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Tuesday, 28 May 2013

"Inappropriate Use of Technology"



No electronic devices during school hours
CC licensed photo  shared by Flickr user Daveynin


Recently, some older students in our school "smuggled" a personal electronic device out into the hallway and they used it inappropriately.  I don't think I need to go into any details, there are hundreds of ways to "use technology inappropriately".

The result is that our principal has decided to ban personal electronic devices from school property.

I understand his frustration and the pressure he must be under.   But I am not convinced this is the solution.

In my class, I have a BYOD policy.  In the past nine months, I had one student bring his phone out to recess because he forgot that it was in his jacket pocket.  He then left his jacket outside, with the phone still in his pocket.  He begged to go back outside to get his jacket.  Luckily, the jacket was still there.  I also had one student take a video of another student who was dancing in a silly manner while we were getting ready for home.  I was in the classroom at the time.  I took his device away for a few days because we have a strict policy in the class that video taping only occurs with teacher permission.

Other than that, I have had absolutely NO issues with their electronic devices.  They come in in the morning, they put their devices in a cupboard which remains locked throughout the day (it also houses our class laptops and iPads).  When we need the devices, we take them out of the cupboard.  It's that simple.

I have done a LOT of EXPLICIT teaching up front about appropriate use of technology and responsible digital citizenship.  My students have a mantra: "What goes on the Internet, stays on the Internet."  They know that they shouldn't post anything they wouldn't be proud to show to their grandmothers.

They also know how to be cautious and protect their personal identity.  They know the dangers.

I don't believe banning electronic devices is the solution.

Let's face it: Kids (and adults for that matter) have been known throughout history to use communication devices inappropriately.  Give a kid a can of spray paint, and he may paint a mural, or he may paint a racial slur.  Give a kid a marker and she might create a title page or she might write her "frenemy's" name on the bathroom wall.  I've picked up a lot of inappropriate notes that have been passed around on paper in my day!  Should we ban paint, markers and paper?  What about the almighty pen?

I know, the scope, and therefore the damage, is so much greater with the Internet available to them.  But as soon as they step off school property they are using the technology.  Are we any less responsible because it happens outside of the school day?  Isn't it better to take our heads out of the sand and teach responsible digital and global citizenship BEFORE the inappropriate usage starts?  Aren't we responsible as their EDUCATORS to teach them how to use digital devices for their benefit rather than to their detriment?

Today I showed my students this TED Talk by Sugata Mitra.  I'm guessing everyone is familiar with it, but in case you aren't, please take the time to watch this video.  More than anything else, this video helped me to understand the power of creating a child-driven learning environment using technology.





I welcome your input on this issue.  It is something we have to face and make decisions about more and more often these days.



Wednesday, 22 May 2013

More Fun with Grade Six Probability Concepts!

I had so much fun teaching Math today!  We are still working on Probability concepts, and on Friday, I had the students play a game I call "Odds and Evens".  Students work with a partner and they each have a number cube.  They roll their dice and add the sum.  One student chooses to be "odd", the other "even".  If the sum is even, then the "even" person scores a point, and if it is odd, the "odd" person scores a point.



Each pair of students conducted fifty trials.  Then we tallied all of the trials for the class and determined the Experimental Probability.  Next, I showed them how to create a tree diagram for the two dice, and we determined all of the possible outcomes.  Students could see that if you found the sum of the two dice, exactly half of the total number of outcomes were even, (18/36) and half were odd.  So we called this a "fair game" because each student had a 50% chance of winning. 


Today, they played the "odds and evens" game again, but we changed one of the rules.  Once again, they each had a number cube and they played with a partner.  This time, when they rolled the dice, they had to find the product of the two numbers rolled.  Again, one of them had to choose "even" and the other "odd".  I asked them first to predict whether or not they thought this would be a "fair game".  They all believed that, like with the sum game, this would be a fair game.  



It was so fun walking around the room and listening to their conversations as they played.  They weren't long into it when I started hearing:  "This game can't be fair!"  So I walked around the room asking them them questions:
  • Do you still think this is a fair game?  Why or why not? How can you tell?
  • Why do you think "even" is winning?
  • What is your experimental probability? Is it what you expected?

It was so much fun to walk around the room and hear the learning as it was happening.  They were so excited when they discovered that both numbers rolled had to be odd in order to end up with an odd product!

