Interesting Quote

I came across an article while working on my inquiry project on calculators entitled Reform, Tradition, and Synthesis by Thomas W. Tucker. I also discuss this in my conclusion, but I would like to comment on something he says when talking about technology. He says:

It pays to heed history: Technology always wins. The world may have been better when people walked instead of driving cars, but that is irrelevant. As long as there is gas, people will drive cars, and what I really care about is that they drive them sensibly. The mathematical world may have been better when people did arithmetic or graphed functions on paper on in their head instead of on a calculator, but that is irrelevant. As long as there are batteries, students will use calculators, and what I really care about is that they use them sensibly (p. 910).

This is such an important statement that I had not thought about before working on my inquiry project. Starting out, I was making calculators out to be the bad guy, but I was wrong. Calculators are an aid to mathematics (if used properly), not a replacement for skills and your brain. Tucker makes a very valid remark when he claims that technology always wins. He's right, where have we ever seen an instant where technology was tossed to the way side? Cars, computers, cell phone, IPODs and calculators are all pieces of technology that will never go away, we just have to learn to use them and incorporate them into our classrooms. Yes, that`s right, I said cell phones! Even cell phones can be incorporated (educationally!) into the classroom. When we say that we want students to use their schooling outside of the classroom, then why are we prohibiting the items that they use outside of the classroom? Something to think about!

My inquiry project: calculatoruseinmath.weebly.com/

References:

Tuckers, T.W. (1999). Reform, tradition, and synthesis. The American Mathematical Monthly, 106(10). 910-914.

Many Teachers Can't Do Math, Let Alone Teach It

The title of this newspaper article definitely drew in my interested when I first read it. I first thought it was a stab at all math teachers in general, but after reading the article I understood its purpose. Teachers are getting very little preparation to teach the subjects they are required to teach and math is one of the main ones. Not everyone can do math easily. At least with social studies or English (not to bash either of those subjects) you can almost pick it up as you go. And these courses do not lead in to one another. If a child does not understand social studies in grade 7, it will not affect their understanding for grade 8. However, since math builds upon previous concepts, a child needs to have a grasp on previous years in order to move on. Since spiraling is taken out of the new junior high math curriculum, the course goes on to assume that all children remember how to do the items from the previous year without any reviewing. Maybe in an ideal world. I seem to have gone off on a tangent. With that being said, teachers who are uncomfortable with math may not be preparing students to move on to the next level. And it is not their fault, they were not adequately prepared in university. I honestly cannot pick one course that I did in university that I can say prepared me to be a math teacher. My math  methods course was half decent, but we only spent a short amount of time preparing lessons and ``teaching`` to our peers. It was okay, however, because I was strong in math. I picked up the pieces where I had to. I often have primary/elementary teachers come up to me and ask me how to do certain problems and concepts. Children can pick up on it when teachers are uncomfortable. The first year I tried to teach dividing decimals with base ten blocks was a nightmare because I did not understand the base ten method. I was not taught that way and I was not prepared in university to teach it that way. I did however take the time to learn how to do it and the following year it went flawlessly, but I knew I had to teach it again to the students from the year before. Had they have gone on to another teacher, unless I had told them, there would have been an assumption that they knew how to divide decimals with base ten block. The article also blames the curriculum for being too much about discovery and less about practice. In order to include both, we need to have less topics to cover in a year span. There is just not enough time to allow for the discovery of every topic while still giving children time to practice with them. The math curriculum that is currently being taken out of the high school program is the one that I did in grade 10. That was the first year for it then. From the beginning, teachers complained that there was not enough practice in the book and it was expecting students to have previous concepts that they had not. It took eleven years to replace the curriculum.

Resource:

http://www.theglobeandmail.com/news/opinions/opinion/too-many-teachers-cant-do-math-let-alone-teach-it/article2183700/

Calculator use in the Math Classroom

Since I have begun to dig deep into my inquiry project of calculators in the classroom, I am finding myself encouraging children to use calculators less in my classes, even for calculations I would once have let them use it for. It seems to be building their confidence as they are asking to use the calculator less and they do not complain as much when I say it is a no calculator day.

