Logarithm Questions Around the Room

December 15, 2014

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Here’s a lesson that worked for me recently. I had six logarithms questions posted around the room. I gave each pair of students some sticky notes and asked them to go around adding to the posters. Each answer had to be different, clearly. (I didn’t even specify that each answer had to be different, actually, the students just assumed that.)

I love that students were out of their seats and talking to each other. They were more energetic about these questions than they would have been about a worksheet. And they were automatically noticing generalisations as the activity went on and more answers got added to the posters. Also the group feel to an activity like this spurs lots of students to try creating an example that is a bit harder than they would suggest normally.

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This was a good activity just like this, but I added a little more. Later in the lesson I took pictures of the posters with my iPad. They are set to automatically upload to iCloud, so I accessed them on my classroom computer and could show them on the screen. We talked about a couple of interesting sticky notes and students noted the ones they thought were incorrect. A few of my students like notetaking more than others, so they copied a few examples.

a mathematics lesson that worked

 

Since posting one of these pictures on twitter, I have been featured by another teaching blog: Resourceaholic. My idea is one of five “gems”; the other four are (also) amazing ideas!

I am glad that the sticky notes idea seems to work for others; a few others have tweeted to say they liked it. Thanks for the feedback, Emma Cox and MathSparkles!

What worked for you recently?


Productivity: Never Wait Again

November 22, 2014

Waiting is a great pain of my work life. In my day, I regularly wait: for the bus, for the photocopier to finish, at the printer for my documents, by the microwave for my lunch to heat, for a doctor’s appointment, for someone who is late, for my tea to brew, and many other things.

I have decided that I will wait no longer. No, I can’t hurry up the photocopier or tardy person, but I can use my time more usefully.

how to get stuff done as a teacher

When the waiting is a bit longer (like for an appointment or the bus), pull some reading out of your briefcase. Could you always carry an article or book or your eReader? While at the hospital this week I made it though this article about promoting deep learning (pdf).

When the waiting is a minute or two (like for the microwave or tea to brew), do a little job. Could you refill the tea canister while you are waiting or wipe down the countertops? Is the shared work fridge in need of a little sorting out? While making hot beverages in the staff room I usually wash my hands and tidy the dishes.

When the waiting time is unknown (like waiting for a colleague or queuing), try to do a few discreet stretches. Calf raises are easy; while standing, push up onto your toes for a few seconds, then release down again. Tense and release muscles up and down your legs and arms. Or, if there is anyone nearby, use it as a chance to catch up and build a stronger relationship.

And even if there is nothing to do when waiting, thinking is something you can do! Plan and visualise how the rest of your day or week can be successful. You could think ahead to the next lesson you will teach, or mentally run through the next series of lessons to see if one will lead to the other successfully. I often think ahead to my next meeting in the week and make notes about how I want to prepare.

This also reminds me about research years ago that figetity people burn more calories, which is reported on here. I think doing something while waiting is a mental version of fidgeting. It keeps your mind healthy.

What do you do while waiting?


Completing the Square: Starter Question

November 16, 2014

Here’s an idea that worked for me last week. My A-level class learned how to complete the square earlier in the year and I wanted to know if they still remembered how to do it. Instead of asking them to just do a couple of completing the square questions, I put this up on the board.

complete the square

This appeals to me as a starter question because it’s more broadly accessible than a couple of examples and also allows for more in-depth extension work.

1. For the student who sees this and thinks, “Oh no! I can’t remember how to complete the square,” there’s a quadratic expression there for them to have a go at. While I’m circulating I can give tips to these students.

2. For the student who thinks, “Oh yes! I know how to complete the square,” there is a quadratic expression there for them to try and also permission to make up any quadratic expression at all to try. While I’m circulating, I’ll encourage them to proceed to generalisation.

3. For the student who thinks, “Oh yes! It is possible no matter what the quadratic expression is,” there is the permission there to say why and give evidence. While I’m circulating I can ask questions and push them to generalise with justification or evidence.

a mathematics lesson that worked

 

When I was writing this question I was trying to create something that would push forward my students’ thinking no matter what they could remember about completing the square. I think this worked for me and my students and I hope I can think of more good questions like this one!

