Tag: Mathematics

A World of Mathematics

That’s the claim of Mathigon.  If you love mathematics (and who doesn’t), be prepared to spend all kinds of time at this web resource.

I actually stumbled into the World of Mathematics by accident but, wow, I’m so glad that I did.  I wa actually looking for some origami resources and fell into a link from the Mathigon website titled http://www.mathigon.org/origami/.  Like what so often happens, when I find a wonderful resource like this…

I’ll back off to the root of the website and poke around.

According to the About page, the site was designed by Philipp Legner and you only have to spend a few moments on the site to realize the passion for mathematics, particularly for the visual, that drives the design.  You’ll be exploring for hours.

Major categories of:

  • Symmetry and Space
  • Numbers and Patterns
  • Combinatorics and Logic
  • Probability and Games
  • Motion and Matter

open the doors for further exploration.

Who doesn’t like a good fractal?  Lots of gorgeous pictures when you explore.

And what would a good mathematics resource be without a discussion of the irrational pi?  My memory recalls 3.1415926 accurate to seven decimal places but that pales in comparison to the first 50 000 digits.

Mathigon has presence on all the major social networks including an extension for Google Chrome, if you’re so inclined.

Some of the resources are still under development.  Mathematics lovers, teachers, and students will definitely want to explore and keep reference to this site.  The site definitely digs into the topics deeply but I think that you’ll find a little something for everyone.



Fantastic Mathematics Resource

So, when Donna Fry gives an order, I do it!

The OAME (Ontario Association for Mathematics Education) has assembled a fabulous collection of mathematics resources that they’re calling mathies.ca.  It’s a really handy collection or games, tools, activities, and support pages for students and parents.

With all that’s assembled here, this should be the one stop resource for Ontario students and parents looking to bring mathematics into the home learning space.  If you’ve been a user of the CLIPS resources, you’ll recognize quite a few of the activities.  Heck, there may even be a few that you don’t recognize.  As a former OSAPAC Committee member, it was terrific to see links to The Geometer’s Sketchpad and Gizmos.  Some of these resources aren’t immediately usable as they’ll require a login / password to access since they are Ministry of Education licensed but instructions about how to get access to the codes are provided.

Some of the links let you download the software to work with locally.  Others run directly from the web.

As a mathematics lover, it’s just fun to play around with many of the activities.  So many of them are just fun to play with.

I’m always a sucker for a good calculator and I just had to check them out.  The computer science mentality naturally draws me to activities like taking the square root of a negative number or trying to divide by zero.  Just fun stuff that were standard for testing things…  I really like the ability to have quick access to a graphing calculator.  You do have to have Flash installed on your computer for some of the activities.  Hopefully, plans to develop for devices that don’t support Flash are under way.

This is an incredible collection of mathematics resources and, as Donna notes, needs to be shared widely.  Please take the time to do so.


An Interview with Kyle Pearce

Kyle Pearce is a secondary school mathematics teacher at Tecumseh Vista School in Tecumseh, Ontario.  He uses social media to promote the great things that he’s doing with his students and also to provide insights into innovative ways to teach Mathematics.  I think the title of his blog “Tap Into Teen Minds” speaks volumes about his philosophy as an educator.

Doug:  Thanks for taking the time to be interviewed, Kyle.  I’m sure that you’ve got some great ideas that can be appreciated by the readers.

Kyle:  Thanks for having me for this interview, Doug.  I really enjoy making connections with other educators in mathematics and across the curriculum to find great strategies to make learning more enjoyable for students.

Doug:  Tell the readers where we first met.  What were your first impressions of me?

Kyle:  The first time we met was back at the University of Windsor in the Faculty of Education.  It must have been in or around 2006.  I remember you being very approachable and down-to-earth when it came to introducing effective teaching practices.  I enjoyed the experience thoroughly!

Doug:  The Faculty of Education class where we met was the Computer Studies teachable.  Are you able to use any of that course in your present environment as a teacher of mathematics?

Kyle:  The Computer Studies teachable course was a great experience because it allowed me to see some of the huge differences that exist when comparing the way a mathematics course is delivered and a computer science course.  When I was at the Faculty, most math classes were traditional with a teacher writing a note on the board, students copying, and then 20 minutes at the end for students to start their practice.  Your course allowed me to see a more project-based approach to teaching.  I am still trying to move more to that side of the spectrum and I know that your course gave me the insight to try making that shift in mathematics.  That being said, I feel that I left a lot of knowledge, experience, and opportunity on the table at the Faculty because I just didn’t have the same passion for education as I do now.  That’s one regret I am not so proud of.

