Sunday, 26 March 2017

Visual Math

Making Math Visual

I recently went to a lecture by George Hart and Elisabeth Heathfield (They have instructions and information on their website for many classroom activities).  I was inspired to see how George takes math and makes beautiful sculptures.  We got to try to make a Polylink triangle.  I have to say, I was not successful at that point. It takes me a while to get my mind around 3D objects and in the time we had, I couldn't quite visualize it yet. I did eventually figure it out (perseverance is something I do have) and have made several more.  

I was also fascinated by the hyperboloid.  Curves from straight lines - how cool  is that? So I made one at home too.
Looking down into hyperboloid

I brought these into my classroom to challenge and inspire my grade 8's.  We tried to make the Polylink with card stock but it is not stiff enough.  You really do need to use the craft sticks.  Some of my students really liked the hyperboloids though, so we started with small skewers which turned out okay.  I then got a group the large marshmallow roasting skewers, and that turned out great.  

Math can be about the beauty in the visual, and, is not just calculations and procedure.  

Saturday, 21 January 2017

Tools in Class Part One

Tools I Use in Math Class - Part One

Well, I fell off the blogger wagon.  Time just seemed to disappear this week so I won't make my goals.  But, back at it.   
"Success is not final, failure is not fatal: it is the courage to continue that counts." - Winston Churchill.
There are many tools - digital and some old school - that get used on a regular basis in my class.  I am lucky to have access to iPads and Chromebooks so the digital tools are an option for me.  This post is part one of two where I give my "old school" aka non-digital options. 

Tools include:

  • Exercise book - this is the warmup book where students do practice questions or some number talk thinking. It is "old school" but sometimes you just need to use pencil and paper.
  • Coil notebook - this is what we use for our Interactive Notebook (INB).  We do foldables and various other notes.  Students use the left page to practice and do upgrade questions, or add extra information.  I also take a photo of my master notebook to put into a shared folder so students who are absent, need help with notes or don't have their notebook at home can access the pages. 
    Example of page from INB

  • Vertical Whiteboards (VWB) - these are 2 feet by 4 feet and are a great tool.  Studies have shown that students will write on a non-permanent surface on average in less than 30 seconds while it typically takes more than 2 minutes to start on paper.  It is also more environmental than using chart paper all the time.  I have found that there is more work done, and less "decorating".  The students can use them to present their work to other groups or to the whole class.  If I want to keep the evidence I just take a picture with the iPad.
  • Personal Whiteboards - these are great for quick check ins and can be used to hold up answers so you can see who knows the answer.  Students are much more willing to answer the question when using whiteboards. I can also choose one for "the favourite form" or "the favourite no" to display on the document camera to use as a lesson too.  The downside to either whiteboard is the number of whiteboard markers I seem to go through.  I am currently collecting the dead ones to determine how many I actually go through in a year.  Eraser tip:  I buy the microfibre cloths from the dollar store, and cut them in half.  The work great, are easy to store, and in the summer I just wash them up.  
  • Chart paper - Sometimes you need to use a large grid, or you want group work to be displayed for a longer period of time on the wall.  This is when I find the chart paper useful.  (It is also good for creating anchor charts - good activity for the students is to develop the anchor chart for a topic then have the class choose which one to display on the main bulletin board) 
What are your favourite tools to use in class? Drop a comment! 

Saturday, 14 January 2017

First Week Back

Back for 2017

It is the first week back after the break for the holidays. I was refreshed after the break but already I can say I am exhausted after only one week.  So my blogging challenge has suffered a bit.  I have not been writing every day this week to the amount I had hoped for when I started (unless thinking counts ;-) ). 

This blog is titled Math Mayhem, but a Math teacher is more than Math.  I loved John Spencer's post a little while ago that included what he hopes would stop in 2017.  One of those things he hoped would stop was about treating teachers like villains.   It got me thinking about all the things teachers need to do besides teach which is really what teachers love to do (although I myself really do love to plan).  

