36 Students on a Bus

Reading my post entitled "MET Building Futures Workshop" I alluded to a problem we were asked to solve.

"There are 36 students on a bus. There are 8 more boys than girls on the bus. How many boys and girls are there on the bus?"

Here are at least 6 different ways to solve this problem.

PROCEDURE 1 (Keeping the sum constant-36)

( STEP 1) Choose two numbers that add to 36. (e.g. 20 + 16)
(STEP 2) Find the difference between the numbers. (e.g. 20 - 16= 4)
If the difference is less than 8, then add one to the larger number and subtract one from the smaller number. Return to (STEP 2) (e.g. 20+1 = 21 16-1=15 >>> 21-15=6 and so on)
If the difference is greater than 8, then subtract one from the larger number and add one to the smaller number. Return to (STEP 2)

PROCEDURE 2 (Keeping the difference constant-8)

(STEP 1) Choose a number equal to or less than 36. (e.g. 25)
(STEP 2) Add or subtract 8 from this number to obtain your second number. (e.g. 25-8=17)
(STEP 3) If the sum of these two numbers is less than 36, then add one to each number and return to (STEP 3) OR If the sum of these two numbers is greater than 36, then subtract one from each number and return to (STEP 3) (e.g. 25+17=42. 25-1=24. 17-1=16. 16+24=40 and so on)

PROCEDURE 3 (My strategy)

Divide 36 by 2. >>36/2=18. Divide 8 by 2. >> 8/2=4. Add 4 to 18 to find the number of boys. Subtract 4 from 18 to find the number of girls. 18+4=22 boys. 18-4=14 girls. Verify (22+14=36 / 22-14=8)

PROCEDURE 4 (solving algerbraically)

Let X=number of boys.
Let Y=number of girls.

X+Y=36
X-Y=8

Solve for X in X+Y=36. X=36-Y
Substitute X=36-Y in the other equation X-Y=8 >>>
(36-Y)-Y=8
36-2Y=8
-2Y=8-36
-2Y=-28
Y=-28/-2
Y=14
Substitute Y=14 in either equation.>>> X+Y=36 >>> X+14=36 >> X=36-14 >> X=22

PROCEDURE 5 (graphing)

Let X=number of boys
Let Y=number of girls

X+Y=36
X-Y=8

Solve for Y in both equations

X+Y=36 >>>
Y=36-X

X-Y=8 >>>
Y=X-8

Plot Y=36-X and Y=X-8 on a graph. Where the two lines intersect is the solution.

PROCEDURE 6

Add 8 to the number of girls so that the number of girls and the number of boys is now the same.
Adding 8 girls brings the new total to 44 (36+8 added girls)
Divide 44/2=22.
Subtract 8 from 22 to find the number of girls. (22-8=14)

THERE ARE PROBABLY MANY OTHER WAYS TO SOLVE THIS.
If fact, I can think of at least 3 other ways right now.

The point?...

Don't tell your students formulas to solve problems. Let them discover them on their own. And the ones they do not discover, you need not worry because if your classroom is collaborative and cooperative, they will learn these other ways from their peers.

What do they even need teachers for anyways? :)

MET Building Futures Workshop

After attending the literacy, numeracy and assessment workshops I had some time to think on the long drive home. I was very impressed with the numeracy presentation put on by the literacy and numeracy secretariat of Ontario. I became familiar with this organization during my obsessive drive to find as many videos of teachers teaching and found one of the best online resources. http://www.curriculum.org/secretariat/literacy_en.html The other really good one I found was eworkshop.ca. http://www.eworkshop.on.ca/cfmx/edu/core.cfm?p=home.cfm&L=1

The speaker made a wise decision. Rather than talk briefly about the hundred and fifty thousand topics relevant to mathematics instruction, she choose to spend most of her time discussing one of the most important. She presented the class a problem to solve.

"There are 36 students on a bus. There are 8 more boys than girls on the bus. How many girls and boys are there on the bus?"