Doug:  Your school is a Pre-K to 12 school, and was designed to be so from its opening a few years ago.  What’s it like to teach secondary school in such an environment?  

Kyle:  I think it is an excellent platform for education.  Cost savings aside, why wouldn’t we want to have a huge chunk of our family of schools right in the same building?  There were some growing pains that caused conflict due to some having a difficult time accepting change, but overall I think it provides great opportunities for student leadership and improving education from K-12 through professional learning communities.

Doug: Do your students have recess envy?

Kyle:  Ha!  Something I have never asked my students, but should!  Some of the secondary students in the first year had an issue that they needed to get over in regards to whether they were in high school or still in elementary.  Now, after 3 years, I think the original pessimists have finally realized that the model is solid.

Doug:  Related to that, do you have any sense as to what it feels like to be an elementary school teacher in a K-12 school?

Kyle:  There was a bit of hesitation on both sides between staff members in the first year, but I think that has passed.  I’m not too sure as to what the cause was, but we have professional learning communities such as the
Middle Years Collaborative Inquiry where 7-10 teachers are together multiple times a year and I can see some great things happening there.  Making an effort to take a walk down there when you can to say “hello” can go a long way and I have built some strong friendships because of it.  Our grade 8 teacher, Craig Guthrie and I are picking each other’s brains all the time to try and better align our grade 8 and 9 math courses.  Our collaboration has even led to a TLLP project for this year that brought iPads into his classroom.

Doug:  You’ll now be taking in Grade 9 students that are accustomed to that school.  Do you find that they transition differently?  Better?  Worse?

Kyle:  I’d like to think that the students moving from grade 8 to 9 in our school feel more comfortable with their surroundings, but I haven’t visibly noticed a difference.  We still have one other school, AV Graham that feeds our school and students making a switch from the separate and public systems that still allows students the opportunity to expand their circle of friends.

Doug:  You’ve been a huge fan of iPads in the Mathematics classroom.  If I was a fly on the wall of your classroom, what would I see on a regular day?

Kyle:  I work hard to maximize the use of the class set of iPads that are housed in my classroom.  When I first began, this was done to eliminate the amount of paper we were using through the
TIPS4RM and 3-Part Lesson approach that Mike Smith and Dave Bracken from my previous school found to be so successful for students taking applied level math.  Originally substituting what I was doing with a SMART Board and paper resources with a class set of iPads, I began finding ways to augment the learning by allowing students to instantly share their work via Apple TV, receive instant feedback and share their work with me and their parents daily.  Trying to modify and redefine what it means to learn math in a 1:1 classroom is still a work in progress, but individual student math blogs is my current focus.

Doug:  How does this differ from teaching without them?

Kyle:  Going digital with 1:1 iPads has allowed me to cut out the stuff that doesn’t matter and add photos, video and interactivity on a daily basis.  The 75 minutes that used to seem like forever has now turned into a snap.  Until I can find funding to support a take-home 1:1 iPad project, I don’t think I will be able to fully maximize the potential of the iPad in the classroom.

Doug:  How did you manage to get such a terrific environment for your students?  Can others replicate it?

Kyle:  Back in 2010, I had submitted a proposal for a
Teacher Learning and Leadership Program grant from the Ministry of Education and the Ontario Teachers Federation.  This grant is made available each year and is typically due by mid-November, assuming the funding continues.  It is a great opportunity for teachers to apply to fund an idea they think will improve the learning in their classroom.  Definitely worth the time and effort!

Doug:  Tell us about some of the applications that you use with your class.  How did you decide which ones to use?

Kyle:  Our “home-base” is an app called
GoodNotes.  Since math does require that students gain an ability to write using algebra and complete solutions, I typically create a PDF file called a Math Task Template in order to give students a way to organize their thoughts throughout the lesson.  However, most days involves a bunch of App-Smashing (i.e.: using multiple apps to complete tasks) in order to get the job done.  This is our first year using Google Drive as our cloud storage option since students are also posting work to Google’s Blogger blogging platform.  Improving student communication often times involves screencasting apps such as Explain Everything or Doceri, while clicker-replacement apps include Socrative, eClicker or Naiku.  Other great app suggestions for productivity include Evernote, iMovie and BaiBoard, while math specific apps that deserve a look are Dragonbox, King of Math, OhNoFractions, Free Graphing Calculator and Algebra Touch.

