A visual summary of our travel today.*
Automobile ☑️ Train ☑️ (sort of)
*All times are EDT
Wednesday, 11 March 2015
Planes, Trains, and Automobiles
*All times are EDT
Thursday, 19 February 2015
eLC Road Trip (Technology Enabled Teaching and Learning)
Prologue
Feb 9th
I grabbed a bite to eat and charged up my phone. En route to my gate I checked the board only to discover that my flight was going to be delayed by a couple hours. After FaceTiming (is that a word now?) with my wife and kids I decided to try and make the most of my time at YYZ by having a little fun on Twitter with what I could discover in the airport. I also found a unique Estimation 180 problem, and finished recording the video I needed for my moving sidewalk math lesson. The next morning, on my way to Atikokan High School, I couldn't pass up the opportunity to stop and snap this pic as the sun rose over the height of land hill.
Even though I had a terrific experience in Hamilton, it felt great to be heading home.
To kick off my eLC travel adventures last week I decided to head to Shebandowan Lake Sunday evening, since I had a Monday morning flight booked out of Thunder Bay. The solo drive was pleasantly uneventful and it gave me a chance to listen to a number of TEDTalks podcasts on my iPhone. The one that resonated the most with me was David Grady: How to save the world (or at least yourself) from bad meetings.
Feb 9th
Well rested and enjoying a cup of coffee at YQT from Tim Horton's who, by the way, had shot a commercial in my town late last year.
I fired up my laptop in an attempt to take care of a few items in my inbox. Since I was going to be offline for a couple hours I stashed a math article into iBooks that I had been emailed, knowing it'd give me something to pore over during my flight. I also Tweeted this in an attempt to make visible what lengths some of us go to in our attempts to juggle home and work.
I fired up my laptop in an attempt to take care of a few items in my inbox. Since I was going to be offline for a couple hours I stashed a math article into iBooks that I had been emailed, knowing it'd give me something to pore over during my flight. I also Tweeted this in an attempt to make visible what lengths some of us go to in our attempts to juggle home and work.
Your flight from Thunder Bay to Toronto leaves at 10:40 am. What time would you wake up in Fort Frances to make it on time?
— John Gibson (@jgibson314) February 9, 2015
On my way through security I was randomly selected for the full screening which meant I was given the choice of either a full body search or getting scanned in the tube...cool! I've never been selected for this before so I chose to try out this scanner thing, and to be honest I was really let down. After the scan, the security agent summoned me out and told me to look at a screen which didn't show anything :( I guess I was anticipating a Total Recall kind of full-body skeleton x-ray. While in the air I had time to "read" the youcubed math article and compose a response by way of blog post on my iPhone. The rest of the day was spent planning SeLNO, connecting with other eLCs from the North and coordinating the TELT school visits for the next day.
Feb 10th
I felt very privileged to spend the day in the HWDSB enrichment program's learning space led by Zoe Branigan-Pipe and Beth Carey http://360.io/rP6xeb. What impressed me the most, even more than how comfortable and inviting the class felt, was how integrated the use of technology was for the learners. While everyone was getting connected, one student was happy to teach me some cool online tricks like Google Gravity, and how to customize the Google homepage with code (which he learned "just by messing around"). Once the students had access to the class Google doc via "The Hub" they were off to the races, researching, reading, and discussing what they learned about the oil sands as "local global citizens" in preparation for their debates. The process of how they developed their team's position was fascinating as they bounced back and forth between creating their arguments independently in a shared document, and working together to organize and critique what they came up with, which included assessing the validity of information from various webpages. Setting up the shared document as a table so that each group member had their own cell to compose in was an excellent strategy to keep content organized with simultaneous authoring.
Although the room was littered with examples of various other forms of technology, from a turntable to tablets, from Legos to a Makerbot, it was apparent that these tools weren't what drove the instruction, rather it was that the technology was used to foster their inquiry. Having an extended period of flexible time (other than using the gym) with the students, allowed for the teachers to go much deeper with the student learning rather than trying to fit everything into a specific schedule or bell pattern.
