I was so pumped after my 3rd teacher workshop of the year that I had to take a picture. 

Earlier this year I did my first math workshop.  Here was the description: 

Are your academic & applied grade 9s disengaged? Learn how other teachers and I transformed our teaching practice utilizing the spiral curriculum to increase retention of math. By using a combination of Dan Meyer's problem-based 3-act math, collaborative white-boarding, and Knowledge Hook's online technology, students are more engaged and rediscover an enjoyment of math. Come and learn how to efficiently implement one or any of these strategies to jump start your classes' retention and engagement! 

I checked quite often (even though I know it was unhealthy to) to see how many people were attracted to my description. It was crushing.  Even on the last day leading up to OAME, there were 3 people who signed up for my session. I managed to console myself by stating that it will be easy and having fewer people is  a good way to start one's first math workshop.  I also managed to convince myself that because it was on a Friday and it was the last session of the day...most people wouldn't come anyway.  So I managed to not take it personally.

Boy was I wrong about the number of people.  I had 30+ show up to my session!  Well, this OAME “Endlessly Spiralling  through Grade 9 Math” was much better than my previous two presentations on “To Blog , where No Blog has Gone Before”. 

There are a couple comparisons that are important to note here:

·         

• After two workshop presentations, I think I got the hang of it.  I went from a 1-way presenter of  disseminating information to an interactive teacher/facilitator that talked and listened to the audience.  I sometimes would lead a discussion with the audience but also lean on the experience of the audience as well for input or further expertise.  

• I’ve been using blogging as a tool in the classroom for over a year whereas I’ve been spiraling for only 9 months.  However, I am much more comfortable talking about spiraling in math than I am about the use of blogging in the classroom. 

• I used Pear Deck many times in the classroom before I did my math presentation vs my blogging presentation. 

Here is some feedback on my presentation.  Looks like about 7 people answered this first question, even though over 20+ attended.  Not everyone fills out feedback forms:    

Leading a discussion with fellow educators and administrators requires a very different than I had developed teaching teenagers. One of the biggest difference I learnt was that there was a curriculum when teaching the students versus no curriculum when at a workshop.  At a workshop, the content discussed better be useful for the audience or else it’s a failure.  In the classroom, the content discussed often isn’t the teacher or student’s choice, so we just have to make the best of it.  As a result, I started my presentation using Pear Deck to interact with the audience.  I used to only use it to get to know where everyone is from, which age group they most affect etc….

This time I used it to ask what they expected out of the workshop.  It became evident as I was browsing through their comments that some of my expectations and their expectations didn’t align.  I went through the list and acknowledged each one of their expectations; I would defer some, promising to get to it later in the presentation, and others I would answer on the spot.   A few questions I wasn’t within the scope of the presentation and I apologized but at the same time used this as a segue to the fact that I wouldn’t get offended if anyone left early.  This portion was informal in nature and opened up the floor quite a bit.  

I spent only 3 hours explicitly preparing for my OAME presentation whereas I spent days preparing for my blogging presentation.  It’s amazing that out of the 7 people that responded, 3 stated that I was ‘somewhat organized’ and 4 stated that I was ‘well-organized’.  However, upon reflection, I’ve actually spent a lot more time preparing for this presentation than the 3 hours beforehand. 

When I went to George Couros’s presentation back in October, he stated that he formatively spent 5 years writing on a blog getting feedback from all sorts of people around the world.  He would get his ideas refined and learnt how to wordsmith. 

Something similar happened to me here – I blogged about spiraling for 7 months beforehand, and I could whip together a presentation in 3 hours and then speak about it in an organized, confident manner the next day.  Normally I would have much trouble talking about my experiences, but blogging helped me refine my thoughts so that when I spoke, it wasn’t a big jumble.  

Wow.  I was thinking that OAME was hiding negative feedback at first here, because there seems to be only one person answering these questions now.  However, I looked back up and saw that there is still some negative feedback, so maybe? 