I asked them to conduct 40 trials.  (I like to use different numbers of trials so that they get used to finding percentages with different denominators.)  When they had completed all of their trials, they calculated the Experimental Probability.

I then asked them to find the Theoretical Probability for the experiment.  It was very interesting.  They all made their tree diagrams correctly.  They all knew that there were 36 possible outcomes.  And yet, out of 10 groups, only 2 correctly found the Theoretical Probability.  They all determined that there were 27 even outcomes and only 9  odd outcomes.  But they used 40 as their denominator again.  

The last step in the question asked them to find the Theoretical Probability for 500 trials.  They understood they needed to use equivalent fractions, but as they had been using a denominator of 40, their answers were not quite right.





During the consolidation, I asked one of the groups with the wrong answer to step forward and explain their theoretical probability.  The two groups who did it properly, at first, began to doubt themselves.  Why did most of the class get a different answer than they did?  A lively conversation ensued.  But soon enough, they realized what the majority of the class did wrong - that they had used 40 (the number of trials in our experiment) vs 36 (the total number of possible outcomes) for their denominator. 

I'm hoping that because they constructed their own understanding and clarified their own misconceptions, it will be understood and remembered! 

Thursday, 16 May 2013

Teaching Probability Concepts



CC licensed photo  shared by Flickr user Duncan Hall

This week we started our last unit in Math.  It is our Probability unit.  I always feel like this unit is our reward for all of the hard work and amazing learning we've accomplished throughout the year.  This is my favourite unit, and it is usually my students' favourite unit as well.  I'm not a very big text book user on any given day, but for this unit more than any other unit, the text book only makes rare appearances. (I once heard Trevor Brown - course director in Mathematics Education at the OISE/University of Toronto and York University and an Associate Professor at Tyndale University College - say that "Math is not textable".)

I believe that children learn about and develop an understanding of Probability through experience.  For this unit, we play games and conduct experiments. We make observations and we record data.  And then, together, we look at our results and we try to figure out how best to represent what we witnessed mathematically.

Children can't succeed with this unit unless they have a firm grounding in proportional reasoning.  If you put in the time exploring fractions, percentages and decimals; if you make sure that students understand the relationships between fractions, decimals and percentages, then your students will be very successful with Probability.

We are only three days into this unit, and my students keep saying "This unit is so easy".  What they don't realize is that it is only easy because they are using all of their knowledge about proportional reasoning to make sense of Probability.

Yesterday, I taught a lesson adapted from an activity from Marilyn Burns' Math Solutions course.  I love this activity because it teaches students how to compare the Theoretical Probability to the Experimental Probability. Here is the original experiment.   I adapted it by having my students compare the results of two different spinners.  Each of the two spinners had three colours, but on the first spinner, red represented half of the spinner, and the other two colours each represented a quarter.  On the second spinner the three colours each represented a third of the spinner.




For our "Minds On", we determined the Theoretical Probability for each spinner as a fraction.  (Theoretical Probabilty = Favourable Outcome/All Possible Outcomes).  Then we turned that fraction into a percentage.  Once it was a percentage, it was easy to determine how what the Theoretical Probability would be for 100 trials for each colour on each spinner.  Using equivalent fractions, we discussed how the numerator would change depending on the number of trials.  Then we discussed how the percentage probability could be written as a decimal and placed on a number line where 0 is "impossible" and 1 is "certain".

I had the students write their predictions for the different number of trials on their personal white boards so I could quickly gauge who was understanding and who was not.

Then came the fun part - the Action.  We had ten pairs of students working together.  (One thing I've learned over the years: make your group sizes according to how many jobs there are to do.  One recorder and one spinner means two kids in a group).  Each group did fifty trials on each spinner.  They recorded the results on grid paper I had made especially for the activity. It looked like this:




You can see the students' individual whiteboards lying on their desks.  We use these all the time. They use them instead of "scratch" paper.  But mostly we use them for quick formative assessment. 




Once everyone had completed fifty trials for each spinner, the students cut out their strips and we attached all of the reds together, (they cut out strips but leave the "x's" on.  We glue subsequent strips via the "x"), then all of the blues, then all of the yellows keeping the results from the two different spinners separate.  (The children said they looked like long strips of ticker tape.)  In total, we had done 500 trials for each spinner.  Looking at the long strips we taped to the wall, it was apparent that for the first spinner, the red strip was twice as long as the blue and yellow strips, but for the second spinner, all three strips were just about the same length.