Feb 11th
Rather than going deep with one class, day 2 was an opportunity for me to experience a wide variety of Technology Enabled Learning and Teaching from SK to grade 8 at two different schools. On our way to Dr J Edgar Davey Elementary School we leveraged our connectedness to social media and picked up a coffee for our gracious host ;)
Although the room was littered with examples of various other forms of technology, from a turntable to tablets, from Legos to a Makerbot, it was apparent that these tools weren't what drove the instruction, rather it was that the technology was used to foster their inquiry. Having an extended period of flexible time (other than using the gym) with the students, allowed for the teachers to go much deeper with the student learning rather than trying to fit everything into a specific schedule or bell pattern.
Feb 11th
Rather than going deep with one class, day 2 was an opportunity for me to experience a wide variety of Technology Enabled Learning and Teaching from SK to grade 8 at two different schools. On our way to Dr J Edgar Davey Elementary School we leveraged our connectedness to social media and picked up a coffee for our gracious host ;)
I'm having an @shareski moment: T-6 minutes until the eLCs arrive, & I spill coffee right down my shirt. #GoodJobAviva
— Aviva Dunsiger (@avivaloca) February 11, 2015
The first room we were in was an excellent demonstration of a variety of iPad apps with a small group of ESL SK students. The students explored letters, sounds, pictures, and stories independently and as a group with the support of the teacher. What I really liked about the apps was that they gave the students instant feedback. For example, when drawing letters they had to be constructed from top to bottom (something that is/was a struggle for me), and if a student was having difficulty it was easy for the teacher to see this and then provide support as needed.
Next, we observed a grade 5 math class of which I have mixed feelings. Not about the class itself, which was fantastic, but about the effective use of technology in math. Personally I prefer DOING math using pencil and paper, where I can quickly (and messily) sketch, scrawl, and revise my thinking as I struggle though a problem. I find drawing and writing to be much more challenging on a device which then makes the problem solving process more time consuming, as well as limiting to creativity. However, we did see some ways that the technology can be a huge asset, like when the students who were using Explain Everything recorded their voices to describe their thinking as they solved the problem, and then submitted a digital copy to their teacher. I guess my ideal math class would be a blend of high tech (sharing work, recording thinking, Desmos) and low tech (pencil & paper, concrete manipulatives).
After the nutrition break we went into Aviva's grade 1 class, which I have already enjoyed visiting daily through her Twitter feed and blog posts. The biggest takeaway for me was how fluently she used technology to document both instruction and student learning. Snagit was used to record the rich discussion with the class at the SMART Board surrounding their structure problem, iPads captured their progress in pictures and videos, then through a mix of Twitter, WordPress, and YouTube all of their learning is shared with the world. In her reflection about the day Aviva came to the conclusion that "maybe the most valuable 'resource' that we have in the 21st century classroom is 'time.' with which I wholeheartedly agree.
Anne and I then ventured off to Ancaster High School to join a few other eLCs in a couple intermediate science classes. I was really curious to see what a school of 300 grade 7 & 8 students with BYOD and a 4-1 ratio of school devices would look like, but to be honest it was very similar to what we have going on in a few of our schools. I spent some time talking individually with students as they worked on their labs, and it was Google Drive that seemed to be the most valued tool for the students. Using it meant that students always had access to what was going on in their classes (even if they were absent), it allowed students to collaborate at school or abroad (unless they are visiting a country that filters Google), and it was an easy way for them to submit their work.