I also find that in my Math 3103 class, I am encouraging them more to use common sense and estimation rather than try to remember rules and tricks. I believe these to be important skills to build on in this course and it is something they will take with them outside of school. They are learning more to decide if a question makes sense or not. This may be a skill that one would think a Grade 12 student would have, but in reality most do not. I am always told by some students that even after doing 3103 they are using calculators less as they find it faster to just do it in their head or estimate correctly.

I strongly feel that a calculator should be used a tool to aid you with complex calculations, not one to replace math skills.

Lead Discussion

Gloria and I lead the discussion for this week on the course site.

New vs. Old

When comparing the two schools of Amber Hill and Phoenix Park, it made me wonder if there really is enough DI happening in my classroom. It is no trouble to see that not all students felt comfortable or felt they could learn from just one method alone. I really like the project based method, but I don’t know if I would be able to give so little guidance or tolerate so much idle time from my students. I try to incorporate both traditional methods and both “newer” methods (for lack of a better word), but I still do not reach all students. Another issue I have is that of CRTs and public exams. How are we expected to teach students using the newer methods, yet 50% of their mark in certain senior high courses is a paper and pencil test. Until the department changes standardized testing, I feel that most teachers are going to continue to “teach to the test” and this means that we will not be reaching all of our students.

When Good Teaching Leads to Bad Results

I found the article "When Good Teaching Leads to Bad Results: The Disasters of 'Well Taught' Mathematics Courses" by Alan Schoenfeld very interesting and he has definitely outlined a critical issue in mathematics. I always find myself sitting on the fence when it comes to issues similar to this one. On the one hand, I believe children learn best when they explore and there are activities and they find math fun. On the other hand, I believe there is a place for old school mathematics with your proof and your algorithms.

Schoenfeld (1988) describes of an instant where a math problem would have only taken the students five minutes to do, but because they had to outline their process and follow the correct format, it took them 15 minutes. I would like to compare this instant with that of writing an essay. Any child can throw a few ideas on a piece of paper and call it an essay. However, in the higher grades, it would not be accepted as a proper essay unless it had proper paragraphs, an introduction, a conclusion and so on. Why should math be any different?

Jumping back on the other side of the fence, I agree that children have trouble connecting the bits of pieces of math that they learn together. They choose to memorize instead of understand. I like how Shoenfeld does not blame this on teachers, he blames it on the curriculum. I long for the day when children are grouped based on ability, not age, and everything they learn they will find relevance in the world around them. Until a curriculum is designed for us that allows this and standardized testing is not used to criticize us, we will do the best we can with what we have.

Why Teach Mathematics?

Growing up I have always loved mathematics; I found it interesting, it came to me naturally and I really enjoyed numbers. (I had a student ask me yesterday: “Miss you really like numbers don’t you?” Yes, yes I do!)

I first decided to teach mathematics because I was very passionate about it and I wanted to share that passion with students. I also knew that there was a lot of negativity about math in schools and I wanted to make math fun and enjoyable again.

I believe that mathematics that young children learn should be relevant to them: math they would encounter every day. As they grow older, math should begin to prepare them for an adult mathematical world.

I came into the teaching profession just four years ago, thinking that I should teach math the way it was taught to me (notes on the board, questions from textbook). After all, I had learned perfectly that way. I realized in that first year, that I need to change that mindset, because not all children learn that way. As each year has gone by, I have experienced more and more with discovery and allowing students to develop their own methods and ways to remember things.

So why should we teach mathematics? Even after reading the article, I am not entirely sure of that answer. My first thought was because students will need it as adults. My second thought was to teach children to be thinkers. And as I write this, more and more reasons pop into my head: prepare them for university, etc.

