What is mathematics anyway??

When I thought about what mathematics is, the first thing that comes to mind is numbers; adding, subtracting, multiplying and dividing.  I also think of problem solving, geometry, and measuring. However, to give an actual definition of mathematics is quite a challenge.  

In our book, mathematics is simply described as “the science of patterns and order”-meaning all mathematics is is simply learning the basic skills and interrelationships between those skills, then building on them.  

According to Van de Walle, doing mathematics is solving problems by generating strategies, applying them and discovering whether they make sense.  To begin this in a classroom, Van de Walle goes on to say that a teacher must pose worthwhile tasks , then create a risk taking environment where students share and defend their ideas. A student can use many was to come up with a mathematical answer.  As long as the process is valid to get the proper answer, this is considered mathematics.

To “think mathematically” means to use mathematical skills and ideas to justify certain things or solve problems.  My son is five and he loves hockey.  When he isn't in school he lives for the sport.  Each morning when he wakes up, he comes into my room and grabs my iPhone to check the NHL scores.  This morning he said “Leafs beat the avalanche 5-2, they got three more goals than the avalanche”.  This was thinking mathematically.  Although he didn't realize it, he was using his numbers and more and less to explain to me the hockey news.  He then went on to tell me that the leafs had now “won six games in a row because yesterday they won five games in a row but they won last night so now it’s six, right Mom?”. We use mathematical thinking so much from the time we play with blocks putting the proper shapes in the holes to fit into a bucket.  We may not realize that this is what’s going on, but it’s such a gigantic part of our society. I think it is natural for people to think mathematically even though they do not know they are doing so. However, as teachers, we have to engage children and make them want to learn more about mathematics so that they can extend their mathematical thinking to solve many problems not only in school and work, but in society as they go through life.

Do Schools Kill Creativity?

This YouTube video by Sir Ken Robinson is a speech he gives at a Ted conference about how we should be creating an education system that nurtures creativity.  He states that creativity, in his opinion, is just as important as literacy and the education system today is destroying people’s capacity to be creative.  I do believe, from what we are learning in our education classes that this is slowing being changed.  We learn more of a holistic approach to teaching rather than explicitly teaching most subjects.  There are some parts of every subject that I believe have to be explicitly taught but creativity is a very important part of a child’s learning and development.    

My favourite statement that Sir Ken makes is that our education systems are a that children are not frightened of being wrong, they will take a chance, he continues by saying that one will never be creative unless that are prepared to be wrong.  He continues to talk about how our education systems are now focused on being right and that making a mistake is wrong.  

When I attended primary/elementary school in the early nineties, all of our mathematics assessments were marked right or wrong; there was no such thing as 0.5 of a mark, or getting marks for showing how you got to your answer ( we were never encouraged to show the steps on how we came up with a certain answer).  As I spend time watching the students during my observation days it seems that the teachers are doing the exact opposite, they are more focused on the students showing the steps they take to get the answer to a math problem, rather than getting the correct answer.  I, as well as many people in the education field know that there is more than one way of finding the correct answer to a problem, and by taking the time to show the steps they take to show how they are getting an answer, whether that answer be right or wrong, is a step in the right direction.  By showing their “work” , It is much easier for a teacher to pick up on where a child is struggling and also for a child to see, once the teacher corrects the work, where he or she is having trouble.  
I’m not sure how I feel about there not being a “right” answer.  There is usually a right answer, however the way that the person gets to that answer, or learns the process(es) to get to the right answer can be completely different for many students.  We, as educators should be very aware of this and get to know our students so that we can use different methods to make the students enjoy what they are being taught and use those strategies to promote learning for all types of students.

http://www.youtube.com/watch?v=iG9CE55wbtY#t=1096

When I sit back and reflect about primary and elementary school I have little to no memory about my experiences and the things that I do remember lack detail.  My lack of memory may have to do with the fact that I had mostly good experiences in primary and elementary school;  I did not struggle in school, I had a lot of friends and was well behaved.  Another reason may be because I started school 25 years ago.

I can remember putting the dates on the calendar every day in Kindergarten.   I remember seeing numbers posted on the walls and number charts, they were made by the teacher. I can remember seeing and memorizing multiplication tables and having “speed tests”, which were a competition between everyone in the class to see who could complete a list of multiplication or division questions the fastest.  I also remember having geometric figures in class and learning the names of each shape.  I can remember using pizzas to learn fractions.

I cannot remember something in particular that I loved about math.  I also can’t remember something I hated about math.  There’s not one thing that I liked more than another.  As I said earlier, I was good at math in primary and elementary school.  My parents always told me how well I did in math.  I know, personally that I didn't struggle because the teacher never came over to help, I never had to ask questions or get help and I did extremely well during class assessments.  I always completed my work ahead of most people in the class and moved on to other work  I remember in grade three completing the math book and being given the grade four math book to work on while the others finished the grade three book.  , When it comes to best and worst memories there is nothing specific that comes to mind.  I remember loving math, because I was good at it, but I cannot remember something I didn't like about it.   

From what I remember about the teacher during math class she would teach a concept, show an example or two and then I would do the work assigned.  She would normally sit at her desk and if a student needed help then they would go to her desk to get the extra assistance  I can’t remember any of my teachers being enthusiastic about math, however, I cannot remember them being enthusiastic about any subject area.  They were also not unenthusiastic, they were mostly neutral about everything, so it seemed to me.    

The only assessment I can remember in primary and elementary school was worksheets and testing, always marked in a red pen.  The tests usually included typical add/subtract/multiply/divide question, word problems, questions about fractions,graphing and geometry.  You were either right or wrong, there was no in between when it came to most of the questions on a test.  

Math in high school was more of a challenge for me.  When i was in grade nine they were just putting the AP courses into the high schools.  They (the school) decided that it would be a great idea for about ten of us to skip grade nine math and go right into grade ten advanced math.  The plan would be for us to then do grade eleven math in grade ten, grade twelve math in grade eleven and AP math in grade twelve.  That was a HORRIBLE decision.  Skipping a full year of math instruction was not a good idea.  We were not prepared to do grade ten advanced math.  We all ended up doing horrible in grade twelve advanced math and many of us repeated it in grade twelve to receive a better mark.  That experience ruined my love of math.  I do like math now, but not like I did in primary or elementary school.   

I did take math courses in university, 1090 and 1000, I didn't do that well on 1000 because at the time I thought socializing was more important than studying.

I use math a lot in my daily life, from grocery shopping, banking, measuring furniture to fit in rooms, calculating how long it might take to drive my son to a hockey tournament.  I was a chef for eight years, three of those an executive chef of a golf course.  I used math every day for food costing, labor costs, ordering from suppliers, recipe conversions...I could go on and on. I actually don’t think there’s a whole lot you don’t use math for,  I do enjoy math now, and I am looking forward to seeing the way the math program is taught in the primary and elementary grades today.

Welcome to my math blog! The purpose of this math blog is to share ideas, thoughts and resources that may come from class or outside of class during the winter 2014 semester.