Rich activities = A day off?

I was talking with some other teachers about all these job action situations currently happening in our province.  Basically we have to get in no earlier than 15 minutes before our first class, and we're rushed out at 5 minutes after our last period.  If you are a teacher, you'd know how tough that is.  Some schools are even encouraging teachers to only mark and plan during school hours.  This is where this comment came up:

"I just make up an activity..."

Ok sounds good so far

"Have the kids do it..."

Uh-huh

"And then I take that time to mark..."

Oh I see -- wait what?

There are couple of things I am seeing here.  First of all, of course I realize that activities are better than just students doing worksheets all class.  I also realize that if teachers are being restricted in their ability to mark, something creative has to happen -- But I just have some problems with throwing an activity at the kids and then doing my own thing.

Even if it's a rich activity.

I sincerely believe that there's real value in teachers being an active part of the learning community.  Even when kids are doing activities, I am never on my chair checking e-mails and reading the news.

I interact with them, ask questions, make them confused, and then encourage them to think out of the conclusion.  Sometimes I guide them and support their thinking, but most of the time I walk around and cause them problems.  Well maybe problems is the wrong word... maybe chaos is better.  Just kidding there also.  What I mean is, students think through the activities and problems, and I ask "what about this" "what about that" "what if" "will this always work"... etc.

Besides the chaos that I throw in each group, I also constantly give them feedback.  Each student requires different kinds of feedback at different stages of their understanding.

I saw this on a wall at some point, and I took a picture of it.  It pretty much describes what I am talking about:

Students don't need to be fed answers.  They need to develop their own answers.  They need to develop their own questions too -- but some require more guidance to be able to produce their own answers.

But let me get back to my original topic.  I find my membership in the classroom learning community to be valuable.  I am not trying to say that I am super important, but I believe there is a lot of things teachers can do, and should do, when students are engaged in an activity.  I also believe that during these types of activities, there is an excellent opportunity to obtain valid and authentic information on student learning and student understanding.

If I'm just sitting and marking, I'm going to miss all that!

But with all that said... if job actions come down... I am not sure how creative I can be with evaluations and planning...

[Random] Shop girl; Money; Cube for teachers

Saturday morning.  This is actually the first Saturday in a long time where I am waking up later than usual.  I've been far too swamped with grad school and teaching to give myself free time.  But let's shove my self-pity comments aside.  That's not what I'm going to be talking about.

I stumbled onto the web, searching for some refreshing things to look at.  I read through several blogs on my google reader, checking out several bloggers that I usually follow, but lately haven't really had time to read: Dan, Fawn, Lisa, Sam... etc.

It was definitely enjoyable.  Between flipping through the pages (not literally), it struck me that I want to see if there were bloggers like me that's actually from Ontario -- using our curriculum.  A lot of the bloggers I follow are from the states, and their mathematical content and curriculum discussions are different.  Of course, there are lots of parallels, and I extract whatever I find useful all the time (ah the power of the human mind), but I thought it wouldn't hurt to just google some new searchers.

I then came across this blog post by shop girl.

She's not an education blogger.  She appears to be a blogger that just happen to be an educator.  No matter, I read on.  Besides being a captivating writer, she also stirred up several of topics that I can relate to and find fascinating.  Some stuff she mentioned, and others just products of my random mind.

In the midst of all the chaos surrounding the current strike action/teacher union/government issues, it was refreshing to read about a passionate teacher*.  Or as she puts it, an "Ontario occasional teacher."  It is tough to get a job in Ontario.  I can't speak for other cities, but in Ottawa, where I am, the competition is fierce.  Just becoming an occasional teacher and getting on the supply list is a huge battle.  Then once you are a supply/occasional teacher, receiving a long term occasional teacher where you teach a class for an extended period of time is even more of a battle.  Then from there to a permanent hire is another difficult road.

Within the past few months, I've been casually following the news articles about union vs government (probably not the most appropriate phrase for this).  "Casual" is actually a subjective word that I feel fits my stance more.  While the war wages, and sanctions are established for what us teachers can and cannot do in order to support the fight, I have basically maintained a relatively nonchalant attitude.  It's not that I don't care about standing for the freedom and rights of people.  I get that.  I have no problem supporting that.  It's just that my motivation to stand behind the fight is strictly about the principle and the rights.

I'm kind of an oddity when it comes to finances.  I have objectively analyzed myself several times, so I'm going to try to put words here that will hopefully resemble my conclusions.  My motivation has never been finances or financial security.  Not to sound like a unicorn (crazy animal that don't exist), but I don't care much for money.  I understand that society value of money.  I understand how to work with money.  I understand the concept of money.  But I just can't bring myself to caring for it.  In fact, I sometimes find myself actively disgusted by (a) money becoming a primary driver for society, and (b) the corruption of money in terms of education, motivation, and entertainment.  Okay, my second point is a mess of a phrase, but I couldn't think of a quick way of summarizing that one.  By "the corruption...education, motivation, and entertainment," I mean seeing students and parents seeking "future careers" based on monetary security instead of passion.  I mean seeing people abandon ideas and concepts because they don't bear immediate fruit for financial gain.  I mean the way that monetary incentives have corrupted people's desire to do things for the sake of doing things.

