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Maths Teachers at Play 94

It is my turn to host the Maths Teachers at Play blog carnival this month (check out the last edition hosted by Manan at MathMisery).

Tradition dictates that I start the post with some cool facts about the number 94, so here are a few:

  • 94 is a Smith number. This means that its digit sum is the same as the sum of the digits of its prime factors. \(94 = 2 \times 47\) and \(9+4 = 13 = 2+4+7\).
  • The aliquot sum of 94 is 50 since 94 has 3 divisors excluding itself, namely 1,2 and 47.
  • 94 and the integers either side of it are all semi-prime.
  • It is the 4th 17-gonal number, and so is a number of the form \(\frac{1}{2}(15n^2-13n)\).
  • 94 is non-totient.

There were some great posts submitted this month, and in no particular order here they are (with a few additional posts that have read and thought were pretty cool!)

  • Recently both the UK and the US have had lotteries with larger than usual rollovers. Manan (@shahlock) wrote this amusing post about the Powerball lottery to celebrate.
  • Julie Morgan (@fractionfanatic) has shared this post on a “tried and tested task” as part of the #MTBoS12days blog challenge. In it she describes using RedAmberGreen tasks to level the challenge of questions on a topic.
  • Lisa Winer (@lisaqt314) has shared this great post titled¬†“Teaching (and Learning) Grit by Having Students Solve the Rubik’s Cube”¬†where she describes watching the tenacity of students develop over solving the Rubik’s cube. I think this is a great side effect of a puzzle. In this article she also links to an article about an American teacher Dan Van der Vieren which I found interesting.
  • In “Math Beyond the Textbook” Tracy Kmosko (@TrayKay11) submitted a post contains a load of links for various non-traditional materials for maths instruction. I particularly like the website about outdoor maths.
  • Rodi Steinig has shared this lovely¬†post¬†recounting the conversations that took place during a “Math Circle” session with 15-16 year olds looking at the concepts of one-to-one correspondences and infinity. There have been a couple of other posts from her that follow on from this one¬†here¬†and¬†here.
  • Learning too Teach” is the first in a series of 5 posts by Melanie where she provides a deeply personal reflection on a mathematics subject knowledge enhancement course she has undertaken during her training to become an elementary teacher. I really enjoyed reading this.
  • Denise Gaskins (@letsplaymath) has shared the great animation by Tova Brown about Hilbert’s Hotel paradox. I hadn’t seen this before so thank you for sharing.
  • Stuart (@sxpmaths) reposted this interesting piece on board games that hide maths well.
  • Colleen Young shared two posts that have proved popular this month: one on using colour when teaching algebra¬†(I was also interested to learn about the Trace Precedents feature of Excel) and this one on multiple choice questions.
  • I found this post by John Trump on counting the legal positions in the game of Go fascinating.
  • Two posts from “A Thomas Jefferson Education” have been shared. The first discusses “7 steps to Successful Math” and one more generally about teaching and learning mathematics.
  • Stephen Cavadino (@srcav) wrote this short inspiring post on him giving an FP1 conics question to a non Further Maths student who successfully answered it.

That’s it for this month, make sure you check out the next one when it is posted which will be hosted at “Life Through a Mathematician’s Eyes“.

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Visualising the Normal Distribution

A short post tonight with a Geogebra resource that I used when teaching the Normal distribution to my year 12 further mathematicians.

I find that the hardest thing when learning the normal distribution and the linear mapping to the standard normal is that students can’t visualise the areas they are trying to find and how they relate. Because of this I made a small Geogebra app that shows how the areas from an arbitrary normal distribution correspond with the areas on the standard normal. It also proved useful for visualising the effect of changing \(\mu\) and \(\sigma\).

Screenshot 2016-01-25 22.28.21

This is available as a webpage and you can also download the geogebra file from this link.

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Call for MTaP Submissions

Following on from Manan’s great last issue of the “Maths Teachers at Play” blog carnival I am hosting this months issue, and will be publishing next Saturday.

Please submit any posts of your own (or others that you have enjoyed reading) either through this form or to me directly either by email or through Twitter. Technically the deadline for submissions was yesterday but as I am a little un-organised at the moment I will take submissions right up till when I publish ūüôā ¬†As it says on Denise Gaskins’ site (she organises the carnival) “We welcome entries from parents, students, teachers, homeschoolers, and just plain folks”.

I look forward to reading your submissions.

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Thoughts on Times Tables

For most of January people have been talking about the new Times Tables tests being introduced into primary schools by the Government.

There has been much negative press about these, which personally I think is unwarranted.

