Solving Problems

I had an amazing lesson with my year 9 class today!
They’re such a beautiful bunch of kids – we get along well and they’re all so keen.

We’ve been working on solving linear and quadratic equations and we’re about to move onto simultaneous equations. I decided to introduce them to the concept and the mathematical ideas that they’re going to need, without actually telling them that they were doing these scary things called simultaneous equations.
I also wanted to force them to practice communicating mathematically, because they can always do with some practice.

I split the class into 5 groups and gave each group a problem that they needed to solve and would explain to the class later in the lesson. Some problems were harder than others so I strategically gave those to my stronger students.

The decorations on this mobile weigh 480g.  Find the weight of each diamond, star and circle.

The decorations on this mobile weigh 480g.
Find the weight of each diamond, star and circle.

How tall are the adults? How tall are the children?

How tall are the adults?
How tall are the children?

How much would one doughnut cost? How much would one muffin cost?

How much would one doughnut cost?
How much would one muffin cost?

What do each of the animals weigh?

What do each of the animals weigh?

What is the value of each of the coins?

What is the value of each of the coins?

Within a few minutes every group knew what the answers had to be, but they’d figured it out by trial and error. Now the fun part – forcing them to find another way to figure out the answers, and be able to explain their method to the class.

I gave a few hints but largely they worked really well together and had some really great discussions. Then each group got up in front of the class and explained how to solve their problem and answered questions from the rest of the class.

We had about 20 minutes left so I handed each student one of these game cards:

I asked them to choose values for x and y, substitute them in and then write their answers. Then they switched with someone else in their groups and had to try and guess their numbers. They started with “nice” numbers (small and positive) and then started challenging each other by choosing negative numbers and decimals.

Most students were just using trial and error, but a few were starting to experiment with substituting. Before we left I asked students to raise their hand if they liked trial and error as a way to answer a question. More than half the students raised their hands. Then I asked if anyone had been frustrated with using trial and error once the numbers got “trickier”. Almost everyone put their hand up. I told them that next week we’ll start looking at more formal ways to solve simultaneous equations.

As if to prove my point, one of my boys then called out “Miss! Miss! I’ve got one for you to try and solve!”. He handed me the card and it only took me a few seconds to use the elimination method in my head and come up with x=-0.5 and y=0.2.

They were amazed: “wow!” “what? No way!” “miss you’re a magician!”

It was brilliant! I ended the lesson with “that’s what I’m teaching you guys to do next week!”

Conduct an Investigation

I’ve just finished the topic of Data with my year 8 class and it was massive.

We looked at interpreting and drawing different types of graphs, misleading graphs and data, types of data that can be collected, ways of collecting data, organising data into frequency tables, ways to plot data, and summary statistics to help us interpret data. All up we’ve spent just over 6 weeks on this topic.

To round everything up nicely and to try and bring all these concepts together, I decided to have my students conduct an investigation where they need to collect data then organise, display and interpret their results. We spent 90 minutes working on this mini-project in class, and i’ll give them another 45 minutes next lesson to finish it all off (and make it look pretty!)

Here it is if you’re interested (i’ll post some finished posters when they’re done)

Point and Laugh (at yourself)

As a teacher you need an abundance of lots of things – pens, whiteboard markers, patience… but you also really need an abundance of self-esteem.

There will be times when you take a step backwards and trip over a bin.
When you get excited and a little too animated when talking to the class and accidentally fling a whiteboard marker across the room.
When you try to say “measures of centre and measures of spread” but get tongue-tied and instead come out with “measures of sprentre”
When you walk the full length of the playground before realising that one of the lenses from your sunglasses is missing.

These moments will have in students in fits of giggles pointing and laughing.

When this happens you have two options:
You can try to regain your composure and with a straight face and fight to regain control of the class, or you can join in – admit it was pretty funny and laugh at how ridiculous you looked.

The first option will solidify the moment in your students minds as that one time when you embarrassed yourself. They won’t remember how to find the area of a circle, but they’ll remember the moment you went to lean on a desk that wasn’t there and almost fell on your butt.

The second option shows students that you’re human, a little (or a lot) clumsy, and hopefully sends the message that laughing at yourself is healthy and that no one is perfect.

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But even if you somehow manage to never find yourself in a situation where you’ve made yourself look like a complete dork, the students are judging you anyway. Students will critique everything about you, with both positive and negative feedback. I’ve had students comment on my outfit, my weight, my jewellery…
They make you wonder if they paid any attention to the maths at all, or if they just spent 20 minutes critiquing you personally.

The ability to easily accept compliments, and even more easily brush off criticisms is invaluable as a teacher.

If you’re honestly comfortable with who you are, they can’t use your quirks and clumsiness (or fashion choices) against you.

