MathematicsAndCoding

I had seen pictures like this before as it is the classic way of representing how the different types of number relate, but I wasn’t totally happy with any of the ones online. 

So I decided to make my own.   

 I used this in a Year 10 Sixth Form taster session. I will post more about this later in the week. 

I created this image in Geogebra because of how easy it is to draw ellipses and use LaTeX symbols. The file is available here. 

Because of my numerical analysis background I am very passionate about teaching coding alongside mathematics. In particular, I don’t think the A Level syllabus really does justice to the numerical methods component of the course. As most real life problems have to be solved approximately I think that numerical methods are incredibly important, but that teaching them without coding them up is silly!

I have always found that once I have coded something my understanding of a method has vastly improved. Because of this, if there is time I think it is good to expose A Level mathematicians to a bit of programming.

Python is the ideal language for this as

1. It is freely available across Windows, Mac OS X and Linux.
2. The documentation is fantastic,
3. The syntax is relatively straightforward.
4. In it’s simplest form the Python interpreter can function as an advanced interactive calculator.
5. It contains all the functionality of a modern professional program language (i.e. it is not just an academic curiosity)

I believe that number 4 in the above list is one of the big advantages of Python over a traditional compiled language (such as my favourite language Fortran or C++) as this can make the whole concept of learning a programming language for the first time a little bit less terrifying. For students, being able to see almost immediately what the commands they have just typed is very powerful – it must have been awful learning to program with punch cards!

For my first programming workshop with my Year 12 Further Mathematicians I chose to use the IDLE interpreter that comes with Python due to it’s simplicity.

  
With the Python Shell (the rightmost window in the above picture) you can type commands one-by-one and explore Python interactively. Launching the editor window you are able to write programs and then run them with the interpreter. One restriction of Idle with my school’s setup is that I cannot import my own modules – because of this for the next Workshop I will be using PyCharm. 

I gave my students a 6 sided worksheet, with some notes and examples to work through. See below for an example of the type of exercises and the full worksheet is here. 

 
All my students seemed to really enjoy doing a bit of coding, and I was really impressed with how well they got on. I’ve seen 2nd year undergraduates struggle more when they are introduced to Matlab than they were 🙂 

If you fancy having a go working through the sheet, the codes for the exercises are all contained in a tarball which you can download here.

I will write again about the future workshops.

At the weekend I suggested the idea of a Twitter Maths Journal Club. MY intention is for this to run along similar lines to the fantastic Twitter Maths Book club (@MathsBookClub) (blog is here).

I have set up a twitter account specifically for this, so please follow @mathjournalclub to stay up to date.

The plan is as follows: every couple of months a journal article will be selected by a poll and we will then have a twitter discussion for an hour one evening, about a month or 3 weeks after the article has been selected. This will be on a day where there isn’t already some kind of mathschat or #mathsTLP taking place.

As a lot of academic articles are pay-wall protected our choice will be a little limited – so either articles that have open access for a particular journal issue, free to access articles or articles where there are high quality pre-prints available on the author’s website.

My intention is to allow people to suggest articles for the poll on the following month, but to get things started here are the articles on the first poll (together with their abstracts)

• How Ordinary Elimination Became Gaussian Elimination; Joseph F Grcar – Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method — that Euler did not recommend, that Legendre called “ordinary,” and that Gauss called “common” — is now named after Gauss: “Gaussian” elimination. Gauss’s name became associated with elimination through the adoption, by professional computers, of a specialized notation that Gauss devised for his own least squares calculations. The notation allowed elimination to be viewed as a sequence of arithmetic operations that were repeatedly optimized for hand computing and eventually were described by matrices.
• Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Examinations; Ellie Darlington (Teaching Mathematics and its Applications) – This article describes part of a study which investigated the role of questions in students’ approaches to learning mathematics at the secondary/tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics questions in England and Wales to focus on requiring students to demon- strate a routine use of procedures, whereas those in first-year undergraduate mathematics primarily required students to be able to draw implications, conclusions and to justify their answers and make conjectures.While these findings confirm the need for reforms of examinations at this level, questions must also be raised over the nature of undergraduate mathematics assessment, since it is sometimes possible for students to be awarded a first- class examination mark solely through stating known facts or reproducing something verbatim from lecture notes.
• A Glimpse into Secondary Students’ Understanding of Functions; Jonathan Brendefur, Gwyneth Hughes & Robert Eley (International Journal for Mathematics Teaching and Learning) – In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students’ intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able to do so. Instead, these students tend to represent the physical characteristics of the situation. In addition, we discovered that middle- school students had sophisticated ideas of dependency and covariance. All the students were able to use their models of the situation to generalize and make predictions. These findings suggest that secondary students have the ability to describe covariant and dependent relations and that their models of functions tend to be more intuitive than mathematical – even for the students in algebra II and calculus. Our work suggests a possible framework that begins describing a way of analyzing students’ understanding of functions.
• Bridging the Divide – Seeing Mathematics in the World Through Dynamic Geometry; Hatice Aydin & John Monaghan (Teaching Mathematics and it’s Application) – InTMA, Oldknow (2009,TEAMAT, 28,180-195) called forways to unlock students’ skills so that they increase learning about the world of mathematics and the objects in the world around them. This article examines one way in which we may unlock the student skills.We are currently exploring the potential for students to ‘see’ mathematics in the real world through ‘marking’ mathematical features of digital images using a dynamic geometry system (GeoGebra). In this article we present, as a partial response to Oldknow, preliminary results.
• Using Geometric Images of Number to Teach Mental addition and Subtraction, Peter Lacey (Mathematics Teaching) – no abstract available.

