Last thoughts

Teaching is a very complex career. One is propbably always questioning what they are doing in the classroom and if it is the best for their students. I was very intrigued by the approach the teachers at Phoenix Park took with their students. The open ended projects and all the responsibility placed on the students was something new to me. These students gained a great deal of knowledge which they could transfer from one problem to the next. The teachers did what they could to interest the students.  Boaler (2002) makes a very positive statement about the teachers in saying," They adapted different problems for different students, and they helped students navigate their way through the problems"(p180). The teachers were there for guidance but ensured that the students thought for themselves independantly. Amber Hill on the other hand had a total traditional approach. They used the old chalk and talk and there was not much of a diverse atmosphere in the classroom. According to Boaler (2002), "many students appeared to be disadvantaged in the face of new or applied situations"(p177). They were so used to the structure and learning a procedure whereas they completed problems using that taught procedure. They were not able to think outside the box.
My own teaching methods involve a little of both approaches. I do not have open ended projects all year and I definitely do not stand up and lecture and then just assign questions out of a text book. I do guide the students, I introduce them to topics and I show them how to use different formulas or equations. However, the students are contantly involved, they are constantly questioned and I do  not give them the way to get the answer. I do guide them and ask them questions which leads them to figuring out how to get the final result. I do have projects and group work and my students are required to think outside the box. I always try to relate the new things we learn to what we have learned before and I try to make my lessons meaningful and interesting for the students. I am not comfortable, however leaving them on their own to work all year as the Phoenix Park teachers did because I am to afraid of the high percent of our evaluations that must come from a paper and pencil test.
Boaler, Jo(2002) Experiencing School Mathematics. Lawrence Erlbaum Associates. New York.

Ability Grouping

I do not believe in ability grouping. It takes away from students motivation. If I were placed in a low ability group I would feel that I was stupid or slow and would not feel the need to work hard as I had been branded as a low achiever. Students learn at different rates but as teachers it is our responsibility to adapt to that and use differentiated instruction as a tool to meet everyone's needs. At Amber Hill the ability grouping eliminated the teachers use of DI. As Boaler(2002) states, "When teachers place students in ability groups, however, they often forget that students are at different places in their mathematical learning, with different strengths and needs, they assume that the students are now a homogeneous group and differentiation is not required"(p157) This takes the diversity out of the classroom and we know that students are supposed to bring diversity. We have a variety of learners in our classroom and differentiated instruction is mandatory in order to reach all their needs.
Slavin(1992) states, "Ability grouping is ineffective. It is harmful to many students. It inhibits development of interracial respect, understanding and friendship"(p14) Students need to feel connected and a sense of belonging. If we do not push them to do their best then they will settle for less. We cannot put a label on a child that determines what they are capable of. If we do this at an early stage then we are eliminating the growth that can occur within a child. For instance, I know a student who did not care much for school. He was placed in the basic stream in high school, there was not a whole of confidence in his ability. After 2 years from the time he graduated he went back to obtain his ABE. He then went onto MUN and has just graduated from Med School. I think that ability grouping was a factor in his behavior in high school. If the school did not have confidence in him well how could he have it in himself, and it is obvious the potential and ability was there.
Boaler, Jo.(2002) Experiencing School Mathematics. Routledge NY
Slavin, Robert.(1992) Why Ability Grouping Must End" Achieving Excellence and Equity in American Education. Johns Hopkins University.

Real world and math

In chapter 7 there was a very interesting discovery regarding students at each school and how they viewed math in class and math in the real world. According to Boaler(2002), "The Amber Hill Students appeared to regard the worlds of the school mathematics classroom and the rest of their lives inherently different"(p120) They did not believe that what they did in the classroom related to their everyday lives. They did not think of math as something you encounter everyday but were only familiar with the math that they learned in the classroom. I think this is important for us as teachers to think about. We must try to make math a reality for our students. Teaching from the text and confining your lessons to the classroom will not cut it. We need to make the math matter to them, make them see how it could help us outside the classroom and discuss the math that we are surrounded with everyday.
If we engage students in their learning by allowing them to see how math is related to the real world then I believe this will increase their motivation. According to Conner and Gunstone (2004), "Willingness is closely linked to motivational constructs." I believe students would be more willing to learn if they feel there is a point and that what they are learning will help them in their lives.