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Communication

Each week we run a maths homework centre for any student in the school who wants help with homework or study. Two students from my strongest year 9 class come each week to help year 8 students as part of a program that requires them to complete a certain number of hours volunteering.

Today I overheard a conversation between one of these year 9 students and a girl from my year 8 class who was attempting an algebra question:

S1: Is it 10x?

S2: Why do you think it might be 10x?

S1: Because there’s an invisible 1 in front of the x that’s on its own

S2: How does that help us?

They figured out the answer was 9x, not 10x, but it was so nice to hear my students parroting both my questioning techniques and my explanations. I always try to encourage them to communicate effectively using mathematical terms but to hear it from them when they don’t know I’m listening makes my day.

The happiness ratio

What’s that theory about the balance between negative and positive comments? Something along the lines of “for every negative comment you need to make 10 positive comments to balance it out”. It’s not that I ever doubted this, but I think this week has really made me understand it – because the ratio is the same for lessons. For every lesson that fails, every class that you walk out of feeling deflated, you need a whole lot of good lessons to balance it out. And I count myself lucky that I have four great classes, but then there’s my 5th class.

This class only has 16 students, which seems amazing until you look a little closer. I have some students completing the Life Skills course (they cover different content to the rest of the class) and many of the other students have very poor literacy levels and diverse learning needs. I always have at least two lessons running at a time – often it’s more like four. Some students in my class are the most renowned for poor behaviour in their year group. Occasionally we have good lessons, usually we struggle through them with lots of complaints and a few arguments and students held back after class, and then there are lessons like yesterday.

We’ve just started probability so this is one of the rare times where we all work as a class on the same topic, and all start at the same level. Looking good so far – I only have to plan one lesson, so I can make it really good. Unfortunately it’s a double lesson (90 minutes) which is hard for these students, but I tried to mix things up with a few different activities and a game in the last 20 minutes.

The lesson completely flopped.

I don’t know if it was the lesson, my management skills or just a bad day for the students, but I think we all left with a headache. Sure some work was completed (how much they truly understood is a different question) but I had students written up for incomplete work, disrespect to me and to their peers, and for storming out of the classroom.

I’m incredibly grateful for my other classes who give me something positive to focus on and who balance out the happiness ratio.

Maths Trivia

A while back I had one of those days where there were a whole heap of things happening in the school that my students were involved in, so my 45 minute class with 34 students was reduced to 30 minutes with 10 kids. Rather than teach new content that I would have to re-teach I decided to give my students (and myself) the afternoon off and play a maths trivia quiz!

I made up some maths trivia questions, grabbed some lollies for prizes, and we had a tonne of fun getting really competitive.

 

They did make me feel incredibly old when not one student could answer the question “The quote “the limit does not exist” is from which movie?” – and even when I told them only 2 had seen the movie!

Why Algebra?

It’s the start of the new year, and I’m getting to meet all of my new classes. I’m really excited to be teaching a year 11 General Maths class for the first time, and even more excited to find out that I only have 14 students!

Our first topic is Algebraic Manipulation. Sounds like a whole bundle of fun to a group of kids who just told me that more than half of them don’t like maths, and at least 2/3rds of them think they’re really bad at it. Since I knew that at some point most students in the class would probably groan “wwhyyyy do we even have to learn this?” I decided to pre-empt this and have the discussion before we even started.

I started by asking them “So what is algebra?” expecting to get responses about using the alphabet in maths (there were a few along these lines), but I was surprised when students started to tell me that algebra was all about patterns. A good start!

I told them that algebra is a tool (and I think a few agreed with that statement on its own) – a mathematical tool that’s used for two things: describing patterns and relationships, and proving ideas. We had a look at a few formulas that they know already and talked about the relationship that each one was representing. Then I showed then a magic trick.

Pick a number between 1 and 10
Double it
Multiply it by 5
Divide by your original number
Subtract 7
The number you’re thinking of is 3!

And from that ‘trick’ one of the best classroom discussions I’ve ever seen ensued:

Student 1: Why did it have to be a number between 1 and 10? Would it work with other numbers?
Me: Give it a go with other numbers and see if it works!
Everyone picked a new number – bigger than 10 – and were amazed when the magic still worked
Student 2: What if you pick a negative number?
Me: Try it out, see what happens!
There was even more excitement when these numbers worked too
Student 3: What about if it’s not a whole number? What if I pick, like, a half?
Me: What do you think? Will it work or not?
A few nods and shakes of the head. When these worked as well I posed the question:

Will this always work? How do you know?