It would be great if you would like to get involved, if you do please complete the Poll.

I really hope you want to get involved, I think it could be a great thing to do. Please suggest articles to include for future polls.

Update: Poll closes on 24th July

A week or so ago Graham Colman (@colmanweb) asked, on Twitter, for a definition and people’s views on Mastery maths. 

Before I started teaching I found it slightly odd that people were talking about the “mastery curriculum” as a new thing…. Surely, no curriculum would have the intention of not building mastery of mathematics in students. My personal experience of school mathematics was entirely on top sets and I definitely did achieve mastery and fluency with the concepts – it was just a bit boring repeating all the topics almost every year until Year 11. I was quite shocked, to be honest, when I started teaching and saw how weak some students were when they came into secondary school and how little progress some students made throughout Key Stage 3. 

Because of this I was quite keen to get involved in developing a mastery based curriculum for Year 7 and 8. My school has been working in conjunction with others in the East Midlands West MathsHub (@EM_mathshub). The layout of our KS3 is similar to that from ARK’s Mathematics Mastery scheme but not totally the same:

 
I am hopeful that this approach will lead to a deeper conceptual understanding in all students and lead to improved results as time can be focussed on extending students knowledge over time and not just repeating things. 

For a definition of mastery in mathematics as asked for by Graham Colman I think I would say something like:

 “A student has developed a mastery in mathematics when they can apply seemingly disparate  techniques and concepts in novel ways  to solve an unseen problem”. 

In a sense this is what a research mathematician is expected to be able to do. 

Can we expect this of school students?

I think we can, within the confines of the school curriculum anyway – geometrical knowledge could be applied to tackle an algebraic problem and vice versa for example. 

Spending more time and delving into topics in more detail allows students to be more critical, giving them a chance to learn how to evaluate strategies and choose the most appropriate given a particular problem. 

For this to be successful though I fundamentally believe that students need to be yet with the basic properties of number – being able to decompose calculations into stages that facilitate calculation, deep knowledge of number bonds and times table facts. Some people argue that these skills aren’t so important now that everyone has a relative good calculator on their phone – I disagree! As well as being quicker than finding a calculator and then keying in a calculation these skills also allow you to mentally check the whether a result is sensible. 

Last month I read Ian Davies (director of curriculum at Mathematics Mastery) post “Mastery – What it is and what it isn’t!” with interest. I liked how he explained why he felt that he had mastered addition, but not integration (in fact can anyone truly master integration?) He also quotes Helen Drury’s definition of mastery of a mathematical concept – the importance of being able to move between different representations stands out. 

Almost a couple of weeks ago now (I can’t find the original tweet) John McCormack (@JohnJMcCormack) tweeted to me this “bumping” method for subtraction. 

 

I haven’t seen this method promoted before. It makes use of the fact that the difference between 9 and 4 say is the same as the difference between 15 and 10: 

 

Subtracting a number ending in zeros is clearly easier than subtracting a general number from another and this is the inspiration for the bumping method. This is something that I (and probably a lot of people who have a good number sense) do when performing mental calculations, but I wouldn’t have thought to do it as written method. The only difficulty is remembering of the carry.

Here’s another example:

 

John has a website where he has posted some black and white examples. 