Doug:  Do you add/remove apps during the school year?

Kyle:  Absolutely.  It can be a pain if you are not using the Apple Volume Purchasing Program and Apple Configurator, but it is definitely worth it.  

Doug:  Can the students take the iPads home?

Kyle:  Right now, iPads stay at school due to the limited number of them we have in the building.  My hope is to apply for funding to research whether students taking applied math would benefit by having an iPad throughout their school day and for completing work at home.  Hopefully, we can make that happen sometime soon.

Doug:  Do the applications that you’ve chosen change the way that students learn mathematics?

Kyle:  I believe so.  However, it is really important that decision makers at the board and ministry level understand that technology will yield no gains without the use of effective teaching practices and sufficient professional development in technology.  Often times, technology is purchased and sent into schools without adequate training to ensure teachers feel confident and understand how to implement these new tools.

Doug:  We’ve all read about the implementation problems that the Los Angeles Unified School District has had with their rollout of iPads.  How has yours been?

Kyle:  Luckily for me, my class set of iPads were the first in our PC-based board.  Since my project was essentially a pilot, I did the research and experimenting to rollout my class set.  A ridiculous number of hours later, I was very well-versed in the process and still manage the devices on my own.

Doug:  Are the iPads locked down for student use?

Kyle:  We have a Bretford PowerSync cart for storing, charging and syncing the devices right in my classroom.  The iPads are locked down using Meraki Mobile Device Management to restrict students from installing apps with their personal accounts.

Doug  I know that you and I have chatted about the use of Apple TV in your classroom.  How do you have it set up?  What are the advantages of using Apple TV?

Kyle:  The learning experiences that Apple TV brings into a classroom is just amazing.  My personal iPad, projector and Apple TV have allowed me to get rid of a SMART Board that I had been using daily for the previous five years.  Not only can I mirror the screen of my iPad from anywhere in the classroom, my students can do the same from their desks.  In an instant, I can ask a student to mirror their work and the entire class can now see multiple approaches to the same task.  Discussions about how the solution might be assessed on a summative or standardized test and what the student can do to improve are discussions that are held multiple times each day.  

Doug:  You’ve recently become an Apple Distinguished Educator.  What does that mean to you?  More money?  More opportunities?  More responsibilities?

Kyle:  When I found out I was selected as an Apple Distinguished Educator, I was completely honoured and surprised.  Being included in a group of educators such as Dan Meyer is something I still have a hard time believing.  While more money would be a great bonus, Apple Distinguished Educators are not paid, but rather rewarded with professional development opportunities.  Each year, there is an Apple Distinguished Educator Institute that we are invited to participate in and Apple foots the bill.  This past summer, the 5-day 2013 Institute was held in Austin, Texas at the University of Texas and was the best PD experience I’ve ever had.  Throughout some of the ADE experiences, I was recently invited to become an Apple Authorized Education Trainer which does provide opportunities to work with other boards (and yes, the compensation ain’t bad either!).  

Doug:  You’ve also recently made Tecumseh Vista a Google Apps for Education school.  What impact does that have in the mathematics classroom?

Kyle:  I think Google Apps makes organizing digital education as easy as it gets.  Students receive a single Google login for cloud storage, email, blogging, YouTube and any other Google service available.  Best of all, the Google Apps administrator has complete control over all accounts and the restrictions set on each.  For example, we have Google Plus disabled until we can determine whether we can keep student information confidential.

Doug:  You’ve shared a Google Document with me titled “MDM1D Learning Goals & Success Criteria Challenge”.  Can you explain what you’re trying to accomplish with this document?

Kyle:  Until just recently, I realized that teachers in Ontario are the link between the students and the curriculum.  Regardless of how often learning goals and success criteria are promoted through board PD, students may never really understand what the purpose of a lesson is.  The Learning Goals and Success Criteria Challenge is one way I’m hoping we can bring Ontario teachers together to develop some student-friendly learning goals and success criteria to improve student success.  

