Activities for last day before March break

First: Inspired by Dan Meyer's webinar yesterday to begin each class with something interesting, showed this today:

Hans Rosling's 200 Countries, 200 Years, 4 Minutes - The Joy of Stats - ...



Rich discussion followed, as you can imagine. What's in quotations came from them, otherwise I asked and got them to jump in (who's shutting up? I am!)

• "what a cool way to show 200 countries"
• how many dimensions are there to this graph - it's not just two! Has a time element, a country element, a size of country element - did we just look at the Fifth Dimension (and they don't know there was once a fabulous group called that)
• "is that why everything is made in China nowadays?"
• "didn't know WW1 and flu could have that much impact on world population"
• "I'm going to show this to my Contemporary Issues teacher"
• "Where's Congo?"
• "Where's Luxembourg?"
• I love the accent, this one I can't do, but I'm working on it

2. Another fun activity today, one I have used many times, came from the National Library of Virtual Manipulatives, an absolutely awesome resource:

http://nlvm.usu.edu/en/nav/frames_asid_164_g_4_t_3.html?open=instructions&from=category_g_4_t_3.html

They did two puzzles that looked like this:

They manipulated the coloured shapes right on their screen so that they fit perfectly into the two white shapes...you get the idea, it's about proving Pythagoras, something they never cared about before! Even more fun was when they learned what the "print screen" button on their keyboards was for! "OMG it's a picture of MY screen!" They then sent their solutions to me. I had 100% participation. Okay, in one class there was only one kid...still true!

Tonight we're gonna blog, blog, bla-bla-bla-blog! (to be sung to the tune of that Ke$ha song)

Awesome posts and awesome comments from this week:

 From Matthew: His question was just amazing, and funny, pretty much just like himself:

Question:  A man wishes to fly around the earth many times.  He starts from his house and begins flying in the same direction.  Ignoring wind resistance, (his plane is so small it cuts through any wind) and not stopping to re-fuel or eat (he has solar panels with large batteries on his wings, and he is in cryogenic stasis so he doesn’t need food), he flies at a constant speed.  After 20 days he is a quarter away around the earth and 10 000km away from his house in distance.  After 40 days he is half way around the earth and is 20 000km away from his house in distance.  How far will he be from his house after a year of constantly flying around the Earth?

From Amelia: Check out the exquisite use of language:

Today in class we continued going over and exploring yesterday’s notes. We began with going over how to find the two sets of zeroes by using your calculator. You must punch the equation into the calculator and than use the “calc” -> “zeroes” button to manually place the cursor on the left than right side of the zero. Once you have found the first zero (we typically call that the heart zero) we form an equation to be able to find any other zero that is a period away. We must remember that there could be two sets of zeroes due to the l.o.o being above or bellow y=0. This is because if the l.o.o is above or below y=0 than the function on the graph will have two sets of zeroes that are separated by the period, but the sets will be of different but recurring distances from one another.

From Mickael: Just wonderful. Period.

Solving Trig Equations With Algebra and Memory!!!

Today in math class miss Mc Goldrick showed us a way to find the zeroes of equations by algebra and memory. Pushing our math skills even further.
-first of all we started with a simple trig eq. we started off with cos(theta)=-1. Then we had to find which of this angle correspondes to -1. to do so you have to remember the unit circle and find which of the angles has an x coordinate of -1. As it turns out the answer is pi. but not only pi we also have to include all the coterminals.
(theta)=pi,3pi,5pi,7pi… or (theta)=-pi,-3pi,-5pi…
The way to write this as to include all the possible answers is
x=pi+or-(2pi)n,nEN
Simple huh

But my favourite comment was from Charlene:

Today I wasn’t in class, so watching the archive and RIGHT AWAY reading the blog post is a great way for me to catch up! I see both points of view in a matter of one hour.
I’m really relieved not to have to rely on Jeremy’s calculator anymore to find zeros, although I’m having a bit of an issue remembering the angles in the B17, and same for the coordinates that go with it. This might actually be a good thing because it’s going to force me to remember them!

This job rocks. Days like this, I honestly can't believe they pay me to do this.

How to Shut Up

Hardest thing for a teacher, right? Our instinct is to talk, talk, talk, explain, re-explain, draw pictures, do a few back flips, in other words, the teaching equivalent to finding the shortest distance between two points. But seriously, it is time for me to stop talking when I am boring even myself, and I happen to be one of my most devoted fans. I'm talking too much even now! I need help!

