20th blog - class review

Math class in Teacher's College..... To be absolutely honest, at the start of the semester I thought that this course would be the most difficult. It is math remember, with numbers, calculations, statistics, probability..... A difficult subject to say the least. Yet to my amazement, reflecting back on the course now, I have done a complete 180 from the first class and am actually sad to see this class coming to an end.
Way back on day one, we met our teacher, Professor Antosz. He described the course, he had us making a video and blogging.......... two things that I had never done before. It isn't that I am opposed the trying new things, it is just that, I have to attempt these new projects without any knowledge of how to and relate them to the subject of math!!! I must have been a glass half empty kind of guy on this day!

Let me begin with the blog. Going into the blogging activity I wasn't as positive as I would have like to have been. As I said, I had never attempted blogging before, I didn't know what it consisted of, I didn't know what on earth I would talk about? How would I relate it to math? And how would I do a refection on a reflection??? Well to be honest, if you do not try, you will never succeed! Going back over my blogs, I can see a steady stream of progression. One thing in particular that I reflected on when reading over my blogs, was that I didn't want to edit them. I want to go back and see how I improved from one blog to the next. I want to possibly show my future students the progression I made when presented with a novel task. I feel as though I went in blind and in my humble opinion came out smelling of roses. I am not trying to make any promises, however I can see myself continuing with this blog. Maybe tweaking it a little from directly math related, but I have really found myself enjoying this activity. Much more enjoyable than I originally thought it would be.
Next assignment, make a math video..... A math video? Pardon? Well again, if you don't attempt something you can not succeed. I gave the video portion of this course a lot of thought! I would lay in bed at night with my mind racing about what I would do a math video on. I would get up in the morning, sit at my webcam and begin a thought only to have it not turn out the way I wanted it too. This process repeated for weeks, until I recalled a math trick I had learned eons ago. The trick to multiplying large numbers by 5. As soon as this idea popped into my head the video was complete. I will be showing this video to my future grade school students one day! I might actually have them do the same sort of activity, as long as the technological resources are available. The only trouble I had with this assignment was stressing over what to do a math video on..... once that had been established, the project was a breeze.
In my final reflection, I would like to first say Thank You Professor Antosz. Thank you, for thinking outside of the box when preparing to teach this math course. Though there are a lot of students who are stuck in their routines of how they think University courses should be taught, I really enjoyed the diverse nature of this course. I feel as though I am taking much more away from this course than I am from the others. Thank you for the practical teaching tools you have given me! I am sure to implement all that you have taught!
Sincerely,
Wesley

Probability - part 2

Continuing the same series of thoughts as my previous post, probability can be a handful. I have decided to give it the honour of being the only topic in which I blog about twice. The reason being, I want to place emphasis on the difficulty of the material. As stated in the previous post, Professor Antosz had given the class a few sample probability activities the past few classes... they really make you to think. These examples really opened my mind to the complexity of probability!
The second example that the Professor gave still has me wondering. We have a class of roughly 30 students, depending on the day. This past Tuesday our class was full, noting the number of students, Professor Antosz reached into his pocket and pulled out a crisp $20 bill. He wanted to place a bet, with any student willing to take it, that there were at least 2 people in the class with the exact same birthday (not the same year, but the same month and day). One brave soul took the challenge. A simple aside here, I would never place a bet against a math teacher. There job is to educate people in the field of statistics, odds, and numbers. Knowing full well that we were learning about probability, and the math teacher being the one to propose the bet, I quickly shied away.
So the Professor had each student shout out the day and month that they were born. The class was only about half way through (14 - students), when we had a match - there were 2 individuals born on June 30th. The good professor just made himself a cool 20 bones.
The majority of the class was in awe at this development. The professor stated that in group of roughly 30 the odds are high that 2 of the people will have the exact same birthday. Professor Antosz did say that he has been stumped before on 2 occasions, but that he has done this trick over 25 times. Thus this probability example has been a very profitable one.
People tend to believe that because there are 365 days in the year, the odds are very small that someone will have the exact same birthday as them. When two people come the conclusion that they share the same birthday, they are always so surprised. In reality it shouldn't be that surprising,  There are statistics that show that a majority of couples get pregnant around the same time of the year, Christmas, New Years, holidays, the summer.... That being said, in a class of 30 students the odds are good that if you were to make this major with a group of people, you would show a nice profit.
Reflecting back on probability, as a teacher I would like to split the unit on probability into 2 sections. One section taught towards the beginning of the year, the other a refresher towards the end of the year. The key element that I have pulled out of my reflecting on probability is that it is that probability is not intuitive. Our instincts lead us the wrong way when deducing examples of probability. This makes it difficult for young students to grasp. Therefore, I find it essential to bring in a variety of clever problems for the students to figure out when teaching probability. I am very much looking forward to teaching probability in my own classroom someday.