She then had us share the different methods we used to solve the problem. This is a key point. She didn't show us "her" way. She let us find our own ways and through each of us sharing our ideas, we all discovered not only that there were many ways to solve this problem, but that our peers can be valuable assets in exposing us to ideas and perspectives that we would otherwise never be aware of. The problems of our society are complex to say the least. No longer can we rely on rote application of set procedures to solve them. We need creative, new ways to solve problems and we need collaborative and cooperative means to do this. Gone are the days when teachers tell us to multiple 47 x 38 by carrying the one and adding a zero on the second line. The true spirit of inclusiveness demands teachers provide opportunities for their students to be exposed to the ideas and strategies of their peers. It's wonderful to think that inclusiveness can be fostered while solving a math problem.

Waiting To Exhale

3 months to go. Only a month and a half until our second placement and I can't wait. Not that I do not love the 3 hour daily commute to Hamilton or the 2.5 hour breaks in between classes on Tuesdays and Thursdays (after all, I can finish my 200 assignments during these breaks...in theory) but I can't wait to be back with the kids.
One of our counsellors said, "after this program, you will be ready to learn how to teach." Well I may not be ready as of yet but as long as the school boards, faculty, and parents don't mind us learning with actual children I'd just as soon prefer to practice on/with them.

Why I Teach (continued)

Our first practicum has passed by and now the term "bittersweet" is more than a mere cliche; Closer to graduation and yet having to say goodbye to these wonderful children. On my last day, my students presented me with a book. Each page, written by a different student, expressed their feelings (and advice). I have always been touched by the honesty and innocence of children. Their simple words mean more to me than the contrived and insincere words often spoken by adults in an effort to be politically correct, hypersensitive, to hide their true feelings and insecurities or for the myriad of other reasons honesty all too often fails us.

In the words of my students, whose advice is usually right on the money...

"Instead of saying "you guys" say class or boys and girls."

(This was a tough one to get over completely. Students do not need teachers who are friends, they need teachers who they respect and who respect them.)

"Make sure the students undersand the math lesson befor having a test! (Really!)"

"Just do the same as you are doing now. If someone tells you to change something about you I say don't your doing great and your perfect. Just be nice and every one will like you."

"always try your best and don't give up no matter how hard things get."

"Try Not to Get hurt!!!"

"you shouldn't give such long (Bleep) math Lessons"

(2 minutes for every year of age. I had my poor grade five students listening to me lecture for 40 minutes once...(actually twice))

"I don't know of anything you can improve on. You're good just the way you are!"

(blush)

"explain in step by one by one"

"Work hard!"

"have fun when your doing your job or pretend to."

"understand the students be nice to them and always give them a second chance"

"be himself because all students will enjoy him."

"he should be more strict."

(it's amazing when you first realize that students actually need and want structure and discipline.)

"practice your teacher voice more often."

(ditto)

Why I Teach

Social Issues Day

Unfortunately, I was not able to attend Brock's Social Issues Day at the Hamilton Campus but I have had the experience working as an educational assistant in a high school in the York Region District School Board. Over the course of 8 professional development days, I attended many conferences and seminars dealing with sensitive social issues, including issues surrounding students identified with exceptionalities such as autism and psychosocial disorders. It was paradoxical in some respects to be employed by a board that stressed inclusion, religious and racial tolerance and diversity and equality for all students on the one hand, while the special education classes were hidden away in the far corner of the building and the principal and vice-principal made a grand total of one visit between the two to our classrooms that school year.
Inclusion must be far more than tolerance and acceptance of diversity; it must include a concerted effort on the part of educators to include the diverse in the everyday activities of the school while encouraging the mainstream, majority to explore and interact with minority populations within the school and board. We have a student with autism in our class. Grade five students can be very nurturing to their classmates and this is no exception in this class. As a teacher, I will do my best to encourage my students, whether they be in grade 1 or grade 6 to welcome diversity. I hope my effort will lead to students that continue to have this positive attitude into their high school years, unlike the high school I recently worked in.