So okay, I might be a unicorn.  In my unicorn-ness, most of the time I leave the financial side of things to my wife.  That's how much I'm actively avoiding it.  Why am I mentioning this?  The situation with the union vs government has basically forced me to examine things like salary, sick days, leaves, benefits... and it basically disgusts me.  Well, actually, so far I haven't really "examined" those things at all.  I briefly glanced at the existing salary grid.  I briefly engaged in conversations where people were telling me what kind of sick days we currently have and what would be taken away.  I don't really know what's wrong with me, but for some reason I actually get sick just involving myself in conversations about the things that we are trying to bargain for.

And I feel bad.

In order to fight for the thing that I care for - rights of people, concepts of a union of protecting the little guy...etc - I need to care about what it is that is being fought for.  And so this whole dilemma of what I value and what I don't value just nauseates me.

Anyway, that was the first tangent I got into.

The second one relates to something called "Cube for Teachers"

In my random search to find Ontario math education bloggers, I came across this website.  The idea is simple.  it seems like a platform for sharing resources for Ontario teachers.  I have mentioned before that in Ontario there are curriculum documents that establishes curriculum expectations which are basically the big ideas that students need to learn.  I will likely elaborate on this later on, but I can say that I believe the curriculum documents are currently an excellent resource and guide for teachers to deliver key conceptual content for students.  It's a shame that not all teachers are as familiar with it as they should be.  Too many of them are bound by the confines of whatever textbook they use.

This cube for teachers platform seems very interesting.  It seems to allow for a search engine that searches by curriculum expectations, in addition to be a common sharing place.  When I have some more time over the winter break, I will likely explore more of it.  The one thing that I noticed, was the fact that Khan academy was one of the popular links on the side.  I am not sure if Khan Academy videos have changed from when I last saw it, but I imagine that even if they have changed -- it wouldn't be that much of a change yet.  While I am not opposed to the idea of flipped classrooms, I am uncomfortable with the current structure of the videos.  I had mentioned in that previous post that I would make a video this year that would address my concerns.  However, that never became the case.  I was just too busy this semester to do much else.  So I guess I'm officially throwing that on the backburner now.

Ok, so this ends my random post about my Saturday musings!

Update: Check out this article written back in September.  An interesting read that definitely still applies -- and applies beyond just the American Education System.

Be your own hero

I recently showed this clip to my classes.

The idea is simple.  Take responsibility of your own experiences and learning -- be your own hero.

Take a look -- it's a great video that came out of TEDed

[Act 1] What is this... A center for ANTS?!

Have you ever seen the movie Zoolander?  It's this serious and dramatic thriller about a model being brainwashed into assassination.


Just kidding, it's not a thriller... Even though it sounds like it could be.

It's a comedy.

I began with this:

The question that we explored -- and it's really a question that I've been wondering myself several times since watching this movie:

How many times bigger does it really have to be in order to fit children inside comfortably?

Students explored this question and they had lots of fun.  We touched on scaling, exponents, 3D shapes, effectively using the internet as a tool and resource...etc.

Our main technique involved freeze framing segments of the movie so we can get an idea of the ratio of the model height compared to Ben Stiller's height.

So... How would you work this question out?  What is your answer?

I'll edit this post later with what we found!  But... show me yours before I show you mine!

Shape within a shape... Part 1

While I still very much enjoy the aspects of reading education blogs and blogging, and will likely not lose this interest, grad school obligation on top of teaching is just too much for me the past month or so.

I had the opportunity to clear out my afternoon so I can visit the school I worked at last year.

Despite the difficulties I faced with job prospects (where I learned lots about life), that school (and especially my students) has a special place in my heart.

And so even within my busy schedule, I simply needed to make time to go visit my colleagues, and my students from last year.  It felt great to see everyone again.  It was awesome to see academic growth of the kids.  I was also nosy enough to find out how my kids from last year are doing now.