Probability - part 1

The past 2 math classes have given me a lot to contemplate. I have been thinking tirelessly about a few of the activities Professor Antosz has brought up in class. The first being the card trick using 3 cards. The second being the birthday trick. Probability is a difficult strand to grasp, especially for younger students. Most individuals seem to have difficulty achieving the correct answers when dealing with probability. In the case of probability, logical deductions do not work as well. Thinking outside the box, or taking a alternate angle, in my opinion is the best option for obtaining the correct result.
One situation that Professor Antosz brought up in class was the 3 card game. The Professor help out 3 cards. 1 of the cards being the Ace of Spades. He showed us the Ace and then shuffled up the cards. He told us to pick one of the 3 cards (the Professor can see the 3 cards). We chose a card - either the Ace of Spades or 1 of the 2 other cards. At this point the Professor eliminates one of the other cards. Note that he will not eliminate the Ace of Spades. The reason being, that the Ace was possibly chosen by us on our original guess, and if not the Professor will keep it as the 2nd card left.  So now that there are only 2 cards left the Professor asks us if we want to switch cards, from our original choice to go with the only other card left, or to stick with our original selection? He gave us a few minutes to figure out the answer.
I immediately thought that I was smarter than this game and said 50-50 chance its the card we chose in the first place, so I said lets stick with it....I was told to reflect further. Upon further reflection I realized that the odds of selecting the Ace of Spades out of 3 cards only results in a 33% chance. Whereas, when you are left with 2 cards. (1 being the Ace of Spades) the card that was originally chosen is still sitting with a 33% odd of being the Ace of Spades, whereas the other card remaining has a 50% chance of being the Ace of Spades.
Resulting in the correct answer being -> you always pick the other card remaining, because of the better odds!!!!
In a group we attempted this experiment 20times. We always switched to the last card remaining. 14 of the 20 times we were correct and chose the Ace of Spades. The other 6 times we were incorrect, with the reason being that we selected the Ace on our first guess (with only 33% odds). Thus, in playing the odds we switched from the Ace of Spades (with poorer odds) to the other remaining card. (better odds)
As you can see, it can be rather difficult when trying to explain. Especially to our younger students. There are students who will be able to grasp this without difficulty, in that case I would have other probability problems ready for them to attempt while I would repeat the experiment for those still struggling with the concept.
Going back over this concept, you can see why it has had me thinking the past few weeks. Probability is difficult but not impossible. We as teachers need to open and willing to teach it. There is no need to be scared and shy away from material that we are not confident in. The more we try, the more we learn, and the better we can become as teachers.

Geo Cashing

I am enrolled in Teacher’s College at the Faculty of Education at the University of Windsor. As a graduate student, there is an abundance of work to accomplish. Not that I expected Teacher’s College to be simple, from what I had heard all the teachers programs across Ontario overload their students with work. For the most part the work is similar; lesson plans, teaching ideas, group work, case studies, essays …. And so on. Thus far, the previously mentioned has all wrong true.  With that being said, I am fortunate to be in one unique class; Mathematics.  The reason being, the Professor, Dr. Antosz has a different view on how to teach mathematics. One of the different ways Professors Antosz has to teaching is that he assigned us a very unique midterm.  Our midterm was to use Geocaching to locate the exam questions.  When we first discussed this idea in class, to be honest I was a little annoyed. Reason being, I really had no clue what Geocaching was, and my plate was already plenty full at the time.

Given some time to let the Geocaching idea sink in, I realised that this was going to be an opportunity to have a new experience and learn an interesting technique that I may be able to add to my teaching strategies one day. I went into the activity with a willingness to learn and was open to the new experience. Though I had some difficulty determining the co-ordinates; I had a fantastic time out on the hunt for bottles containing the exam questions. I was thrilled to hear that I was the first to locate the set of questions from the Mademoiselle at the Library. It made me proud to know that I was the first to master the co-ordinate questions and find the exam questions. I was beginning to really enjoy this activity.

