lim joe→∞

Teaching, Mathematics and Teaching Math.

Posts Tagged ‘Teaching’

Expectations

Posted by forumjoe on January 10, 2011

To go along with the class discussion on why we study maths, the first lesson needs to discuss expectations. I believe this will help clarify in the students’ minds what they can expect from the course, what they can expect from their teacher, and what the teacher expects from them. If we make this explicit at the beginning of the course, I hope to reduce student misunderstandings about what is required of them.

Here’s the list I’m working on, but I’m sure it’ll grow over the next month.

Expectations:

What can you expect from this course?

  • This course will hopefully teach you what you need to know to pass the course, to survive subsequent years of mathematical study.
  • Does not teach you how to be a good mathematician!

What can you expect from your teacher?

  • I will always attempt to be prompt and reliable.
  • I will always be available to help; before school, after school, at lunch and recess.
  • I will always do my best to help you learn the content and to get the best results you can.

What do I expect from you?

  • I expect you to be polite.  You should show respect to your fellow students and your teacher.
  • I expect you to not waste my time. This sounds selfish, but if you waste my school time, you’re not taking it from me, you’re taking it from other students who need it.
  • I expect you to not disrupt the learning of others.  Everyone has the right to a hassle-free environment.
  • I expect you to use the feedback on tests and homeworks effectively.  This is what I do it for.
  • I expect you to take advantage of my availability.
  • I expect you to do work at home above and beyond what is called for by the homework*.

Homework is a bit of a separate issue, and I’ll be making my expectations of homework submission clear at another time.

 

Does this sound fair to the students?  Would you have liked it if a teacher made this clear when you were at school?  Should there be more expectations in any category?

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Why is Mathematics a core subject in school?

Posted by forumjoe on January 1, 2011

Mathematics contains much that will neither hurt one if one does not know it nor help one if one does know it.

– B. Mencken, 1715

In order to get my students to think a bit more about what they’re studying and why they’re studying it, I’m going to ask them the above question… Why do we study mathematics?

And I’m going to get them to really think about this. First individually, then in groups, but not in the way that can be brushed of with “Because its important”. However, if I’m going to ask my kids this question, I’d better have some idea about what the answer is, so I decided to do some research and discuss the results here.

It is my belief (though I can find no factual evidence of this) that 90% of careers and occupations use no maths higher than Year 8 level. Beyond addition and subtraction (which cash registers and calculators can do anyway) how much maths do you really need to survive in society these days? Why do we force students to study maths beyond this level? Sure, there should be maths classes covering calculus and algebra and trigonometry in highschool for those students who WANT TO BE THERE, and these should be wonderful, happy places where students creatively solve problems and learn about the world, like Lockhart envisioned.

Mathematics is looked at by society at large as a “necessary evil”. Why is it necessary? Do schools make Mathematics a compulsory subject because society sees it as necessary? Or does society see it as necessary simply because “everyone has to do their dues” in the mathematics classroom as a child. Parents expect their children to study maths because they themselves studied maths as a child. But if they’re not going into a career that requires maths, why do they need to study it?

The SIN rule
The Mode of a dataset
The Volume of a right prism

When will people ever need to use these things unless they get a job in a field that requires it? The only reason to understand these concepts in maths is because they’ll need to build on their understanding next year. It’s a repeating cycle. “You need to learn [x] because it will help you learn [y] next year”

Cut The Knot’s manifesto – http://www.cut-the-knot.org/manifesto/need_it.shtml – has a great collection of quotes on this issue from throughout the ages, for both sides of the argument. Here are some interesting ones that I’ll be showing my kids to start discussion on this:

J. B. Mencken, De Chralataneria eruditorium, 1715 (quoted in C. Fadiman, The Mathematical Magpie, p. 256):
Mathematics contains much that will neither hurt one if one does not know it nor help one if one does know it.

Has anything changed since 1715? I think many people would agree with this statement today.

Fran Lebowitz (b. 1951), Social Studies, “Tips for Teens”, 1981.
Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra.