My week:

Had a few good Breakout Room activities this week, and found that things go much better if I:

• keep reminding myself that I must not do it for them
• remind myself again
• have a good activity - just easy enough and just challenging enough and just fun enough
• keep it to 2 kids per room
• have the slide up before I put them into their rooms
• tell them to write on their board (either one writes and the other verifies, or both split the work and write, then verify)
• go in to take snapshots every few minutes and keep my mouth shut as much as possible, with the exception of:
• ask who is writing (hint hint kids I should see some writing)
• ask who is checking
• ask is there consensus
• tell them to investigate any differences and remember sometimes there is more than one good answer
• give warning when I'm about to bring all back (they hate it when that voice suddenly and way-too-cheerfully informs them "You have been moved to the main room")
• once all are back, compare snapshots
• ask them to explain differences in answers, procedures

The activities I used:

• In Tech Sci Math gr 11: explorelearning student exploration guide for Vectors gizmo, to be filled in while using the gizmo:

• Tech Sci math gr 10: investigation of optimization problem, my own creation, basically each BOR tries to find the best possible combination of hyoptenuses in a problem like this: 

                      and then organize their findings in a table like this:

• Sci Math gr 11: gave a trig equation to solve, using graphing calc. Here are some actual snapshots:

What was really cool about this one was that different rooms got what looked like different answers, but once we all got together in the main room, they discovered that they were all right by looking at each others' snapshots. Now that was cool. Good teaching moment. Pat, pat, Audrey.

I need two things:

• to put together/find more activities. Lots of great suggestions for concrete and rich math activities thanks to Dan Meyer:

https://www.ncetm.org.uk/public/files/224/improving_learning_in_mathematicsi.pdf

(the good stuff starts on the page titled "The Types of Activity", which is thumbnail 20, but page number 16.)

• To be blunt, I need to shut up! That is just as hard for me as it is for them to un-shut up. But until then I am that teacher in Ferris Bueller's Day Off. Which, by the way, none of them has ever heard of. Wow.

Re-orientation Day

The test results were pretty much the same as always. But I shouldn't really be thinking this way. The whole point was to improve the quality of the learning, and that may or may not include improving the quantitative measurement we call tests. I guess the old teacher in me just can't help but hope for that fantasy where EVERYONE gets it. Plus, it's early in this experiment.

The fact is, the connection I feel to and amongst the students in the blogging classes is much stronger than in those that are not blogging. Could be because the blogging classes are the more motivated students anyway.

I have one class that is so non-participative I could swear I'm that pathetic teacher in Ferris Bueller - "Anyone? Anyone?"

THAT'S the class that should be blogging their little non-participating hearts out!

First test after starting the classblog

Test today on the material that coincided with the start of our classblog. I am very interested to see if the results are any better....

End of chapter review:

Gave a totally different kind of review last Friday. Instead of me writing out a whole review outline and telling them what's on the test, I just told them

"You already know what's on the test because:

a) You've been writing the review outline since we began the scribe post
b) You've been supplying me with sample test questions too"

So we went through those sample questions, and as we went I tried to get them to come up with harder ones, or ones that were combos from different days. Like instead of "What's the ordered pair for pi/4?", or "What angle is coterminal to 11pi/3", combine them into "What's the ordered pair for 11pi/3?", which is a combo of Jeremy's and Shelley's questions.

Also tried to get them to see their own progress, for example, when we began with converting radians to degrees and vice versa, they had to use that proportion to do it, but now they have angles like pi/4 or 2pi/3 burned into their memories. Now I can ask "What's 3pi/4 in radians?", and it's just right there. That worked sort of well.

I had anticipated that they would have been more involved and active in the review than they were, because they had been more involved than usual thus far, but it was a pretty subdued class.

Maybe I overwhelmed them. They might never have had to do this much thinking from the teacher's end before.  Another factor might have been that lots of them weren't actually there - some areas had school closures due to weather.

Next time:

To show progress:
Use an old screenshot of how they used to have to work it out, before they were familiar with the big picture. Compare to what they're doing now. They will see the progress instead of having to listen to me tell them about it.

To get them to make up combo questions:
I will identify the questions by name, like "Combine Jeremy's question with Shelley's question". Might make it more fun and make it really about ownership, too.

To avoid overwhelming them:
Instead of doing a smorgasbord of every blogger's question at the very end, we'll try generating questions after 2 or 3 days, a la "Improving learning in mathematics", by Malcolm Swan. Even make it part of the discussion at the beginning of class about last night's blogger - now that we all know how to do this, let's crank it up a notch....

Now to my corrections....

Blurring the lines

Today’s post will have some movie references in it, because I love movies. In case you do too, you might recognize references to Madagascar, Ben-Hur, and Jerry McGuire. There is a point to this....