Doug:  Are your mathematics teaching colleagues on the same page as you with respect to technology?

Kyle:  The teachers in my department have been completely open to integrating technology into their classrooms and we continue to learn together as we try to make learning math as relevant and enjoyable as possible. Quite a few math teachers across our board are using SMART Boards and class websites to get digital and make their lessons more engaging.  I’m confident that if we ever move towards a 1:1 iPad program in our board, we’d have a significant amount of buy-in from teachers.

Doug:  On Twitter, you’re known as “Mathlete Pearce”.  You’ve got to explain that handle to our readers.

Kyle:  My wife Chantal has always referred to me as “Mathlete” any time I get mathematical in a conversation.  I think she heard the term on a movie way back when we were dating in university.  Now, I call my students mathletes on a regular basis.

Doug:  Thanks so much for taking the time for this interview.  I know that you’ve had great success to date and I wish you all the best for the future.  It’s great to see students from my University of Windsor class get jobs.  That’s not easily done these days.

Kyle:  I can’t tell you enough how grateful both my wife and I were to find jobs straight out of the faculty.  Flattered that you took the time to interview me for your blog as I know that educators still flock to access your educational resources and insight (including myself!).  I’m sure we’ll catch each other on Twitter before too long!

Stay in touch with Kyle’s learning by following him on Twitter.  You’ll find him as @MathletePearce.  Kyle also blogs regularly, sharing his thoughts, ideas, and resources for teaching secondary school mathematics at http://tapintoteenminds.com/.

A Puzzle to Drive You Nuts

I’ve always enjoyed a good puzzle.  The more it makes me thing the better.  I love logic and a good mathematics puzzle is hard to beat.

On a cold and rainy day, I decided to go looking for one.  And, I found a good one.

Matchmatics is a faithful replication of the math activity that drove me nuts (but in a good way) in elementary school.

Remember this?

A mathematical puzzle with the digits and the operators created by matchsticks.

I remember them being drawn that way in the textbook and, if you were lucky enough to get a textbook that didn’t have the answer already written in it, you reproduced the question in your notebook and then solve it.

The solution can be reached by moving one of the sticks so that you end up with a mathematically correct expression.

In the iPad version, just pick a stick and move it into place.  When you get a correct solution, it’s time to move on to the next puzzle.

An additional challenge is to do a screen capture as you solve a puzzle.  In this relatively simple one, I completed the equation by changing the six to a zero.

Want to drive yourself nuts?  Want to challenge those learning math?  Download and give it a try.  Oh, by the way, it does keep score so speed of solution is important.  If you’re like me, you’ll ignore that and just want to solve the puzzle!

The free version contains 10 puzzles and three different challenges for solution.  Beyond just playing it, in the classroom I would use it as a launchpad for students to create their own puzzles and challenges for classmates.

A full version of the program is also available for $0.99


This Week in Ontario Edublogs

It’s been a while since I’ve taken the opportunity to highlight some of the great content that Ontario bloggers are creating.  It’s not that I’ve given up reading the blogs – I still enjoy them daily – but I took the time to do some other Ontario things.

The list of Ontario blogs that I know about is available here through this Livebinder, which by the way is a great way to read them all.  All of the links take you to the blog embedded in the Livebinder so you don’t get lost.  In addition to the list of bloggers, there are also two list of Ontario Twitter users that you may find helpful.  List 1 has 499 people and List 2 has 38 and growing.  Recently, I’ve been spotting a number of new names and I’ve been adding them to the lists as I find them.  So, don’t let anyone tell you that nobody uses Twitter!  If you’re an Ontario educator and want your blog listed or your Twitter name added to the lists, just go here and complete the form.

Here’s a bit of what I had the pleasure to read this week.


How to Share a Dropbox Folder in an iPad Classroom

If you’ve heard about Dropbox but are in need of a little inspiration and a tutorial to get you started, head over to Kyle Pearce’s blog.  He’s written a combination tutorial/editorial about how to use it and, at the same time, why you should be using it.  He’s done a great job with text, screen captures, and embedded movies to give a complete guide.

If I could offer another read, I recently wrote a post called Deja Drop.  It extends a previous post I had made about using Dropbox as a hand-in folder and offers ideas about how to use it with an iPad now that iOS6 has been released.

I totally agree with Kyle – there are so many advantages to using Cloud storage and you can’t beat the feature set of Dropbox.