For me there is no need for tests to put undue pressure on children, or increase anxiety – it is all about how they are presented to the children by parents and teachers. I can remember being told by my Granny (who was a maths teacher) to “go in and enjoy it” when I talked about tests and I can never remember hating maths tests. Of course I realise that some children may not particularly enjoy tests, but the “children hate tests and they make them hate maths” talk that is common is a massive stereotype and not universally backed up with any evidence. I believe a more pressing issue is the projection by teachers of their anxieties about tests onto their pupils; understandable since they are often judged these days on their pupils performances on high stakes national tests. I certainly don’t see why a new times table test will lead to children not enjoying mathematics!¬†In addition, I feel that not expecting all children to be able to know their times table facts by the end of primary school is just symptomatic of having low expectations.

But, all of these problems are to do with how tests are interpreted or the results used, not with the tests themselves. This distinction is important to me as I always enjoyed doing tests in maths lessons – they were a time where I could just do maths as opposed to being bothered by other things. A nicely designed test is an opportunity for a child to express themselves mathematically – sadly this seems to be a rare thing…

However, I am a little unsure about each individual question having a time limit. If a student is anxious about maths then their performance in this test is likely to be an underestimate due to the anxiety getting in the way. I’ve only really just started thinking about this issue and came across this paper¬†which is interesting reading – I will add it to the next #mathsjournalclub poll.

Apologies for the slightly rambling nature of this post – it’s more an attempt for me to put some thoughts down for myself than anything. For me fluency with multiplication facts underpins so much of later mathematics, even A-Level students who are weaker at these basic skills struggle.

As a final aside, I was discussing this with an old colleague and we think it should be known as “The Multiplication Matrix” instead of “times tables facts”.

 

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The Fourth #mathsjournalclub Discussion

On Monday the 11th of January we discussed two articles from the ATM’s Mathematics Teaching journal special edition on Assessment.

A storify of the discussion is embedded at the end of this post.

@PGCE_Maths shared a great article from nRich which though aimed at Primary teachers I think is worth reading regardless of the phase you teach in.

I am taking suggestions for inclusion in the next poll (which will be going live on Friday 22nd January) – please get in touch with articles (that aren’t behind paywalls).

On the 11th of January we discussed two articles from the ATM Special Edition of MT on assessment (available at http://www.atm.org.uk/Special-Edition-MT249)

https://storify.com/tajbennison/mathsjournalclub-discussion-4-an-atm-special#publicize

 

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#mathsjournalclub on the 11th January

As written about here, on Monday 11th January at 8pm there will be a special #mathsjournalclub chat to discuss two articles from the¬†special assessment edition of ATM’s¬†Mathematics Teaching Journal.

Here are a couple of things from each article that I think could make discussion points and may provide a bit of focus as you read the articles.

  1. “Encouraging students‚Äô formative assessment skills when working with non-routine, unstructured problems: Designed student responses” by Sheila Evans¬†
    1. Do you use exemplar student responses to develop mathematical thinking in your classes?
    2. Do you think this would work for your students?
    3. The responses in this particular example are designed to stimulate particular ways of thinking – do you think this is a good thing? Is it better than sharing actual pupils work?
  2. “Assessment: Beyond right and wrong” by Matt Lewis¬†¬†
    1. The authors make the point that levels are only proxies for mathematical competence – could we test in a different way to get more meaningful data.
    2. Should we do more teacher assessment in later keystones?
    3. Have you had experience of using a comparative judgement methodology when marking tests?

I really hope you can join us tomorrow – I’m looking forward to a good discussion.

 

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2015 – A Year of Blogging in Review

As a quick post for New Year’s Day¬†I thought I would share my top 5 blog posts of the previous year.

  1. Maths Journal Club РThe first post about #mathsjournalclub. Get involved in the next discussion on the 11th January for the ATM special edition chat, details are here.
  2. John Mason – Another ATM Session¬†–¬†Here I wrote about a fantastic morning that i spent in Leicester at the joint ATM/MA session led by John Mason. He presented some great ideas for use in the classroom, I was particularly interested in his ideas for developing mathematical thinking in those students with weak numeracy skills.
  3. Another MyMaths Post¬†–¬†This post proved very popular over a couple of nights in September as it detailed a particularly bad piece of content on a MyMaths lesson. To MyMaths’ credit, they then did change it within a day!
  4. Carnival of Mathematics 127¬†–¬†In October I hosted the 127th Carnival of Mathematics that is organised by the Aperiodical. There are some really interesting links in this, so take a browse if you haven’t already.
  5. An A-Level Calculated Colouring¬†–¬†In the run up to Christmas I shared a resource for A-Level that I had created. All of last year my classes had been asking to do a calculated colouring so for the last lessons this term I produced an A-Level calculated colouring. This has been downloaded many times and I am very grateful to the people who pointed out slight mistakes.

Over the course of the year I have really enjoyed posting on this blog, and it looks like I have been fairly regular:Screenshot 2016-01-01 00.42.47

For the #summerblogchallenge I managed to post every day for 49 days which I am quite impressed with – I’m going to try and do this again next year. I am hoping to post more next year, and definitely share more resources which I haven’t been that good at doing this year.

Thank you to everyone who has taken the time to read my posts during the last year – it means a lot.