The brainy thing floating around in my head today:

These days, the best things happening in my class are happening outside of my class.

Some of those things are happening because I have insisted on them, like commenting on voicethreads, posting on our classblog, commenting on those posts, and responding to articles on our discussion board. All of these are evidence that someone, maybe only one person mind you, but someone is thinking about math when there is no math class going on. And that’s a great thing to know! At the very least, that means a little less time needs to be spent in the next math class getting everyone back up to ramming speed. At best, these extra-curricular math-tivities are having an impact on what happens when we do get together again, because then we have something to talk about besides homework. We talk about what one of them did, and what we all thought about it!

But then there are things happening that I didn’t insist on, or even suggest to anyone to do. I’m getting emails like “I figured out the answer to the bonus question – is this right”, “Can I use what we did in class today in my project because I think it fits in”, “ I didn’t understand this part of that article so I tried to work it out – please tell me if this is right”. Not from everyone, mind you, still from a small group that I pretty much had at hello, but it is an improvement over previous years, when the number of emails that I got like this was approximately zero. At the very least, these kids are getting to sink their teeth into something fun.

At any rate, for some kids, there is no longer a clear line separating the time they’re learning math from the time they’re not learning math. It’s no longer a digital situation – a one or a zero – it’s more analog, a little of this, a little of that!

Maybe this is a glimpse of what customized education would look like? They are choosing what they will learn, when they will learn it, and how long they will spend on it. And of course, the most manageable time and place for this to happen is between classes, otherwise I would have to manage potentially 30 different kids learning 30 different things during a one-hour math class. How to get this kind of thing happening with the not-so-motivated-and capable? Don't know yet. How might one manage the goings-on between classes...well, maybe blogs?

However education looks in the years to come, I suspect blogging will become a major player. It is an uber-customizable activity! It just might be the ideal tool for anyone who is looking to blur the lines between, say, math and art, or between school and fun, or even between learning and living. For example, just by blogging, I am showing the world who I am, that is, not just a math teacher but a student, a photographer, a music lover, a gardener, a film buff, (there it is!) etc etc, and so it is anyone’s guess where the teacher ends and the student begins. Would the same thing happen when students blog about their lessons? Well, today, as we were processing Andrew's blog, Steve commented that Andrew's sense of humour was all over it! You can't help but imprint yourself in your writing, no matter who you are!

Other brainy things:

Things I want to share:

I received "37 Interesting Ideas for Classblogs" from my fabulous principal, Dianne Conrod, about classblogs, and it is the reason I was inspired to try voki.

A free handbook of math class activities, with the theory behind it, "Improving Learning in Mathematics" thanks to Dan Meyer.

And finally a video, "Nature by numbers" that is the best imaginable example of the blurring of lines between math, art, science, and music! Many thanks to Darren Kuropatwa for the tweet about this beautiful video!

Hi it's "me"!

So once you've joined voki you can customize a lot more!


The next time I post on the classblog I'm going to use this. I CANNOT wait to see their reactions!

Just joined voki. Apparently I can embed this here. This is the closest I could get with what they had - none of the glasses were right, and wildly out-of-control curly hair wasn't one of the options either. But my eyes are green!


Wow, cool. You can click on the pink play button on the lower left to hear "me". Not sure what I'm going to do with this but it's fun!

Mining for math

The rundown on what the kids are so far doing and not doing on the classblog:

Well the kids' posts are continuing to get better and better! Jeremy's post contained a lot of info, but there were lots of misuses of the vocabulary, and there was no picture in it. Fred's included more math symbols, tables, and an embedded graph. His command of the languages, both mathematical and english, was obvious. He also asked an original question, that is, it wasn't similar to anything I had asked in class:

Then we compared the 2 graphs and found them to be almost exactly the same except for 2 differences.
What are they?

As for the comments.....they are all starting to sound alike....Wow great post, I like the way you organized the info.....no doubt this is partly because they are hesitant to critique each other, but they are likely just not used to writing about their math THINKING. Or thinking about their math thinking. They aren't addressing anything remotely mathematical in their comments, for the most part.

A few exceptions, of course. Jeremy's answer to Fred's question:

Now about the difference between the Sin and the cosin function, the cosine function intercepts the y-axis at 1 and the sin function intercepts at 0 Also, The sin function always crosses the x-axis at either pi or 2 pi ( or more if mroe than 1 turn occured), in other words, it crosses the x-axis at 0/360 degrees and 180 degrees.

What I have done and will have to get better at:

Well, I realized that I have to get over my hesitation to correct and critique, if I want them to, which means I have to model not only the types of comments I want them to make, but the tone, the respect, the we're-all-in-this-together way to give constructive criticism.