My list of things to do this week included; Boys basketball practice (two of which were at 7 am), computer contact activities, staff meeting (where I was presenting a Number Talk), 7/8 teacher meeting, planning, and marking.  That is just the school stuff.  I also have a life outside of school. 

I still have to do breakfasts, lunches, walk/feed/play with the dog, exercise, clean, sleep (ah the elusive sleep), shop and do a little TV/reading.  

So it has been a busy week.  

January/February are two of my busiest months of the year.  I coach Boys basketball so practices and games take up about 6 hours a week. It is also end of term 1 so those final assessments, and marking need to be done as well as some chasing to get work not yet submitted.  And then report cards need to be written which take about 30+ hours of time to do. IEP's need to be done for term 2 (thankfully my school has great administration and a terrific SERT who help us out a lot with this task). 

I don't have kids of my own other than my 4 legged one :-).  I don't know how teachers with kids manage it sometimes.  

It is no wonder that we get sick.  I, knock on wood and the bottle of Oregano oil, have been lucky not to get sick this year.  

Next week I start conferencing with my grade 8 students.  Several were worried about it.  I mentioned that to Debbie, my friend and LST, and she suggested that we do a fishbowl role play of both a prepared and unprepared conference.  It was great, and Debbie did awesome in preparing herself as one of my students. 
Debbie,  this is for you!

Many students told me afterwards that they felt a lot better about having their conference after seeing it.  We created anchor charts during our debriefing time.  
Conference Anchor Charts
As I have mentioned in my post on Standards Based Grading, I want my students to be aware of their learning, and take ownership of it.  My goal is that by doing the conferences (which are new for me too), that they will look at their assessments as more than a mark, but a way to learn what they need to improve.  

Do you conference with your students?  If so, do you have any tips or suggestions?  Post in the comments as I'd love to learn from your experiences. 

Wednesday, 11 January 2017

Standards Based Grading

To SBG or not to SBG, that is the Question

I have been doing an exploration into Standards Based Grading.  Many things I have read have shown that feedback without a grade has a bigger impact on student learning than just grades.  Students typically look at the grade, and only the grade, and then put the assessment away.  The goal is to get them to read the feedback, understand it and then improve their understanding.  

It has been an interesting transition, and the students are still trying to get their mind around the the fact that I don't assign grades explicitly as a percentage but rather I give them a proficiency level.  
I have been marking with the focus on feedback and growth.  Students have the opportunity to fix mistakes and improve their level of proficiency along the way. This requires a little more time from me as I need to give feedback for everything assessed.  It also requires students to take on more ownership for their learning, and for some of them, that is a new experience.  

The other piece to this, and we'll be trying this out this month, is the student conference.  Grades are needed on report cards.  The students need to conference with me to discuss what marks they think they should get and most importantly why.  They must also come with a next step, or, how can they do better next term. 

It is a trial.  I think it has been going well.  I was using a spreadsheet that I modified from John Orr, but double entry of marks (one in the spreadsheet and one in my paper mark book) got to be overwhelming so it has fallen by the wayside for the moment.  

I will be continuing this through term two, but I may not give them the proficiency level as they have begun to only look for it instead of the feedback now.  They will get the proficiency level when they ask and can explain their feedback. 

Saturday, 7 January 2017

Number Talks

Talking about Numbers

One of the ways to encourage students to think about Math is to encourage number talks regularly.  These discussions encourage students to process their knowledge, expand their conceptual understanding and communicate their thinking so that others can understand.  They can also be useful diagnostics to see what misconceptions or concepts are known before a topic is explored in class.  These talks can be individual, or group activities but I find it best, especially for those introverted students, to start them off with at least a few minutes of individual think time.  They can be done as a purely mental math task such as a dot card talk, but some questios may take some drawing or calculating to come to a solution. Typically a number talk is less than 15 minutes.  I have found that they can take an entire 30 minute period if the discussion really gets going.  You can choose to let the Math take you along the journey or you can set a timer and limit the time spent. There are many resources for this available to use.  