It took a long time for the students to complete all of the trials.  But taking the time was worth it.  This morning we started our math lesson with the Consolidation of yesterday's experiment.  It wasn't long before they were able to explain to me that the more trials they did, the closer the Experimental Probability approached the Theoretical Probability, and as one of my students shouted, "that is just so cool!"

We were ready for a challenge after that!  So for our Action today, I gave the students percentages for certain colours, and they had to work in groups to devise spinners that would result in the correct Theoretical Probability represented by those percentages.  In a sense, it was working backwards from what they had done yesterday.  They quickly realized that making spinners with 10 sections was the easiest way to complete the task since they had been given percentages.

As an Exit Ticket, I gave them an Open Response questions from last year's EQAO Assessment.  My students found this question "easy".

Exit Ticket: Connor has a bag of coloured tiles. There are 1 green, 3 black, 5 blue and 6 red tiles. He reaches into the bag and chooses 1 tile without looking. What is the probability that the tile is not red?
Justify your answer.


Show the value of the probability on the number line below.

0 ____________________________________________________________________ 1



I am loving teaching this unit.  When I take the time to create lessons that I enjoy and can be enthusiastic about, my students also enjoy the lesson and share my enthusiasm.  When we are all having fun, everyone learns!

Wednesday, 15 May 2013

EQAO Musings

The countdown has begun; there are only seven teaching days left until we begin our EQAO assessment.

I know there are many teachers out there who are very against EQAO testing, and I fully understand their arguments.  I recently read a post by Andrew Campbell that gave me plenty to consider on the whole EQAO question.

However, notwithstanding Mr. Campbell's points, I believe that the EQAO provides educators with some very useful and powerful information.  Taken as a whole, it does show us patterns of achievement so that we can see -  as a teacher, as a school, and as a board - where we need to change our practice.  It is appalling that our minority groups don't perform as well as their majority counterparts.  But that just tells me there is more work to be done in closing the achievement gaps for these students.

When comparing two schools with similar demographics, it is interesting to note when one school is outperforming the other, (which happens often).  As a teacher, I want to know: What are they doing in that school?  Is it something I can and should be doing with my students?

I'm ashamed to admit this, but knowing that the EQAO test is looming over us, I am motivated to never give up on my students.  Case in point - we recently had a Measurement test in Math.  A full third of my students struggled with finding the area and volume of triangular prisms.  If I didn't know that they would be tested on these concepts in June, I might have said "oh well, they'll learn it again next year".  But that EQAO test makes me accountable.  It is not acceptable for 33% of my students to not understand these concepts.  So I reassessed my teaching, and retaught the unit to these students using different teaching strategies.  The EQAO assessment provides me the impetus to keep on trying. I shouldn't need that impetus, but I do.

It is fairly common practice for teachers to teach students "frameworks" for answering Open Response questions on the EQAO.  But I've had experience scoring (they are "scored" not "marked") the EQAO assessments, and I discovered that these "frameworks" don't work.  Typically, the students who used a four-square model to answer Math questions didn't do well.  The curriculum suggests that we teach students to use a 4-part problem solving model.  This model works, forcing students to use a framework does not.  Just because they draw a four-square on their paper doesn't mean that they will be able to work through the four steps of problem solving.  They actually have to have deep understanding of the Math concepts to answer the Open Response questions.

Likewise, I've seen many different frameworks used when answering the Reading Open Response questions, such as "point, proof, comment" or "APE" (Answer, Proof, Extension).  These don't work either.  In order for the students to be able to respond to the questions appropriately, they have to comprehend the text.  Nothing else works.

So when I hear people complain that teachers are just teaching to the test, it bothers me.  In my experience, taking time to teach students frameworks for their Open Responses is a waste of time.  We need to spend every moment helping our students to develop deep understanding of the content areas. We need our students to be able to construct their own understandings of Math concepts and written texts.  That is the trick to helping them succeed.  

I have found over the years, that while the EQAO assessment might not be perfect, and it might not be scored perfectly, it does do one thing very well.  It assesses how well we are teaching the Ontario curriculum. It has forced me to teach that curriculum better every year and to constantly improve my practice so that everyone in my class succeeds.  I just wish it could happen during the very last week of school, because trying to teach 10  months of curriculum in 9 months does not seem fair or just to me or my students.  And I've learned the hard way that you have to teach ALL of the Science and Social Studies curriculum as well because often the Reading and Writing activities are based on the content areas.  Without those under their belts, the students don't have the necessary background knowledge to succeed.  These days, we are moving at break-neck speed; and that isn't any fun at all.