To cap off the day we were treated to an open discussion with a group of students about the use of technology in their school. It was interesting to hear them offer solutions to most of the problems that we encounter as we become more reliant upon being connected to the internet and our devices. Some of their suggestions included:
-printing off study notes before tests
-store vital content locally on the device as well
-continue printing and handwriting as a skill
-read books to gather information
-take time away to detach yourself periodically from your devices
-develop social skills like being able to have a face-to-face conversation
-students will take more ownership if devices are 1-1 instead of shared
-for some classes technology isn't always an asset eg: math work
And like most of the teachers I know, their biggest technology request is for faster, more reliable internet access.
Epilogue
Well my journey home Wednesday evening didn't exactly go as smoothly as my travel to Toronto. After bypassing the massive security line thanks to my Nexus card :)
-printing off study notes before tests
-store vital content locally on the device as well
-continue printing and handwriting as a skill
-read books to gather information
-take time away to detach yourself periodically from your devices
-develop social skills like being able to have a face-to-face conversation
-students will take more ownership if devices are 1-1 instead of shared
-for some classes technology isn't always an asset eg: math work
And like most of the teachers I know, their biggest technology request is for faster, more reliable internet access.
Epilogue
Well my journey home Wednesday evening didn't exactly go as smoothly as my travel to Toronto. After bypassing the massive security line thanks to my Nexus card :)
I grabbed a bite to eat and charged up my phone. En route to my gate I checked the board only to discover that my flight was going to be delayed by a couple hours. After FaceTiming (is that a word now?) with my wife and kids I decided to try and make the most of my time at YYZ by having a little fun on Twitter with what I could discover in the airport. I also found a unique Estimation 180 problem, and finished recording the video I needed for my moving sidewalk math lesson. The next morning, on my way to Atikokan High School, I couldn't pass up the opportunity to stop and snap this pic as the sun rose over the height of land hill.
Even though I had a terrific experience in Hamilton, it felt great to be heading home.
Monday, 9 February 2015
Youcubed, Fluency, and Basic Facts
One of my colleagues forwarded me a link to Jo Boaler's Youcubed article Fluency Without Fear without any indication of his viewpoint regarding its content. I really appreciate an unbiased sharing of information when the person believes it is worthwhile. Whether it's "holy cow, this is the coolest thing ever" or "can you believe this garbage" or more likely somewhere inbetween, personal comments can poison the readers opinion especially when coming from a higher tier on the organizational chart. So please, if you haven't read the article, click the link and do so before reading the rest of this blog post. Technically, I didn't actually read it to begin with, my iPhone read it to me.
At first listen, I had somehow developed the misconception that the article was saying the learning of basic math facts was not necessary to develop fluency, and that it was causing anxiety and fear in early learners. I was mistaken. After rereading the article I would say that this line best summarizes her stance: "Teachers should help students develop math facts, not by emphasizing facts for the sake of facts or using ‘timed tests’ but by encouraging students to use, work with and explore numbers."
I am a big fan of Jo Boaler's work with growth mindset in mathematics, and I agree with much of what she says about the need for developing number sense, as well as the memorization of facts not being what math is about. Check out Maths is not special for more about this last idea.
However, I strongly believe that the recall of some basic facts can be immensely valuable when learning mathematics which supports Boaler's statement that "mathematics facts are important." Specifically, addition up to 10 + 10 and multiplication up to 10 x 10 comprises some of the knowledge needed to be fluent in number sense. The author illustrates this when she admits that she doesn't "stop and think about the answer to 8+4", and in each of the cited 'number talks' multiplication facts of up to 9x10 are used as building blocks in solving the more abstract computational problems.
There are numerous analogies between learning English and learning math, so I'll throw my hat in the ring and start at the beginning with counting. Even before my daughter could recognize numbers, she was able to count, much like how she learned to talk before learning the alphabet. I like to think that learning her ABCs was akin to her learning to count from 1-20, and by 10s to 100. As she learned to read by sounding out words, she needed to be taught that c-h makes a "ch" sound, whereas in math she learned that 2-3 makes twenty-three. Likewise I think of sight words as a corollary for basic facts. As a budding reader she could sound out the word "choose" every time she saw it, but eventually she progressed to the point where it became a sight word for her. In math, when she was given 2+3 she was quite capable of counting to get the answer, but eventually she saw this as one of the "ways to make 5."
