Shift in Perspective

At the beginning of this course I was under the impression that mathematics had to be taught in a textbook manner. I experienced math as a strict textbook course that didn't really allow for "outside the box" thinking. Throughout this course, the idea I have of mathematics as a subject and in teaching mathematics has completely changed. 

As I mentioned in a previous blog, I never enjoyed problem solving and I was always intimidated when the problems were wrote on the board. After this course, I actually throughly enjoy problem solving now because I've learned to look at it in a new light and experience it in new ways. I see problem solving as not a separate section within a math course but as an approach in teaching mathematics all throughout the curriculum.

I also now realize that student's must learn through mathematics instead of being taught directly how to "perform" mathematics. Mathematics is not just a subject in school, it's a way of thinking and it's all around us in our everyday lives. I've learned the importance of not focusing on what answer students obtain but rather put focus on the process of obtaining that answer. I also see the importance of holding off on jumping in when students are struggling, it's okay to struggle! It's how we learn. I also see mistakes as a great value in mathematics because it provides great learning opportunities for all students as well as the teacher. 

I'd like to create a math learning environment that supports risk taking and values making mistakes as a learning experience. I'd use problem solving and open ended problems throughout the curriculum and teach it in a way where students can adapt it to solving everyday problems. I'd like to create real life situations in the classroom where student's can apply their mathematical thinking instead of giving them traditional algorithms on worksheets to complete.       

The classroom would be arranged in a way that supports collaboration team work, and active learning. Desks would be arranged in groups and at times would be pushed to the perimeters of the room to create space for the student's to be physically involved in problems. I'd also have manipulatives available around the classroom for student's to use whenever they need them. I'd also make sure to lay some manipulatives at student's desks while solving problems as a way to get them used to using them and to cut down on any embarrassment of using them. 

I've learned a great deal in this course and I'm happy of the shift in my perspective. I feel now MUCH more confident with approaching the subject and (almost) prepared to teach it. :)

  

K-6 Mathematics Resources

In class we were able to explore Math resources from kindergarten to grade six. I thought this was a great opportunity because it opened my eyes to the various resources available to teachers.

Primary Resources 

I noticed from Kindergarten up until about grade three, the math resources we're much more vibrant and colourful. I also noticed the math resources didn't really seem like the math that I was exposed to in those grades, the math was more disguised. The content in these resources contained more stories and it seemed much more relevant to children's lives. I really enjoyed the resources for kindergarten. I actually felt excited about teaching math when I looked through all the different books that covered many topics in storybook form. In these resources mathematics is displayed in everyday life, its not just a subject in school, it's everywhere we look.

Elementary Resources 

By the time we reached the grade four station, the mathematics was looking more similar to the math that I experienced while in school. The resources contained less images, less stories and colour and just seemed boring! I found it really hard to even investigate the various resources in these grades and I frequently found myself turning the pages without taking anything in (which may be what elementary students experience).

Overall, I really enjoyed the resources for the primary grades and I'm looking forward to using them. As for the elementary grades, although there are great resources available, I will definitely look for additional, more student relevant and appealing resources.  

Front Matter

We were asked to look the the front matter in the curriculum guide and write about what we found interesting or surprising. The first thing that caught my attention was when I was reading through the Belief's about Students and Mathematics Learning. The guide stresses that mathematics learned should build on students prior knowledge and experience. This means that the mathematical content must be relevant to the child in order for them to construct meaning and understanding. This somewhat came to a surprise to me because when I experienced math in primary and elementary it didn't seem relevant or meaningful other than when it came to completing a test. I remember frequently questioning the purpose of most of the math I encountered in school.

Secondly, while reading through the Instructional Focus section, I noticed this statement; 

• By decreasing emphasis on rote calculation, drill and practice, and the size of numbers used in paper and pencil calculations, more time is available for concept development. 

