Thoughts on readings for week ending Oct. 5 -Forward, Introduction, Ch.2

I am very interested in reading the text and learning of the findings of the study carried out of the two vastly different schools and the different approaches to teaching mathematics.
I teach grade one and feel that my students learn best by being engaged in math activities that connect to their experiences. I encourage learning by allowing them to figure things out for themselves, by praising their mistakes and seizing moments to create more math problems to solve. I see my students learn most through interactingh with each other, playing games and exploring.
Then I come home to my children, one in Grade 8 and one in Level 3. My Gr. 8 girl (if gender has any influence) is complaining that she has a math test on Friday that she feels she will fail as her teacher stands at the board all class and puts up examples for them to copy. My son (level 3) is currently at a math tutor. He is capable, but does not listen well in class and does not practice the necessary skills (my diagnosis of his lesss than acceptable math marks). He has not provided me with much information on his math classes, but at curriculum night last week, his math teacher showed us the 300 page Practice Exercise workbook that is recommended at a cost of $25 as the text book that is provided is not adequate. The teacher also provided us with some websites where students get additional math instruction and practice. Sometimes his tutor will show him how to solve something in math but tell him not to tell his teacher that he knows how to do it this way!
Sorry if I am ranting...but there seems to be too many incongruencies between math in primary grades and math in high school. Are we creating six year old confident problem solvers who by the age of 12 are taught that there is only one correct way to do things and that they must do it over and over just like everyone else in the class????

What is math and why do we teach it?

Lakoff and Nunez (2000) refer to a romantic view of mathematics where a mathematician is someone who “is more than a mere mortal-more intelligent, more rational, more probing, deeper, visionary” (p.340). This is contradictory to the ideas on creativity expressed by Robinson when he compares the abilities of professors with those of dancers. He stresses the recognition that all people have intelligence or a talent in some areas. Not being strong at math does not make a person any less intelligent than a mathematician. It is simply their talent, or the area in which they are intelligent. Each person has the capacity to be highly intelligent in something, but not necessarily the same thing. This is an important notion for educators and something that needs to be shared with learners. My own children will often say how smart a classmate is I always correct them and restate that the person is smart in math or biology or merely more capable at studying and listening.

Despite agreeing that math is not everyone’s strength I do feel that math needs to be taught to our students, but more efforts need to be made to help them make connections to their own lives and to see the relevancy of studying math. I love to share with my little Grade One students the book Math Curse by Jon Scieszka (1995) just as an example that math is all around us and necessary to explore. We all use money, follow patterns, count, measure, compare and so on. I do not think that people connect all of this to mathematics. Students need to see these connections so that the study of math has more purpose for them. All will not become mathematicians, but all will need to use math. Musicians, actors and dancers need to keep time, carpenters must measure, cashiers must count money, etc. Davis  (1995) states that there needs to be a change in a math teachers thinking and actions from working to explain math to working at affording students experiences to interpret (p.23).

References

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

Lakoff, G.  & Nunez, R ( 2000)  . Where mathematics comes from. Basic Books: USA.

Math autobiography

My first mathematical memories are of the counting rhymes “One, two, buckle my shoe….” and “Ten little, nine little, eight little Indians”. I do not know who taught these to me but I do remember chanting them as a young child of 4 or 5 years old.  I am glad to see that I was exposed to both counting forward and back at an early age.

What I remember most about primary school mathematics is doing many pages of written work which I did enjoy. Teachers did a few examples on the chalkboard each day and students did many examples of the same concept in their exercises copied from the math text book. All work not completed in class was assigned for homework. Correct answers were called out in class the next day and we corrected our own books. Story problems were present at the end of most text book pages. I recall disliking them. At the end of each chapter we had a test.

Elementary school was a repeat of more of the same. For the most part I did enjoy math and achieved high grades. I grasped new concepts easily and loved doing the written practice.  To study for tests I always redid many examples of calculations from the current unit of study.

In grade 8 I continued to do very well in math, but many of my classmates found it difficult. I am not sure if the concepts became more difficult or if the teacher was unable to explain them adequately. After the usual chalkboard demonstrations and assignment of seatwork I set about helping my peers understand  the day’s math lesson. (I think the teacher counted on me for this! As I recall it being a daily occurrence and I was somehow labeled as “the brain” in the class. )  I listened and practiced and already seemed to have a knack for teaching! When I relay my on an individual basis Grade 9 experience you will see I was not the “math brain”.

In Grade 9 I was automatically placed in what was then called Honors Math. I got 60% in the first test and was demoted immediately to the regular stream.  It was a little blow to my ego, but I continued to listen to math instruction in class and practice the necessary skills daily and nightly.  I also continued to help my peers on occasion and enjoyed the work. Thus I continued to do well in math, always achieving A’s.

Onto university where I had my career as a primary school teacher all planned, therefore I needed only one math course … it was maybe something like Teaching Math in Primary Grades. I recall making absolutely no connections with math or anything else during this course.   The instructor was a male in his 50’s who did not speak English clearly. I recall only being so grateful that I did not have to do the brutal math courses that my friends had to do in first year as they pursued studies in Engineering and Commerce. It always bothered me that students were so ill prepared for university’s introductory math courses.

As a Grade One teacher I love teaching mathematics. I can have a lot of fun with it and so easily incorporate it into everything I do. I spend a lot of time connecting math to their everyday lives. We count how many days we’ve been in school, who is tallest, who has the longest and shortest names and so much more. I enjoy doing hands on activities with my students, they learn so much from each other. I spend a lot of time trying to have them explain how they know things and encouraging them that it is okay to have strategies to find out what we do not know. I am trying to bring my little students beyond answering that they know something “because”.  I give my students lots of praise and call them “Great Mathematicians” when they solve problems
One of the most valuable mathematical experiences I have had as a teacher has been conducting individual math interviews with my students. I have used observation and paper pencil activities as forms of assessment in the past, but the clearest picture of what  a student really knows is best seen when you get to talk to them on an individual basis about math and how they do things and know things.

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