Microteaching

A lot of my colleagues had the opportunity to teach lessons before their microteaching experience. I had not had this opportunity so while my colleagues, councillor and camera watching, I taught my first lesson; Features of Informational Texts; Magazine Articles. After some initial fiddling with the overhead projector (Note to self: practice working the overhead BEFORE your lesson), the lesson progressed with a few points worthy of mention. I used the term "you guys". Too familiar to instill much respect from my students. I made the mistake of asking "Would anyone like to answer this question?" followed by no volunteers. (lesson learned the hard way.) Finally, I would get into the habit of repeating my student's responses. It is now clear to me why this practice is not a good idea. 1) It takes up time. 2) It discourages students from paying attention to their peers. (why listen to them when the teacher will repeat what was said?) and 3) It does not encourage students to project their voices and speak up. I have made a good effort to eliminate this practice in my other lessons.
I honestly went into this lesson expecting to make lots of mistakes and learn a lot of "what not to dos" and believe me, there were a lot of them. I did not in the least feel disappointed with all my mistakes. I know how difficult it is to be a good teacher and so I am realistic how long it will take to become one but when I watched the tape of this lesson back at home, I felt really good. I saw a teacher that had good mannerisms, involved the students in the lesson and had good rapport with his class. I felt like a teacher for the first time. It was a good feeling!

My Grade Five Class

That's right; MY grade five class. I only see these twenty four students, their teacher and their educational assistant two days each week but they are MY class. I take my responsibility to facilitate their learning and growth very seriously. It will never be cliche to state that parents and guardians entrust their children to educators and it will never be cliche for teachers to believe that they can make the world a better place but we can only help make the world a better place if we take our responsibilities seriously and ensure we have the knowledge and skills to help children learn. The immense workload at Brock, unbelievable as it sounds, it not nearly enough to make us great educators. If all we did was complete the assignments and do the readings, we would not be good teachers. Pre-service programs stress critical reflection and I try to spend an hour every day reflecting on my teaching knowledge, skills and experiences. With extreme effort I may complete the year and enter a career next year as just an OK but inexperienced teacher. After a couple of years, maybe I`ll be a good teacher and after five or ten years, maybe even a great teacher. For now, I will try hard to be a great student. Great teachers never stop learning; from current research, other educators, parents and just as importantly, from the children they teach.

The First Week

The hour long drive from Toronto to Brock's Hamilton campus gave me a chance to reflect on my personal and profession journey. When I was 6 I wanted to be an astronomer. I am still fascinated by the beauty and breadth of our universe but when I was 12 I told my mom that I wanted to be a supreme court judge. She told me that I had to become a lawyer first and I was intent on that career choice right up until my third undergraduate year when I decided that the legal profession was too corrupt to suit me. I left university and entered the family business selling furniture for 5 years before my inner voice shouted that I was destined for more than sales. I became an air traffic controller for 3 years before leaving to answer that pesky little voice again saying that I needed to make a bigger impact on the world. There are not many people who can say they left their career to enter education because it was less stressful! They say the most stressful job in the world is the president of the United States, followed in order by a nurse working in a burn unit, an air traffic controller, and a teacher! So here we are.
Working as a special education assistant last year, I know that education is far from the easy job many people think it is. We get summers off, two weeks for winter holidays, another week for march break and all those professional and snow days without the kids but...we need them! My colleagues and myself were counting the days until summer break way back during the first week of May, and not because we didn't enjoy teaching children but because it was hard work and we needed a break to recharge. On my way to Brock last Tuesday for our first day, I was excited more than anything to begin classes. I felt that same excitement in many of my colleagues I met in our counselling group, both my peers and our councillors. The first week, as expected, did not really go into the methods and practices of good teachers. Administrative tasks were extensive and hopefully completed. I was able to get to know a few of my fellow classmates and look forward to meeting and getting to know all my classmates better in the following 8 months.
I want to become a teacher because children need more good teachers. As a male entering the primary-junior stream, I am very aware of the great need young children, especially young boys, have for positive male role models. I am also aware of the need within myself to make a strong and positive impact on my community. Through teaching, we WILL all impact hundreds and perhaps even thousands of children throughout our careers and lives. Let's make it a strong and positive impact!
In the words of John Lennon, whose memorial in Strawberry Fields I was able to visit in NYC last month..."Imagine all the people, living life in peace...Imagine all the people sharing all the world. They may say I'm a dreamer but I'm not the only one. I hope someday you will join us and the world will live as one."