Monday, August 19, 2013

From T.V. to Math Class

The one thing that every kid has in common is that they watch t.v. (although some more than others). So when I was assigned to teach a Locally Developed Math Class, I tried every way possible to make connections to what the kids are surrounded by every day. For the Money unit, we were learning how to estimate prices... so what better way to engage the students, than to have a Price is Right game show right in the classroom!

Here it is below for anyone interested... you can use items from the school, home, or to make it more interesting, take a little trip to your closest dollar store. The kids were all involved (even the ones who refused to usually participate because of low confidence in the subject), there were lots of laughs, and lots of application of knowledge learned. 

Estimating Prices
The Price is Right Game

The contestants from the Contestant Row who guesses the cost of the item, closest to the actual price without going over, wins it and has the chance to play in the Final Showdown.

Buy/Collect 6 items:
-have the students write the price they think it is on their cards
-show the cards, the closest without going over qualifies for the final
-before entering the final, they need to go to the board to answer a math/ real life situation question for an additional prize (pencil or pen, or candy…). Have the audience answer the questions too, and they will be the judges to tell them if their answer is right or not.
*If you are calculating a price on the calculator, and the final answer is 16.5, how do you read this?
*You are working as a cashier. A customer purchases a candy for 65 cents, and gives you a dollar for it. How much change would you give them? Describe 3 different ways that you can give them this change.
*The cost of a water bottle is $1.65. Round this price to the nearest half dollar. Round the price to the nearest full dollar.
*You have a grocery list with 10 items on it. List 2 reasons why it would be helpful to estimate the cost of each item before going to the store.

-after doing this for 6 items, there will be 6 students in the semi-finals; have them one at a time draw 2 notes from a hat. In this hat there will be multiple notes with different amounts of cents on it. The 2 students that have the closest to a dollar without going over (have students all add these up in their notebook), goes onto the Final Show-down
-the final show-down will include dividing the class into 2 groups… and the last 2 left will go head to head trying to estimate the cost of multiple items (without going over), while the others will be their teammates to help them out.

Every Graph Tells a Story

It's one thing to be able to plot points on a graph, but its a very different skill to be able to understand what it all means and communicate it in words.

Distance-Time Graphs (Plotting the distance moved over an interval of time, be it seconds, minutes or hours) are a lot of fun to teach for this story-telling reason! Since there are so many ways and reasons why things move over a period of time, students can work together to produce some concrete evidence of understanding in an interactive and creative way. Here's how I have done it in a classroom once before:

*Students will work in pairs. They will create a narrative that involves something/someone moving at different speeds and different distances, with reasoning as to why. It needs to be a minimum of half a page. They also need to make an answer key (on a separate page) that is the graphed version of their story. You can incorporate technology by having students make animated videos or actually record their movie.

*Students will then swap their stories with their partner, and try to graph it.

*After this is done, they 2 students will work together to compare the partner's graph with each answer key. They will discuss any indescrepancies, and ask the teacher if unsure who is right.

This activity involves not just consolidating their understanding of the topic, but problem solving and practice of effective and clear written communication.

Here is one of many examples found on google.

Extra it helping?

At my school, Math Extra Help is provided twice a week after school. Always the same days, always the same times. However, despite this consistency, advertisements of it around the school, and teacher recommendations to specific students, this resource is never used as much as it should & could be by students.

Then came along the Online Extra Help. All the students need is an OEN ID number, and they have access to live help, between certain times, online. Nice and accessible from virtually anywhere. When asking my students however, only 1 has ever tried accessing this resource.

Why, if there are multiple ways of accessing help, are students not seeking it out? Especially those who need it most? Think back to your least favorite subject in highschool. Did you not count down the minutes of class time left, every single day? Would you ever consider re-visitng that subject after school, just to better succeed? These students aren't always looking to succeed, they are just looking to survive through the semester.

This is why Khan Academy is an effective resource to not just "suggest" students to use, but to embed it into your lessons. By embedding these resources into the lessons, it makes the student access them in order to complete an expectation of a teacher. Removing the voluntary aspect of "extra help", and putting it into an activity, it will be an effective way of ensuring each students' needs are met.

Thursday, August 8, 2013

More on math and farming....

I guess I will be getting a reputation of only thinking about farming, but it is my life and I teach in high school that is probably more than half farm raised students (sorry!).  Here is a good read on how math is important in farming.  It is something that I will probably use with my classes in the future.

A quote from the report..."The math used in farming is sometimes unnoticed.  The calculations and formulas require mathematical knowledge and farmers use their problem solving and money management abilities daily.  Farmers use more advanced math to calibrate machines and irrigation pumps.  Basic geometry, proportions, multiplication, and measurement skills are used everyday by farmers."  