After a short silence a student tentatively offered the answer “algebra?”
Me: Yes! So we want to pick a number, but we don’t know the value of that number yet. How do we represent it?
Ss: x!
Me: Do we have to use x?
Ss: Nope, you can use any letter
Me: Good. But it doesn’t have to be a letter – it can be any symbol – I could draw a picture of a fish if I really wanted to

Then we went through the process using x (and fish) and showed that our original number divides out, so it’s completely irrelevant.

One student picked up on the fact that we didn’t need to subtract 7 – we could have finished the trick with one less step, but we decided that it makes the trick look more impressive it there’s an extra step in there.

If this lesson is any indication of the year to come, it’s going to be awesome!

Student Survey

I made it to the end of my first year of teaching! Phew! There were lots of stressful moments and a few tears, but mostly the year was filled with amazing moments engaging with students on both a personal and an academic level.

I’ve taken a break from the world of teaching for the first few weeks of my holidays – no planning, no blogging, no twitter. But this week I need to start gearing up for the new year – and what better way to start than by looking back at last year.

Inspired by a number of bog posts I’ve read (including Tom DeRosa’s end of year student surveys) I decided to create my own survey to have students fill out in the last week of school. I wanted to get feedback from the people who matter most to me – my students.

This is what I came up with: End of year student survey

Handing them out, I was the most nervous I’ve been since my first week of teaching. I prefaced the survey by telling them that one of the best ways for me to improve as a teacher is to ask for their feedback on what I’m doing well and what I could be doing better. The survey was anonymous to encourage everyone to be honest.

Waiting for all the surveys to be handed in felt like the longest 15 minutes of my life, but the feedback was overwhelmingly positive!

In the first column, the only negative feedback I received was to the statement “Miss Davis knows me well” – with 4 students disagreeing. I’m ok with that. As much as I would love to know all of my students really well, it’s not always going to be possible when I’m teaching over 100 students.

A lot of the more negative responses to the rest of the survey were tied into personal learning styles – some students wrote that I assigned too much homework, while others responded that assigning more homework would help them do better.

Other comments related to aspects of my teaching that I’m aware that I need to improve, but I haven’t quite figured out a system that works for me yet – like checking homework more often and providing feedback more regularly.

Some of my favourite responses to a few of the questions:

If you found out that your friend/family member was going to be in Miss Davis’ class next year, what would you tell him/her?

“Miss Davis is an excellent teacher… she makes you challenge yourself”

“Go to class willing to learn, because if you do you will learn heaps”

“You’re in a great class and you have a great opportunity to do well and learn lots”

“She is a good teacher that works hard for the students”

“Get your homework done because it just keeps building up!”

“The homework is all important even if it doesn’t seem so. It helps A LOT when it comes to test time”

 

I hate it when Miss Davis says…

“The homework is due tomorrow”

“You have a test in two weeks”

 

One thing Miss Davis should do more often is…

“Hand out lollies”

“Sing Ricky Martin”

 

What is the one thing you will remember most about this class?

“The easy-to-follow lessons”

“All the help provided”

“Helpful Keynotes and a friendly teacher”

“The 90 minute sessions that seemed like they never ended”

“Miss would sit down and help one of us if we didn’t quite get it”

 

Anything else you would like to tell me?

“Please take our class next year”

“You are very supportive through school work and personal problems”

“You are a really nice teacher and you have a visible passion for mathematics”

 

Sharing is Caring

I’m more than a little late with this one… but here’s my contribution to mission #8 for Explore the MTBoS: Sharing is Caring.

All year I’ve been talking to my maths colleagues with about this wonderful world called the MathtwitterBlogosphere… maybe babbling is a more accurate description of what I’ve been doing:

“Did you make this activity up?”
“Nope, I found it on the MathtwitterBlogosphere!”

“Thats a really cool website”
“I know! Someone from the MathtwitterBlogosphere tweeted about it!”

It was only the other day that I realised I’ve only given a proper explanation of the MTBoS to two of my colleagues, but a lot more of them have (unknowingly) seen the benefits of this community.

A few weeks ago we were teaching the topic “Graphs of Physical Phenomena” – starting with basic travel graphs, then moving on to more complex graphs that involved variable rates. After finding this website, I decided to have students make their own videos. Working with another teacher, we formed a plan. We started with a quick lesson looking at graphs that depicted cars accelerating, or a runner who was slowing down as he got tired – gradually introducing language like “increasing at a decreasing rate”. Then we watched 4 Graphing Stories and students became more confident working with these complex graphs.
Then came the fun part. I borrowed a pile of different shaped glass flasks from the science department, and had students film themselves slowly filling them up with water (holding a ruler next to the flask so we could see the height of the water). As a class we then sat down and graphed the height of the water as a variable of time – drawing a quick sketch of what we thought the graph might look like, then a more accurate graph as we watched the videos. The activity worked amazingly well, and full credit was paid to the MTBoS for the wonderful idea. I’m hoping that my continual mentioning of the MTBoS will help some of my colleagues become more open to the idea of an online professional learning community.