Ultimately, I think all math teachers would agree that we want our students to develop a solid grasp of the "basic facts" without scaring students off of learning mathematics. Maybe for some, myself included*, rote memorization works, but for others we need to be willing to patiently use other strategies.**
*I still remember learning my times tables in Mr. Bradley's Grade 4 class (6 x 7 was my nemesis) as well as how to write a cheque, fill out deposit/withdrawal slips, and doing enrichment with patterning.
At first listen, I had somehow developed the misconception that the article was saying the learning of basic math facts was not necessary to develop fluency, and that it was causing anxiety and fear in early learners. I was mistaken. After rereading the article I would say that this line best summarizes her stance: "Teachers should help students develop math facts, not by emphasizing facts for the sake of facts or using ‘timed tests’ but by encouraging students to use, work with and explore numbers."
I am a big fan of Jo Boaler's work with growth mindset in mathematics, and I agree with much of what she says about the need for developing number sense, as well as the memorization of facts not being what math is about. Check out Maths is not special for more about this last idea.
However, I strongly believe that the recall of some basic facts can be immensely valuable when learning mathematics which supports Boaler's statement that "mathematics facts are important." Specifically, addition up to 10 + 10 and multiplication up to 10 x 10 comprises some of the knowledge needed to be fluent in number sense. The author illustrates this when she admits that she doesn't "stop and think about the answer to 8+4", and in each of the cited 'number talks' multiplication facts of up to 9x10 are used as building blocks in solving the more abstract computational problems.
There are numerous analogies between learning English and learning math, so I'll throw my hat in the ring and start at the beginning with counting. Even before my daughter could recognize numbers, she was able to count, much like how she learned to talk before learning the alphabet. I like to think that learning her ABCs was akin to her learning to count from 1-20, and by 10s to 100. As she learned to read by sounding out words, she needed to be taught that c-h makes a "ch" sound, whereas in math she learned that 2-3 makes twenty-three. Likewise I think of sight words as a corollary for basic facts. As a budding reader she could sound out the word "choose" every time she saw it, but eventually she progressed to the point where it became a sight word for her. In math, when she was given 2+3 she was quite capable of counting to get the answer, but eventually she saw this as one of the "ways to make 5."
Ultimately, I think all math teachers would agree that we want our students to develop a solid grasp of the "basic facts" without scaring students off of learning mathematics. Maybe for some, myself included*, rote memorization works, but for others we need to be willing to patiently use other strategies.**
*I still remember learning my times tables in Mr. Bradley's Grade 4 class (6 x 7 was my nemesis) as well as how to write a cheque, fill out deposit/withdrawal slips, and doing enrichment with patterning.
**Feb.14 Update: Kyle Pearce illustrates this at http://tapintoteenminds.com/2014/04/13/memorizing-multiplication-tables-hurt-help/
Tuesday, 27 January 2015
Today Was "Actually" a Good Day
This morning I had fun doing math. We warmed up with the "Sign Post" problem which I was all over trying to solve it mathematically, until someone figured it out with Google...this kind of sucked the fun out of doing the math, but I'll give HB credit for finding the solution albeit a little too easily for my liking. Check out http://www.agoogleaday.com/ for its daily puzzle that provides some more challenging work in using your search skills.
I made up part of a denominator in a chocolate bar problem at our Regional SIM session, and I'll admit I was a little stressed. As a "math guy" I feel that there is an expectation that I should be able to answer math problems quickly and correctly especially in front of 150 educators. I know I should be more comfortable with making mistakes, I just don't know anyone who WANTS to be wrong. So for participating I was rewarded with an 85% Cacao chocolate bar...a little bitter, but still yummy!