The report gives lots of examples that you could use in a math class, from rates, to percents, volume, formulas uses when spraying crops, profit problems that related to linear relations, how farmers create mathematical systems of equations and inequalities to help them make decisions about which crops to plant in which fields, etc.

An interesting little read for sure....

we need to be able to compute without computers!

I recently watched the following video on Ted Talks….

The speaker was Conrad Wolfram, and he speaks about how we need to stop teaching calculation in math, but instead use computers.  His theory is that there are 4 steps in teaching and making math engaging for students, and those steps are:
1.       Posing the right questions
2.       Converting the real world problem to a math formulation
3.       Computation
4.       Then converting the math formulation back to the real world for verification. 

He believe that we should be using the students for 1, 2, and 4, but that we should be teaching them how to use computers for the computation part.  I am easily persuaded by good speakers, however I am not so sure that I agree with this.  I come from a farming family, where my husband is a cash cropper, and is part owner of a farm supply.  Him and I discuss often how important math computation skills are important in his sector of the world, and I can only assume that it is not only the farming world that needs people that can compute WITHOUT COMPUTERS!  

What do we need to know?

So news flash, the most common words ever said in a math class are "when am I going to use this is real life?".  So I guess the real question is, when are you going to use it in real life?

I'm not saying that math isn't important, I'm actually saying the exact opposite.  Math dictates our lives in ways that many people don't understand.  That being said, there is something to be said about the fact that there is a certain level of abstraction between math curriculum and the "real world".

So here comes the problem: we (collectively) don't understand the math that, at the end of the day, controls our lives.  Watch this video from Michael Moore (I know, I know, don't judge).
And that's just one bumbling man who actually works in the business.  Our financial future is controlled by math that the vast majority of people do not understand.  That ignorance trickles down to our daily lives as well.  Ask a grade twelve student about compound interest, listen to their answer, and then realize that in a year or two they will have a credit card.   When you read statistics like the average Canadian carries $3500 in credit card debt, it becomes a worrying proposition.

So what's the solution?  How do we make math relevant, and how do you teach some math that is kinda just "trust me, this is really important... someday."

I don't know.

Wednesday, August 7, 2013

Change for the better?

In checking out some blogs for ideas, I have discovered that there are two very distinct views regarding how mathematics should be taught in schools.  Not surprisingly, these perspectives contradict each other.  It seems like teaching math properly has always been a debatable subject.

I have been teaching for quite a while, and if you include my time as a student, I have a lot experience with the education system…long enough to realize that pedagogy is a relatively cyclical process.   I remember the “new math” debates when I was a kid.  There were improved ways to divide numbers because the “old” way was outdated, and there was a better way to round decimal numbers that I still remember to this day.  If the accompanying whole number was odd, then .5 was rounded up just like we have always done.  However, if the whole number were even, the .5 would round down, yes DOWN!  Look at how well that idea caught on!

So, over time, I have witnessed a number of new ideas which have come and gone, with the effects still in evidence to varying degrees.  Have math skills improved?  Depends on how “skills” are defined.

Personally, I feel that today’s student has a much better understanding of how and why mathematical concepts work.  Given opportunities to explore and investigate relationships, current math pedagogy encourages a student to question, compare and suggest alternative ways to resolve a problem.  Most students feel comfortable and confident when searching for solutions to complex and challenging real-life problems.  They ask questions and debate perspectives using appropriate vocabulary.  Many are excited about their learning and are capable of solving challenging problems.

On the other hand, some “true mathematicians” are saying that students cannot apply the correct algorithms when solving math problems.  These people want students to use standard algorithms because they are effective and efficient.  According to some profs, current students’ math skills are greatly diminished because they are using ineffective tools to problem-solve.

In the end, math education is always evolving.  I guess it just depends on where each educator is in the process, however, students deserve to understand what they are learning.


I Missed Math!

Last school year, I didn’t formally teach math.  For the first time in ten years, scheduling resulted in somebody else teaching math to my class.  And I realized how much I really enjoyed teaching the subject because I really missed it.

For me, math is all about the relationships that exist and trying to help students discover the relationships on their own.  It is about exploring everyday situations where math exists and recognizing that math is an intrinsic part of our day.  It is seeing the light suddenly appear in students’ eyes when they see and understand the connection that I’ve been leading them to and they “get it”, all by themselves.  It is about students finding links that have always been there but now are revealed.

Math instruction is convincing every student that they can “do” math.  It is helping to fill in gaps that exist so that confidence develops.  It is challenging students to solve problems without adult intervention.  It is connecting mathematical understanding to the world around us.  It is finding a way to assist each student by teaching to their strengths and supporting their weaknesses.  It is making sense of our world through number relationships. 

As I work through the various assignments connected with this course, I am becoming more aware of the amazing resources that exist and the important role that I play in making math come alive for all of my students.  After my hiatus, I will return with renewed vigour to math instruction this fall.  Boy, I missed math!