I’d be really interested to hear what you think of this method – I quite like it, but I’m not sure I’d want to teach it as the general method for subtraction.  

Would you teach this method and why? Do you have any examples where you think this will be helpful or where it won’t work?

After having to set my alarm for 04:30 in the morning to make the train I needed to get into London and enduring an annoying rail replacement bus I’m glad to say that #mathsconf4 was fantastic; as the previous ones have been!

Before I describe in a bit more detail I want to mention the only negative aspect – no breakfast pastries. If you know me you will know that I get strangely excited about that kind of thing, so this was very sad. The cute little pot of jam that was given to me by (@tessmaths) did make me very happy though.

I’ll try to briefly describe the best bits of the sessions I went to, and leave the detail to the people who them!

Speed Dating 

The day started with speed-dating to swap activities. In the past I haven’t been great at this, and always wish I had recorded what I had spoken to people about more. So this time I was more planned (I shared my Further Pure 1 geogebra conics task which I have described here) and wrote down the great things I was told about:

Dawn Denyer (@mrsdenyer)  shared her worksheet for low attaining groups which has the answers for each question somewhere in a grid for them to find and know they have likely done it correct. I’m going to try this with some of my classes.

Deb Friis (@runningstitch) talked about the idea of using the “boxing up” technique to get students to write number stories, structured like they would write a story in English. I have seen this technique before from @HelenHindle1 of Growthmindsetmaths.com, but I really liked seeing how it could be used in conjunction with a problem solving lesson to structure pupils thinking without guiding them on what to do.

Japleen Kaur (@japleen_kaur1) talked about using the date as a starter similar to the Commonly known Four Fours problem. I think this is a great starter if you are moving rooms and need something simple students can do whilst the computer loads etc as it reinforces key skills. If as Japleen does it is done regularly it could become a good habit to ensure maths is happening straight way. I liked how even her Sixth form class found this useful.

For the last person I spoke to someone I wasn’t already following on Twitter; Jen Chan (@JenJenDes) showed me a learning grid for area and perimeter. I keep meaning to try these after I had been shown one in my school by an English teacher, so it was good to see an example of a maths one!

Mark McCourt 

Mark delivered the keynote this time round, and it was nice to have a change from the last two, especially as Mark is always an entertaining speaker. He was speaking on the subject of “How can we improve Mathematics Education for all”. His starting point was the fairly depressing assertion which is – we can’t. He discussed Japan, which is seen as a high achieving nation but still reflects on their maths education system and wants to find ways to improve it.  He showed this quote from Japan:

“[If in Japan], the aim of mathematics education is to make pupils hate mathematics, then in this point we may have succeeded”

He also used another quote that I like to refer to from a paper by Jeremy Hodgen (@JeremyHodgen), who is now at the University of Nottingham and co-authors:

“For every aspect of mathematics education linked to high performance in one country, a contradiction can often be found elsewhere'”

This quote led nicely into Mark’s main point – the importance of culture. All the High performing Shanghai countries have a very different culture to ours and this has a massive impact – what works in one place may not necessarily work elsewhere. I was really interested to hear about the paper where the high performance of western born children of East Asian descent was investigated. Tim Stirrup ( @TimStirrup) kindly supplied a link to the paper and I will definitely be reading this during the next week or so.

Mark ended by saying that something that teachers can do to improve maths education is for them to be “intelligent, independent and not just tow the line”. I whole heartedly agree with this.

Now onto the workshops!

From Euclid to You

Emma Bell (@El_Timbre) delivered an excellent session looking at some books in her impressive collection of old maths books. She has uploaded a padlet containing her source materials here.

The mention of Euclid’s elements led to an interesting discussion about Euclid’s five postulates and which ones are used when answering a variety of geometry problems from across the key stages. Maybe we should bring more history into our lessons? I know I don’t mention the postulates in a regular lesson on shape!

Emma also shared a great problem concerning birds from Leonardo of Pisa’s (Fibonacci) book “LiberAbaci” from 1202. I think I may write a separate post about this as it is a good introduction to under-determined systems…

There was a lovely quote from a 1958 book where Bodmas was described as a “travesty of mathematics”. I liked this whole page of division questions phrased in different ways

And I thought the way this question concerning the days between different months of the year was particularly nice:

I recommend that you take a look at Emma’s padlet where the presentation can be downloaded with some of the source materials. Emma has also shared an essay she wrote during her PGCE on proof – I’ll try to have a read of this at some point. Thinking I should also share a 6 lesson plan I wrote on circle theorems during my ITT – I’ve not looked at it since!!