Nevertheless, I guess the respondents finished off the survey at the end, which showed I did an ok job:  3 people said it was ok, 3 people said good, and 2 found my session to be great!  I still have to work on things as only one person would recommend me as a speaker – now I have something to work towards.  Looking back – I have to work on my content.  I am not very knowledgeable about the changing math education.  My goal is to read Jo Boaler’s “Mathematical Mindsets” this summer and hopefully I’ll have a better scope and understanding of what her student Dan Meyer was going towards.    

Except….I forgot to apply to run workshops for 2016/2017 year as ultimate took up my entire life from May to June.  You live and you learn I guess.    On to the next year!  Can't wait to start tomorrow!

Math and Work

Balance.

If there is one thing I've learnt over the years, it's that balance is key.



Teaching math comes out with all sorts of different instructional strategies and technologies.

However, attaining fluency in math is just like anything else - practice is key.  Today's learners are less and less receptive to repetitive drill and grill - which is fine.   Drill and grill is for the assembly line workers of the 1900s.

The way English is taught in schools when I attended was that it was never really explicitly taught.  English was always implicitly a part of the curriculum from what I could remember.  Even grammar.  I was taught English in many different contexts, whether it was experiential by going out to the local fair or interacting with people from other schools in the collaborative learning environment.  Sure, there were some explicit grammar lesson to keep things in balance, but the learning occurred without me even realizing it.

I have been trying to attain this balance in the math classroom with those 3-act problems introduced by Dan Meyer.

Introducing a problem through a vague video is that first step.

Inviting the students for any questions or comments about the video is the hook.  Sometimes those videos are something that they would recognize from their world (ie:  a videogame) or sometimes the video can be about an abstract math concept.  I have to balance the context of the problem with their world and the 'outside' world to both connect with them and also teach them about something outside their world.

Spiraling through the curriculum is also a form of balance.  We stay long enough on a topic such as linear relations to challenge their attention span, but also switch to 2D measurement perimeter and area to keep them engaged.   We provide problems that vary and cross the different strands to show that math is not just one dimensional.

However, after problem solving we must go back to do some focused learning.  Usually in the form of worksheets that focus on a particular skill, I find that students have a little more motivation to practice the skill that we just introduced through the video that we just problem solved.

It's interesting to see them focus on practice and drilling and grilling.

One of my friends, who plays in a band for a living, stated that music and sports are probably the only subjects that students 'practice' anymore, where they are willing to try and do it over and over and over again.

The students still need practice.   I tried to vary the practice in a few different ways - with the use of whiteboards.  The whiteboards are super important as they are MEANT to be erased, which encourages students to try - regardlesss whether or not they fail.

Balancing differentiation.  These are the only two things that I have seen work consistently.  But it's hard to pull it off.

Iterations Improving the Proficiency of my 3-Act Math Delivery

NOTE:  This is a late post - supposed to have been published last month but I've only recently found time (during exams) to post it.

For today's lesson, we turned to Dan Meyer’s video question on which cup contained more juice.  Here's my powerpoint that goes with it:  

It is a splendid 3-act problem that inspired some interesting questions.  However, the quality of their questions has decreased since September; the questions had more depth, and their observations keen.  Now, they are just giving me the question that I am looking for.  Wasn’t the whole point to emphasize the questioning to clearly define problems a little more?  It looks like I’ve fallen hard into my habits and have prized THE answer as opposed to prizing the question and problem definition. 

Wow, blogging really forces me to reflect more than usual.  It just dawned on me that the reason why the question quality has been decreasing since September is that I don’t answer all of their questions.  There were so many quality math questions that were generated by the students from the videos in September but I ignored the most quality ones because they would probably take a day to answer. 

I have placed 100% more importance on following my scheduled spiral curriculum than their curiosity. 

Looking back, I should have made more of a compromise, and actually followed through with at least a few of their questions.

It would show a lot more teacher willingness to venture into the unknown and really value their questions.  Following through to try and answer their questions would actually demonstrate how I learn – one of the most important things to model.   Instead, I’ve trampled on their curiosity and lost that opportunity to be a role model of a real learner. I feel really badly now. 

But, can’t be ruminating now, can we?  I’ll just change it for next semester.

So I’ve digressed.  Going back to the 3-act question:

After receiving their questions, I specified the question that we were going to answer today.  Which cup has more, and by how much? 

Here are their guesses as a completion to act 1: 

It’s interesting to see how many of them chose that cup A and cup B had the same amount. 