Boaler, Jo.(2002) Experiencing School Mathematics.New York
Conner, Richard. Gunstone, Lindsey(2004). Conscious Knowledge of Learning. International Journal of Science Education. v.26 p1427-1443

Chapter 6

I found it very interesting to read chapter 6 and realize that all that practice Amber Hill students received in textbook questions and paper and pencil tests that they did not excel on the GCSE exam over the Phoenix Park students. The students from Phoenix Park were rarely exposed to the exam and had a very worry free atmosphere. They completed open ended projects and barely did any traditional textbook questions. As Boaler(2002) states, "The students at the two schools developed a different kind of mathematics knowledge"(p104). The Phoenix park students were able to apply what they had learned in a broad range of questions. Amber Hill students on the other hand wanted to see questions that they had seen or were familiar with from class as their knowledge was triggered by cues or knowing that a certain procedure had to be carried out for a certain type question.
I was also amazed regarding the facts about the students who were off task or misbehaving in a Phoenix Park classroom. According to Boaler (2002), "a comparison of NFER entry results and  GCSE results show that these students did not underachieve on the GCSE examination in relation to other students"(p103). I was concerned while reading chapter 5 and completing my discussion that the off task students who wanted to learn through the traditional approach were being left out by the Phoenix Park teachers. It was evident this was not the case as they were not worse off than the other students on the exam. They were actually learning and even having to take on a small amount of responsibility themselves helped them develop a knowledge of mathematics and they were able to apply it. This goes to show that even the reluctant students will learn when we allow them to take responsibility for their own learning and explore mathematics concepts.

Boaler, Jo.(2002). Experiencing School Mathematics.New York:Routledge

Thoughts

This week I am going to express how I am feeling about my classes today. I am finding that most, but not all my students have lost interest in school. It has become a place where they show up and aim to pass their courses but are not putting in a lot of effort. There are some students who I know can attain an 80 but are settling for a 60. I make phone calls home, have discussions with students but still I am seeing a lack of effort on the students part. In math we complete projects, have inquiry discussions and I feel I am fighting at times for the students to participate. I assign practice work where you might see half the class complete. I am calling home for late assignments and with the new assessment policy I have to accept these whenever they come in. With the new cheating policy in the eastern school district I must give a retest to a student I catch cheating. I feel that the students do not see a  reason  to work hard and put forth their best effort forward as we are catering to their every need. I am feeling frustration and needed a place to express this. I was wondering how many more people out there might be experiencing this with some of their classes/students? Every night I spend time making up lessons, coming up with interesting ways for the students to learn and in return I get little back. I care about my students and want them to do well. This is why I do stress as much as I do, I am not one who settles but aims for the best.

Schoenfelds article

After reading Schoenfelds article it has opened my eyes to some things that may be going wrong in a math classroom. There are many times when I have taken courses myself where I was told or shown how to go about a certain question. It was not explained to me why we were carrying out the procedure we were but only guided through the steps. I had to go beyond the workings myself to find the understanding or go to the teacher on my own time.
In some math courses, especially the public courses students reach in grade 12 there are many objectives to cover. There is a pressure put on teachers to get the material covered on time for that big 50% exam. As stated by Schoenfeld(1988) the textbook does not often help. "Most textbooks present problems that can be solved without thinking about the underlying mathematics.."(p16) I often did feel this way as a student. I would open the textbook, begin practicing following the procedures that were presented by my teacher. I always try to explain things to my students during a class. I make them understand and I attempt to relate it to the real world.
I found it interesting when the example of division was shown, where the same number was added together and divided by the number of those same values there were. The fact that some students would add it all up and divide, not realizing this was not necessary. I can see some of my students doing that, but I see many of them picking up on what was going on because they do understand. We have encountered problems where they can solve a problem my merely taking the square root of each side. There are others who end up carrying out the quadratic formula to solve for x. This lets me know who the students are that actually do understand when we discuss operations and those who cannot grasp it but only follow a procedure.