Things got a little hazy here for a while, but a slide deck referring to the optimization of a rectangular dog pen struck a chord with me. When explaining to a colleague what I was pondering they suggested I should ask other people. Alrighty I thought, lets tweet this to Grade 9 math teacher extraordinaire Kyle Pearce:
On to exploring Grade 9-12 math tasks, and to be honest I was unimpressed. Perhaps it was my initial dismay, or thinking about the Dog Pen problem, or focusing on classifying the tasks in front of us, but I TOTALLY overlooked what appears to be a real gem.
In the afternoon we had some great sharing and discussion about what, as math coaches/numeracy facilitators, we had been working on with teachers in our boards and what we were seeing in their classrooms. Lots of good stuff happening and I promised that I'd share more of the resources I'm really enjoying for math instruction: * this is off the cuff, so I'll probably come back and update it more later. I'm still struggling with how best to curate.
Starters:
Estimation 180
Math Talks
Visual Patterns
Math Arguments
Graphing Stories
Would You Rather
Problems:
Bedtime Math (I really like the App, and so does my 5 year old daughter)
1001 Math Problems
Problem of the Week (CEMC)
YummyMath
NRICH
3-Act Tasks:
Dan Meyer
Geoff Krall
Kyle Pearce
Robert Kaplinsky
To wrap up our day seven of us were meeting for a social discussion when an impromptu game of Farkle broke out! It was the fist time playing for almost all of us, and it was a lot of fun, and a little competitive. Plus some really great mathematics discussions took place during the game, mostly focused on number sense for scoring and probability for making decisions. What is the probability of getting Farkled? Congrats to the birthday girl for winning.
To cap off the evening I was fortunate enough to experience firsthand a simple reminder why math is so important in real life:
Dinner Bill - $16.49
Drink Bill - $9.39
Total - $36.00 (calculated mentally by the waitress)
"Math never ends" - me
I made up part of a denominator in a chocolate bar problem at our Regional SIM session, and I'll admit I was a little stressed. As a "math guy" I feel that there is an expectation that I should be able to answer math problems quickly and correctly especially in front of 150 educators. I know I should be more comfortable with making mistakes, I just don't know anyone who WANTS to be wrong. So for participating I was rewarded with an 85% Cacao chocolate bar...a little bitter, but still yummy!
Things got a little hazy here for a while, but a slide deck referring to the optimization of a rectangular dog pen struck a chord with me. When explaining to a colleague what I was pondering they suggested I should ask other people. Alrighty I thought, lets tweet this to Grade 9 math teacher extraordinaire Kyle Pearce:
@jgibson314 For my 1P students, we look at a visualization through investigation, not an actual proof —> http://t.co/RD5Pt2xf5t #mathchat
— Kyle Pearce (@MathletePearce) January 27, 2015
Boo Yah! *Bonus - I just learned how to embed a tweet conversation into a blog.On to exploring Grade 9-12 math tasks, and to be honest I was unimpressed. Perhaps it was my initial dismay, or thinking about the Dog Pen problem, or focusing on classifying the tasks in front of us, but I TOTALLY overlooked what appears to be a real gem.
The sum of two numbers is
28 and their product is 5. What is the sum of their reciprocals?
It wasn't until debriefing afterwards when a colleague pointed out this problem did I see what I had missed. This question is not a simple component of factoring a quadratic...so tomorrow I'm going to revisit this and see if I can figure out its solution. Also, thanks to MC for sharing about a teacher who let his class choose if he should use the mean, median, or mode to calculate their grade. What a great application idea for students!In the afternoon we had some great sharing and discussion about what, as math coaches/numeracy facilitators, we had been working on with teachers in our boards and what we were seeing in their classrooms. Lots of good stuff happening and I promised that I'd share more of the resources I'm really enjoying for math instruction: * this is off the cuff, so I'll probably come back and update it more later. I'm still struggling with how best to curate.