I found this statement surprising because this illustrates a completely different environment when it comes to mathematics compared to what I experienced while in school. For example, when I was learning multiplication it was entirely based on drill and practice and on memorization. I've been able to see this change during my observation days. Instead of memorizing times tables, students are learning many different kinds of methods to figure out multiplication solutions. Class time is based more on the process of obtaining solutions rather than coming up with answers as fast as possible. 

As I continued reading I came across the Instruction Time Per Unit section. I found this section interesting because it provided a visual of a time line and a recommendation for how much time to spend on each unit. I really like this resource and I think it would be extremely helpful for new, less experienced teachers while planning their school year.   

Overall, I think the front matter of the curriculum guide is an excellent resource for teachers. I think it's especially beneficial for future teachers to be familiar with and to understand in order to begin thinking about the kind of classroom environment that is the most suitable for all needs. 

So What?

As a future teacher I need to be thinking about what's important for my future students to experience and learn in my classroom. When it comes to Mathematics there are Principles and Standards that have to be incorporated in the classroom. So what? Why are these things important to consider? Why should we care?

After looking through chapter one of our textbook, the first thing I asked myself was what is the NCTM and what does it have to do with teaching mathematics? NCTM stands for the National Council of Teachers of Mathematics. This organization is the base of all mathematical curriculum in Canada.  

Why is this organization relevant to my teaching career?

The NCTM released the updated document, Principles and Standards for School Mathematics in 2000 which is still causing a reform of mathematics in school's today. This document provides the basics of what to teach when it comes to mathematics. 

The following lists and describes the standards and principles that were mentioned in the document.  

The NCTM list six fundamental principles that corresponds to high quality mathematics education. These include: 

1. Equity: High expectations and support for all students

2. Curriculum: A "coherent" curriculum, as an integrated whole, focused on big ideas  

3. Teaching: Teachers have to understand what they are teaching, they have to know the ways their students learn and the individual development of their students and provide content, tasks, and strategies that aid in the students learning. 

4. Learning: Mathematics must be learned with an understanding, not just by performing tasks. Learning must be able to transfer to new experiences and students must be able to evaluate their own learning and ideas. 

5. Assessment: Assessment should be based on meaningful information. Teacher's should be constantly assessing to measure students growth and understanding and to guide instruction.  

6. Technology: Technology should be used to enhance students learning; aids in solving problems not possible without and allows for increased exploration. 

So what?

These principles are important for me to be aware of and understand because they describe what a mathematical environment must look and feel like. Your classroom should be built upon these principles.

The NCTM also outlines The Five Content Standards. These are a common set of strands of mathematics that appear throughout the grades.

1. Number and Operations

2. Algebra

3. Geometry

4. Measurement

5. Data Analysis and Probability 

So What?

These content standards outline the content topics that repeat throughout the grades. You would have to be aware of these in order to plan units or to be prepared for substitution days. 

The Five Process Standards are also explained (How you perform the content)

1. Problem Solving: emphasis doing mathematics by solving the problems

2. Reasoning and Proof: Emphasis logical thinking; why does your answer make sense?

3. Communication: Being able to talk about, describe and write about mathematical ideas

4. Connections: Being able to see connections within and outside of mathematical ideas. 

5. Representation: Emphasizes the use of symbols, manipulatives, diagrams, charts, graphs to represent mathematical ideas.

So what? 

The process standards describe how students solve mathematical problems as well how they think mathematically. It's important to understand these standards because teaching must reflect and be based upon them.

The Teaching Standards

1. Knowledge of Mathematics of General Pedagogy

2. Knowledge of Students' Mathematical Learning

3. Worthwhile Mathematical Tasks

4. Learning Environment

5. Discourse

6. Reflection on Student Learning

7. Reflection on Teaching Practice. 

So what? These standards help you envision your role as a teacher that creates an environment that supports the Principles and Standards.    

After looking through chapter one for the first time I was overwhelmed by all the principles and many forms of standards. Once I went through each one individually and looked and at the overall idea to these standards and principles, it all became clear and relevant. Knowing about all the standards and principles allows me to feel more confident about teaching Mathematics.   