Upon completion and submission of the exam, I look back on it and realise that this was one of the most rewarding tasks that I had to do during Teacher’s College. Have you ever had an exam where you were outside in the fresh air scouring the grounds of the campus in order to locate the questions for an exam?  A truly unique experience, if I had to say so myself.  Another thing that took from this activity was that it doesn’t necessarily have to be applied to mathematics. The Geocaching could be used with any and every teachable material across the entire curriculum.  

I really would like to thank Professor Antosz for furthering my knowledge of Education. Each and every day we learn new things.  On this day in particular, I learned how to Geocache.

1-million vs 999 thousand

I was thinking to myself the other day, would I rather have 1 million dollars or 999 thousand dollars?
It seems like an easy answer, does it not? Doesn't everyone want to be a millionaire? I know that the music group the Barenaked Ladies wanted to be millionaires. Their success with that one song alone more than likely propelled them to such extravagant earnings. But the real question here is would I want the distinction of being a millionaire.... or maybe just well off with 999 thousand dollars.

Upon further inspection the millionaire tittle alone would open more doors. Like mentioned above, I would be distinguished as a MILLIONAIRE. Not only would I be wealthy I would be rich..... I would be rolling in the dough! A millionaire would be the choice..... right? On the other hand, with 999 thousand dollars I would only be a thousand bucks short of a million. I would still be, figuratively rolling in the dough... but without the tittle of millionaire..... the decision might be hard to choose between. But it would be awesome to be the one too have to make the decision.

In the end, after great thought and reflection..... I would choose NOT to be a millionaire. I would rather have 999 thousand dollars. The reason being, the distinction of a millionaire would be too difficult to cope with. There would be far too many expectations. Everyone and their brother would be crawling out of the woodwork looking for a handout from the millionaire. It is not that I would not help out if I were a millionaire, heck if I had 999 thousand dollars, I would be more than generous and fruitful with my money. I just do not think that I could personally deal with the expectations that a person with a bank account with that many zeros has to deal with.
In the end I will chose to have 999 thousand dollars....... if someone wants to toss me another 1000 dollars...... I'll just keep it in a separate account.......  

superstition - numbers

Am I superstitious? I don't think so.... When it comes to walking under ladders, seeing black cats, or breaking mirrors... I definitely am not. I have done or seen each and everyone of those things multiple times.
Numbers on the other hand are an entirely different story.
The reason I believe that I am superstitious when it comes to numbers is because that I have been involved in competitive team sports my entire life. I have had various numbers throughout my career. If my memory serves me correct here are a list of the numbers that I have sported: 3, 6, 7, 8, 9, 11, 13, 14, 19, 21, 49, 55, 77.
There very well could be other numbers but those are the ones that stick in my mind.

Would I chose any other number than one of the listed above???? Sure, but I would prefer one from above.
Now the real question should be "Does the number make a difference?" The correct answer in my opinions is 'DEFINITELY"
I've done a lot of reflecting on this throughout my lifespan. The number one reason why the number on the back of the jersey plays a incredibly large impact on the player is CONFIDENCE. 
I can assure you that if you are in a slump in whatever sport you are playing... if you change up your number you will immediately have 1 of 2 outcomes.

1. You will play much better - You will thus stick with your new lucky number.
2. You will play much worse - You will go right back to your old number, be more comfortable and play better again.
The final verdict on number superstitions is that they are real..... they have been proven over and over thousands of times. Confidence or maybe coincidence helps a great deal with the belief of this superstition.

Mean, Median, and Mode

In my placement I was fortunate enough to be able to teach my Grade 7/8 class central tendencies.

Some students, if not all had done a smaller unit on these central tendencies in prior grades.... however all the students had difficulties distinguishing between Mean, Median, and Mode.

A quick summary of what the Mean, Median, and Mode are....

Mean: -- Also known as the average.  The mean is found by adding up all of the given data and dividing by the number of data entries. 

Median:  -- The median is the middle number.  First you arrange the numbers in order from lowest to highest, then you find the middle number by crossing off the numbers until you reach the middle. 
Mode: -- this is the number that occurs most often.

After my first lesson, I was reflecting on how I could get these 3 key terms to stick with the students.... I knew them, but solely because I had used the three M's so many times over my 20year career as a student. 

It wasn't until the next day at recess, or now known as 'nutrition break' that I was given the answer. I was in the classroom with a student who was absent the previous day. He was a 'busy' 8th grader who enjoyed talking out and disrupting the class. I was conducting the previous days lesson. When I was discussing the central tendencies, I said Mode. The student blurted out "MO-MO" for no apparent reason.... I didn't react immediately.... instead I did my own personal quick reflection... seeing this as an opportunity rather than a time to reprimand. I finished the lesson and let the student go outside for the rest of the nutrition break.