Starters:
Estimation 180
Math Talks
Visual Patterns
Math Arguments
Graphing Stories
Would You Rather
Problems:
Bedtime Math (I really like the App, and so does my 5 year old daughter)
1001 Math Problems
Problem of the Week (CEMC)
YummyMath
NRICH
3-Act Tasks:
Dan Meyer
Geoff Krall
Kyle Pearce
Robert Kaplinsky
To wrap up our day seven of us were meeting for a social discussion when an impromptu game of Farkle broke out! It was the fist time playing for almost all of us, and it was a lot of fun, and a little competitive. Plus some really great mathematics discussions took place during the game, mostly focused on number sense for scoring and probability for making decisions. What is the probability of getting Farkled? Congrats to the birthday girl for winning.
To cap off the evening I was fortunate enough to experience firsthand a simple reminder why math is so important in real life:
Dinner Bill - $16.49
Drink Bill - $9.39
Total - $36.00 (calculated mentally by the waitress)
"Math never ends" - me
Monday, 19 January 2015
Coffee Conundrum
What's wrong with this picture?
If you thought "hey, there's two pots but not even enough coffee to pour one cup" then we are on the same page. Terry Tate does a great job of reminding a coworker about proper coffee pot etiquette in this Reebok Office Linebacker commercial.
This very useful pitcher in the break room fills the coffee pot...
To be honest it's not a big deal, but what I'm really wondering is why does it get like this? I know some days are hectic and you grab a cup and go without having time to make another pot...no problem. For most of us I'm going to assume that this isn't the case, and my best guess is that it's because they may not know how. To be more specific, they may not feel comfortable for fear of making the coffee too strong or weak.
The goal of this post isn't to rant (maybe a little bit), it's to present a real world math problem with a meaningful solution, so let's get down to business.
What information do we need?
What information do we need?
The coffee can label includes this recipe...
To make it quicker than using a tablespoon, we have this scoop for the coffee grounds...
How many scoops do we need to make a full pot of coffee?
*Extension: How much do we save by brewing our own coffee?
*Extension: How much do we save by brewing our own coffee?
Saturday, 10 January 2015
Cutting Up a Pineapple In 5 Steps (With Geometry)
A big shout out to @trianglemancsd whose blog, Talking Math With Your Kids, and his Which One Doesn't Belong is the inspiration for this blog post.
I think it's pretty cool that my 5 year old likes getting involved in the kitchen, so last week it wasn't a big surprise that she pulled out her ducky stool to see how I was going to cut up a pineapple.
Step 1: cut off the top and bottom
Me: What shapes did I make?
Layne: Circles.
Step 2: cut off the skin
Me: What shape do you see now?
Layne: ...a hexagon?
Me: Close, how many sides does it have?
Layne: Eight.
Me: What kind of animal has eight legs?
Layne: An octopus.
Me: Yeah, so what do you think the name of this 8 sided shape might be?
Layne: Octogon.
Step 3: cut into 8 segments
Me: Now what did we make?
Layne: Triangles!
Step 4: Cut the core off of each segement
Layne: Trapezoid!
(I don't even have to prompt for for this one)
Step 5: cut into bite size pieces and eat
Tuesday, 9 December 2014
Halloween AfterMATH
With the passing of another All Hallows' Eve it's time to eat some treats, and take down the decorations in preparation for the next holiday season (only 49 days until Christmas*). As I'm walking through a local store on Sunday I notice the following display:
Sweet! I can figure this one out on the fly. I grab my KitKat bars and head to the check out, but on the way I see:
I put back the KitKats I had already picked up and grab the box of 50 chocolate bars, box of 50 cheezies, box of 50 chips, and go pay. On the way home I start to second guess myself and wonder if I made the right choices.
How do you think I did?
How many of each type of chocolate bar are in the box of 50?
*originally drafted on November 3rd*
*originally drafted on November 3rd*
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