Reflection on nature of mathematics

What is mathematics and why do we teach it?

The three required readings for this week, raises the questions of what mathematics is and why do, should, or would we teach it?

 The first reading The Theory of Embodied Mathematics from the book Where Mathematics Comes From by Lakeoff and Nunez,  discusses how some have a world view that is a part of their identity in believing what the authors have called Romance of Mathematics. Some points of the Romance are that mathematical truth is universal, absolute, and certain; that mathematics would be the same even if there were no human beings; and that mathematicians are the ultimate scientists. The authors state that beliefs like these intimidates people and leads many students to give up on mathematics as simply beyond them. The author’s goal is to make mathematics more accessible and give a more realistic picture of the nature of mathematics.

The second reading What Kind Of Thing Is A Number? Is an interview between John Brockman and Reuben  Hersh.  Hersh believes that mathematics is “ neither physical nor mental, it’s social. It’s part of culture, it’s part of history. It’s like law, like religion, like money, like all those other things which are real, but only as part of collective human consciousness” (Hersh, 1997). Hersh separates philosophers of mathematics into two groups which he calls Mainstream and Humanists and Mavericks. He states that Mainstream sees mathematics as inhuman or superhuman but Humanists see it as human activity. Hersh believes that “math is something human. There’s no math without people” (Hersh, 1997).  He lists three possible philosophical attitudes towards mathematics. These are:

1)      Formalism- math is calculations, has no meaning, follow rules to come up with the right answer, is connected with rote- your given an algorithm; practice it for a while; now here’s another one.

2)      Platonism- math is about abstract entities which are independent of humanity, helps to make mathematics intimidating and remote.

3)      Humanism- math is a part of human culture and human history, brings mathematics down to earth, makes it accessible psychologically, and increases the likelihood that someone can learn it.

Hersh believes that interaction, communication is essential and that students should interact not sit passively.

The third reading Why Teach Mathematics to All Students by Brent Davis addresses three questions. These questions each fall into a different question category.  Question one is a teacherly question: Why do we teach mathematics to all students? Question two is a rhetorical question: Why would we teach mathematics to all students? Question three is a hermeneutic question: Why should we teach mathematics to all students? A teacherly question already has a determined answer; a rhetorical question expects no answer whereas a hermeneutic question allows for interpretation of an answer and can be expanded on.  Davis believes that the first two cannot be questions at all because they either already have an answer or no answer can be given. The answer to all three questions however seem to come down to we teach mathematics because we have to.

After reading these three articles I believe my stance on mathematics is humanistic with a hint of formalism. I believe that math is social, cultural, historical but also physical and mental. This view comes out in the way I teach my students. I try to involve them in their own learning, always encouraging and prompting them to try different ways to approach and find a solution to a problem. I consistently use peer tutoring and small groupings allowing students to explore and discuss what they think with others. However, there is a touch of Formalism in that I believe that math does involve calculations and it is possible to come out with the right answer sometimes by following certain mathematical rules. This is one area that as teachers we have been changing our methods of teaching over the last few years. I learned long division in school by following rules.  Now, I teach my students that the algorithm is just a method of showing your calculations not how to solve the problem.

Math needs to be connected to the real world for students. It has to have meaning to their lives. I had a student in my class one year who had absolutely no interest in any subject in school. He wanted to be outside, especially on the long liner with his family. Whenever I could, I used problems with him on calculating crab catches or payroll for the workers on his boat and he would have no difficulty digging in and finding a solution. This made sense to him whereas how much would it cost to buy 20 apples at the price of .35 cents each didn’t interest him. He didn’t like apples and had no intention of buying them.  Math does have a humanistic philosophy for me. By making math interesting and relevant to the students’ real life wouldn’t we make it less intimidating and therefore more attainable for them?

References:

Lakeoff & Nunez.  The theory of embodied mathematics. Where Mathematics Comes From.

Brockman, John. (1997). What kind of thing is a number? A talk with Reuben Hersh.

Davis, B. (1995). Why teach mathematics? Mathematics education and enactivist theory. For the Learning of Mathematics, 15 (2), 2-8.

All references retrieved from http://criticalissuesmathed2011.blogspot.com/  September, 2011.

Reflection on Video of Sir Ken Robinson

Reflection on video of Sir Ken Robinson

                Sir Ken Robinson asks the question “Do Schools Kill Creativity?” As I viewed the video posted by Dr. Stordy on our course blog and the video posted by a classmate (Jonathan) on his blog I could see clearly that some of the points Sir Robinson made are true in my school.

                Sir Robinson presents the ideas that children have a large capacity for innovations and that they will take a chance. Children start off not being afraid of being wrong but then as they grow older and approach adulthood this changes and by adulthood they are afraid to be wrong. Sir Robinson wonders if we are educating our children out of creativity and I wonder this as well.

