18 October 2014

5 Maths Gems #10

Have you ever wondered where the word mathematics comes from? Me neither. But this is actually quite interesting:

Latin mathematica was a plural noun, which is why mathematics has an -s at the end even though we use it as a singular noun. Latin had taken the word from Greek mathematikos, which in turn was based on mathesis. That word, which was also borrowed into English but is now archaic, meant "mental discipline" or "learning", especially mathematical learning. The Indo-European root is mendh- "to learn." Plato believed no one could be considered educated without learning mathematics. A polymath is a person who has learned many things, not just mathematics (source: Math Forum).

So my fellow polymaths, here's my weekly maths gems. Creative maths teaching ideas, inspired by the great minds of Twitter.

1. Etymology
On Tuesday @letsgetmathing led a great #mathscpdchat about literacy in mathematics. There's a useful summary of the chat here. I've written a post about developing maths vocabulary before but now I have a new idea to share.

There's great value in talking to students about the etymology (origin) of mathematical words as they arise. It helps students make connections and builds on their understanding of mathematics. Our role as teachers is to enrich our students' lives with knowledge, and knowledge of etymology is both interesting and important. This fantastic article (a must read!) says "Etymology provides a safety net of de-mystification. When all the words you hear are new and confusing, or when those around you put old words to strange purposes, a grounding in etymology may help".

Thanks to @CParkinson535 for telling me about etymonline.com. I've taken the following excerpts from this website, just to give you an idea of the kind of thing you could share with your students:
  • hexagon (n.) 1560s, from Latin hexagonum, from Greek hexagonon, from hex "six" + gonia "angle" (see knee).
  • locus (n.) (plural loci), 1715, "locality," from Latin locus "a place, spot, position," from Old Latin stlocus, literally "where something is placed," Mathematical sense by 1750.
  • vector (n.) "quantity having magnitude and direction," 1846; earlier "line joining a fixed point and a variable point," 1704, from Latin vector "one who carries or conveys, carrier" (also "one who rides"), agent noun from past participle stem of vehere "carry, convey" (see vehicle). 
  • binomial 1550s (n.); 1560s (adj.), from Late Latin binomius "having two personal names," a hybrid from bi- (see bi-) + nomius, from nomen. Taken up 16c. in the algebraic sense "consisting of two terms."
Thanks also to @the_chalkface for sharing the list of words below, most of which I'd never heard of. Although we should always endeavor to use accurate mathematical vocabulary when we're teaching, some of these words may be a step too far!

2. Plickers
I've never paid much attention to interactive voting systems before because my school doesn't own the necessary devices. The idea is that students simultaneously respond to a multiple choice question or opinion poll using a wireless system. The teacher can gather and analyse their responses instantly.

I can't give my own opinion on their effectiveness as a teaching tool, but benefits are listed here as: improved attentiveness, increased knowledge retention; poll anonymously (unlike a show of hands); track individual responses; display polling results immediately; create an interactive and fun learning environment; confirm audience understanding of key points immediately; gather data for reporting and analysis. So they are similar to mini-whiteboards for formative assessment, but they have some clear advantages. The main disadvantage is the purchase and maintenance cost. 

I've been reading a lot of tweets and posts about Plickers lately and am keen to try it out. Plickers is a free app for your phone or tablet. Print and distribute voting cards and ask students to hold up their card in the correct orientation to indicate their answer. Scan the room with your phone to collect the data. You can load up questions and students' names on the user-friendly Plickers website

I've read some great ideas to make this work well in maths. One is to permanently stick the cards to the back of students' books (from this post) and the other is to use a separate PowerPoint for the questions to give you more flexibility (from this post) - this means you can use diagnostic questions from @MathsDQs

I'm going to try using Plickers at school soon and am thinking about running a session at the National Mathematics Teacher Conference on Pi Day 2015 demonstrating Plickers (amongst other things). Please let me know if you think this would be helpful.

3. Misconception board
@amyjscudder shared her interactive display for tackling misconceptions in this blog post. It works like this: create a true/false board in your classroom and stick a statement on it that represents a common misconception. Underneath the question are two small whiteboards - one for students to write their name if they think the statement is true, the other for students who think the statement is false. What I like about this idea is that students can easily switch their answer from one board to the other if they learn something that changes their mind. At the end of the week the answer is revealed and discussed. Helpfully, Amy's post provides some example statements to get you started.

4. Feedback
Now that Ofsted have helpfully clarified that schools don't need to micromanage teachers by imposing prescriptive and time-consuming marking policies, let's have a look at some practical tools for feedback that you can use during maths lessons. This brilliant blog post, written last year by @dan_brinton, is full of great ideas. You may have seen some of these before (like fantastic feedback plasters) - here I'm featuring two ideas that are new to me.

First - Dot Round, an idea which came from @Doug_Lemov’s post 'Has Anyone Tried a “Dot Round”?' and also featured in @LearningSpy's post “Marking is an act of love”. The feedback method is described in Dan's slide below. I think this could work really well in maths.
Second - Verbal Feedback Stampers. I've seen stamps used before but not in the way described here. The key point is that when you give your students feedback during lessons - whether it be about their method, their workings, a mistake or a misconception, you stamp their work and they write down what you said. They then correct their work. The idea is from @shaun_allison's post 'Verbal Feedback Given...'. I like this because it means my students will really have to listen to my feedback and acknoweldge it - no more empty nodding - and the stamp will act as a reminder of the conversation.

@shaun_allison's blog is always full of great ideas. In his most recent post 'Success with low ability students' I like the idea of a 'portfolio of excellence' in which students display examples of their best work (this could be work they really struggled with).

5. More Post-its!
The amount I talk about posts-its, you'd think I'm sponsored by 3M! Here's two more post-it based activities I've spotted this week.

The first idea is inspired by something I saw on Pinterest (I'm not sure where it originated so apologies to whoever took the photo shown). In a Pythagoras lesson, or any topic, you could put questions on posters around the classroom. Students answer on post-its and stick their answers under the question. This has similar advantages to the 'Stuck Post-its' I featured last week in that you'll be able to see which questions remain unanswered, but in addition you'll be easily be able to keep an eye on workings to check understanding. 

The second idea is from @eatf105. At the start of the year put up a large 'literacy board' showing the letters A to Z. If a student hears a new keyword during a maths lesson, they can take a post-it and add the keyword and definition to the A to Z board. Because post-its often fall off, this might work better on a pinboard - students could pin up an index card instead. By the end of the year you'll have a student-made wall of keywords and definitions.

What I've been up to
My post on teaching trigonometry has been very popular this week.

I've also started writing Bitesize Gems (should have called them Midget Gems - thanks @taylorda01!). These are designed to be printed onto postcards to provide flashes of inspiration to busy teachers who don't read my blog. I intend to convert all of my previous gems posts to Bitesize Gems and am aiming for a collection of 100.

I've also been exploring my new subscription to MathsPad. I love their cleverly designed resources, like this new rounding worksheet.

I'll leave you with a fantastic joke shared by my good friend (and maths rival) from school @MikeMJHarris who is now developing software for mathematics education. I’ll be sharing this joke with my Year 12s when we cover convergent geometric series.

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