Aug 24 2014

Resources for Students

One of my personal resolutions for the coming year is to carry on with my practice of using resources that students can then refer to or use at home if they wish. Mathematics notes and calculators are a good example of such resources.

To consider an example, early this term with the Further Mathematicians I will be studying matrices and I will let them know the sources of any resources I use in lessons. I use a blog to provide the details of my students’ homework so I can simply add the links to their homework page. Sometimes where there are several useful resources I think maybe of interest to a wider audience I also add a post to Mathematics for Students, see for example, Polar Coordinates. In fact I think I will do that more this year.

To return to matrices, some useful resources include the following:

On the AQA website the Teaching and learning resources page for A Level Further Maths includes three online textbooks under the Resources for students heading. For example if I want a worked example of finding the inverse of a 3×3 matrix then we can look at Chapter 5 of AQA’s Further Pure 4 text. This also has an exercise with the answers at the back if they want additional examples.

$The Math Centre$

The Math Centre

More sources of notes and examples include Chapter 9 on Matrices and Transformations from the CIMT Further Pure Mathematics A Level material, Just the Maths, the Math Centre and The HELM Project. If you have not come across the HELM Project before, the project was designed to support the mathematical education of engineering students and includes an extensive collection of notes which include clear worked examples. You can see on the list that a very small number of titles (that you are unlikely to want A Level) are ‘not ready yet’; for the sake of completeness I discovered the complete set hosted by the Open University. To access the Open University resources you will need to create an account (easy and free), this will also give you access to the numerous free online courses.

Obviously we need to keep an eye on the specification when looking at alternative sources of examples but surely that can only be a good thing, particularly for our students who will be off to university in the near future.

Matrices is an example of a topic where it can be very useful to check work with WolframAlpha; I have created a new slideshow of Matrix Examples to add to the WolframAlpha slideshow series so we can easily check any work.
The series is on Mathematics for Students also and a post including the matrices resources discussed here has been added also.

Aug 15 2014

Learning Names

I have written on this before but something coming up again soon for UK teachers and no doubt many readers are already doing this – lots of new names to learn! Something we all need to do at the start of each year, learn the names of our classes as fast as we can! Certainly I think this is worth spending time on and should be a priority, we want our students to know that we know who they are!

I used name cards last year and will certainly use them again for the coming academic year. These are simple to make from an A4 piece of paper which can be folded in half and then folded in half again. Students can then write their name clearly on one side of the card. The other side of the card visible to the student could be a reminder of anything you want; the above illustration shows the card I used for a lesson observation with a class I was unfamiliar with. For my own students I have the details of when homework will be set and handed in and the address of the blog I use to post details of homework. In case it’s useful this is the Word file for the above example.

There is plenty of useful advice for learning names, these suggestions might be helpful:

I was interested to see a suggestion to seat your class alphabetically by their first name rather than surname in one article; that could be worth a try.

TES – Learning Names on New Teachers

Learning Students’ Names from the University of Nebraska includes many suggestions. I might try a variation on suggestion 15 here with younger students, perhaps they could try and think of a mathematical term which begins with the same initial letter as their name, Colleen calculator, Tina triangle….!

On the subject of names it is worth mentioning the lists compiled by the Office for National Statistics. In fact the top names for England and Wales for 2013 were published on August 15th 2014. This pdf details the key findings from the data and includes Excel files to download various tables. There are clear infographics showing the changes from 2003 to 2013 for girls and boys.

Anna Powell-Smith’s website England & Wales Baby Names has details of names chosen by parents in England & Wales each year from 1996 to 2013 (based on the ONS data discussed above), using this site makes it easy to see the popularity of a name over time, we could search on Colleen for example (or this link for the US version)!

I think teachers and students can also be users of the baby name statistics because in my experience it goes down very well with students! What’s in a name? is a lesson from the the Census at school site; the lesson is suggested for Year 7 (age 11-12) and learners are asked to investigate popular first names and do a survey for their class on the image of first names and to report their results. This involves data collection, presenting data and designing a survey. Another suggested lesson which I have have successfully used myself is Baby Names from Stats4schools. The lesson involves students investigating the popularity of names and asks whether names get more or less popular over time.

Students might be interested to see how their school compares to the ONS data.

Further websites offering Statistics on names:

Entering a name into WolframAlpha shows US Statistics for that name and gives the etymology of the name and notable people with that name.