The Best of the U.S. 

This session was delivered by Craig Jeavons (@craigos87) who talkedabout some things from the States. Maths educators from the U.S. are very active on Twitter and maintain a directory of members of the MtBOS community here. Craig explained that he liked using stuff from the States as they are culturally similar to us and their Common Core State Standards (pretty controversial over there) are actually quite similar to our new curriculum.

I’ve used the websites estimation180.com and grapthingstories.com before. I find graphingstories really good when working on real life graphs, with all ability ranges – some of them are actually pretty tricky. The fact that the website is american also provides a good excuse to look at imperial measurements. I’ve only recently come across the website openmiddle.com, and am curently putting some of their questions into my school’s new Year 7 mastery curriculum. As the name suggests, each question has the same start and end point but there are multiple ways to get to the solution (i.e. an open middle). The website is really useful as it categorises the questions by their Grade (remember that a US grade 6 is the same as an English Year 7), and goes up to the end of high school. I really like this question:

Craig then talked about Robert Kaplinsky’s Depth of Knowledge (DOK) charts, for example the one below which I hadn’t seen before 

I’d heard of the DOK as an alternative to Bloom’s Taxonomy (I’ve always been pretty derisory of Blooms to be honest!) before but I hadn’t seen it applied to maths topics before – very interesting and lots of questions OpenMiddle questions in the grid too. I think it would be nice to have something similar for all topics really.

I’m also grateful for Craig pointing out the curriculum maps on emergentmath.com. These link to the Common Core Standards and contain some links to great activities, such as this one “Square Roots go Rational” from NCTM. I’ve bookmarked these for a proper explore during the summer holiday.

Tweet Up

After a great cooked lunch (thanks LaSalle, the lamb stew was really good!) it was time for the tweet up. I played a very minor part in helping run this, all organised by the wonderful Julia Smith (@tessmaths) and with Dawn Denyer (@mrsdenyer) providing us all with some great T-shirts. 

From Left to Right: Dawn Denyer, Nicke Jones, Julia Smith, Emma Bell, Martin Noon, Danielle Bartram, Jo Morgan and me.

We had lots going on, including Jo’s lowest integer game, the QR Cubed Cube, a photo booth, some lovely  O-Level questions. Make sure you come along to the Tweet Up at the next conference everyone had fun – here’s Beth (@MissBLilley) with her folded cube:

What I Learned from Teaching new GCSE content to Year 10 and 11 Students

This session was delivered by Sarah Flynn, a head of department who is also a maths advocate for AQA and as such helps schools in delivering AQA content. I was hoping that there would be more discussion on ways to teach some of the new content, but it was definitely good to look at some questions on topics (mainly graphs and Venn diagrams) that are going to be in the new syllabus and see exam questions from the Linked Pair Pilot programme. We discussed the following question:

 The question asks you to estimate the distance travelled by the snowboarder and state the units of the answer. I was surprised to learn from Sarah that the mark scheme said that the graph should be approximated by 5 shapes – seems like overkill to me! I need to go away and look at the mark schemes for these kind of questions before teaching to get an idea of the error bounds and what is expected. During this session @MissNorledge showed me this trick for finding the exact trigonometric ratios for 0,30,45,60 and 90 degrees.  

I hadn’t seen this before, and generally aren’t keen on tricks – I’d obviously prefer for students to just learn them or be able to derive them, but I do think this is pretty neat!

For me the take home message from Sarah’s session is to not underestimate the students. They may be able to do some of the questions that we feel are more challenging even if they don’t manage the more “basic” questions.

The past papers from the Linked Pair Pilot are worth checking out, there are some quite nice questions, such as this one from 2014:   
These questions do generally seem less challenging than the questions in the new specimen papers though!

The Art of Leading a Mathematics Department

I was really looking forward to this session by Amir Arezoo (@workedgechaos) and it definitely didn’t disappoint! I decided to go this one as leading a mathematics department is something I aspire to, and I thought it was worth getting some tips early 🙂 I was annoyed though that this session was blocked against Martin Noon’s (@letsgetmathing) session about marking – luckily he tweeted out a link.