Nevertheless, act 2 came along, and with those measurements and the conversion ratio the students went about to work. 

After about 15 minutes of discussion and hard work on large whiteboards, the students put their answers on at the front.  Only 10% of them got the right answer:

 The stumbling point for many students was the CONVERSION!  I have to find another way of teaching conversions as I have been repeating it throughout the year and it still hasn't sunk in. 

In truth, the fact that many of my students weren’t able to complete this question in pairs disappointments me. 

I made this question into an entrance card to repeat for tomorrow in hopes that the students will get it during their second try.

I will take it up and repeat a similar question as an assessment on the next Friday. 

Update:  They did very well on their assessment.  I wonder if they’ve gained any ‘permanent’ skills along the way in this process or if they've just memorized the process.  I will only find out later I guess especially with that EQAO coming up soon.  

EQAO - math standardized test - the time is here..

Wow.  We just finished the EQAO and it looks like it's been quite a success.  The students, according to my marking, have scored the highest they ever have compared to the previous two times I've taught the course.  In their feedback of how they felt about writing the EQAO, the students reported a high level of satisfaction upon completing the test.

The success comes as no surprise as I've never had engagement like this before.  However, it just feels pretty good to have this spiral curriculum and 3 act math pay off.

Well, of course, I think in order to really see if all of this did work, I should compare their grade 6 math EQAO marks to their grade 9 EQAO results to see if I really did make a difference.  We'll have to wait until next year for those results.

I'll just have to wait, then.  

Inquiring the Surface Area of a Sphere Through the Peeling of Oranges!

It's getting closer to the winter break, so it was great to have some hands-on activities to add some spice to the classroom for my academics.

It seems like my applied class is getting all the engaging and interesting approaches to math, so this was quite refreshing for myself (and especially these academic kids) to have this tangerine activity to explore the surface area of a sphere.

First thing we did was take a good look at the tangerines and noted its differences from a perfect sphere.  We then went on to talk about how perfect mathematical spheres don't exist in the real world since once one gets into the atomic level, things just aren't continuous.  This sort of statement really bothered some of my students  that one went home and told their parents.

Nevertheless, upon noting the clementines' (lack of) sphere-like properties, we proceeded to take a guess as to its surface area in terms of its radius, and thus area of its 2D ('projection'?)  version.   Each partner made their guess:

Looks like they their estimation skills are almost en par with my applied students' skills which has been honed through the Dan Meyer's 3-act process.  That...or they looked at the formula sheet or remembered the answer from their elementary school days.

Let's see how they did:

 I guess they couldn't be bothered to peel that other portion there to get its true surface area?  I guess I should have done more teaching and less snapping of pictures here, as I could have demonstrated that by peeling the skin into smaller pieces would more accurately depict the surface area.  Right now, much of the 'surface' area is used for the third dimension of height severely downplaying the true surface area of this orange. 

 That clementine there looks quite tasty.  I must mark these students' self regulation skills to be excellent in their ability to stay on task without eating some juicy fruit.

 Now that clementine looks quite symmetrical...and tasty.

Ahh, "four" circles!  The 'true' answer.

Now this group featured a student who made the best notes ever and another student drew some of the best art on evaluations.  The illustrations left behind were both profound and thoughtful.  It's no small wonder that they took the time to rip the orange peels into symmetrical sizes to create the above work of art.

Anyways, this activity proved to be quite memorable.  It's a good one and one that I'll continue to do every time I teach grade 9 as it somewhat demonstrates how the surface area of a sphere is 4πr^2 or the equivalent of the area of four circles.   

A Student Teacher, Teaching the Teacher

A Lesson on Felicia

I have ALMOST given the full reins to my student teacher lately every Thursday when she comes to volunteer. 

I use the word ‘almost’ because a student teacher never truly has their classroom management tested as they’re walking into a classroom with established norms and systems in place that hopefully protect supply/student teachers. 

I’m also in the room while she teaches, which affects the management of the classroom.  

On a separate note, for the first time in eight years, I can say that my applied classroom norms extend strongly even when I have a supply teacher (given the comments they leave behind).  That’s how receptive my students are this year. 

