What is MATH?

When I think about the word Mathematics, I think about its basic concepts such as addition, subtraction, multiplication, and division. I believe that these are my preliminary thoughts because these are the concepts that are so recognizable to me and are skills that I have used so often in both my school days and everyday life as well. I think that these are the building blocks to the bigger ideas which included mathematic techniques such as algebra, geometry, probability and other higher level concepts that I was taught going up through high school.

Since I have started university I have begun to build on my mathematic knowledge by becoming exposed to a number of different math courses such as, number theory and combinatorics. I think that as a result of this exposure that I have broaden this understanding of the bigger idea of mathematics and that it continues to do so because of this course. I now feel that mathematics is more about exploring, thinking about what makes sense and not so much about if the answer is right.

The article “What Kind of Thing Is a Number?” A Talk with Reuben Hersh, talks about how math is usually considered to be either internal or external. That it is first assumed that what is math is such a simple question to answer but the complication that is really involved is sometimes unnoticeable at first glance. I found that Hersh expresses his thoughts of this in an enlightening manner. He conveys that math is an enormous part of our culture that it is neither physical nor mental but social in nature. That math is part of so many things within our culture such as the law or the money we use. I think that this is easy to see when you stop and think about how math is used in our everyday lives, that it is not just a skill that we are presented to in schools and that is its only purpose is to drive students crazy but has a deeper meaning that we all sometimes take advantage of. When I think about it from thinking about the amount of time I have to get ready in the morning to figuring out what meal is cheaper at a restaurant the numbers and other materials used with the understanding of math is around us and in constant use. I think that children need to be explained and aided in the comprehension of the importance and constant use of matematics.

Article Review and Textbook Website

Today in class we got into groups of two and read the article: Mathematics for the moment, or the Millennium? Education week commentary 29 (xvIII) March 31, pp 30 & 34. After we were finished reading our teacher gave us the opportunity to discuss our thoughts and what we gained from the reading. She also explained that this is important to do because different people gain and can perceive a piece of text in a number a different ways. I personally thought that this was a very interesting article because it dealt with a research study done on two schools that investigated the different mathematic teaching styles. One school was taught math by using a project-based style. This style was a done by having students work in heterogeneous groups and had a very laid back atmosphere; however the other school used a textbook style that was very strict and had the students use mostly memorization and learn procedures and formulas. It enlightened me when I read the results that the project-based school did better in the tests, I was expecting it to be the other way around. This helps to reinforce my feelings of using this method of teaching in the classroom when teaching mathematics. I found that the writer was well spoken and that the text was very easy to read also she never once said directly that one method was better to another only providing the reader with the facts. Also I thought that it was impressive how not once did the writer diminish the work of any teacher from either of the schools.

We also got the opportunity to look at two blog postings by Elaina Johnson. I was very impressed with the amount of work that she has put into her blog as well I was captivated at the way in which she has incorporated the use of a blog into her classroom. I think that since we are in an age that is so technology based that this is a great way to introduce her class into the use of computers and a great way to relay information back to parents.

The last thing that we got to look at before the end of class was the textbook website. This was very first time seeing this site and I found it very helpful the way that we were explained how to use it and the different recourses that it could provide for us now and as future teachers. For example the black line masters that provides a number of different activities that could be used in my future classroom and a literature section that provides a list of a number of books that could be used to aid in the teaching of different math units. I think that it is wonderful that this site makes this information available. Also I really enjoy how when after reading a chapter in the text you can look up that chapter on the site and get an overall summary which will be especially useful when studying for the midterm.

Novel : The Number Devil

Today in class we were introduced to the novel the number devil. I think that this novel would be a great resource to use within any primary/elementary school classroom to aid with the understanding of mathematics. After Mary read us just a small portion to give us just a little glimpse of what this novel was about I became mesmerized. This is definitely a book that I would use within my classroom; also the fact that it is so versatile and you can use it in both primary/elementary increased my fascination to this novel. It also covers basic concepts, infinite numbers, prime numbers, numbers that expand and the challenges surrounding calculators just to name a few.

Today in class we also got to get hands on and had to put our thinking caps on which I found to be very exciting. We got into groups and each group was given an amount of sand, we were then expected to find out how many grains of sand were there. Me and Veronique who was my partner thought about a number of approaches before we actually started, we finally ended up by filling up 1 cm cubes we ended up with 14 cubes being filled then we emptied one of the cubes out and further broke down the amount into half’s until we were only dealing with a tiny amount of sand that we were able to count the grains. When we were given the chance to walk around and see the other approaches that some of the other groups used I was amazed to find that there were so many different attempts that had not even crossed my mind. I quickly realized that children need to be exposed to this type of activity to understand that there is not always one right answer or one way to reach a specific answer.

Observation day

On Tuesday’s class we were given the opportunity to talk about our observation day that we had on Monday. We began this by getting into smaller groups with people that we were not sat with or had not previously had a similar discussion with. When we were into these groups we chatted and shared our experiences that we had with both the teachers and students in specific consideration with mathematics. The methods used and the interactions and response that the students had. After we had all a chance to share amongst the group we returned to our previous setting arrangement and be a whole class discussion. Mary began by asking students that were in grade kindergarten classrooms, then grade four etc, and some students openly made comments about mathematics in there observation day. She had also accompanied the discussions by showing us visually the textbooks for math for each individual grade. I found this discussion to be very enlightening because it gave me the chance to hear about some of the methods that different grade levels and schools responded and addressed mathematics.

My observation day took place in a grade five classroom here in St. John's. I was so delighted to get to be a spectator to the introduction of capacity. The teacher began the unit by talking about previous knowledge that they had about millimetres, centimetres and meters. Then she talked about the related units that would be using which included millilitres, litres and kiloliters and she discussed the relation between the units. She decided to do an activity as a whole class to get the students motivated and interested in the new unit. She set up a table in front of the classroom and had it lined off with a number of different shaped containers such as a water bottle and juice container. The teacher had the students write down an educated guess and arrange the containers, which were numbered from the one that would hold the most water to the least. Then she had a number of student measure the amount and then the teacher reviewed and converse over the findings.