An Teaching Out Loud Exclusive: I’m A Big Boy Now!

There are three great ingredients to look for when reading a blog.

  1. Good news
  2. Cryptic messages
  3. Humour

Stephen Hurley’s recent post had them all.

In Ontario, there seems to be a scorecard passed around educators to let you know when someone is approaching the 85 factor.  Stephen rationalizes some of his personal thoughts in a post that includes all the successful ingredients.


Between a rock and a hard place

I’m really bad at reading blogs and not commenting immediately.  For that, I apologize to all whose blogs I have enjoyed but neglected to leave a post.  But Tim King’s recent post struck a nerve with me.  How many times is the computer science teacher weighed down with the responsibility of being the go-to person in the school when something computerish breaks?  I know that it happened to me many times and I think that’s why I found my head nodding as I read Tim’s post.  My scenario was like this – I was in the middle of dealing with a student’s problem and a colleague came between the student and me mid-conversation, looked me straight in the eye and complained “My printer doesn’t work”.

In the rush to have everyone class computer savvy, students and teachers are at times, pushed into the deep end in implementation without learning to float first.  Thank goodness for the computer science teacher.  I’ll just go bug him.

And yet, we still do it.  Are computer science teachers just that noble?


Minds on Math – Learning as a Community

In September, I had the chance to interview Shannon Smith when she was just a Newby in her role as principal.  One of the things that we discussed was her use of social media and how would it extend to her new school and its community.  She promised that she would be very transparent with parents, staff, and students.

Can it work when the day-to-day workload kick in?

Shannon’s school recently had a professional learning day and they were “all-in” for mathematics.  It would have been easy for her to have blogged “We did math stuff”.  Instead, she shared a complete set of details about what happened on that day.

I really like it.

If I’m a parent in that community, I know that the staff is dedicated and now I know what might be happening in my child’s math class.  It’s a great read and if any other principal is wondering what sharing with the community could be (other than when the next hot dog day is…), this is a perfect model.


The Trustee Dilemma

Trustees are people too.  In theory, they make the decisions that set governance and policy with school districts.  As you know, many things have been thrust upon local school districts by the Ministry of Education this fall.  The one voice that we seldom hear when it comes to this situation is that of the individual trustee.

We hear from teachers, we hear from the federations, we hear from the government, we hear from the school district, we certainly hear from newspaper reporters, and of course from the public that reply to their opinions.

But what about the lonely trustee sitting around the table at board meetings?

Robert Hunking took the time to share his thoughts about what’s happening in Ontario now.  For a completely different perspective, you should take the time to read this post.


This was a fun post to write.  I get a rush reading the great things that Ontario Educators write about.  Please check out the above and all the great things happening and made available through the LiveBinder.

Missing the Forest for the Trees

I bugged good friend Ross today.

I was working with a teacher analysing some data generated for some of their PLC (Professional Learning Community) discussions. It was an awesome time and we chatted about trends, type of graphs, how to tell a story with statistics for people who aren’t statisticians, and much more.

We were using the Ministry of Education licensed Fathom software. For my money, it delivers on the promise that we always heard about spreadsheets. We were always promised that spreadsheets would allow for the “what if” scenarios. It does; but you typically have to develop and test a formula for it to happen. Fathom is so much easier for some things. Drag and drop an attribute on an axis and voila a graph. Drag and drop in a different location and other things happen. So, you quickly get to the discussion rather than muddle around with formulae.

So, we’re messing around with a graph with more than one attributes and I was asked the question

“It’s great, but if the legend went from 100-0 instead of 0-100, it would be so much better.”

No problem, thought I. We’ll just drag it around or modify it here or there. Nada. Not even close.

Now, I’ve worked with Ross’ mathematical genius mind before but he wasn’t around. So, I figured – what the heck, I’ll drop him an email and he’ll get back to me hopefully this school year. Crafted the message and then went back to noodle scratching.

Out of the blue, there’s a message. Yep, it’s from Ross. Nothing like having a mathematician on call.

The solution was so simple that a child could do it. However, this old child was looking for answers in all the wrong places. The suggestion was embarrassing.

“Why don’t you just multiply every element in the range by -1?”

Not only had I missed the forest for the trees, I wasn’t even in the same general area as the forest.

It’s great when you have your own supports just an email away.

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