Given that thought, I think the math curriculum is too jam packed full of topics that try to satisfy all these reasons why we should teach mathematics, that it is too much for students. Students are lacking basic skills and mental math which are so important to every adult, because we spend very little time teaching (or going back to) these topics. The high school general math curriculum (it is in the process of a much needed change) was teaching children about abstract math that they would never use. Instead they should have been taught how to do their income taxes, balance their chequebook, etc.

I am always torn when I have to write something like this, because I love the difficult math that children always complain they will never use again and I can see all the benefits of teaching it, but on the other hand, I see children lacking so much in the areas that they will 100% use again.

What Kind of Thing is a Number?

When I first started reading this article, I was thinking to myself that this guy way thinking WAY too much into mathematics and why this was that and why things were how they were. I often find it hard to sit back and be philosophical about things. After I continued reading on for a bit, the article reminded me of the philosophical thought of "If a tree falls in a forest and no one is around to hear it, does it make a sound?" that raises questions about observations and knowledge of reality (Wikipedia, Oct.12, 2011). Hersh says "There's no math without people. Many people think that ellipses and numbers and so on are there whether or not any people know about them; I think that's a confusion" (Brockman, 1997, p. 1). I'm one of those people who would say that yes the tree makes a noise because if there was someone there they would hear it. The same goes for the math, I believe the math still would exist if people were not around, it just would not have a name. All humans have done is name it. However, it certainly makes me think more about the philosophy of math, that's for sure.

There are three philosophical attitudes towards mathematics: Platonism - some abstract entities; Formalism - calculations only, there is no meaning; and Humanism - mathematics is part of human culture (Brockman, 1997, p. 4). Hersh feels that humanism is the only educational friendly philosophical attitude of education and that it "brings mathematics down to earth" (p. 4). In other words, it is just what we have been calling making math real for children. We have been saying for years that we have to relate math to the real world for children in order for them to have a connection to it and find it meaningful to them. Having only been teaching for 4 years, I am finding myself more and more heading in this direction. My first year out, brand new to the whole thing, I resorted to the way I was taught with notes and questions, maybe a scattered activity. As each year went by, I felt more comfortable allowing children to discover formulae and why certain things happened the way they did. The children enjoy the math more this way and then they are much more likely to remember it.

The Romance of Mathematics

I believe the following about mathematics

·         Mathematics is an objective feature of the universe; mathematical objects are real; mathematical truth is universal, absolute, and certain.

·         What human beings believe about mathematics therefore has no effect on what mathematics really is. Mathematics would be the same even if there were no human beings, or beings of any sort. Though mathematics is abstract and disembodied, it is real.

·         The mathematics of physics resides in physical phenomena themselves - there are ellipses in elliptical orbits of the planets, fractals in the fractal shapes of leaves and branches, logarithms in the logarithmic spirals of snails. This means that "the book of nature is written in mathematics," which implies that the language of mathematics is the language of  nature and that only those who know mathematics can truly understand nature.

I think this affects how I teach mathematics in that I am constantly trying to show students how real mathematics is and where they can find mathematics in places they never thought. When a child thinks of nature, they do not think of mathematics, so I like to show them how different things can follow different mathematical patterns. Some develop a greater appreciation for mathematics because of that.

Sir Ken Robinson

I found this video particularly interesting as we do often find that the Arts are the first subjects to go when courses need to be cut for a small school. By doing this, we are already limiting some of our students' interests. With regards to teaching mathematics, I believe that we should alow students to express their mathematics in creative ways. Let them show you what they know through pictures and stories or anything at all that allows them to be creative. We have to accept that fact that not all students were made to study quadratics and exponential equations, it's just too bad that the standardized testing does not allow for the students to be creative in their knowledge.