That just means that next year, my students will be wild and out of control, doesn’t it?

On the other hand, my student teacher is incredibly talented and is in her final year of teachers’ college.  I have learnt much from her style, approach and her creativity; case in point, take a look at her lesson on Felicia that she made up:

The question, I could see, resonated with the girls in my classroom.  I guess after questions involving video games, Usain bolt, etc. this was something new. 

My student teacher and I coordinated through my spiral curriculum well as the question was just a touch out of their comfort zone as they just finished learning solving equations and we’ve been through perimeter and area about two times before in previous spirals. 

The question was challenging as they got into groups of two or their ‘rate of change’ partners.  This question demanded the large whiteboards.   

For some reason, the students have been naturally lately looking to group their pairs into group of 4s and 6s.  I immediately broke up the group of 6 as I know that group was just too large.  I let the group of 4 stay as I knew that particular group of 4 worked well.  I still, prefer pairs, so I'll probably split them up next time.  

However, I wanted to see how well they worked and learnt; the next day, I went over it briefly and summarized positives and negatives of each group in terms of their process work, communication, without stating the answer. 

To truly assess how well they worked, I put up the question again.  Now, usually I am not a fan of re-doing a question, or re-assessing the same question, giving multiple opportunities, and doing it in groups…but I’ve been reading so many positive reviews of it that I decided to truly try it again.

It actually worked.

For thinking style type questions, putting the students in groups and allowing multiple opportunities created an environment of learning.  The majority of students actually tried it on their own (except the bottom 5% of the class where collaboration occurred immediately..) before starting to compare answers.  Upon finding differences, these students went through learning conversations where they justified each other’s work. 

For a question that we did yesterday and that I took up earlier, it took almost 20 minutes to get it done.  Some students didn’t even finish.  I guarantee you, as I walked around the classroom listening to their conversations, none of them were fooling around. 

Mind you, I still hesitate at the thought of doing summative thinking questions in groups with my academic students because I know the ‘Mr. Shin caught your mistake’ current environment I’ve set up would cause more of my students to copy off other students as opposed to learning it. 

I am really going to have to rethink my teaching as I found that those rich discussions that the students had with each other is worth designing the curriculum for.    

What’s hilarious is that the education world made this discovery about math education about 5 years ago when Dan Meyer first landed in a TedX talk.  Education has already moved on from this to the next phase – but at this point, the latest stuff is too progressive and far left reaching for me. I've never been an innovator; I've always been a late adopter myself to make sure the 'latest' trend actually sticks around and works with the common teacher.

Maybe if I was an elementary school teacher, I would make the jump ASAP to the latest educational trend; but as a secondary school teacher where post secondary institutions require a certain level of standardized skill, I don’t think I could ever make that jump.  

Maybe in another 5 years I’ll make the switch if it has proven to be more than the latest trend.

Things just move so fast. 

Anyways, I’d like to take this opportunity to thank my student teacher for using her beautiful question as a springboard into student learning as well as mine.  

Success! Students Create, Solve, and Assess Equations all on Their Own

I just marked the students' test on spiral #9 which included a) volume of pyramids and b) solving equations.

Volumes of Pyramids
16/22 members of this applied math class achieved level 4 or higher on this multi-step pyramid that involved using the pythagorean theorem first.  Since this is the third time spiraling through pythagorean theorem, this high success rate is not surprising.


Solving Equations
Regarding the solving of equations - take a look at what they produced on the test:

Needless to say, they aced the other questions where they had to solve my equations.  However, their formal LS and RS checks needed a little work, and during their reassessment next week, they hope to capture that portion of the test. 

It shows that the formative peer work they did the day before worked.  I didn't have to do any marking to provide the feedback that they needed.  This community that the students have created in the past 3 months have allowed them to embrace their mistakes.  The amount of learning was exponential as the students were making their own questions on their whiteboards and discussing with each other their own individual problems.  They found each others' mistakes and they would justify to each other why it was a mistake.

Some students thought that a decimal/fraction answer was a "mistake"; they went back and "corrected" the question that they created so that the solution was an integer.  The process of critical thinking necessary to justify and correct it was fun to watch; however, I have put in a mental note for the students' need that a real number (non-integer) is a number too.