I also bumped into some students that mentioned that they follow my blog.  So here, guys, here's a special blog post for you all :)  Thanks for the warm welcome, guys!

~~~~~~

When I made this blog, my intention was to allow myself to explore mathematics education, philosophy, and mathematics.  I have not really explored mathematics yet.  I have come across interesting questions... but since everything that I am doing is more focused on education, I have not had a chance to fully explore interesting questions.

So here it is, my first blogpost about a question that intrigues me!

Instead of outlining how I've tackled this question, I am just going to pose it and comment on it instead:

This picture above was actually just a random picture that "somewhat" relates to the question that I've been exploring.

So I was sitting around, and suddenly a question hit me.  If I have a cone, how do I cut a circle into it so that what I've hollowed out has the same volume as the part remaining?

Let me elaborate by using a different way to explain this problem.  Imagine you have a cake in a shape of a cone.  Imagine you are cutting it with a circular cookie-cutter.  Assuming you overlap the center of the cookie cutter with the center of the cone, how big does the cookie cutter have to be in order for the volume to be the same for the 2 pieces that you've removed?  See below for a crappy visual that I made up:

Initially I thought this was a relatively easy problem.  I posed the problem for other math teachers in my department to try -- and I haven't really gotten a good response on it yet.  They haven't had a whole lot of time to tackle this, and they probably have other things on their plate, but it doesn't really diminish the fact that this interesting question is definitely more difficult than I initially thought.

so... what do you all think?

There are lots of extending questions that we can ask from this as well... I've also found a lot of related interesting results... but I'll save that for the next installment!

[Act 1] Pillar problem + going outside

Man...  no matter how hard I try, time seems to be fleeting when I have more responsibilities than usual.

Here's a short post since I miss spending time on this :)

So there's this interesting pillar close to the entrance of our school:

So... the questions naturally flow in.  What is it for?  what is the volume of this thing?  how much concrete or rock do we need for this?  can we fit a person inside that hole?

These types of questions were exactly the questions that my class came up with as well.  I actually did a lot of asking around to find out where this was from.  It turns out that these (there are 2 of them) used to be pillars which held up a giant log that prevented construction trucks from coming through.  There used to be a lot of construction around the area.  Time passed on, and the log started to rot, so the city removed it before it became a hazard.  For a long time, this weird shape became the symbol of the community.  Now it is no longer a symbol for the community, but it remains as an artifact and no one removed it.

I am new to the area and new to the school, so when I first saw this weird thing it definitely intrigued me.

In any case, our class had excellent discussions.  I let them to think about:

1. what would we need to find out the answers that we want? (volume + surface area)

2. what is the best way to measure this?

3. what kind of calculations would we need?

We did lots of planning inside the class.  Each group came up with an idea as to what to do.

Then we went outside and did it:

I took more pictures, but I only provided this one.  I am still a bit concerned about privacy and whatnot, so I had to carefully pick a picture like the above.

After we went outside, we came back and finished up our calculations.

All in all, it was great fun :)

On the next day I also talked about other methods that we could have done this.  Using a picture and using the idea of scaling, for example.

Note the umbrella...  I brought in the umbrella the next day so we did measurements with that as well.

The best part about this activity was definitely going outside (for them and for me).  And it was exciting to come up with answers that were extremely similar between the groups (with some help from me).

Linda Darling-Hammond on Performance-Based Assessment

This is an old but great video on performance assessments in areas of the world, and the conceptual underpinnings of their tasks and assessment systems.

It's from the 2008 Forum for Education and Democracy.

Have a look!

Math Education -- A Lifestyle

Going to ramble some philosophical musings.  This blog was initially created with a space to not only retain my journey in mathematics and mathematics education, but also my own fascination with philosophy (hence the title of the blog the Pai Intersect)... I feel like I've been a bit lopsided since I haven't really done any posts on pure mathematics or philosophy.  So... here it is...

I definitely would not have foreseen the extent of integration of mathematics education with my life.

I read about math education, work on math education, research about math education, create daily lessons...   and beyond the occasional fatigue induced sitting-and-staring-at-the-wall-because-I-am-intellectually-spent moments, I truly do enjoy it.

And when I enjoy it -- it doesn't feel like work.  In fact, reading blogs and certain aspects of planning lessons  (like supplementing my Ninja Board) has become my past time.

There seems to be a strong desire to separate work and life... but that seems to operate under the assumption that work is not part of life.  "If you're working, you're not living life," or "working is preventing me from really living my life" are things I common hear about these subjects.

I really don't see a problem with the two being one and the same -- integrated, mutually supporting each other.

Of course, when I do get the courage to object to people's adamant distinctions between work and life, I often get the response of: It's great that you currently think this way, but trust me, it will fade.

I completely understand that may be a possibility, since the uncertainty of futures makes their response absolutely unfalsifiable, but I suspect (and strongly hope) that statement will fail to represent my future.  For my own sake, I think I will try to come up with some reasons for this:

1. I believe the mindset of seeing work and life being one and the same will help prevent immediate attribution of frustration only to "work."  Sure, I can be frustrated at some aspect of work, but I would not be able to charge this negativity to the category of work since I have not established a clear separation between "work" and "life."