Phwoar, no such thing as Algebra!? But what about… oh. How about… hmmm. Surely… no, ok. Maybe you’re right.
Algebra is a great mathematical tool. It’s great for solving mathematical problems and it is a fundamental building block for many subsequent mathematical concepts. But if someone doesn’t learn it, or doesn’t understand it, will it affect their ability to contribute to society?

R. P. Boas, Jr., If This Be Treason…, Amer Math Monthly, 64(1957), 247-249.
When I was teaching mathematics to future naval officers during the war, I was told that the Navy had found that the men who had studied calculus made better line officers than men who had not studied calculus. Nothing is clearer (it was clear even to the Navy) than that a line officer never has the slightest use for calculus.

So now, perhaps, we are approaching the crux of the problem. Why is this so? Why does studying calculus help in an occupation that has no use for calculus? I can think of a whole bunch of possible reasons, but I don’t really know. Hopefully this is where my research will lead next.

There are lots of great quotes in Cut The Knot’s manifesto, and I encourage you to check them out. Many have anecdotal evidence about how studying mathematics helps develop the mind in ways useful for many careers. I shall leave you with one of my favourites. Benjamin Franklin, in 1787:

It seems to me, that if statesmen had a little more arithmetic, or were more accustomed to calculation, wars would be much less frequent.

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Do things to post about

Posted by forumjoe on June 24, 2010

I promised myself that during Term 2 (which I’ve just started) I’d post one thing a week on my blog about my teaching. If I wasn’t doing at least one thing a week that was interesting, exciting and different then I’m doing something wrong. Right?

Enough excuses about teaching a curriculum I haven’t taught before, or being only new to the profession. If I’m not innovating then I’m doing something wrong. Right?

*sigh* If only. Last week I posted about my survey, and hopefully I’ll get some more responses there. That will sit and gather data for a while. This week? Reports.

Reports

How do you find reports? I’m new to this game, I’m not good at writing them. Combine that with being a bit of a perfectionist who agonises over the right choice of words at the best of times, and this week I’m feeling like a zombie. Every spare minute I get, write a report. 8 hours at school a day, and then four hours at night writing reports.

I’ve just finished my 50th one (out of 95 I’ve got to write). Word tells me that I’ve written 4,682 words so far. That’s 93 words per report. 93 words to sum up each precious cherub I teach, what they do right, what they do wrong and what they can improve, plus a few little motivational ones in there too. I know it’s an important part of the job, and parents value this information like diamonds. But by crikey, I’m tired.

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Finding Motivation – The Mathematics RPG

Posted by forumjoe on June 14, 2010

{I’m getting a few visitors from Riley Lark’s Virtual Conference on Soft Skills which is great to see. Hi, everyone.
If you’re a teacher and you’ve got a few spare minutes, I’d really appreciate it if you could fill out a survey for me. I’m gathering data about teachers around the world, and I really need more responses from everywhere. There’s only a few questions about how many hours you work, so if you want to help out go to this post of my blog. Cheers!}

Five students, Huh?

I have one Year 8 class that is specifically modified to give attention to those students who need it most.  Five students in the class, with modified content that is supposed to be “within their grasp”.  These are students with identified difficulties in learning mathematics for various reasons.

Although there’s only five students in this class, there’s still a larger range of learning styles, abilities and personalities in this class than in a normal-sized class of 24.  I have to diversify teaching methods and content just as much, if not more, compared to my other classes.  But the biggest problem of all is motivation.

Motivation?

Yeah, motivation.  It’s hard to describe how these students look at the mathematical world, although I’m sure anyone who’s taught a similar class will understand. There’s nothing you can possibly do to make it interesting (not even the WCYDWT suggestions I’ve tried) because a probable response will be a shrugging of the shoulders and a “who cares?”. They’re all awesome kids, and I love them all, but I know I’m not reaching them. Just going through the motions and teaching them what I can. Anything they do pick up is a bonus. It’s a sad state of affairs.

A lack of motivation leads to other problems.  Organisation was an issue, with many students not even bringing anything to class most days.  Absenteeism was high from this class at the beginning of the year.  General refusal to attempt anything asked of them

But over the last four weeks, I have at least got them to look forward to coming to Maths class, which is something that 4 months ago I would have thought impossible.