I'm glad that none of my students have stated any racist or sexist or any other inappropriate comments; but they certainly are 'fractionists'.  I have to figure out a way to expand their thinking on this one.  

The whiteboards' non permanent surface is a boon for students as there is no eraser mark, white-out, or need for an official eraser.  It encourages students to just write out their thoughts, display their thinking, and promote discussion. 
 
I wish I had employed the spiral curriculum since my first year of teaching with these applied students, as this success rate has been absolutely unbelievable.

At the same time, I have a couple factors that are exaggerating the spiral curriculum's success:

1.  I have motivated kids.  My level of engagement is even higher than that of my academic classes.  Dan Meyer's 3 act math had something to do with that.

2.  I have students with extremely strong learning skills this year.  My classroom management micromanaging at the beginning has paid off continual dividends that the students reap every day. 

Hooking Students into Solving Equations

As I approached this topic - it scared me.  Typically, my 9 applied students don't take this concept of solving equations very well.

However, it went extremely well.  Better than I thought.

All my work emulating Dan Meyer has paid off, as they gobbled up this math lesson with such focus and creativity that amazed even me.

The community of openness, willingness to make mistakes, and the growth mindset was on full display.

I started off with the typical Pearson textbook problem on a Powerpoint, and had them figure out in any method how many spheres are in the bag, assuming that this was a balance.  It's my attempt at having them recall some prior knowledge:  

 Then, I had them try out this question:

I asked them - "What is the difference between this question, and the previous question?"

Student: "It's more complicated."

Mr. Shin:  "Yes it is more complicated.  There are many ways that this question is more complicated.  Can someone elaborate on why the second question is much more complicated?"

Students:  "Uhh...more spheres, more items, and more bags on both sides."

I then went on to explain that there's a method to "simplify" (bad term to use, I'll admit.  I have to ask my colleagues for the proper term.  They're much smarter than I on the formal aspects of mathematics) complicated equations like the second picture  to become simpler equations like the first picture above.

A little bit of a hook was made to some students, but as usual - not all.  Well, at least I got some without having to use any symbols or use of any math.

At this point, though, I had to introduce the use of symbols to solving simple equations on solving equations.  I made sure though, that they as a class were able to predict  each math line that would pop up on the Powerpoint before I flashed each line on the screen.

Continuing on to use think pair share and whiteboards for the next two questions makes sure that at least half of my 22 students are able to get some portions of this concept.

On day two, we built equations.  They made up their own equations using cups and cubes.   I also encouraged them  to draw out questions for their partners.

Talk about students being leaders in their learning - giving them the responsibility to create their own questions.  Fractions and decimals came out as partners answers others' questions - it was very interesting that they would take it back and try to 'fix' it as if there are problems with fractions.

However, going through that exercise of integer answers only really made them think creatively.

This is why I like the applied classroom - they take liberties on things like the money bags up top and even this:

Bunny rabbits and money bags are so much more interesting than spheres.  Money bags is better conceptually though, than the rabbits who have eaten candies, but at least they're taking their artistic liberties.

And...they're really into it - a few of them started on their homework from Knowledge Hook right away on Friday night, and there is NO red square so far.  One video was watched for clarification so far...good news good news.

 I guess the real test is:  how many more 9 applieds will they even attempt their homework by Monday? 

 
Stay tuned! 

Causality vs Causation and an Intro to Graphing

The second spiral was a short introduction to relations.  I started off with the concept of a rate, and created my own version of the "pumping gas" problem from Mr. Orr's "tap into teen minds". 

One of the best things that Mr. Dan Meyer stated about this was how the video can be used as a 'hook'.  Boy, did I underestimate the power of this hook.  Combine this hook with open ended questions, and Dan Meyer was absolutely correct - all sorts of learners participated, even the weaker math students.

The video even out the playing field and it was magical to have such engagement in an applied classroom.  In all of my eight years of teaching (I know, I'm young), I have never, ever seen this.

Another thing that has me pleasantly surprised - were the questions being asked.

"What car is it?"
"How many litres can your car hold?"
"How many litres did you put in?"
"How big is your car?"


"How much did you pay?"