2. I have discovered an enjoyment in casually dabbling in different aspects of professional development that some may label as "work."  Reading blogs, for example, is not an obligation but a relaxing venture.  Google reader may pile up with lots of "unread" posts sometimes due to my busy schedule, but all I have to do is wipe the slate clean with "mark all as read," and I am home free!  Well I try not to do that, since I do want to see some valuable opinions that I may have missed, but I've definitely just browsed and skimmed through the posts if they don't immediately catch my attention (or were too intellectually demanding for whatever state of mind I was in).  Having a clear goal in my research, and reading interesting research studies have also been mostly a positive experience for me.  This is likely because I don't feel pressured to really obtain a "degree."  I am far more interested in the puzzles that constitutes my research questions (for some reason writing this sentence reminded me of the TV Show House MD).  So I think my non-chalant attitude towards these aspects of life will contribute integrating "work" and "life" even in the future.

Reason number 2 is a particular interesting one.  It's not that I am refusing recognizing my responsibilities -- it's more like I am choosing not to be bogged down by these perceived responsibilities and obligations.  Instead, I am focusing on my reasons for wanting to take on these responsibilities.  I am teaching because I love it.  I am reading blogs because I enjoy thinking about teaching which I love.  I am doing grad studies because I am interested in finding out more about this thing which I love called education.

So why fuss over what I love?  Why tease out the specifics of what I love attribute only the positives to "life," and the rest to "work?"

To my future self -- Maintain this attitude of choosing to think about work and life as one of the same, and we'll live much happier.

Or I'll disown you.

[AnE] Open question + closed questions

In Mathematics Assessment, I believe there is a real need for a large variety of "open" questions.  But let me elaborate on what I mean here before I get tomatoes thrown at me!

Open questions are questions that are "framed in such a way that a variety of responses or approaches are possible." (Small and Lin 2010)

And that's exactly what it is.  Closed questions are questions that only lead to one answer - and most of the time the skills that they test are quite limited.  Questions like the following examples would be open questions since it provides a wide variety of ways of answering it:

Open question:
Example 1:
Two lines are perpendicular to each other and intersect at the point (10, 5).  What might be the slopes of these lines?  Explain your thinking.

Example 2:
Write an algebraic expression involving one variable and at least three terms that can be simplified by using exponent principles.


On the other hand, the following would be closed questions since they allow for limited approaches toward finding the answer.

Closed question
Example 1:
Determine the derivative of the following function: f(x) = 3x + 10

Example 2:
Determine the slope of the line connecting the following two points: (2, 5); (-3, 10)

Note that the difference between open and closed questions don't necessarily dictate the amount of time taken for each question.  You can have an elaborate closed question that consists of lots of words like the following example, but it would still only have one correct answer:

Bill wants to earn extra money selling lemonade in front of his house.  It costs $1.20 to start his business and each glass of lemonade costs $0.06 to make.  He plans to sell the lemonade for $0.10 a glass.
a) write an equation that represents his cost
b) write an equation that represents his revenue
c) graph both equations on the same set of axes
d) does bill make a profit or lose money for 20 glasses sold? 35 glasses sold? 50 glasses sold?

What makes open questions effective is the fact that students are allowed to demonstrate their understanding of their own volition.  On the one end of the spectrum, they provide opportunities to demonstrate in depth understanding.  Students need to understand so much more in order to be able to answer these questions. But because of the nature of the open questions, these questions naturally come with multiple entry points so students who may struggle with some concepts still have the ability to start answering the questions.  So it addresses the other end of the spectrum, since students who struggle with some major concepts still get the opportunity to demonstrate what they think they understand.

By the way, I am definitely not saying that closed questions are not useful -- they definitely still are.  I am just arguing for incorporating more open questions as an additional source of assessment of student achievement.

I highly recommend this book for those who are interested.  The book also recommends some strategies for turning your existing closed questions into open questions.  That is so much more effective than just having a wealth of questions (or "question bank:).  Afterall:

Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime
-Lao Tzu (old Chinese Proverb)

Small, M. and Lin, A. (2010) More Good Questions: Great ways to differentiate secondary mathematics.  (not going to bother citing it properly!)

Ok so let me summarize the main reasons behind my suggestions towards incorporating more open questions in our assessments:

1. Open questions allow for multiple opportunities for students to demonstrate their learning
2. Open questions allow for multiple entry points for students with different levels of understanding
3. Open questions arise more naturally and thus are inherently more fun (like these act 1 questions that students come up with themselves)
4. Open questions allow for student ownership of their own understanding and encourages them to organize, mediate, and combine the skills and concepts in order to present their answers.

I am sure there are more benefits of using open questions that I am missing -- but hopefully I've made a convincing argument for incorporating open questions.

[Act 1] Exponent introduction

Going to keep this one short.

How do we effectively introduce the idea of exponents and powers?  Our first idea was to think about what things have exponential growth that actually matters to kids.  So we first thought of youtube videos.  Viral videos potentially grow because 1 person tells many people, and those people tell every more people... and so on.  There's a link to be drawn there.  Not a tight link, but a strong enough one that can lead to some good solid introductions.  So we decided on this video:

Look at the number of views (right now):

Awesome.  Lots to talk about there.

Then on my drive home I kept thinking about it -- and a story that I've heard a long time ago struck me.  Wasn't there a pennies on chessboard story that involved exponential growth?  Well more correctly the "wheat and chessboard problem" that involves geometric series (as I found out through a bit of digging).