So, first thing in each class, I now upload the post onto our eboard, bring up anything useful that has already been put into a comment by one of them, ask if anyone has anything to add/change etc, then I have at it myself. The first victim of this was Jeremy. After I'd made a few corrections, I asked him, "I hope you don't feel Jeremy, that I am tearing your work apart!" and he said "No, it's ok, I wasn't sure about this part!". Hmm...he was maybe hoping for this? Then as I went through my list of corrections to Jeremy's post, others started to say "Oh yes I noticed that too" or "Wouldn't it have been better to call that an angle instead of a radian".

Here are a few things I will look for from now on in the posts:

• is everything that was in the lesson in the blog
• is the vocabulary and notation correctly used
• is there a sample question
• is the overall organization good, easy to follow
• is their personality evident in their writing
• is there anything new - new symbols, new type of thing inserted
• are there any citations missing (Fred uploaded an image from a site and didn't give the url)
• did they make any observations about the content, how interesting it was, how it was presented, how it connects to something, etc

What I will look for in their comments:

• did they notice any of the above
• did they answer the question with any depth at all
• did they make any observations about the content, how interesting it was, how it was presented, how it connects to something, etc
• did they ask anything that would enrich their understanding

Meanwhile, back at the voicethread:

I'm finding that the voicethreads lend themselves to problem solving more than they do as responses to the powerpoint lessons. I have had them contribute one step, with explanations, to a situational problem that they are all working on. It's partly a way for them to check in with each other for reassura, collaborate with each other, and for me to document whether or not they are actually working. Plus, again, it's just great for us all to see each other occasionally! Closest we'll get to f2f!

Playing around again...trying to embed a voicethread:


OMG I did it! So this is a voicethread. It's like a movie that's part slide show, and part responses to the slide show. All you have to do is click the play button right under where it says "comment".

Had an opportunity to talk to a group of B.Ed. students at McGill today about online teaching as a career choice. It was fun, and I think, I hope, one or two might just be reading this. I hope they found it interesting, even if only the part where my daughter called me, twice, during my talk, to ask if I could take her shopping....:)

Aha moment!

Just realized as I was in class, that if I want certain things to be discussed about a post, I need to have my own observations at the ready. Eg. Juan's post used the symbol for pi, instead of what I just typed, the word pi. Hey Juan (I should have said) how did you do that? It also had a link to a pic - did anyone notice that? No? Well then next time let's embed the picture right into the post. And how about that abbreviation for the big seventeen - B17 - applause for Juan that's a great idea!...this is what I need to do!

Transparent learning!

A revealing post

Shelley's post on the unit circle was a real eye-opener, for the simple reason that it was the first one that took place on the weekend. (It was also a very good post!) Many of the kids commented that reading her summary during the weekend (or Monday morning) helped them recall what we were doing last Friday, and therefore made it easier to get back into the swing of things on Monday. It never even occurred to me! How many cases of Monday morning math funk have gone undiagnosed all these years? During our discussion in class on Shelley's post, I asked her if she had found it helpful to have had to summarize the lesson. She made a point of saying "Yes! REALLY helpful!" Very interesting.

This must be what Darren Kuropatwa means when he says that the posts and responses can make our students' learning transparent to us. Things are being revealed in a very organic, non-contrived fashion through these posts.

Still not sure how to mine their posts and comments for the math, though. I am very hesitant to make any corrections myself to their posts. It's a pretty public thing they're doing. It seems like it could easily turn into just another thing for me to put x's and checkmarks all over, like a test, and then they will be hesitant to do it. Ideally, we want them to make the corrections to each others' work, at least that was what I understood. Fortunately, one class (interestingly, the class that Shelley was not in) did point out the few things that needed to be fixed with her post:

• that it was missing a sample question
• there was one mistake ("-90 is coterminal to 275")
• some of the terminology and notation was not quite used properly ("a circle has a radius of 1", "an angle theta0")

But what do I do if no one sees a mistake? Maybe I'll give them the first crack at it, then step in if I have to. But maybe I also need to help them find ways to give each other constructive criticism, or at least set the stage so that they are more comfortable speaking their minds about someone's post.

More and more it seems like this is less about math than it is about emotions and relationships! One student joked that math class was more like therapy these days! At least I hope he was joking...

Update on McGoldblog

The third post was from Abby. I think hers has set the bar a bit higher. She wrote: (my italics)

Today in class, we continued our lesson on radians and degrees, and how to convert from one to another.