Textbook chapter 1 to 3

As I began to read the text I started to think about my own teaching methods. At Amber Hill it is obvious that they are following the more traditional approach where there is an obvious barrier separating students from teachers and definitely the principal. There was not a whole lot of interaction between either.According to Palinscar(1998), "interactions such as those achieved through classroom discussion are thought to provide mechanisms for higher order thinking". At Amber Hill the lack of communication that was occurring within the classroom will hinder such development.


Phoenix Park on the other hand did foster more communication. The principal along with the teachers were constantly interacting with the students. This type of interaction will allow for higher order thinking.

I try to use a balance of both schools. Due to the high percent of students marks being based on the paper pencil test as well as the vast number of objectives that have to be covered by June it would be hard to use the project inquiry discussion all year but in no way is it useful for me to get up at the board doing a chalk and talk all class. I do present objectives and examples but I also give the students time to explore ideas on their own using the investigation approach. I also get students up to the board to lead discussions. I think that for now my balance is working. I would like it if there was not such an emphasis on the paper and pencil testing.

Palinscar, A. (1998). Social constructivist perspectives on teaching and learning. Annual Review            

                      Of Psychology, 49, 345-375.

Reading 2 thoughts

As mentioned before I had the belief growing up that math is concrete and there is always a right answer. After reading the article involving Hersh I start to think about the nature of mathematics myself. The laws that I learned, growing up and the objects we found the surface area for, well where did all these come from? Who decided a square was a square or a circle a circle? When you really sit down and think about anything in this life, well where did anything come from? After I read this article I start to think and reflect and growing up believing in something, such as math is concrete, then reading an article which questions this is difficult.
In terms of teaching I am going to try to push harder for independance for my students. They do enjoy it when I am at the board doing examples, but I refuse to do that in my class all the time. The students are responsible for becoming part of the class, for contributing and figuring things out on their own. I will get them up to the board more often then I am already doing and I will make them work harder to learn for themselves, not because they must just get good grades.

Reading one and Ken Robinson Video

As I went through mathematics in school I always believed that anything we did in class was definite and true. Any formula, equation or activity I participated in during class was as real to me as the person sitting next to me. My love for math grew stronger every year and I became more biased that math made sense, while the arts courses such as english did not. I thought that there were to many opinions in those topics and that math was concrete. After high school I went on and continued my studies in math because I wanted to do courses where there were right answers involved.
My thoughts on mathematics did not begin to change until I entered the education program and then within my first years of teaching. I realized first of all that there was not only one way to get to an answer. I encountered many people who thought of questions in different ways then I did and worked out problems using a completely different method then myself. When I was a student I thought that what the teacher did was right and it was the only way to do the question. This has helped me tremendously in my teaching career as I encourage the students to investigate problems on their own using their own strategic thinking as opposed to doing everything the way I may do it on the board. There are so many kids that amaze me with the ways that they reach an answer. I allow them to share their thoughts with the class and perhaps they will help other classmates understand the concept better.
Sir Ken Robinsons video opened my mind up to so many thoughts. There are many students I encounter that do not like math. They feel like they don't need to know it and that they will never be good at it. I must realize that these students have talents elsewhere. As their math teacher though I feel the responsibility to focus on math when I have them in the classroom. I am beginning to think about other ways I can still teach them math but help them find out what they enjoy, what they are good at and what makes them happy. When I was in school and still today there is the idea that the core courses are the most important in life while the others are not as useful. This however is not the case and we as educators must help diminish this idea.