Anyway, back to Amir’s session (which I like to think was enhanced by the use of my clicker haha). I loved how he used his wife’s description of him to start the session – “daddy, mathematician, geek and moody” – thought it was really useful that he had split the talk into the following 11 key questions to ask yourself as you take over a department

1. Is your department serving the needs of its students?
2. What is your vision for your students and your staff?
3. Do your staff currently have the capability to meet these needs?
4. How do you determine what is best for your students and staff?
5. What does your curriculum look like?
6. How do you engage your students?
7. Do you and your staff reflect on practice?
8. How do you know that you’re moving in the right direction?
9. Who do you look to for guidance?
10. Why did you become a leader?
11. How do you grow the essentials?

Using a set of questions to frame the talk seemed to really help me to reflect on my views as the session progressed and after.

Amir emphasised that he didn’t believe that recounting what worked for him was useful as what works in one department wouldn’t work in another. This led to a nice tie in with Mark McCourt’s point that context is important – the context of the department within the school / within the community is important. How the community views the importance of mathematics is going to affect how your pupils view mathematics and what your student’s needs are. I was very interested in his mention of a “common calculation policy” and looking at my notes has reminded me to ask him more about this! His retort that “Bodmas is a waste of Oxygen” led to a bit of a discussion between a few of us about why we don’t like Bodmas on Twitter which was good.

Amir shared his experiences of things which didn’t work for him, such as trying to change everything in a department in one go.

When talking about point 5 he referenced the great picture from William Emeny of Great Maths Teaching Ideas shown below

    
The high resolution image is available here. I love this network so much that I have it on display in my classroom. As Amir says, it is important that any curriculum addresses the topics that have the highest weight in this network. He talked about having an open door policy – I really like this idea, and I try to ask for feedback from any other teacher that walks into my lesson.

There really is too much good stuff from this session to write about here – Amir please can you blog about it yourself?

To sum up the main points of the session I will use the same quote that Amir used “Character succeeds where personality only promises” – the human side of leadership is important!!

Other Stuff

Meeting more people who i have spoken to on Twitter in real life was great, and I had some fantastic discussions in the pub afterwards; both with people I have met before and those I met for the first time at mathsconf4. There are too many people to mention here…

I’m also sure I have forgotten many great things from the day too.

It was another fantastic event organised by LaSalle and I can’t wait for the next one.

 

 

The Japanese method of multiplication seems to be everywhere at the moment – Julia (@tessmaths) I noticed had advocated it ( I think prompted by a tweet by @missradders) on Twitter overtone weekend and one of my oldest friends posted a video of it on my Facebook page yesterday asking how it works and if it will always work. 

This method is apparently taught to Japanese primary school pupils (note to self: ask the Japanese exchange pupils when they next come!) as an easy method for multiplying large numbers (larger than the times tables anyway). 

It works due to the way that numbers are written down in base 10. For example, 325 is 3 lots of a hundred plus 20 lots of ten plus 5 lots of one. This along with the distributive property of multiplication allows us to split numbers up when multiplying. If I was working out 24 times 12 mentally I would split it up into two multiplications – 20 times 12 and 4 times 12 – then add the results. Mathematically, this can be written as:

\( 24 \times 12 = (20 + 4) \times 12 = 240 + 48 = 288 \)

The Japanese method takes this a step further and says that both numbers can be split up in this way and so that 

\(\) 24 \times 12 = (20 + 4) \times (10+2) = 20 \times 10 + 20 \times 2 + 4 \times 10 + 4 \times 2 = 200 + 40 + 40 + 8 = 288 \(\) 

To multiply using the Japanese method you represent 24 as two parallel lines, a large gap and then another parallel line and represent 12 as 1 parallel line with a gap then 2 further parallel lines. The lines for 24 and 12 cross each other. Then to calculate the product you count the intersections on the right for the units column, the tens is calculated by combining the two sets of intersections in the middle and then the number in the hundreds column from counting the intersections on the left. 

I think that makes a lot more sense in a picture, so here is another example:

  
Some are harder than others:  

 

In the example above the number of intersections in  the middle is 16 and so 10 of them have to be carried to the left, increasing the number of hundreds from 6 to 7.

For larger numbers this method becomes incredibly cumbersome – what withdrawing all the lines, counting intersections and dealing with the carries. See the example below for two 3 digit numbers: 

 I much prefer the lattice/Chinese/Napiers Bones method myself, but that is for another day. 