The Mathematics RPG – Making the entire course into a game

I started awarding XP to students for things that would benefit their learning (re: Behaviour I wanted to see).  These range from “Turning up to class on time” to “submitting homework” and losing points for things that interrupt the flow of conversation.    I started out by giving each student a list of these instructions, with a list of things they can earn and lose points for. Get the sheet here: 8 Modified Maths – The RPG (if you want an editable doc, just ask).

As additional motivation (since points just aren’t enough) I needed a levelling mechanic and a way to specialise their character.  I designed these fairly simplisticly initially, as I just needed something simple I could run with.

The Effect

I had no idea if this was going to work, but anything was worth a try.  Here’s what happened.

The kids didn’t care.  It just seemed like a boring idea, and they thought they’d have to add up their own points or do some maths or something, and it looked too much like Maths.   But I had an excel spreadsheet ready to go to keep track of their score, and had it on the screen during the first lesson I implemented.  Kids started earning some points anyway (just by paying attention) but no one seemed to care.   At the beginning of the next lesson, everyone who was there on time automatically got 10 points, and something surprising happened.  The two who showed up late were UPSET that they didn’t get the points.  Thought they were disadvantaged by not being early, so they worked harder during the lesson to catch up! I’ve never seen these two kids contribute so much in class all year, but all of a sudden they cared about the game.

And from there it’s built and built and built.  Kids have suggested things that should be worth points (and even some things you should lose points for).  If I really want to get attention I can say that participating in this discussion will earn you 20 XP.  They are really excited at the idea of getting to level to choose a specialisation (none of them have it it yet).  They are eager to come to maths to earn more points to get ahead, or to catch up, it’s really exciting to see.  As a side note, they’re getting better results too, but that’s academic.  They’re enjoying coming to class, that’s the important thing.

What would I do differently?

Nothing really.  Starting simple and building on it makes it easy to get to grips with early.  I plan on adding extra mechanics as we go along, when the novelty wears off (it shows no signs of that yet) The only downside is that it’s manageable precisely because there are five students in the class.  I track scores for everyone, I put the leaderboard up on the screen I can see easily who’s got all their gear, etc.  In a class of 24, this could get pretty damn tricky.  I haven’t decided if I’ll attempt to bring a stripped down version to my larger classes or not, but for the moment it’s working.

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Teaching Around the World survey, now released

Posted by forumjoe on June 10, 2010

I’ve finally finished planning my survey, so it’s time to release it on the world.

If you’re a fulltime teacher, it would be great if you could fill out my survey here:

http://bit.ly/9a5E4M

It should only take 5-10 minutes of your time.

It would be even better if you could tell other teachers you know to fill it in too.  If they’re from another country, awesome, but even if they aren’t then hopefully it will help the word to spread.  My goal is to get at least one response from each continent.

I should point out that this research isn’t for any greater purpose.  I will not be writing a paper on it, or using the results for my own nefarious needs.  This is something I’m interested in after discussing the issue with a few international teachers over the last few months.  I do promise to make all the results public, and to discuss any observations on the results.

Cheers

Remember, pass the link on to as many colleagues as possible!

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International Comparisons of Maths Teachers

Posted by forumjoe on May 19, 2010

I’ve been doing lots of thinking about things like blogging.  I read a few other people’s teaching blogs, and it always seems that they have so much TIME.  Maybe it’s because I’m new to the profession, but I don’t see many Australian teachers blogging about their work to the same extent as British and US.  It got me wondering about the sorts of hours they put in to different roles.  US teachers talk about office hours where they are there for their students to come and ask questions, and this gets used a lot more than my similar time here.  I’d really like someone to describe a typical day of a US Teacher to me to make the survey more appropriate.

So, I’m going to pose a questionairre that I’d like responses to.  I’ve got three weeks Winter Break coming up, so I’ll be able to collate the results if I get enough information.  First I’d like feedback on my questions though.  Don’t answer these questions, just tell me if you think I’ll get valid data, or if I need to clarify things before I publish.  I’ll post a Google.Docs survey when I nail down the questions.

A Survey for Full-Time maths teachers around the world

Country:

Ages Taught*:

How many different class groups do you teach?