   

  

Video Response

Sir Ken Robinson - Do Schools Kill Creativity?

After being introduced this video a few classes ago, I have altered my opinion of the educational system along with my role as a teacher. Sir Ken Robinson analyzes society today, along with the changing educational system in such a unique, yet humorous way that really made me question and analyze the system myself. I'm going to highlight a few of Robinson's points about the educational system that really made me think about my role as a future teacher.  

All kids have tremendous talent and we squander them. 

Children are frightened of being wrong.

Mistakes are becoming stigmatized

If your not prepared to be wrong you'll never come up with anything original. 

Educating people out of their creativity

All children are born artists, the problem is to remain an artist when we grow up

All of these quotes speak about the existing educational system today and what is valued and what isn't. Sir Robinson explains that children come to school ready to explore and experiment but quickly they realize that its not acceptable to stray from the crowd and it is humiliating to be wrong. This means that most students are not going to publicly think or act outside of the norm, therefore a lot of people will not follow their passions and we won't produce creative thinkers.

Sir Ken Robinson made me ponder my future role as a teacher and how I will interact with my students. The video made me think about how children learn in so many ways and how I must be prepared to attend to children of all different needs, abilities and talents and to not punish those who don't respond to traditional teaching methods.

There is a lot to consider when creating a nourishing, enriching and supportive classroom environment. I think a good way to start creating such an environment is by incorporating this quote into your teaching philosophies:

Math Autobiography

I really don't remember much about math in the K to 6 classroom. I can remember having  word problems wrote on the board, having to memorize times tables (which I still remember today), and doing work from the text book. There always seemed to be a standard way when it came to learning mathematics. 

One of my not so fond memories was during a problem solving exercise in grade two. I can remember feeling hopeless when the word problems were wrote on the board. I had a lot of trouble understanding how to solve the problems and we had to work individually and weren't able to ask for help. We were told that we had to figure out the problems on our own. I remember feeling an overwhelming feeling of helplessness and embarrassment when I couldn't figure them out. My teacher would call us up to the board to answer the questions and it was a horrible feeling when you didn't know how to solve it. I still have negative feelings towards word problems to this day. 

Overall, I was average at math. I wasn't good at geometry but I really enjoyed algebra. In high school I had to get extra help throughout the three years. I did get good grades in math but I did have to work hard to get those grades. I really enjoyed doing math that I could understand and once I figured out topics I struggled with, I formed a more positive outlook when it came to that topic.  

I remember in junior high and high school, students would always comment on how they felt like the mathematics we were doing was pointless and we would never have to use things like cos, sin, and tan in real life. I can remember one teacher in particular agreeing with us but they claimed they had to teach it because we would be tested on the CRT's on the topic. The teacher seemed to enjoy teaching mathematics but seemed to also believe that some of what we were learning wasn't relevant to our lives and future. Assessment in math was always formal testing. I don't have any memories about math assessment in any other form than a written math test.  

Math in high school was okay. I had the same teacher for each year and my teacher had a degree in mathematics and you could tell that it was his passion. In university, I did math 1050/1051. I really enjoyed the type of Mathematics that was covered in Math 1050 since it was different than any Math that I had done before. However, I didn't enjoy math 1051 as much because there was a geometry section. I haven't taken any math electives and I don't engage with mathematics in any major way in my life.     

I feel okay about mathematics now. However, I don't feel like i'm strong overall with the subject and I feel like I need to feel more confident in the subject matter. I hope that this course boosts my confidence when it comes to teaching mathematics.

Welcome

Welcome to my blog! This blog's is a requirement for an Education Mathematics course that I am taking. I'm hoping this blog can help me with my future experiences in teaching Mathematics to Primary and Elementary students.
:)
Sherry

(Entirely unrelated...but this is my bunny, Muffin in her Christmas sweater :) !!)