It is so intriguing as some of these questions did not come to my mind, yet each of them are indeed connected to math.  In many ways, my converging mindset could only think of the one question I really wanted (ie:  what is the price of gas per litre?)  I must work on my divergent thinking.

After a day of rates, we went on to the topic of scatterplots.  Now understanding the importance of a hook, I started the students off with a 30 second paragraph of Tyler Vigen's graphs of spurious correlations

The causality vs correlation issue is often a huge source of consternation for those who frequent the forums online, and I just wanted to introduce this common pitfall. 

Hence, my Friday assessment of scatterplots and rates was chicken and crude oil related, much to the delight of some of my students.  Or chagrin.  I'm still learning to read some of them one month through.

On a side note, a few of my students were trying to force a connection in this above relationship depicted by the line graph to make sense and ventured a hypothesis thinking that the chicken was being cooked in the crude oil. 

My mind is still blown that I have such a high engagement level. 

I'm proud of the students.  Let's see how long we can keep this up.

Look ahead:  I'm spiraling back to the Pythagorean theorem by starting off week 4 with  perimeter of composite shapes.  Now that we've completed an initial assessment and a reassessment of week 1, I know exactly who to target tomorrow for individual help.  This is an incredible advantage of the spiral curriculum. 

Assessment of the First Spiral

Even though I've been teaching for eight years now, I turned everything absolutely upside down.  I'm now working with a spiral curriculum, performing Dan Meyer's 3-act math on a regular basis and implementing some serious classroom management techniques that was recommended to me from my last year's mentee.

My first spiral which consisted of Pythagorean theorem, perimeter, collecting like terms, polynomials, area and distributive property was a success by my books thus far.  They did well on certain portions of their assessment, but other not so well.  I crunched a lot of material in 1.5 weeks, and they struggled with the last portion - distributive property.  Or rather, I didn't give enough time to allow for the students to work with it.

Nonetheless - I borrowed some growing success initiatives from my science department, my wife, and another math colleague.

1)  An adaptation of my science department's concurrent credit recovery policy,:  if the students failed the assessment overall, they could get a second hack at the assessment.  They must perform at a level 3 (~70%) for me to bring their marks (all of K, A, T, C) up to 50%.

2)  Wife:  Since I was devoting class time for students to have a second hack at the assessment, I allowed the other students to try to upgrade one question.  My one page double sided assessment had a couple of thinking questions - one from homework which I took up and another one that was a little extension.  As a result, all of my students had 'something' to work on.

3)  After going through the whole assessment, students can choose to look in their binder to help them with any question that they may have trouble with.  I've been trying to give students incentive to keep an organized binder, and especially with this spiral curriculum, we have topics everywhere.  Well, armed with their organized binders, students can now use their binder (at the cost of 50% of the mark for the particular question), students can now and try to get the remaining 50% of the question.

Intro to Pythagorean Theorem

Today, I have officially decided to follow and jump on the Dan Meyer bandwagon by introducing a problem using his 3-acts.  However, I have more specifically jumped on Mr. Orr's bandwagon, as he seems to be the Canadian version of Dan Meyer from what I've read on his blog.

To start myself off on this 3-act business, I have copied Mr. Orr's video on "Corner 2 corner" with this video below:

I requested that the students write down any questions that come to mind - even non-mathematical ones.  I had some trouble amalgamating their questions as well as leading them to the question that did matter - but I have tremendous students that eventually got to the question I wanted:  what's the length of the room from the top corner to bottom corner? 

My favourite part of the whole exercise is the estimation portion.  As per Dan Meyer, it's best to ask students to answer the following:

•  What's a number that's too low? 
•  What's a number that's too high?  
•  What's the exact measurement?

Take a look:

We then discussed a plan of how to find the length of the string.  With some guidance, a couple got the concept.  Reinforcement is definitely necessary tomorrow.  

Instead of giving all the measurements, I felt that my 9s needed some movement - so I split them up into groups and they went about counting the tiles on the ground to calculate the width and length of the class.

We finished it off with some calculations and got the answer.  We have two people who guessed very close to the answer!

I'd say my first 3-act execution was somewhat of a success.  Let's hope I improve on the next one!