Math Autobiography

I started school in 1990, but I cannot really remember a whole lot about mathematics for me in grades K-6. I do remember working out of a workbook that you could tear the pages out of; Math Quest I think it was called. I also remember doing a lot of work out of a textbook and not much in the way of discovery. I am not sure if this was because I grew up in a multi-grade school with three grades in one classroom. We probable had to be given a lot of "busy work". Grade 6 was the first year in a single classroom (we were bussed to another school). I still remember just doing a lot of questions from the book. Since I particularly enjoyed mathematics, I do not really remember a best moment, but my worst moment was probably in grade 4 with a "times table" test. I got all of the 4's wrong and I was so disappointed in myself. The next time we had a test, I made sure I had them all memorized. This has influenced me in that I know there needs to be a motivator for children to want to do well in math. My motivation was that I liked doing well and if that didn't happen, I didn't feel good. Other children's motivators are different. Some need something fun and interesting, others need praise. Each child is different.

I was good at math. I found it easy and it did not stress me out. I did well on tests without too much effort and I was usually pretty quick grasping concepts. The role of my teacher in my math classes was to teach me the concepts and then I practiced the concepts. Most were quite passionate about math. Assessment was always in the form of assignments and tests.

In high school we were the first group to use the Mathematical Modelling books in Grade 10. I found it okay to work with, but a lot of my friends struggled with the book and the teacher. I branched out to Advanced Math in Grade 11 and completed both Math 2205 and 3205 concurrently. I remember more about my experience with 3205 more. That was probably because I enjoyed it more. I felt so confident about 3205 that when I away from school for a week on a school outing, I did not worry about a test I needed to write when I got back. I ended up getting 100%. Math 3207 in Grade 12 was probably my worst math course. I still achieved high 80s, but I was used to getting mid 90s. Work in these courses was still really what people call "chalk and talk". Even though the courses were the beginnings of student discovery, I think the teachers felt uncomfortable with this or felt there was not enough time to allow for that.

I started off with Math 1000/1001 (Calculus 1 & 2) in university and my grades quickly went down to 60s. I had not developed any math study skills in high school (because I did not have the need), so it took me a few semesters in MUN to get my grades up closer to A's. I was not satisfied with my math grades, but I was away afraid to ask for help. I also did Calculus 3, Linear Algebra 1 (which I loved), Linear Algebra 2, Intro to Mathematical Programming, Discrete Mathematics, Real Analysis, Technical Writing in Math, Vector Calculus, Ordinary Differential Equations, Applied Graph Theory, Abstract Algebra (almost killed me), Euclidean Geometry, Projective Geometry, Combinatorial Designs and a stats course. Wow that's a lot of math courses! I only remember the ones that didn't give me nightmares! (And the one that gave me the worst)

I always try to engage math in my life in major ways. It may be nerdy, but I absolutely love solving problems and calculating things. Since teaching, I have improved my mental math abilities (not quite up to par with my parents!) and find myself calculating things in the store without even realizing it.

I chose to become teacher because I love helping people and I love it when people succeed at something they once could not. I became a math teacher because math is my passion and what better way to tell others about my passion than to teach it! I also wanted to make math fun for students. I would often hear complaints about math being so boring and I wanted to change that. I would describe my teaching as evolving. I started off teaching how I was taught (notes and questions), then as each year passed, I have found myself moving more towards allowing children to discover things and allowing myself to incorporate different types of activities into my routine. More and more I am finding students saying "Miss, that was fun!" and that is what I was hoping for. Students will have a better chance at remembering something if they found it fun (like me with my university courses).

I currently teach Math 7, 8, 9, 1201, 2204, 3204, 3205, 3103, Tech7/8/9 and my biggest challenge is perhaps keeping students engaged. This is only my fourth year teaching and I am only just developing strategies that I feel comfortable with so I can deviate away from the boring lecturing and notes. One thing that I think would help me as a math teacher is more freedom in my classroom. I would like to not have to worry about public exams or getting the curriculum finished. I think if I did not have to worry about those things I would be able to incorporate much more in my classroom that children really need and deliver them in ways that they enjoy.

Welcome

Hello everyone! Welcome to my blog, I finally have it figured out! I am currently teaching at Holy Cross School in Eastport, NL and I teach most math from 7-12 and junior high technology. This is my first school and I have been here going on four years. I really love where I am teaching!