What Would YOU Do?

In class this week, our instructor presented us with some scenarios that we may face as we go into the classroom as a math teacher.  We were able to discuss them in groups, then have a class discussion on how to solve the problems presented in these scenarios, followed by our instructor going through what she would do (or has done!).  This is a very valuable activity to do with pre-service teachers as it alleviates some of our fears going into the classroom.  I want to share a couple of the more difficult scenarios and what I learned:

1.  "A student comes to you right before university applications are due and tells you they need an 85% in your class for the program they want to get into. They currently have a 72%."

This was a tough one for me because I am a very empathetic person and it would make me feel so bad if a student said this to me, especially if it was accompanied by tears.  My group discussed the idea of looking at the student's marks to see what's going on.  If the student was an 85% student in general, but really did terribly on one unit, then perhaps, as a teacher, you could allow the student to make up the marks for that unit.  However, if the students marks are consistently in the low 70s, then there's not a whole lot that can be done.  The class discussion and instructor comments brought up the concept of being proactive.  Let the students know right from the beginning of the year that these marks are very important, and not a whole lot can be done to adjust marks later on.  In doing so, you are letting the students know to take this all very seriously, and there will be no surprises later on when you tell them that you can't adjust their mark.

2.  "A student comes to you the day before a test and tells you that she overheard Scott telling a friend that he plans to type his notes and formulas into his graphing calculator.  This way, it'll look like he's using his calculator to do math, but he'll really be reading his notes and getting formulas."

My first thought on this was to simply walk around a lot during the test and keep peeking at what the students are doing.  That way, Scott would likely feel quite uncomfortable cheating because he would know at any given moment that I could walk by and see what he's doing.  However, the class did come up with a couple of other possibilities. First of all, the teacher could have all the students reset their graphing calculators to erase everything in memory.  And secondly, our instructor mentioned that one way of solving the problem is to have a classroom set of graphing calculators that are only used for tests.  That way, you know that there is nothing saved on them.

There were a few more scenarios that we went through, and all of them were quite challenging!  I'm so thankful when instructors give us these types of activities.  I don't know about anyone else, but as far as teaching goes, I'm least worried about the actual teaching itself. What I'm most worried about are difficult situations that may arise.  They may have to do with marks, cheating, classroom management, etc, but those are the things that I think will be difficult.  So, the more exposure we can get to possible classroom scenarios and how to deal with them, the better prepared I will be to go into the classroom.

The Log Loop - An Amazing Way to Remember How to Convert a Logarithmic Form to Exponential Form

This week in class, one of my colleagues did a Grade 12 (U) lesson on Logarithms - specifically on how to convert logarithmic form to exponential form and vice versa.  I don't know about you, but it's always been quite difficult for me to remember the formula.  My colleague presented an amazing diagram that helps students (and teachers!) remember how it works:

Gruen, Amy. (2011). The Log Loop [drawing]. Retrieved from: http://squarerootofnegativeoneteachmath.blogspot.ca/2011/02/loop-for-logs.html

I love tricks like this!  If you can simply remember that you start at the bottom of the diagram, then you can remember the formula!  So the answer to the above would be:  2^3 = 8   And technically, the loop also works to turn the exponential back into the logarithm.  In the example I just typed, the loop would start with the 2, go around to the 8, then finally to the 3, which would result in the order seen in the picture with the logarithm.  Awesome!

Secondly, my colleague got us all to play "Log War".  It was basically the card game War, but instead of just numbers written on the cards, logarithms were written on the cards.  So, we all had to solve the logarithms in order to find out who had the highest number in the round.  This is an excellent way to get students practicing!

I will say though (as I always do), that I do feel it's important to assign some textbook homework as well, just so the students get used to writing out full solutions like they'd have to on a test.  Giving them homework will also give them a resource to use while studying for the test.

Having said that, I truly enjoyed this lesson and I hope to use it in my classroom someday!

Find the Mean Like You MEAN It

In class this week, we focused on grade 11 college math.  This is the course that is generally taken by people who know they do not want to go to university, but are rather headed into a college course.  Two of my colleagues presented lessons for this course and I'd like to talk about the lesson on mean, median, and mode.

I really liked this lesson overall!  My colleague began by using the Smart Board to display a worksheet that tackled the definitions of mean, median, and mode, and how to find each.  This gave the students a good review as mean, median, and mode are first taught in elementary school.  At this point she could have just given the students textbook homework to practice these concepts, but instead she used a card game called "Find the Mean Like You MEAN It"

Found at: https://blog.prepscholar.com/hs-fs/hubfs/Body_mean.jpg?t=1517604014667&width=325&name=Body_mean.jpg

She took all the face cards (and jokers) out of the decks so that we (the students) had decks with cards from Ace (one) to 10.  In groups of 3 or 4, we had to shuffle the cards, and deal 7 cards to each player.  Each player had to find the mean of their cards and write it down.  After 3 rounds, each player had to find the mean of the 3 rounds, and the person with the highest mean won the game.

The game was then repeated only instead of using mean, we could use median or mode.  It's an excellent method to get the students practicing!

This was only part of the lesson, so my colleague didn't mention it, but I do hope that students would also be set textbook questions to do.  After all, on a test, you won't have a deck of cards and you might have word problems that will only be solved successfully if the students have had practice with word problems.

I do like the idea of fun and games in math class, but I also stress that rote practice is useful as well.  Completely doing away with textbook questions is not a good idea in my opinion.  I hope to be able to strike that balance in my classroom.  Some topics will lend well to games, others may simply be better learned through pencil and paper practice.  But I've come a long way even to say that, because before this course, I would have said that all topics are best learned through pencil and paper practice.  It's been great learning about the different ways students can learn and practice math in the classroom.