I was teaching the 2nd lesson of central tendencies right after the break. I began by reviewing the 3 M's. On cue, almost like I had asked him to do it; when I said Mode, the student who was in with me at the break blurted out 'MO-MO' again. The entire class erupted in laughter.

I immediately thanked the young gentleman for helping the class learn a trick to remembering the Mode. I said Mo-Mo-Most..... Mo-Mo-Most often.... so the Mo-Mo is the number we see MOST often.

My very next question was what is MO-MO? Each and every student had their hand up.

Upon final reflection, I knew the trick worked!! I was very happy! The reason being on their final unit test that I gave the class, there were multiple questions relating to Mean, Median, and Mode. Almost everyone of my 31 students wrote down MO-MO when they were answering questions relating to the Mode!

Special thanks to Cole!

Time Flies

Holidays, holidays, holidays......
For some people, this is the most enjoyable time of the year. Visit with family, see friends, sleep in. When I think of the word holidays, the first word that comes to mind is usually relaxation!


I wrote my final exam on Thursday December 15th 2011. Today is January 11th 2012, exactly 28 days have gone by since that exam. It feels as though 2, maybe 3 days have past.
Over the course of the last 4 weeks, I've taught for 5 days, I've completed multiple assignments, I have been to Guelph and back. I have celebrated Christmas 4 times, New Years twice, worked at my old job 5 times and most importantly got married to the love of my life.  The wedding was on Friday January 6th, a week after school had already resumed at the wonderful University of Windsor..... did I mention that I am from Chatham and commute each and every day to school.


Time..... is a set amount of numbers that count down each and every day. There are 24 hours, 1440 minutes, and 86400 seconds. Ample amounts of time...... right? On Sunday evening, I am fortunate enough to be in a men's hockey league. As I got dressed for the game, the gentleman sitting beside me asked how my holidays had gone????? I had to laugh, "Holidays.... no such thing...... not enough time for holidays...." He told me that the older you get, the faster the time goes.
I thought about this for a little while. This can't be true can it. Can time speed up? If you consider 'day light savings time' well then yes time skips an hour. In reality time moves at the same pace it did years ago. The hour glass or sun dial work in the exact same efficient manner.
What I reflected on this I concluded that time does not actually move more quickly. We 'adults' take on more responsibility. We place more on our plates. We overload ourselves with deadlines and commitments that are in set time frames. The more events we have and experience the busier we are.  As a youth, I could find myself board..... at times. Which would lead to me misbehaving or worse, complaining. However..... today I find myself wishing that I had the opportunity to be board.
So, technically time doesn't actually fly.... but the older you get the faster it seems to go...
I can vividly remember as a child hearing my parents say "where did the time go?" I can now relate those sentiments.

pie chart - strings

Last week in math class, Professor Antosz demonstrated a way in which to present a pie graph to the class. The manner in which Professor Antosz presented it astounded me.
The class began with Professor Antosz handing out meter length tape measures to each table of students. It was your typical math class and I did not really give it much thought.
The next step was that Professor Antosz asked students who were dog people. A series of people put their hands up and they proceeded to the front of the class with 2 tape measures.
Then the good professor asked the students who were cat people? Another series of people walked up to the front of the class, again with 2 tape measures.
Finally, Professor Antosz asked the class "Who are bird people?" and a single student proceeded forward with 2 tape measures.
The students formed a circle around Professor Antosz. The students spaced out evenly based on their numbers. The members at ends of the groups held out their tape measures and Professor Antosz held the other end in the middle.
This was a phenomenal way in which to express the size of the pie slices in the pie chart.  Students who have a difficult time taking data and converting it into a pie chart now have a simple visual  way to represent it.

It had never occurred to me before to present a pie chart in this manner. I always had the most difficult time drawing pie charts.  Now I am able!

When I was teaching grade 7 and 8, the students would never choose to use a pie graph to represent their data. They struggled with separating the slices into the right proportions. I am looking forward to going back and showing them this great way to do a pie graph!

Looking back on this excellent idea, I started thinking about other ways to present other graphs. 
Bar graphs - having the number of students stand in a line. Then those students that are in the same group stand vertically beside them.
Histogram - same as above but the students are closer together, possibly interlocking arms!!!

Super COOL!!!