5 Minute Lesson Plans: Area and Circumference of Circles

5 Minute Lesson Plan: Unit Conversions for Area

5 Minute Lesson Plan: 2D Measurement - Composite Figures

5 Minute Lesson Plan: 2D Measurement Formulae

Destination 2014: Magical Maths

Hello, I'm back! I haven't given up on the Destination 2014 series - just had to take an enforced pit-stop while we took our u15 girls chess team to Nationals (where we came 4th in the country, by the way!). But now it's time for the next area of thought - Magical Maths!

While English is my first love, Maths is my first teaching love - it's the first subject I ever taught, and probably my favourite subject to teach. Well, maybe not. I don't know. But anyway I enjoy teaching it.

I've been teaching Maths for four years now, and I believe I am starting to get the basics right. Of course now the syllabus is changing, but I think the underlying principles are remaining the same, and I can teach those. I have a solid selection of basic resources for different topics, and enough headspace to create more as necessary during the year. I have also developed a sprinkling of interesting/inspiring ways of introducing topics and making them come to life which I can reuse each year.

So yes, I think (hopefully without hubris) that I'm a pretty decent Maths teacher at this point.

Now to improve!

The thing about Maths is that it's often awfully dry. Most people don't find the subject interesting for its own sake. They take it because they have to, and hate it most of the time. They struggle with it, stress over it, get poor marks for it. They blame the teacher, blame themselves, blame the system. All in all Maths is a stressful, often unsatisfying subject to teach or learn. Understanding seems to be an unattainable goal.

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The role of the Maths teacher, if anything, is to tie the learner up in knots, confusing them and rendering them complete incapable of making the climb to Mathematical brilliance.

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The Maths itself, rather like Rapunzel's hair, becomes this esoteric weapon which the teacher wields mysteriously, and the learner has no hope of developing for him or herself. But it doesn't have to be. The teacher could teach every learner to wield a weapon. If not the glorious hair of Mathematical truth then at least... the sword of logic? The frying pan of hard work? And once the learners are armed? Well then we can all tackle the tower of Mathematics together instead of working at cross purposes.

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How to make Maths magical? I think the answer is somewhat counter-intuitive. Make it more magical by making it more predictable. Predictability is where the learners will discover the frying pans and swords which will make their Mathematical experience manageable.

Usually I would think that predictability would make a subject boring. But actually I think that predictability cuts down of stress. And cutting down on stress makes learning possible. And once learning is possible - then you can start having fun.

Here are some of the ways in which I will be trying to increase predictability in my Maths classes this year:

1. Structure: Learners need to feel that they know how each lesson/chapter is going to go. I had great results this year when I published a lesson by lesson plan of a chapter before starting. This helped the global thinkers to work out where everything fitted in, and helped the incredibly busy people to plan their workload. And it helped all of us to stay on task.
2. Homework: Unfortunately Maths is one of those subjects where homework needs to be done (and checked in class) every.single.day. I hate this. I find it tedious and boring. BUT. It is necessary. I got it mostly right in 2013, but let it slide a bit (at least the checking part) towards the end of the year when I became demoralised by how many students weren't bothering. That's not okay. I need to find the energy to persist in following this up all year.
3. Independent Work: I want to make a greater variety of resources available to the learners online. This includes extra worksheets and memos, videos, quizzes and so on. I want them to be able to do extra "frying pan drills" whenever they can. In our department we are going to try and make better use of Edmodo to post these extra resources once a week after our subject meetings. This also puts some of the onus onto the learners and parents: if they want to improve, the tools are there.
4. Communication with parents: This is key. It connects with structure, homework and independent work. It links to preparation for tests and exams. The basic principal is this. If the classroom is the battleground of Mathematics, then the home is the training ground. And the parents are the drill sergeants. They just need to know what to do. SMSWEB, Edmodo, emails and phone calls... essential.

I know that despite its title this post hasn't really mentioned much about Maths itself. But all these structural points are what I believe enable me and my learners to actually get the Maths done. Because trust me, it's a WAR out there, and we need to be as thoroughly equipped as possible.

Do you think predictability helps or hinders learning?

yours mathematically

jjr

Dear Government

...in particular the officials of the Western Cape Education Department,

Don't get me wrong, I know you guys are doing a decent job under incredibly difficult conditions. I know I'm fortunate to be a teacher in a wonderful, successful school. 

And I certainly appreciate the need for transparency and teacher evaluation. In fact, I'm all for it.