Firstly, after a discussion on Twitter the other week I’ve decided to delay publishing my workings of the Edexcel exam papers until I know that they are already out there on the Internet. My personal feeling is that the exam papers (not solutions) should be made publicly available (I.e. Not in any secure sections of websites) by the exam boards no more than a week after they have been sat. I can’t see how there is any commercial value in them not doing this, and these days a past paper can’t be used as a Mock (not least because they are released by the exam boards before mocks are likely to take place for A Levels) without students having the potential to have seen them. Having said that, these posts will become password protected before the next academic year – any teachers who want a password just email me. 

Anyway, back to the topic of this post – the Edexcel Mechanics 2 exam; my students were pretty worried about this paper. In light of this I think that the paper was pretty nice – not quite as hard as in previous years, but still some things to challenge the students, especially those who don’t like non-standard questions. 

The paper started nicely, with Question 1 being a fairly straightforward  application of F=ma in conjunction with work done. 

 

I really liked Question 2! The first part is a standard centres of mass of a lamina, but the second part is trickier and isn’t a “standard” question so to speak. As long as you apply the knowledge of what it means for the lamina with the extra weight hanging vertically through a particular line then, with the help of a good diagram, finding the extra mass is a nice problem to solve. 

   

Question 3  is a simple exercise in applying the definition of impulse and then finding out the increase in kinetic energy following the impulse. 

 

Stuart ( @sxpmaths) commented on Twitter that Question 4 is a classic example of the type of question where all intermediate steps are removed (I talk about these kind of questions here). As long as the students are ok at drawing the diagram then the question isn’t any harder than if the diagram had been given. The difficulty is increased though as the question doesn’t guide you through the necessary steps.   
 For Question 5, you’ll see that I made some silly calculation errors in working out the solution to part b – my excuse: it was late!!     

 Question 6 was a (in my opinion) a standard kinematics with variable acceleration question – nothing non standard about this.   The projectiles question was non-standard in the sense that you don’t often see questions with the angle of the particle at a particular (non-initial) point in the motion. Nice numbers hadn’t been used either so you ended up with horrible decimal answers – hopefully students stored the full values in their calculator for subsequent parts. I actually think this should be a requirement, and if they don’t then at most 1/2 marks for subsequent parts – a bit harsh I know. 

  

   

   

The final question  was a really nice projectiles and conservation of linear momentum question finding an inequality for the coefficient of restitution and then investigating further questions. 

  

  

  Overall I think that like most Edexcel papers this year, this paper wasn’t really nice for the students but it could definitely have been a lot harder! 

Whilst I was out tutoring last night I missed a post from Jo (@mathsjem ) about Prisms… There was a debate about whether a cylinder was a prism.

I had always understood a requirment of a solid being a prism was that the base of a prism was polygonal – i.e. made up of straight lines. This means that a cylinder cannot be a prism. However, the formulae sheets from GCSE papers seem to disagree, as this picture from the Edexcel papers shows:

Here we have a “prism” that clearly has curved edges forming the cross section.

I know quite often the volume of a cylinder is taught by referring to it as a prism with a circular cross section, but I haven’t seen any reliable definitions of prism that include cross sections with curved boundary. Instead, all definitions I have seen specifically require that the face is polygonal, for instance this definition from Wolfram’s Mathworld. Here they reference an old book on solid geometry as a source of this definition – Solid Mensuration with Proofs by Kern & Bland – @El_Timbre do you have a copy of this by any chance?

Keith (@MrKMorrison ) suggested that the word prism comes from the greek ‘prisma’ which literally means ‘something sawed’, suggesting the same face throughout, and so a cylinder should be a prism. I think the root of the word is largely immaterial, once an accepted definition is present. For instance multiply is a word in general usage and with a precise mathematical meaning, the root of multiply is the old French (I believe) for increase, but mathematically we wouldn’t use the word multiply to mean this. 

In the grand scheme of things I guess it isn’t really a big deal to call a cylinder a prism – a cylinder certainly “behaves” like a prism, and maybe for lower attaining students calling a cylinder a special prism perhaps helps. For students going on to study maths though I think being loose with definitions can lead to problems, especially once they get to university. 

I alluded to prime numbers in a tweet this morning as being what I think is the most dangerous example of miss-teaching of definitions / miss understanding of a definition. I’ve had so many students (including undergraduates) say to me that 1 is prime because it only has 1 and itself as factors. This is despite the definition of a prime number explicitly excluding 1. I’ve always found this quite odd……

Update: Mike Lawler (@mikeandallie) provides me a link to this nice definition from the Art of Problem Solving