This Wikipedia entry has the top 10 names for various regions of the world.

And just what you always wanted to know, it seems Max and Bella are the most popular names for US dogs – Popular Dog Names – 2013! In fact Max tops this UK list as well.

Aug 8 2014

Resolutions for Mathematics Teachers

Everywhere I look I see references to Back to School (there were signs in the shops before we even finished term!) and I know many of you are already back or about to begin term so I thought I’d post my updated ‘Resolutions for Mathematics Teachers’ earlier than originally planned.

All links have been checked and updated where necessary; in many cases the posts linked to have also been checked and updated with new additions.

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To highlight some updates:

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On gritty students, I have updated the blog post with a video where you can hear Carol Dweck talking about teachers and coaches developing a growth mindset in their students in an interview with Basketball School. Carol Dweck made a couple of points that struck me in particular, 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’.

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A new reference to coding has been added. I recently came across CodeMonkey (a subject I will return too in later posts) which is a superb site for teaching coding and is easy to use for students of all ages. I have previously written about Scratch which also offers us the chance to get some coding into our Maths lessons. There are many topics where we can use a little coding including polygons and making the monkey walk about in all directions it struck me that this would be great for directed numbers!

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I always try to use resources in class that interested students can then use themselves at home, hence the addition of the reference to Calculators and tools. When one of my very good students last year marched into the lesson and announced that she know the text answer was wrong because she had checked it on WolframAlpha I saw the impact of this strategy. She had been working on a problem and was confident in her methods but the text answer had a typo so she turned to WolframAlpha to check. There are so many excellent tools out there for students to explore and check their work, this can encourage their independence in learning.

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A reference to ending lessons well has been added as I recently created a new slideshow on the subject.

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My post on feedback was updated recently including the need to allow time to respond to feedback.

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I learn much from reading various blogs and tweets and about teaching generally not just Mathematics, the reading pages here have been updated to include some favourite blogs on learning and teaching relevant for teachers of any subject. On the subject of reading, have a look at the addition of Nix the Tricks to the Free Books page.

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If you have just returned or are about to return to school then I wish you a brilliant year. If you are still on holiday I hope you are having a well deserved rest…but maybe there are a few useful thoughts here for you when your thought return to school!

Aug 2 2014

Feedback

I have read some great posts on feedback, see Alex Quigley’s Improving Written Feedback and Verbal Feedback Given….. on Shaun Allison’s ‘Class Teaching’. Such a good idea, I couldn’t resist – so I bought myself the stamper and decided to try this with Year 7 – early days yet, but I love the idea so far..

A student in my Year 7 class was determined to find the number of winning lines in a game of 3D noughts and crosses which she did successfully. She drew some clear sketches of the different groups of winning lines and after a discussion with me was the recipient of my first stamp! I was very enthusiastic about her written work on this as you can see from her response! I had explained to the class that if I discuss their work with them, then give them a stamp – they have to write down that feedback as Shaun suggests in his post.

verbal feedback v3

It is important for students to make a note of verbal feedback and I have asked students to do this more often recently, so for example if I am giving any verbal feedback to the class after a test or homework I expect them to make a note of any verbal feedback they believe applies to them.

Something we must do of course is allow students time to respond to feedback, ideally I want a conversation in their books! I acknowledge where a student has responded to feedback by awarding a Feedback Response point (see ClassCharts for recording learning behaviours). We need to allow time in class for students to act on any feedback given; another possibility is to give freedom of choice for homework. My notes for my Year 7 class on our homework blog includes the following:

Note that the independent homework gives you the chance to respond to feedback; for example you might want to try to solve some equations and present your solutions very logically and show that you are checking your work. It may be a response to my feedback or your ‘self-feedback’. When you reflect on something we study in class, sometimes you might think ‘I’d like to practise some more examples’. Your independent homework provides that chance. Remember you could choose any topic, your homework offers you the chance to revise work.

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Staying with the use of homework, it may be appropriate to give a follow up homework allowing students the opportunity to act on feedback received from the first attempt.
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See also: Dollops of Feedback which includes some useful resources on feedback.

The most powerful single modification that enhances achievement is feedback. The simplest prescription for improving education must be “dollops of feedback”.
Hattie, J.A. (1992). Measuring the effects of schooling. Australian Journal of Education (see page 9).