That being said, I don't think I'm going to be able to provide you with all the paperwork to prove that I'm doing a good job. Those daily lesson plans, the teacher files, the evaluation files, the assessment files, the learner book comments... Allow me to explain:

I usually get to school between 7:15 and 7:30 in the morning. That gives me enough time to check my emails and respond to the really urgent ones (usually from parents) before running down to the printing room to do some last minute print runs. Since I am in charge of one grade for Mathematics, sometimes these are print runs of 200+ copies, which I then need to count and distribute to the teachers in question. Sometimes I get a chance to have a quick cuppa before the morning meeting.

The morning staff meeting runs from 7:45 - 7:55, and gives me a chance to check the outline of my day in my diary. I always know who I am teaching, and have a clear idea of what I want to achieve in each lesson. I don't always have time to write it down in a form anyone else could understand. Sometimes I don't even get a chance to write it down at all.

From 7:55 to 8:05 I deal with my home/tutor class, taking register and dealing with any disciplinary, pastoral or uniform issues that require immediate attention. I have a child near tears during register about once a month, and have ten or so minutes to calm them down, while simultaneously preventing the rest of the class from tearing my classroom walls down. I deal with absentee notes, reply slips and excuse letters during this time. I need to send my kids to class not later than 8:02, so that they have time to be punctual for first lesson - and so that I can get my head into the teaching zone. 

I invariably teach in first lesson. From 8:05 on, I have a new batch of students entering my classroom roughly every 45 minutes, all at different grade levels, and all with different needs. There are five minute breaks between lessons. I try to reserve these for greeting students and starting lessons on positive notes, but often issues arising with kids from the previous lesson use this time up pretty rapidly. Depending on how my morning went, I might have an urgent email to send, or a pile of worksheets to dispatch to another teacher. I may need to send an SOS to the school counsellor or grade head about a child. I also need to switch my projector off to give it a rest, and make sure the computer is working well enough to produce my next set of slides or notes. Sometimes I realise at the last minute that a particular worksheet has slipped through the cracks, and I have to McGuiver a solution for the next lesson.

I teach five grades. Out of the 33 lessons available per week, I usually have three or four free for preparation and admin, less than one per grade - including the grade that I lead. Usually these lessons are swallowed up filling out forms about detentions or missed tests, responding to emails from colleagues and parents, preparing and distributing workplans and worksheets, and setting tests and assessments. It is unusual to have a chance to mark during free lessons. Sometimes I have time for a cup of coffee or tea.

In the remaining 28 or 29 lessons every week, I teach. I never give free lessons - there is no time in the syllabus. I seldom have a chance to revise. Most lessons will be taken up with teaching new content, working through examples and then assisted practice. I try to give homework every single day. It is seldom completed by everyone in the class, but I make sure I go through it for those diligent kids who get it done. In the senior classes, this is usually about 20% of the class. In the junior classes it is more like 70% -  a percentage which I have worked hard at increasing, and am very proud of.

I try to make sure that at least half of each lesson is spent working, and answering questions from the kids. I try to make sure that I am supportive and encouraging, especially of weaker students. I usually spend at least 5 to 10 minutes of each lesson coping with discipline issues.

At break I usually have meetings with members of my tutor class, special catch up sessions for kids who were absent, academic support meetings with the "at risk" kids that I mentor or members of the two sports teams which I manage. I try to spend at least 15 minutes of break in the staffroom, eating my lunch - otherwise I struggle to keep my energy high enough to teach effectively. I have break duty once every two weeks.

School ends at 3pm. From 3 until 3:30 I sit in my classroom, supervising classroom cleaning by the kids in my tutor class, and coping with any situations that the kids bring to me as a result of whatever happened during the school day. At least once a week there will be a major or minor conflict to be resolved between two members of my class. Bullying, fighting, pregnancy, drug abuse, parental issues, boyfriend issues, academic issues - I never know what will land on my desk in this half hour. I try to be discerning about which issues need to be passed on to someone else - I am forever grateful for the excellent support system at my school.

At 3:30 I go to my extra mural commitments - either hockey or chess, depending on the day of the week. I have an extra mural every day. If it is a hockey day, I am able to take some marking with me. If there are no crises with the two teams or the coaches (medical, emotional, disciplinary) then I am able to get some work done on the side of the field. I will tutor kids during this time where possible - especially those who have been absent or lazy and have asked me to help them catch up. About once every two months some fairly minor injury needs to attention, but I am fortunate not to have been involved with any serious injuries so far.