What maths question worked for you this week?

 


Learning: Spotting Pattern Everywhere

October 14, 2014

I like this for a maths department motto: “Spotting Pattern Everywhere”. (Thanks to a former workplace for that one. I still love it.) Something I was reading today mentions that a lot of learning, not just in maths, is about spotting patterns. People love making meaning out of the things they see around them. The consciousness researcher Daniel Bor was interviewed in Time magazine talking about this. He calls the human brain “ravenous” for solving problems and making patterns. He says, “We get streams of pleasure when we find something that can really help us understand some deep pattern.”

Bor mentioned people who want answers to the question, “Why?” “The way I approach my job, it’s like trying to solve a really big fuzzy crossword puzzle and when you do put in that new clue and see the deeper pattern, that’s incredibly pleasurable.” I took this as encouragement to help students approach learning maths like a puzzle to be fit together. This could make learning more pleasurable for my students’ brains.

Bor was asked, “If our brains are hungry for information, then why do we tend to see learning as a chore and fail to recognize it as a huge source of pleasure?” He replied, “I don’t know. Obviously, more intelligent people get more pleasure from spotting these patterns, but I think almost every normal person does this. I think it’s a pretty pervasive thing but it’s almost as if we can’t notice it because it’s so pervasive.”

Ways to Make Maths Learning Like a Puzzle

1. Show a diagram and ask, What does this tell you?

I was about to teach about area and volume scale factors of similar shapes. I put this on the board and asked students to discuss what it might mean.

volume sf

2. Ask students to watch you do a maths procedure in silence, then explain to their partner what it was.

Here’s a great example from the nrich website where you watch a very short video of someone summing a sequence, then students are asked to explain what just happened.

Thanks to Larry Ferlazzo for tweeting about this today and making me think more about it.

How do you make learning into a puzzle?


Reading and Writing in Maths: a new version of maths homework

September 15, 2014

This week I will teach a lesson about estimating to my year 9s. The lesson will be a pretty standard one for me: a sequence of tasks and activities, some whole class items but mostly pair work. The lesson will involve some discussion about how and why someone might estimate the answer to a calculation. I’ll be using a few slides, a puzzle, some problems to solve (sourced from UKMT Intermediate contests), and a plenary about a poor guy whose calculator doesn’t display decimal points in answers.

But it’s the homework I want to talk about here. I plan to set a two part homework: read, then write.

1. Read

First students will read an article from earlier this year about two skiers who allegedly tied for first at the Sochi Olympics. Actually, their downhill skiing times were reported as identical due to rounding to two decimal places.

Two skiers tied for first (image: New York Times).

Two skiers tied for first (image: New York Times).

2. Write

Next, students will access a Google form that asks them three questions for which they need to write at least 300 characters (about 3 sentences). Here’s a copy of the form that you are welcome to answer “for fun”. (My students will be using a private version of this.)

I’m excited to see what students write in response to the third question: other examples (outside sport) where rounding of a measurement makes a crucial difference.

I’m interested to see what my students think about being asked to read and write for their maths homework. After reviewing literature and reflecting on my practice last school year, I decided to try a whole range of different homework options this year.

Our school offers the IB diploma for the final two years of secondary school. The maths courses each contain a 20% internal assessment that is a written report. So part of my interest in reading and writing in maths is to prepare students better for writing in maths during the IB diploma.

Have you tried out reading and writing activities in mathematics classes? Please tell me about it in the comments.


Reading Notes: The One Minute Manager

September 9, 2014

When I read I usually take some reading notes (in Evernote) to help me retain the main points and some learnings. I thought it might be a good idea to start publishing these in an occasional series, in case they may be helpful to anyone. They are unedited; just notes that I take while reading about what struck me. There won’t be any commentary, just lots of bullet pointed ideas. Let me know if they are useful, interesting, or both.

