and it now has a host of wonderful new features.

One can now register your school and students, set them quizzes for which they get feedback and so do you! You can read Craig Barton’s own description of the new features here and note the series of videos with clear instructions on many aspects of the site.

Testing this, all seems to be working well. I uploaded students easily using a spreadsheet as described in Craig’s video “How to add Schools, Teachers and Students”

It is very easy to assign one of the many available quizzes for your students or set them one of your own quizzes. Again, Craig has described the process in a video (it takes seconds to do!)
Standard Form

I thought I would try this with a quiz I created earlier on Standard Form and all worked well. I logged on as a student to test this and did very well! At the end of a quiz the student can review the questions, read explanations by other students and could also download the quiz if they wished.

This is certainly a feature I will be experimenting more with. Happily I have excellent students who like to be given further resources which enable them to help themselves.

Another thank you to Craig Barton and Simon Woodhead for creating and developing this outstanding resource. Talking of further developments Craig tells me that a Quiz Preview function (currently an easy way to preview a quiz is to download a worksheet) and a newly improved Data Quiz page will be available very soon.


Since I will be studying the Bivariate Data section on one of our Year 13 (UK age 17-18) Statistics modules soon I was rather pleased to see that it is now really easy to use Desmos for Regression. The video shows how simple it it to use.

I tried this with some data from an A level question then also added another expression and table to see the values predicted by the model.


It is also simple to use Excel – just add the data, insert a chart – choose Scatter, then add a trend line.

Regression using Excel

Regression using Excel

GeoGebra provides us with another option.
Try this ready to use worksheet – find the line of best fit.
GeoGebra Regression
From the GeoGebra manual – FitPoly command  

For another easy to use tool, we could use the PhET simulation.
PhET Residuals

…or we could just pop the points into WolframAlpha and have it do all the work to check our calculations!


Algebra Snippets

Algebra Snippets

Year 11 (UK age 15-16) have mock examinations starting next week so we have been revising.
I have written before on ‘Here’s the diagram …what’s the question? and having studied Trigonometry recently

Here's the diagram....

Here’s the diagram….

the selection of various triangle diagrams worked very well and prompted some good discussion on unknowns we could work out in the various diagrams and what methods we could use.

Algebra Snippets 2
I thought I would extend the idea to Algebra and rather than a diagram just use what I have termed Algebra snippets where I have given for example only algebraic expressions, equations and so on from questions. (Very economical – you can get a lot on an A4 page!) All the vocabulary (which students often ignore!) has been stripped out. So rather like the diagrams idea students have to work out what the question might have been. With the vocabulary missing it is interesting to ask students what terms they think were used in the question. Following our discussions I also showed the students the complete questions. On the subject of vocabulary there are some excellent resources on this page including the very useful guide to exam terminology (I have seen this document around the web – I believe the original is from AQA).

Resources like the above can be fast to create – I created a table in Word then used the wonderful Windows Snipping tool to select my images and copy them to the table. If anyone wants the complete sheet: Word Algebra snippets or pdf Algebra snippets (you’ll see I snuck in a backwards percentage question as well).

I find these are worthwhile exercises and do get students thinking about the various question types and was pleased that some students started commenting on the differences in types of questions.

LinesOne last diagram! Having asked these students if they wanted any particular topics, some asked for equations of lines so in one lesson we started with this diagram and managed to revise equations of lines, simultaneous equations and inequalities as well!

I gave them a copy of the diagram each and used a flipchart to give them some information and ask questions as we went along.

In case this is of interest the complete document is here: Lines & equations revision


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The diagrams here were very easily created with Desmos, note that you can turn of numbers and/or the grid if you wish on Desmos from the Tools menu.