At 5pm, sport is over for the day. I go back inside to finish up on admin before heading home. I usually get home at about 6pm, though I try to do earlier where possible. I am grateful to live close to my workplace - otherwise I would seldom get home before 7pm. I usually have 2-3 evening work commitments per term (PTLs etc...). 

Parent meetings also have to happen during the 3:30-6pm slot, so I have to arrange to be away from my sports practices about 5-8 times per term. Meetings with parents are a great way to communicate, and I try to accomodate them as often as possible. They seldom last less than an hour.

When I get home at 6pm, I am very tired. My husband and I are both teachers, so we are both very tired. If the day has been a particularly traumatic one in terms of the issues that land on one of our desks, we need to debrief for upwards of an hour. We have dinner (usually a defrosted meal that we made over the weekend - if we were lucky), and try to work. I am seldom able to focus on marking or preparation unless it is an emergency. 

As a result, most marking and preparation happens over the weekend, in between sports fixtures. This is also the only time we can see family and friends. Our friends who aren't in education find our social absence difficult to understand. Those who are in education commiserate. Our families get scant attention, despite our very best intentions. 

So please understand that while I'm doing my best to be a decent teacher, your extra paperwork is unlikely to happen. I can barely keep up with the "essentials" of marking and preparation. Please tell me that is more important to you than having your boxes ticked? 

Your sincerely

Belaboured Employee

Teaching Transformations and CAPS

Since the curriculum changed soon after I left high school (2008 for the first batch of matriculants), geometrical transformations (reflections, rotations, translations and enlargements) have been a small but important part of the curriculum in Maths from grade eight through to grade twelve.

If you've forgotten what geometric transformations are then there is a fun free powerpoint with lots of pretty pictures here. There are also awesome notes and visualisation tools here.

Now we have just started grade ten roll-out of a new new-curriculum: CAPS. And we decide to remove ALL transformations from grade 10 to 12. Which is cool...we have to take something out to make room for all the new stuff...

But the problem is that teaching functions (linear, quadratic, hyperbolic, exponential) is really lacking in depth if you teach it without referring back to transformations (I should know, I learnt it without any knowledge of transformations). Functions are so much more sensible if you understand transformations. And Maths should always be sensible. Well, where possible anyway.

Net result: we teach almost all of the transformations (leaving out detailed rules of rotation) in grade 8 and 9. We do basic understanding of physical transformations in grade 8. This means that in a one-two week module in grade 9 we have to achieve a reasonable level of understanding and competency with the rules of translations, reflection and enlargement.

Bear in mind that being decent, hard-working teachers (most days of the week), we don't just want to give them the rules and let them get on with it. We want them to at least have a "hand-wavy" understanding of where the rules come from.

With this aim in mind, I have created a series of worksheets aimed to develop a solid intuition about how the various types of transformations can be represented algebraically. I attach some screenshots of the best bits for your delectation and delight. I will put them on TPT as soon as I've given them a test run (and since it'll be a test run by my whole department it should be reasonably accurate **we hope**)

The aim is to start with what the kids CAN do (writing points as coordinates, physically transforming the shape using geometrical methods...) or at least are supposed to be able to do. Needless to say half of them will have forgotten, which is why I'm planning to use this series of worksheets as "do on your own - now do together" type resources, question by question so that the weaker kiddies don't get completely lost or end up going on their own little completely incorrect mission.

But we need to move very swiftly on to focusing on the coordinates of vertices, and figuring out the relationship between the object coordinates and image coordinates. Otherwise we stay in grade 8 forever...the horror!!

You'll notice that 2.4 represents quite a jump forward. So I anticipate spending a fair bit of time in class looking at the table together and formulating a sensible answer. The second half of question 2 then does exactly the same process all over again with the other translation shown in the image...

Then, after some notes and a fair bit of repetition, we get onto using the notation properly and skipping out the intermediate steps. In other words, actually using the rules which they will now be intuitively happy with.

When we go onto the next installment (reflections), we take the steps a teeny bit faster, and they have to get to the comparison of coordinates a teeny bit more independently. Just to mix things up a bit (and prevent the stronger learners from getting too bored).

I won't bore you with endless repetitions: I do essentially the same thing three times for translation, reflection and enlargement, and a brief version for rotations. The emphasis throughout is on correct notation and terminology, and attempting to make a strong intuitive link between the algebraic representation and the geometric representation.

AND FINALLY...we whizz through a whole bunch of exam type questions. Just to satisfy the endless chorus of "What's in the exam, ma'am??", and of course also to calm the nervous and generally satisfy curriculum requirements. 

What do you think?

Can we get through this in 5x forty minute lessons??

We really need to, so wish us luck!