The One Minute Manger by Ken Blanchard and Spencer Johnson

“The best minute I spend is the one I invest in people” (63)

“People who feel good about themselves produce good results” (19)

One Minute Goals
1. Agree on your goals.
2. See what good behavior looks like.
3. Write out each of your goals on a single sheet of paper using less than 250 words.
4. Read and re-read each goal, which requires only a minute or so each time you do it
5. Take a minute every once in a while out of your day to look at your performance, and
6. See whether or not your behavior matches your goal.

One Minute Praisings
1. Tell people up front that you are going to let them know how they are doing.
2. Praise people immediately.
3. Tell people what they did right – be specific.
4. Tell people how good you feel about what they did right, and how it helps the organization and the other people who work there.
5. Stop for a moment of silence to let them “feel” how good you feel.
6. Encourage them to do more of the same.
7. Shake hands or touch people in a way that makes it clear that you support their success in the organization.

At first, praise things that are approximately right, and help people move towards desired behaviour.
If, instead, we leave people alone and then punish them when they don’t do exactly the right thing, then they start to do as little as possible.

One Minute Reprimands
1. Tell people beforehand that you are going to let them know how they are doing and in no uncertain terms.
the first half of the reprimand:
2. Reprimand them immediately. [reprimand the behavior only, not the person or their worth]
3. Tell people what they did wrong – be specific.
4. Tell people how you feel about what they did wrong – and in no uncertain terms.
5. Stop for a few seconds of uncomfortable silence to let them feel how you feel.
the second half of the reprimand:
6. Shake hands, or touch them in a way that lets them know you are honestly on their side.
7. Remind them how much you value them.
8. Reaffirm that you think well of them but not of their performance in this situation.
9. Realize that when the reprimand is over, it’s over.

Never save up negative feedback, always give it immediately and in very small doses.
Definitely don’t have surprises at performance management time.
“When you ____, I feel ___.” Then reaffirm their worth.

“We are not just our behaviour, we are the person managing our behaviour.” (93)

why does it work?
“the number one motivator of people is feedback on results” (67)

“feedback is the breakfast of champions” (67)
there would be no point playing golf in the dark; people need to know how successful they are being

“most companies spend 50-70% of their money on people’s salaries. And yet they spend less than 1% of their budget to train their people” (64)


Factors Using Multilink Cubes

September 2, 2014

My year 8s (twelve year olds) have been learning about multiples and now it was time to talk about factors. Some of them have not got all their times tables memorised, which presents some difficulty for our unit of work on factors, multiples, and primes. So my teaching assistant and I doled out the multilink cubes and I asked them to make rectangles. I wanted to know if any number of cubes could be made into a rectangle shape, fully filled with cubes (no gaps).

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After the students played with this for a while, I started making a list on the board of all the sizes of rectangles they had made. Then I asked, which numbers of cubes can be made into more than one shape of rectangle? Above are two rectangles with 8 cubes and below are three rectangles with 12 cubes.

2014-09-02 11.53.36

 

Next I introduced the idea of a factor by talking about the sizes of the rectangles and after some discussion we listed all the factors of 12 using the rectangles in the picture above.

After that, students made their own lists of all the factors of some numbers of their choosing. My assistant and I went around to their tables, asking if they were noticing anything. Using their results, we made a table on the board of all the factors of the numbers from 1 to 15 and talked about what they noticed.

Top on their list of noticings were: 1 is always a factor of every number and the number itself is always a factor. These were not obvious statements to my students. We discussed why each was true by talking about making a long skinny rectangle of 1 x __ for any number.

Next lesson is going to be about prime numbers, so I hope that their next noticing is that some numbers have a lot more factors than others.

Do you use multilink cubes in your lessons?

 

 


Is Your Email Signature as Nerdy as This?

July 10, 2014

I was reading blogs and came across this wonderful idea for an email signature.

Even if you think you don’t love mathematics, mathematics loves you.
Don’t believe me? Solve for “i”.
9x – 7i > 3(3x – 7u)

How marvellously nerdy! This is from the blog Math = Love.

Is your email signature as nerdy as this?


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