I edited the video from "Excerpt from the IBM film "Mathematics Peepshow"" a bit and voila

Talk talk talk, discuss discuss discuss... (I may elaborate on what we talked about if I have some time in the future... but for now, use your imaginations!)

Consolidate

Bam...  Act 3:

Analyzing the difference in the Act 1's

My last post involved two act 1's that I put up.

One of them was about the sinkhole that occurred last week.

And the other one was on a few pictures I took at the pet food store.

I wanted to dig a bit deeper on the differences between the two.

The sinkhole picture, let's call it A, is a situation that's hot, fresh, and interesting.  It happened not that long ago, and kids are instantly excited to talk about it.  They had all sorts of questions that popped up.  Since they were sitting in a math classroom, some of them even came up with some math questions.  Perfect.  We meant to do this.

The pet food pictures, let's call it B, is a situation that built with the intention of discussing a particular topic in mathematics.  Kids are still excited to talk about it, but it took having to focus and zoom into the parts we actually "cared" about.  Of course, I still indulged other good questions that didn't have things to do with math, but primarily there was a goal.  The goal was fractions, percentages, value, division...etc.

So therein lies the major difference, I think.  A is driven primarily by an exciting situation that deserves talking about, while B is driven primarily by a mathematical topic that deserves talking about.

Both A and B ultimately achieves the goal of getting students excited and talking about mathematics, but this links to what I mentioned before about spiraling the curriculum.

I have not been able to go full blast just spiraling the curriculum just yet, because there are several factors that prevents me to go off and do it this year.  I would say that A has more of the "spiraling flavour" to it.  It's interesting and the questions that pop up links to multiple areas in the curriculum that I am currently working with:

• speed of the car - linear function
• braking while the car stops - non-linear function
• the size of the sinkhole - volume
• The rate at which the car sinks - linear (or non-linear functions)
• the cause of the sinkhole (outside curriculum but links mathematics to other interesting areas)
• ... and so on

Ideally we would spend a few classes exploring different aspects of this question.  We give them information as they need them.  We measure the length of the car to approximate depth of the car according to the picture.  we make assumptions on the time difference between each picture...etc.

We would then link them back to the strands and overall expectations of this course, and students fill in what they have learned.  They frame and organize what they have learned into the established chunks of concepts.

Instead, we primarily focused on B.  Don't get me wrong, I still love the rich discussions that come out of B.  There are still lots to learn about the aspects of B -- but B was narrow.  B was planned for a more narrow focus on value.

Maybe having both A and B is fine -- and it probably is -- I just wanted to elaborate a bit more on the spiraling concept, and to differentiate it slightly from the other "kind" of act 1.

But regardless of which one I use in the classroom, I love both of them.  I love the fact the students are investigating, thinking, discussing, arguing, and learning.

[Act 1] Compilation (some of the first two weeks)

I've been swamped.  Grad studies + teaching is totally draining me, and it's only the first week!  Hopefully it'll ease up once I gain a bit more traction and I'll be able to Blog a bit more.  I was a bit bummed that I couldn't coach basketball this year, but it seems like I have my plate overfull anyway.

I have been meaning to blog about the various things that I've done in the first two weeks of school - but as time goes on, I feel like I am less and less capable of doing these lessons justice (or even capable of fully explaining what went on in the class).

I don't really want an incomplete description of the activities like my first angry birds post.  Man... I just did too much with that during to fully explain it well in the first post (or I just didn't spend enough time recalling everything I did during class).  I had to follow up with another post that elaborated on some of the details.  Having said that I don't really want an incomplete description... I still want to force myself to present all of them out there.  So the following are some of the "Act 1's" that I've done in the past week or so.

Recently there was a sinkhole on the highway -- east end of town.  I grappled with whether to use this right away -- since it wasn't relating directly to the subject we were talking about.  I decided to do it anyway since it was fresh, hot, new, and exciting.  

Kids recognized the situation instantly and buzz was already building.  I built the situation into learning about asking good questions, and having them realize the power mathematics have in answer these.  Things that are logical.  Things that we can test.  Things that make sense.  So we talked measurements, depth, length, volume, sizes of cars, speed of the car, weakening soil...etc.  Good stuff.  (I'm skimming over a lot of details like I did with the Angry birds post... so don't hesitate to ask if you want more details!)

This is part of the Act 3 that I gave them:

Here's 1 more (I intended on blogging more, but I need to get working on other stuff...)

Simple one with pictures that I took at the pet store.  "Which one has the better value?" was the main one that we looked at.  We got to talking about prices, taxes, percentages, value, fractions...etc.

I then threw this at them

So nice, good opportunity to talk about percentages, fine prints, infinitely multiplying items (going to bring this back later for power) to get more money...etc.

privacy + security settings for the blog world

This post is a bit different from my normal ones.

Recently I posted about the "Ninja Board."  In my initial post, instead of blogging only about what I did, I also included some of my future plans for the board.  I recognized that students may be able to search it up, and started searching for ways to prevent this.

I took myself to many websites searching for ways to prevent for google search.

First I changed this setting here:

Followed by some reading about robot.txt's.... I then changed some settings on custom robot tags (after failing to edit the html on the webpage itself):

Followed by some directions to go to Google Webmasters to request for the archived search results be removed.

Blah... such a tiresome process.  I even took down the post for a while.

After thinking about it for a bit longer, I decided to just removed the content that has to do with future plans for the Ninja Board.

But hey, I don't believe it was a total waste of time!

what I learned from this:

• how to navigate through different functions that blogspot seems to have
• google webmasters is an interesting app that I've never explored before
• we can add custom robots tags!
• some additional knowledge about how search engines work
• to post primarily about "what I've done" and not about "what I plan to do"

Board for Ninjas

*note* a large part of this have been removed due to potential student "googlers."

Last week, about 2 days before class began, I read about this cool "Ninja Board" idea from Jeff Brenneman over at "Trust Me - I'm a Math Teacher"

As you can see from my comments on his post, I was excited.

What I initially envisioned it could be used for:

• Building positive class culture
• Instill some fun into the class

What happened so far:
Great.  Awesome.  I went on to set it up.  The only tricky part was formatting.  I grabbed 2 chart papers, stuck this on top:

And so the first day went on without a hitch (I will try to make another blog post about what happened in the first week... too much to blog about!!!)

During the first period noone really asked about it.  No big deal -- their names aren't on there yet, and they barely know me.  The second class in my third period came, and 2 - 3 kids noticed right away and asked me about it.

"What is the Ninja Board?"

"Good question."  I said, and promptly walked away.

"What is the Ninja Board, sir?"

"That's a very good question."  I repeated, feeling a bit like a robot now, and smiled at the student who asked the question.

"You're not going to say anything, are you."

"Probably not."

Second day came, and I put up some names from each class on their respective Ninja Boards.

The font was actually a bit difficult to find.  I needed something that looks great, but still readable.  I settled on "Brushed," "brushtip-c," and "Levibrush."  (I don't have the specific link that I got them from anymore)

Finally some people from the first class asked about it.  I gave them the non-answer once again.

My second class started getting really curious towards the end of last week.

During a group work activity, one student came to me and asked:

"omg just tell me what it is, I'll give you anything you want."

"Anything?"

"yeah!"

"ok..." and everyone went silent in the room.

"It's a Ninja Board."

Some groans and giggles, and they went back to work.

What is yet to come:
On Monday, they will see that some students have these instead:

Along with the following "unlocked achievements"

And this is where I deviate a bit from what Jeff's doing in his class.  I think mine are a bit more geared towards positive classroom behaviour (didn't award points for asking about the ninja board, calling me evil...etc).  I also have the same unlocked achievement list in both classrooms.

**Content removed due to potential spoiling of Ninja Board for awesome student "googlers"*

Right now I have been taping these names onto the ninja board every day.  I think I am going to go out to construct something will be easier for replacement.  I will probably blog about that evolution later on.

*click here to see an update on the board*

Global Math Department - Math conferences

It has been a crazy first week.  I keep having ideas about what to blog about, but I keep storing it away in my Evernote since I just couldn't find the time.

So this is just a quick post -- more will be coming this weekend about the details of my first week, and I am excited to share a lot of interesting stuff!

Megan Hayes-Golding has taken the lead on this very awesome Global Math Department.  I only heard about it earlier this week, and was fortunate enough to immediately sign up for the conference on Tuesday talking about Geogebra scripting.  I use geogebra for functioning, geometry, and general overlaying-pictures-then-do-cool-math-things-with-it, but I have never tried the scripting function.  I was unable to completely follow the examples that were given at the conference using big marker, but it was definitely a valuable experience that opened my eyes to possibilities.

If you are reading this then you're probably interested in math education!  Go on to the big marker site and sign up for some of the conference!  The next one coming up is described as the following:

Lisa Henry will lead a panel of presenters who will share their favorite review games. Presenters include Lisa Henry (An Old Math Dog Learning New Tricks, @lmhenry9), Kim Hughey (Math Tales from the Spring), Julie Reulbach (I Speak Math, @jreulbach), Alisan Royster (@G8rAli), Remi Smith (The Math Smith, @reminoodle), and Sue VanHattum (Math Mama Writes, @suevanhattum).

RSVP in advance or show up on Tuesday (9pm ET) at https://www.bigmarker.com/globalmathdept/sept4

DO YOU HAVE COMMENTS OR SUGGESTIONS? GO HERE TO GIVE US FEEDBACK. 

Make sure you sign up if you have time!

[Activity] Angry Birds (part 2)

A quick elaboration on angry birds...

My last post about angry birds was lacking a bit.  I was severely jetlagged (still a bit now, but definitely better), and my memory was failing me.


Here are some of the other things we did with the following picture












*note* the following are all consolidation from the different groups that came up with different methods.

We talked about how we would find the vertex and the equation of the path so we can predict whether it will hit the pig (predicting act 3).

We threw a graph on the picture right on the smart notebook file.

We talked about what units we should use and we decided on "red bird."  in other words, the height of the red bird was 1 unit, and the width of the red bird was 1 unit.  (so we were counting by birds which was interesting, and the whole unit concept was fantastic to talk about)

We talked about what we would need in order to obtain an equation that would help us predict the result.

We talked about where the "x-axis" should be.  The common decision was to use the black part of the slingshot as a straight line for the x-axis.  We then threw a straight line there so we can see the x-axis.

We then established 0 (at the slingshot), and used the cloning tool to make many little red birds to help us measure our "red bird" unit.

I had another picture that showed the path until mid air, so we took that into account and measured the vertex.

then came crunch time and we sorted through some math

Finally arriving at the equation which hits the middle of the wood plank that the pig was leaning towards.

It was fun!

Why Learn Math?

I love love love this 3rd prompt from math blogger initiation.  Students are almost always surprised by how much I love answering this question.  I've been meaning to talk about this topic for a while now, and now I have even more excuse to do it right away.

I am sure you have encountered The Question in a mathematics classroom before.  "Why do we have to learn this?"  or "When are we every going to use this?"  or some variation of this.