Per week, how many hours are you in class, teaching students?

Per week, how many hours are you at school for?

Per week, how many hours do you spend on Pastoral Care?

Per week, how many hours do you spend in staff meetings?

Using keywords, what else do you do in your school time not covered above?

Per week, how many hours do you spend at home marking or preparing?

Per week, how many hours do you spend reading/writing/contributing on the Internet with other teachers?

Any parts of your job that you feel important that aren’t covered above?

Any other comments?

*The Primary/Secondary schooling divide is different for countries, and “7th grade” means different things in different countries, so I’d rather get the range of ages taught as a more comparable metric.

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Steven Strogatz's Opinionator – NY Times

Posted by forumjoe on May 18, 2010

I’ve just spent an evening reading and re-reading Steven Strogatz series of Opinionator editorials in the new york times: http://opinionator.blogs.nytimes.com/category/steven-strogatz/

I’m absolutely amazed at Strogatz’s ability to explain complex mathematical topics in a way that is understandable by most adults.  The links he provides in his notes sections go to incredible websites that provide hours of enjoyable and informative perusing.  The sort that makes me feel happy about reading about Maths at 10pm at night.

I really wish I could find a way to make my kids read these articles and understand them, but I’ve realised that’s impossible.  By definition, if I show my students an article, they will think it’s boring maths and switch off straight away.  Maybe if I print them out and get the students to paste them to the back of the cereal packet?

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Back at school – Day 0

Posted by forumjoe on February 3, 2010

So, over the holidays I did lots of things, but not much of them to do with teaching or planning. I’m now at my new school, and this is day 0. The last two days have been staff only days with lots of seminars and meetings and stuff, and this afternoon, finally, I get some time to myself in my office to organise my workflow and my classroom. I’ve spent some time setting up my work laptop to be just the way I want it (including getting all my contacts up to date from all sources). My organisation method is for another post, but right now I’m setting up my classroom to be how I want.

Finding some good maths posters for the classroom is difficult. There are a few old tattered ones in the maths office, but they’re fairly bland and boring for the kids. I ask you, all you teachers out there, what do you decorate the walls of your classroom with?

Tomorrow the kids come back. I’m having fun drawing a massive maze on one of the poster-walls, and sprinkling the important school notices (like uniform policy, fire drill procedures, etc) as walls of the maze. Should get the kids looking at them a bit more, and might provide a talking point.

Oh, and I got my timetable. I’m teaching grades 7-10 (11-16 year olds) with some classes of each. It’s going to be a crazy year, I’ll keep you posted on my sanity at regular intervals

I haven’t even had a chance to read teaching blogs yet. That’s my job for this upcoming weekend.

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Start here…

Posted by forumjoe on January 7, 2010

For the record, so I can look back and see where I was at professionally it’s this:

After one year in the profession, I don’t think I’m a very good teacher. Sure, lots of my kids got good marks last year, and I think I developed a good professional relationship with my peers and my students and their parents. I think even one or two of my lessons might have been engaging and interesting for my students. The most important thing for me at the moment is that I don’t mind this, because I’m trying my hardest. Teaching is easy, GOOD teaching is hard, and I’m confident that I’m improving constantly. But I also feel I could be improving faster, for which I’m going to be doing a shitload more reflection this year. I’m going to make a prediction now that if I look back on this paragraph in a year, or five years, or 20 years, I’ll say to myself “Huh, I still feel just like that now”. I don’t think it’s a bad place to be though. If I ever get complacent about my teaching, I’m not doing it right.

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Disconnected Metablogging

Posted by forumjoe on January 7, 2010

I’m not big on New Years resolutions. I usually make some superficial ones that I know I’m going to achieve easily. Things like “I won’t drink any alcohol for all of January” or “I’ll do more gardening this year than I did last year”. Those two seem to be the main recurring ones, actually.This year, I’m doing it differently, and I’ve decided I’m going to improve myself in every way I can. I’m not calling it a New Year’s resolution, because that implies I’ll stick with it for a while until I decide I don’t want to any more. And the simple rule that I’m living by is that when I’m sick of it, that’s when I’ve got to start doing it differently. This happened with my running, it’s amazing how easy it is to do exercise when you’re not running up and down the same road, with the same thoughts in your head. Taking an iPod and a dog and going on different routes makes life so much more interesting (especially if it involves trespassing)!