Math Autobiography

During my time in grades k-2 I remember sitting at a table that was round. All the students faced each other and we were always working together.We used red, yellow, green and blue counters. I remember helping some of my classmates to count in kindergarten and the teacher would go around to each table, helping us and saying good job when we could do the work or if we were being helpful to someone else. I did a lot of worksheets in math from kindergarten up. I will never forget the stickers that we got on each sheet and how we would compare the stickers with one another. Many people in my class would have to count on their fingers. I could do it all in my head. When I was in about grade 3 we would always say our times tables out loud. We would have a quiz every Friday on them. In elementary I remember taking apart an orange and counting pieces of pizza and pies when we did fractions. I always loved my math class especially when we did activities and group work. I had a few teachers who would let us go to the board and show the rest of the class how we completed some of the homework questions.
The best memory I have of my math classes were the group work activities. This includes simply completing a worksheet because I always loved to help others. I found when I explained it to someone else it help me understand and retain the information a lot better. The worst memory I have surrounding math is the year I completed math 3207. At this point I was in grade 11 and graduating early. I had to take so many core courses plus complete some at home. The math 3207 was not going to be a factor in my chances at a scholarship so I always left that course until last to work on. I did not do as well in it as I would have liked and that was upsetting to me. However, when I took my first university course in math and had the time to focus on the material which was similar to the 3207 course I enjoyed it and had a much easier time with it. As an adult I realized that I cannot push things to the side because I don't think they are as important. The course did not turn me from math it simply made me want to work harder.
I believe I was good at math. I always had good grades and really enjoyed all my courses. I could do math in my head that my other classmates might not be able to do. I had excellent grades in my math courses at MUN and I did well in the higher order thinking problems as well.
Within my classroom most of my teachers, especially as I got older introduced concepts and provided examples by writing on the board and standing in front of the classroom. When they assigned work most would pace around the room checking on everyone. If they saw there was a student making a mistake, they stopped and helped. I did have a few teachers who sat at the desk while we worked, correcting or doing some other activity. I think these are the teachers perhaps who may or may not have liked math but were not engaged enough in the course to be a constant help to the students.
In most of my classes assessment included worksheets, assignments, quizzes, unit tests and portfolios which contained our journals. The journals allowed us to express math in words as opposed to using numbers most times. We had to explain concepts and answer questions that made us think outside the box. As mentioned before in the younger grades we had many worksheets that were handed back to us with stickers. The tests came later in school.
In high school we did less group work and less activities. There were a lot more classes where we sat and watched the teacher work and then we were assigned seat work ourselves. Much more of our assessment was based on assignments and tests. The word curriculum and getting it covered came up a lot more as most of us had not heard the word when we were younger. I still enjoyed math because I like to work on problems. Many students however did not look as enthusiastic and were complaining most times. The question was always brought up to the teacher as to how this would help us in life.
In university I completed a math minor. This included math 1000, 1001, 2000, diff equations- 3260, discrete math 2320, math 2050-linear algebra, finance 2090,3331-projective geometry, and of course my methods courses during education.
I engage in math during my life by teaching it everyday. I was, while I taught in Alberta and will be part of a math professional learning community at my new school. I take care of my bank accounts as well as other financial issues in my life where I must use my knowledge of mathematics.  I have made many purchases in my life where once again I need to be aware of interest rates and so on.
As I teacher I chose to teach math because I have a passion for it. I enjoyed it in school and I want to help others enjoy it as well. I am happy teaching math as opposed to teaching something that I may not be interested in and I would be teaching it just because it was a job. In my classroom there is an atmosphere where students are not afraid to ask questions. They know that no question is the wrong or stupid one. Everyone feels comfortable expressing their concerns and are not afraid to ask for help. I get my students to participate in activities and group work. I always ask the students what they prefer and there are times when my instruction at the board is a majority vote. They like it when I introduce topics and go through examples. I don't simply just do out the example on the board but we go through it together and I will constantly ask questions throughout the process. I try to make everyone feel part of the class.
I am responsible for teaching grade 9 math along with all the high school academic and advanced math courses. The challenges I face are trying to get those students who are convinced they hate math and are not good at it, to become interested and try to do better. I attempt to build up their confidence levels by making them feel good about themselves when they are getting things right. Even when they do things incorrectly I tell them that this is a mistake anyone could make and we work through the problem again where I simply guide them leading them to the correct answer which in turn makes them feel much better.
The one thing that will and has helped me as a math teacher is constant collaboration with others