• We know that the number of degrees in a circle is 360, and the number of radians in a circle is 2(pi).
• So then, we have a proportion, 360^o/2pi^r=theta^o/theta^r , which could be used to covert radian to degrees or vice-versa.
• This could also be reduced to 180 degrees/(pi)radian=theta^o/theta^r .
• To find how many degrees is 2 radians, we would replace theta^r with 2 using the formula above and cross multiply. So theta=180*2^r / (pi) , would come to approximately 114.6 degrees.
• To be exact, just multiply 180*2, leave pi as is, and we get 360/(pi).

• To find how many radians is in 30 degrees, replace 30 by theta degrees instead, which I’ll leave you to figure out – exact or approximate amount.

Arclengths -another new thing we learned.

• If we have an angle, we get an arc or a section of the circumference. This is called the arclength.
• And the bigger the angle, the bigger the arclength. :O
• If we take 360 degrees of the circle, the arclength would then be the whole circle, or its circumference. And its formula is C=2(pi)r.
• a (arclength) = 2(pi)r when theta=360. From this, we get a proportional formula similar to the one with radians.
• 360 degrees/2(pi)r = theta^o/a , or 180/(pi)r=theta^o/a

Another sample question:

• If we had r=5cm, and an angle=45 degrees, find the arclength subtending this angle. Mrs. McGoldrick also gave us a formula for arclength: a=theta^r*r , but it can only be used in radians.
  Hope you all have a radiant rest of the day.

Things I love about this:

• She didn't leave any content or formulas out
• She put in subtitles
• She asked not one, but two questions
• Her personality came through, especially at the end with the "radiant day"!
• The clarity of it suggested to me that it was a pretty well-done lesson (pat on the back for Audrey)

Things I would like to see in the future:

• diagrams - slides from the lesson or their own
• colour coding
• worked out examples
• math notation - how the heck do you get that into a blog post - to find out

When we discussed Abby's post, many things came up - math things, that is. For example, one question was not properly answered so we corrected it, or rather, Fred worked it out because I knew he did have the right answer. It all just seemed so much more relaxed and natural than when I am once again trying to get them as enthusiastic as I perpetually (and probably annoyingly) am.

Today's lesson was on the unit circle. Introduction to. Here's the powerpoint for the lesson that Shelley will be blogging about this weekend (lucky girl!):

feb 4 unit circle intro  

I know....97 slides! But don't worry, that's only because I show each little step.....you'll see. Enjoy!

More coolness!

Found out how to embed an actual powerpoint using scribd! This is a powerpoint I made a while ago that was inspired by a post at the fabulous website http://www.betterexplained.com/.
Intro to Calculus Using Circle
You can see the slides just by clicking on the little arrow at the bottom of the window, right next to where it says 1/20. There were animations in it originally, but maybe scribd doesn't support those? Another thing to find out....

test

Just playing around here - finally figured out how to make a powerpoint slide into an image that can then be uploaded into the post - I am so happy right now it is probably a bit weird!

The Constant Gardener

Gardening in February?

Last night I found myself excitedly checking all kinds of different sites - the McGoldblog, then the voicethread, then the discussion post, then explorelearning to see the assessment results. I felt like I do during gardening season, when I check to see what's blooming, what new weeds are sprouting, or what's just plain pretty to look at.  It certainly is a lot of fun to see what the kids have said, and they are making me laugh outloud sometimes. As usual though, not everyone is participating, which is discouraging. It seems like I am still only reaching those kids that I know are always with me anyway, and don't get me wrong, it's great to be connecting with them in new ways, but I was hoping to see the invisible ones emerging from the shadows. Only the first day of the classblog, so I guess it's a bit early to get discouraged!

Class procedure day after first post:
Yesterday I began my class by looking at Kristopher's post, thanking him for it, giving positive feedback on the length and amount of detail, and asking if anyone had anything to add or share about it. Then I told them there was one tiny mistake in it, and gave them a minute to try to find it. All it was was that sohcahtoa was spelled sohcahtao. Normally, I wouldn't make a big deal about spelling, but this one could lead to some pretty nasty math mistakes. No one found it, and I was wondering if perhaps no one wanted to, because they might feel it was not their place to correct a peer? Just a thought...

Post #2
Yesternight's blogger was Catherine. Her post was not quite as detailed as Kristopher's was, but I have a feeling that the lesson was a bit short on content anyway. I got hung up on showing them something that I hadn't planned to show them - where the exact values for sin, cos, and tan of 45, 30, and 60 degrees came from. I had a feeling that it would affect the posting. Maybe it was boring, too! This is kind of like getting instant feedback from the kids on the lesson. Scary.

What's next?

I'd like to be able to embed my powerpoints here so I'm trying that out with scribd. Wonder if I'm donig too much at one time? Am I the flower or the weed?