So how will my teaching change? Hopefully, a lot, and hopefully, this blog will be a catalyst.

I’m about to start my second year of teaching. I read a lot of teaching blogs (both Maths specific and others) and I find them all amazing. Eye-opening, uplifting, crazy, intelligent, irrelevent, irreverent are all words that describe posts I’ve read over the last year. But even the ones with “early-career teachers” are still from teachers that have been in the profession for four years. I’ve been in it for one, and that one was so hectic, so crazy busy, that I hit the ground with both feet running and didn’t get time to pause. I read so many great things, so many things I want to do, but can’t even imagine having the time to implement in my life. And everyone says this is normal for a beginning teacher!

My three biggest excuses for not posting more are:
1) Dial-Up internet – Yeah, I know, it’s 2010 and no one is on Dial-Up anymore, right? Wrong. Well, as good as anyway. I have to turn the modem on whenever I want to read something on the internet (the first hassle) and I pay per megabyte. Apalling, I know, but what’s more apalling is that I let this be an excuse. Unless I stimulate my mind by reading things, it doesn’t get thinking and it doesn’t get writing. I feel my life is so severely crippled by a lack of always-on internet, and it depresses me that I rely on it so much. And yet, I need to accept that this is who I am. My mind needs stimulation, and the way I’m accustomed to getting that information is through blogs, political essays, theorems and white-papers. Even if I got the information from *ahem* BOOKS, it doesn’t have the immediacy to prompt me to jump on the computer and write about what I read.

2) I don’t have the time – This is stupid, I should stop playing computer games and spend the time writing. It’s amazing what a good “To-do” list does for your motivation to get things done. I’m one of many people who spend too much time saying “I should do something about x” when I could just get up and do x. This is the one area I’m focussing my improvement on this year. I will not make up excuses for putting something off (which is why I’m posting this blog at 1:05 am when I should be asleep)

3) I don’t have anything to write about – I know lots of people who cite this as a reason for not having a blog, and just as many more who carry on blogging regardless. How can I make my posts interesting and useful? Well, I’ve realised the first isn’t important. I don’t care that no one reads my blog, because this is now my journal. My personal journal that lets me document my life as a teacher. As long as this is useful to me, that’s all that matters. Throughout my teacher education at CSU, I was told the importance of Reflective Practice. That is, that everything you do as part of being a teacher gets reflected on and (hopefully) improved. This might be done with scientific method, but it doesn’t have to be. After every lesson, ask yourself what worked, what didn’t work. If you’re trying something new, ask why? What do you hope to achieve? A simpler term for this practice is “Looking at yourself with a critical eye” and there are plenty of resources, research papers, textbooks and tales on how to do this right, but no one can do it for you.

Already I feel crippled by my lack of internet. I’m doing this post as a rant, and haven’t yet referenced anything or anyone else, and I hate it. I could mention the blogposts that Maz and Taiters discussed (which I followed and read) because it really is mental stimulation and reading that creates a desire to write. And I probably should. But on the other hand, that would require going into the loungeroom, turning the modem on, finding the pages, making sure I reference them right etc. And having unrestricted net access just causes more distractions.

So this is the blogging I’ll do in January. Disconnected. Writing posts without looking at the internet, then just uploading them when I next check my email. It will be a challenge, but hopefully it will be useful. Maybe the following morning I’ll post a followup, finding the links, paying my dues. Maybe I won’t. But I am determined to keep this up. Even though I’m on summer holidays at the moment, I’ve got a lot of things to do with my teaching. All centre around the words of “Get organised”. So now I’ve begun to get my blog reading and writing organised, (in the manner of getting motivated and recognising the excuses I make), next step is around managing resources. I’ve got a pile of paper-resources and a drive of electronic ones, and they need to be sorted in a way that they can all be found quickly and easily when I need them. I might do a bit of reading, then a bit of planning, then put it into practice, then discuss my results online (including
self-reflection), and seek feedback from others. That seems like a good pattern, lets see if it works.

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