Some classes seem to have it pop up more than others.  Some lessons seem to call for the questions.  If you quickly google these questions, almost always Math pops up as the subject in question.

If you find yourself faced with this question often - then I have a treat for you.  I am going to go through the many ways that I have answered this question, and the many reasons why we learn math. (of course, I don't claim it to be comprehensive).

1. Math improves your critical thinking skills

This is the answer I use the most often.  There's actually multiple ways of approaching this one - because follow up questions can always be asked: "why do we need critical thinking"  Well, now doesn't that seem like an easier question to answer?  It's almost like a straw man fallacy... except they made the straw man!

Okay, so this first response is the fact that understanding mathematical concepts and ideas are ways of training the mind to think in different ways, to different extents, and within different capacities.

Last year (also my first year teaching), we did push ups together in the first lesson (we did it together because I didn't want to just make them do it.  Plus... I kind of like push ups).  I preemptively asked them the question:

"When are we ever going to need this in real life?"

Do you see where I am coming from?  With some quick prompts, students realize that it is exercising their muscles, making them healthy, promoting better self confidence and image...etc.  But then I flip it around (if they haven't done it themselves already):  That's exactly the same with math.  We might not need the specific topics covered in mathematics, but they improve our thinking skills, make us healthier, and can promote better self confidence and image...etc.

If push ups are not your thing... then maybe this next one is:
"If you can dodge a wrench, you can dodge a ball."

If you can think through difficult logical/mathematical situations, then you are preparing yourself to think through other difficult life situations.

2. Math as your defense

This response also applies to the general idea of critical thinking.  Not to mention it can be considered as part of the first response.

What do the following have in common?

They are all protective suits of some kind.  There are lots of influences around the world now that is fighting for our beliefs, effort, time, money...etc.  There are lots of advertisement and ideas that uses mathematics, mathematical concepts (and if you want to go general and tap into other subjects - technical jargon, complicated terms...etc) to persuade us.  Having a solid understanding of the concepts and ideas are a way of creating our own protective suits against these influences.  Knowledge is power.

3. Math as your offense

Similarly in the same fashion, we can also think about increasing our ability to explain things in better ways.  We can supplement our ideas, knowledge, and beliefs with creative and convincing facts.  Facts that can come from mathematics (or other subjects can be associated with this response, once again)

4. Diversifying your portfolio/Because you don't know if you'll need it/enjoy it

There are 2 parts to this response, and is tied my second favourite way to respond.

Part A

"When do I ever need this stuff?"  That's a great question that maybe noone can answer.  But wait, not even you can answer this, and that's the point.

There has been a steep academic inflation over the past few decades -- and it's not done climbing.  Jobs are harder to find (even for us teachers), academic requirements overall are increased, and general day-to-day knowledge include ideas unimaginable by humans 100 years ago.  Mathematics is the basis for sciences.  Logical thinking, which is a large part of mathematics, is the basis for almost all disciplines.  So then the answer here should be a bit clearer.  By learning mathematics, we are extending opportunities and possibilities.  Opening doors instead of closing doors.

Part B

The question of why do mathematics usually comes with a sense of resentment.  It comes with a student's history of disliking math stemming from their struggles, lowered self esteem, "bad" teachers... etc.  But that doesn't mean they actually know, for sure, that they hate math.

Afterall, how can you hate something you don't fully know about or understand?  That's right, you can't.  It's like hating an unknown person that you've never met or heard about.  Mathematics is not just one thing.  It embodies infinite ideas, possibilities, concepts, and opportunities for learning.  There is an "ah-ha!" moment at the end of the struggling tunnel that you might find absolutely delicious.  You can't give up before you get there!

We don't know what our future holds.  Maybe we will find passion in something that requires mathematics.  Maybe we will find passion in some area of mathematics.

Don't let your past haunt your future.

p.s. there is a great poster that outlines what jobs need what aspect of mathematics.

5. Mathematics is a common language

There is a main idea from this video.  And that is to obtain a common ground in which to discuss things, organize things, and understand things.  Mathematics is one of those things.  It is naturally found everywhere. It is understood in almost the same way across our globe.  It is truly a universal language.  Understanding mathematics lets you open your eyes to the beauties of the world that you may not even be aware of!

~~

These 5 responses, and variations of them, are answers that I've come up with on my own (I think a lot... maybe too much), and have tried answering with.  Sometimes it comes as a planned prelude to a lesson (in which case it might come equipped with videos or pictures), sometimes it comes as an immediate response to a student, and sometimes it comes as a lengthy discussion with a friend (who may hate math).

Let me know what you think or if you have anything to add or if you want to discuss any of them (because I love talking about this topic)!!!

Singapore Math - Successful Meeting!

As I mentioned in these last 2 posts, one of my honeymoon destinations was Singapore.  I had wanted to contact their Ministry of Education to set up a meeting to talk about their math education.  My wish was granted!  There were some small hiccups along the way, but what's important was that I got some questions answered.

I had drafted some short questions to ask, and they were the following:

1. I read that you have made problem solving the main focus.  How do you achieve this?
2. How are your secondary mathematics curriculum structured?
3. What are the sample lessons like in a typical secondary math classroom?
4. How are students assessed and evaluated?
5. What do your textbooks look like?

Unfortunately I did not get to talk to a specialist on these topics.  Instead I had a meeting with someone who was knowledgeable about everything in general.  I won't put in any of my opinions in this post.  Instead, I will just try to summarize what I've learned.