Saturday, 11 May 2013

Blended Learning in Their Eyes

I finally got around to having a class discussion about Blended Learning.  I wanted to hear from my students: what did they think of Blended Learning? Do they like it?  Do they find it helpful?

This is what they had to say:


  • Most of kids don't always pay attention to the teacher; but kids pay attention to what is on the Internet, so if you didn't pay attention in class, you can learn what you missed on the D2L (our learning management system). ~ one of my English Language Learners
  • I like Blended Learning because it can help you get ready for tests, everything you need to know for the test is on the D2L.
  • Using the D2L is helpful because if you forgot a text book at school and you have homework, you can just message your friends and ask them to email you the work.
  • I like the D2L because I work better on the computer; I have trouble spelling and using punctuation so doing my work on the computer and submitting it through the Dropbox means I can do my work better.
  • If you are sick and you miss school, you can just go on the D2L and find out what you missed.
  • Kids mostly use the Internet and video games for entertainment these days, so when you learn from the D2L it is more like entertainment and doesn't feel like school. This particular comment was reiterated over and over again, especially by the boys in my class.
  • Kids pay more attention to what is in front of them, using digital tools makes kids pay more attention.


Overwhelmingly, the students in my class love Blended Learning.  They are already expressing their concerns that next year, with a new teacher, Blended Learning might not be an option.  They find learning this way more engaging, and it places them in the driver's seat, giving them more control of when and how they learn.  Using a learning management system, like the D2L, they now have greater recourse when they don't understand something. 

We've had a lot of fun experimenting with Blended Learning this year.  My students asked me, back in January, to "flip" my class.  A flipped class is when you provide the introduction to a lesson via a video or link on-line that students can access at home as homework prior to a lesson.  It gives them background knowledge, so that when they come to class, they are ready to start the "action" or "working on it" part of the lesson right away, while the teacher is there to provide support.  So often, teachers stand in front of the class lecturing, and then students have to do the practice work alone at home where they don't have the teacher's support if they run into difficulty.  The idea with a flipped class is that the students get the "lecture" at home, and then they work on the practice at school while the teacher is present and able to scaffold for them. 

Some of my students had heard about flipped classrooms and they wanted to try it out.  It didn't work that well for us.  Invariably, some students didn't do their homework, i.e. didn't watch the video or access the links, and other students didn't understand the videos or links.  So I still had to address the information one way or another prior to the "action" part of our lesson.  But it wasn't a total failure.  The students who didn't understand the videos went home and watched them again AFTER the lesson, and said that they made sense now.  They realized that they need some "background" knowledge to understand the videos.  Likewise, I think the lesson went more quickly and made more sense to the students who had watched the videos prior to the lessons.

What we learned was that it is helpful to have the information available for the students to access on-line both prior to and following lessons.  That is what I have continued to do all year.  Some students choose to always access the information prior to the lesson so that they are "primed" for learning.  Others prefer to access the information after the lesson to "top up" their learning.  Either way, it puts the students in charge of their learning and that is the goal.  They are paying attention to whether or not they understand.  They are monitoring their learning. 

I believe strongly that every teacher should somehow incorporate Blended Learning into their teaching.  If you teach in Ontario, your board can probably get you access to the Desire 2 Learn (D2L) learning management system that I have been using with my students.  But if you don't, Edmodo is another great option.  It looks similar to Facebook, and allows you to input your students into classes and groups so that they can access content and submit work electronically.  

But even if you are not ready for a learning management system, you can start small.  You can create a class blog where you share information that is happening in class, upload videos for your students to access, and links for them to use to supplement their learning.  There are so many on-line supports for learning, it seems wasteful not to give our students easy access to them. And if you are intimidated by the thought of managing a blog, please don't be.  I knew NOTHING about creating and managing a blog last June.  I taught myself using on-line supports via the "help" button and Youtube. Trust me, no one can be less computer savvy than I was last June. 

Consider having your students use some digital tools to collaborate together, like Prezi, Google Docs, or iMovie.  Many students are already familiar with these tools and are using them for fun at home.  Encourage a student to become the "expert" on a tool and teach the rest of the class how to use it.  You don't have to be comfortable with these tools for your students to use them successfully.  

The greatest thing about Blended Learning to me is that it is not only more engaging for the students, it makes teaching much more fun as well!