I learned a great deal from reading Jo Boaler (Mathematical Mindsets and What's Math Got to Do with It) and using her website  I have also read other books such as 
Making Number Talks Matter by Cathy Humphreys.

Here are some of my favourite resources online:

Which One Doesn't Belong

This is a visual of four things.  The students are asked which one doesn't belong to the group or find a reason for each one not to belong.  Choose whichever version works with your students and the time you want to use.  If you create your own, you can submit it as well.  Many also show up via Twitter ( so it is good one to follow.  I project it onto the whiteboard and as the students give their answers, I write it beside the option. 

Example of a WODB
Estimation180 - Lots of great stuff here.  Some of my newest ones to use though are the clothesline activities.  If you haven't tried one, I would suggest doing so. 

FractionTalks - new one for me, but I like the options.  There are various categories such as square.  The How-To section explains how to use them very well. 
Example of a Square Fraction Talk

Open Middle - These are lots of ways to search for problems.  It is US based so you need to be aware of how the Standard Core compares to your curriculum if you are in Canada or another country (check here Canadian Correlations) - this is just what it says, visual patterns, and there are over 200 of them to choose from right now.  Recognizing patterns can be done with any grade though some of them are more exponential in nature.  It can extend into Algebra by asking for a particular term number or for the equation.  
Example of Visual Pattern

Would You Rather - Give two options and students need to justify their choice.  Really encouraged Math language and discussion.  
Example of a Would You Rather

Tap Into Teen Minds - Kyle Pearce has been doing some amazing things with this site and many of the animations make great number talks.  The students get a visual and the Math which activates that cross brain activity that really helps them to understand the process and not just an algorithm. 

There are also a lot of great tools that can be used to aid in either doing the number talks or to gather data before, during or after the discussion.  The conversations and observations are useful data to record.  How to effectively and efficiently gather that data, especially in rotary classes, is where I am currently trying to grow.  Any ideas you would like to share on how you do it? (Please leave a comment below - would love to hear about it. )

These include (but are not limited to):
  • Personal whiteboards
  • Vertical Whiteboards
  • Google Forms (Using their quiz feature or using Flubaroo add-on)
  • Google Slides
  • GoFormative
  • Peardeck
I will discuss the tools I use in a subsequent post.  

What are your favourite Number Talk resources?  

Monday, 2 January 2017

Happy New Year!

Happy New Year Everyone!  

As we begin a new year and everyone thinks of resolutions, the prevailing idea in education is to set goals instead.  What are your goals this year?

I have decided to try to blog more often as my goal so here I am, on January 2nd, beginning that process.  I believe I read that "writing improves reading and reading improves writing".  I read a lot - prodigious is a word that comes to mind - so I have the reading part covered, but I don't write much even though I do like to do it.  I have accepted A.J. Juliani's 30-day Blogging challenge in which I intend to write everyday and publish at least twice a week. Will you join me? 

There is also a trend to choose your one word for the year using #oneword2017.  Overall, I chose innovation as my word for the year.  I think it encompasses everything.  It means to create change by creating something, improving something, designing something in new ways.  For me, innovation is about practical things like how to use technology in new ways, but also about how to change my teaching practices to better meet the students where they are at right now.   I will try new things.  Some of them may work and some will not, but failure is part of growth.   
I heard a quote recently "Failure is an option, but failure to deliver is not."  I really like it as I feel it has a great deal of meaning for students today (or it should). I wish I knew who said it originally.  

What is your one word for 2017?  

Friday, 23 December 2016

Official Formative Educator!



I know it is not a real word, but it is appropriate I think!  Thanks to GoFormative for acknowledging me as a Formative Educator.  I love the tool, and the students are comfortable using it.  It makes gathering data and sharing student work with the class anonymously simple and straightforward.