In the case of one particular teacher, my mentor, I’m making a more direct effort to get her involved in the MTBoS – we sat down for about half an hour on one of the last days of school this year, and I showed her around a bit. I showed her some of my favourite blogs, some others that I think she might find really useful, a whole pile of virtual filing cabinets, websites like Estimation 180, as well as emailing her a copy of Nix the Tricks. Maybe a little overwhelming for a half-hour session! She’s told me that she’s going to spend some more time exploring in our 5 week holiday. After all that she’s done for me as my mentor this year, I really hope that I can show her the wonders of the MTBoS as a small way of giving something back to her.

Maybe next year I’ll introduce them to Twitter.

A Day in My Life

Mission #7 for Explore the MTBoS: record the details of one day this week. So here we go… a sneak peek into my Monday.

6:10 – My alarm goes off, but I decide to lie in bed listening to the pouring rain and dreading going outside in it. Get up, check twitter while eating breakfast, shower, pack lunch and head out the door at 7:40.

8:00 – Arrive at school and check my emails – no extra classes today, phew! Print off worksheets for the days lessons, and an assessment notification for my seniors. Print off some work for a casual covering a colleague’s class and check in with a teacher who’s class I have once a fortnight (today!).

8:25 – Weekly staff briefing. A run-down of what’s happening this week. The highlights of this week include a chair and desk audit on Tuesday, evacuation and lock-down drills on Wednesday, and lots of room changes due to special events.

8:45 – Head off to our first session of the day. This is where my school is a little different (read: amazing!). Every teacher has a group of about 15 students that they are responsible for looking out for – academically, socially, emotionally… everything. We see these students for 40mins every morning and usually have time to help them with homework and assessments, talk about any behavioural issues, and generally check in with them. This morning though, we’re running numeracy sessions, so after marking the roll students disperse to their numeracy groups. This morning we looked at some probability statements and addressed common probability misconceptions.

9:25 – My seniors! My year 12 Mathematics class has a grand total of 6 students. One student from the other Mathematics class has a free period occasionally when my lesson runs, so he joins us today. I hand out the notification for the test they have in 2 weeks, and we have a quick discussion about it. They work through a sheet that encourages them to think about the geometry of the derivative, and what the concepts we’ve learnt actually mean (how do we know the curve y=4x^2 is always concave up?) and then complete some review questions.

10:12 – Off to the year 7 class that I have once a fortnight – but when I show up their usual teacher is there! Turns out he was asked to cover another lesson, so since he wasn’t getting the session off class to plan, he may as well teach his own class. I shuffle off to teach another year 7 class a lesson that I haven’t looked at yet. Luckily I can wing year 7 probability.

11 – Recess! Back to the staffroom to check my emails again, eat a muesli bar and chat to the teacher I share a year 8 class with about where they’re up to.

11:25 – The staffroom empties out as everyone heads off to class, but I have the session off to be super productive! I work through the pile of exams that I marked the other day (5 hours of marking) and collate the marks. I’ll enter them all into our markbook tomorrow. I have a discussion with another teacher about one of my students who hasn’t handed in an assessment for her class, and make a note to chase it up tomorrow morning when I see him.

12:12 – Year 8 lesson on finding the volume of cylinders. We work out the formula together, then they have exercises and HotMaths work to do. A fairly uneventful lesson.

1 – Lunch. A toasted sandwich and a banana. Tomorrow I have sport and I’m taking some girls down to the pool, so I spend 10mins grilling a nearby PE teacher for ideas on what activities to do with them. Talk to my head teacher about moving students up or down classes next year, and about whether we’re going to change the brand of calculators students buy from the school (a very dramatic decision with some teachers adamant that their brand is better). Duck downstairs to visit the lovely ladies in the finance office to ask about buying train tickets for an excursion next week.

1:35 – Year 9. We’re starting the new topic of graphs – straight lines and parabolas mainly. We start off today with the basics of completing a table of values and graphing straight lines on a number plane to jog their memories (it’s all in there somewhere from last year right??). In the last 10mins I hand back their tests. We went over the tests last lesson, but I had to recollect them to record marks.

2:22 – I spend the last session of the day planning for tomorrow – finalising lessons and printing worksheets.

3:20 – Staff meeting – nothing exciting to report this week.

5 – Head home via the shops to grab some stuff for dinner. Usually I’d spend another hour or two working on lessons for tomorrow or later in the week, but I was actually productive last weekend so I’m a little ahead of myself, which means I have time to sit down and write about my day!

Now its time to make dinner… gnocchi I think.