                Sir Robinson’s description of the hierarchy of education that was put in place because of industrialism and because we were educating children for what we thought would be useful in their future ‘jobs’ is chillingly the same as our education of today. Even though our world as gone through many changes, and is changing daily with regards to social changes, cultural changes, technological changes etc. our education system has not changed a whole lot. We still call our math, science, language arts and social studies core subjects, while the arts (music, drama, art….) are just considered electives or secondary subjects. We are living in a country, a world, where health problems due to obesity is growing rapidly and yet our education system is cutting back on the number of physical education classes in our schedule.

                Just like this hierarchy of education has been around for decades so has the school year from September to June. When children return to school in September (especially children who struggle), we have to spend several weeks reviewing last year’s concepts because they have had such a long break in schooling. Why are we still taking a summer break? Children used to take the summer months to help their parents on the farms or with the fishing. Across Canada today there are few families who need this assistance. So why have we not begun a semester system?

                One part of the videos that struck home to me, especially since our government is implementing an inclusion model, was the part where children are grouped according to their age not ability, or interests or any other grouping, just age. As Sir Ken stipulates, “age is not the only thing that children have in common.”  A child that is born by 11: 59 pm, December 31^st, is considered ready for Kindergarten whereas a child born 12:00 am, January 1^st is not ready until the next school year. This has never made any sense to me.  We have been implementing “inclusion” at our school for the last five years; however this year we are ‘officially’ piloting the inclusion model. I’m hoping that some direction and clarity will be brought to light on what exactly inclusion means for our children because I’m afraid that what we have been doing in the name of inclusion is really ‘excluding’ our children. Just because a child is sitting inside the four walls of a ‘regular’ classroom does not mean they are feeling included. If I were sitting in one of my son’s engineering classes, where I could not understand anything that was being taught, I surely wouldn’t feel included would I?

                I really hope that we can get to the point where we are putting the interests and the needs of the child first. Where we can allow our children to be creative and have “original ideas that have value” (Sir Ken Robinson, video).

               

Gloria

Math Autobiography

Math Autobiography

                I have very vague memories of my time in K to 6. I remember that I did like math class better than any other class. I don’t recall any particular math classes but I remember that we used text books. In K to grade three they were consumables and I loved working in those. When we got to grade four we had hard cover text books and all our work had to be completed in exercise books. Assessment in elementary consisted of unit tests which I always scored well on. My teachers explained concepts from the front of the room using the board and then assigned practice questions for the class to complete. My teachers would go from desk to desk helping anyone who needed help. I don’t remember any of my teachers showing any passion for math class. I got the impression that it was just something they had to teach.

                One of my worst memories was at the beginning of grade ten. I had changed schools and had signed up for honors math because I felt I could do it. The principal came into my class, knelt down in front of my desk and said he thought I should do academic math not honors. I was so intimidated and embarrassed that he was expressing this IN my class with all the other students present that I just nodded my head and it was done. I was put in academic math. I excelled in this math, scoring high A’s but no one ever suggested that I do honors math. Even though I did so well in academic math, this situation caused me to believe that I wasn’t good enough at math to continue with any higher level. Therefore when I began university I shied away from as much math as possible.

                When I look back at this situation I wonder if it had something to do with socio-economics. My dad had become ill and our family was forced to rely on social assistance throughout my high school years. I had to bring a ‘welfare slip’ to school to get my books. Students with slips were looked at as having lower potential intelligence and lower potential for future success.

                After my children were born, I became interested in math again. All three of my sons had a natural ability for numbers and problem solving using patterns and numbers. All three are math lovers. My eldest is working as a mechanical engineer in Medicine Hat, Alberta, my middle son is in his 5^th year of mechanical engineering at MUN, and my youngest who graduates this school year as decided he too wishes to study engineering because it is using math. These three young men are my success stories of the importance of math. Working with my own children throughout their young years and seeing their passion for math sparked my passion for math again.

                I love to teach math more than any other subject. Science is my second favourite to teach. I love how we can now use a hands-on approach. There are so many manipulatives that we can use to help children learn math and to have fun while doing it today that wasn’t available when I attended elementary.

                What both surprises and frustrates me is the number of 8 and 9 year olds who already hate math when they get to my class.  I hope that I can be a part of rekindling the love of math in the students that I teach. I think that allowing children more choice in the strategies they choose to solve a problem, the use of manipulatives, and peer/group working will help spark the interest. I can’t change the world in a day but I can help one child at a time.

Hello

Hi, this is my first attempt to use blogger. Welcome to all my classmates in Education 6630. I have no idea how this blogging works so if someone in my class can find me and respond to this post I would be so grateful. Good luck to all of you.