Answers:

1. This question was not answered that well.  It seems that problem solving has been made the focus.  Most teachers still have their own individual touch to the lessons, so it was difficult to identify how it is achieved within each classroom.  It seems that the problem solving is primarily driven through textbooks and/or each teacher's approaches.

2. It is an interesting way of organizing.  The curriculum is separated by topics, but there are different levels of mathematics that students can take.  In Singapore they have standardized testing, and after elementary school, an exam score is collected and those are given to parents for consideration.  Each high school specializes in different areas.  So if your child is excellent in mathematics, but not humanities, then there would be a selection of schools recommended for your child.  The scores are ways of helping this.  The specialization is similar to the structure in Universities.  On top of this, students have 3 main streams that they can enter.

N(T) Level - Normal Technical Level, I was told.  These are for students who are doing courses that would be structured to be more application based.  This takes 5 years to complete

N(A) Level - Normal Academic Level.  The in-between level.  This takes 5 years to complete.

O Level - Ordinary Level.  These are for high academic achieving students.  This takes 4 years to complete.

Within each level, like O level, there would also be differences between each classes in terms of academic rigor.

3. I was not able to get a sample lesson since these differ from class to class (as I expected, I guess?) and depends on the teacher.

4. Students are primarily assessed through tests (I cringed a bit when I heard this, but that's ok.  There are still plenty of other things I can learn from this experience)  Students have 4 semesters in each school year.  At the end of each one there is either a test or national exam.

5. I was directed to a book store that pretty much specializes in selling textbooks.  When I got there, I was extremely surprised to see that 4 years (or 5) worth of material has been condensed into either 1 or 2 books.  They are not even that thick!  I opened them up and found it to mainly be summaries of concepts, followed by exercise questions.  While the questions are well made, I was a bit surprised to see that there are no activities within the textbooks being outlined.  I am guessing that these textbooks are meant to supplement, and that the teachers do their own activities?  I bought 3 of these textbooks for reference.  I have not had the chance to go through them all yet.  Something good caught my eyes in each of the textbooks that I bought (which is why I bought them...).  They are tremendously cheap!  Less than 20 dollars per book, compared to the 100+ dollars for the textbooks that we buy here.

All in all, it was a good experience.  We had some good conversations about their education system.  There were definitely things that I liked, and aspects that I did not like as much.  It was unfortunate that I could not set up something more substantial where I would be able to see a good lesson from a teacher (similar to the Japanese lesson studies that are out there), but maybe next time.  My wife was already a bit angry at me for taking time out during our honeymoon to go meet with the Ministry of Education for 3 hours.

[Activity] Angry Birds

Recently returned from my honeymoon -- so that means I will soon be writing up lots of blog posts!  I've discovered that there is so much that I want to blog about.  I just hope I will have time to blog about it all!

This probably won't come as something new for most math teachers out there, but I thought I'd throw in how I approached the topic.

When Angry Birds first came out late 2009 - 2010, it made a huge wave.  It made me a bit jealous because my phone at the time was a flip phone that barely performed the "phone" function.  When I finally got an iPhone (I don't remember exactly when that was...), Angry Birds was one of the first apps I downloaded.  I immediately went ahead to creating activities for Angry Birds.

What I did
I had 2 classes to try my activities on last year.

This picture was waiting students as they entered the room.  "What's the first question that pops into your head?"

I gave them some time to talk, get excited, argue, discuss, then I collected their responses.

We have already covered a lot of quadratic functions before this point, so it was relatively easy to lead them to exploring that aspect.  A lot of fun things also came out - gravity, angles,...etc.

*here are some more details in what we established in act 2*

We related to graphs, x-intercept, and basically had a lot to talk about when it came to these birds.

I then used the free Angry Birds Chrome to bring up the different birds.  It was a great experience because it is browser-based.  Since I had a smartboard in the class, I was able to put it right on there, and students can use the touch features to play around with the game itself.

I let the students play with them, and have them come up with "what's happening here."

Get Google Chrome if you are interested.  It comes as a free add-on, and you can play without paying a cent!

Here are the different birds I am talking about:

A lot of them generated very interesting discussions.  Even on the front of "what would the quadratic function look like", "how did the function change when you tap them".  The blue bird, for example, they talked about transformation of functions, what the functions would look like, and why did it split in the way that it did.

I don't completely remember what else we did in those classes (I have a memory of a goldfish when it comes to certain things, which my wife constantly reminds me about - which is why evernote has been a lifesaver), so I will stop talking about it there.  There were so many great conversations that happened during class...  which is why I may move to a different way of assessing students in the future.

In any case, I will move onto:

Potential future changes

• The general idea is a catapult.  What about building a real one with a slingshot for us to do outside?  Would that take too much time?
• Use Jing and VideoPad (or some alternative video editing software) to create a video version of act 1.
• Overlay the picture on Geogebra to give it a graph and more interactivity
• Maybe leave the "other birds" for a different lesson.
• I found this picture from a great photographer who does cool picture sessions with his kids.  His name is Jason Lee and here's his Flickr photostream.  I might use this picture in the future as well!  Maybe use Geogebra to separate the kids so it can be moved (or even with smartboard software this would be easy).  This would change the function every time I move the individual pictures.

• Create test questions based on this activity.
• Something that you guys suggest!

*I did more of an elaboration here*