The Way to Teach Math... A Shift in Thinking

     Prior to this course, I didn't really have a personal opinion regarding an adequate way to teach mathematics to primary and elementary students. I had very limited exposure to math in my observation days, which was realistically my only opportunity to perceive how math is taught in school's today. Outside of this, my only thoughts and perspectives extended from math experiences that occurred throughout my own childhood. As illustrated in an earlier blog, these experiences consisted of memorization, quizzes, tests, and short term knowledge that was forgotten shortly after. 

     The big fat x stands for how ineffective and outdated the older methods of teaching math (that I experienced) are. Research clearly shows that there are newer, more improved ways that math can be taught - ways that support transferable, relevant, meaningful knowledge that can actually benefit a student in the real world. These new and improved methods are crucial in order to prepare students, of a competitive 21st century generation, to succeed. 

     In terms of how I envision a math learning environment in my future classroom, I wish to create an environment where students are comfortable, engaged, stimulated, and motivated. I don't want students to have the same anxiety about mathematics that I held growing up. I would like my students to have confidence in math and regardless of if they proceed to enter a field where math is involved, I would still like them to possess a liking for math and problem solving skills that can be applied to any circumstance or situation. Students need to learn how to learn and develop mathematical skills that are useful not only in school, but in the real world.

     In an ideal math environment, I would like technology to be used. I'm a firm believer that technology can benefit learning, so why not incorporate it into a math environment? This is especially important in a generation that functions digitally. My generation lives, eats, and breathes technology, but it seems that the following generation is even more surrounded by technology, so it is essential that as teachers we recognize this and integrate technology and math. 
    Next, I would like to offer a math environment that is interactive. I don't want students sitting in their seats completing questions from text books (how boring). In my math class, math would look more like the following....

I hope I have the discretion, materials, and opportunity to create an updated, fun, 21st century, engaging, and interactive math environment, where I can actively encourage transferable knowledge.

Math Team Teaching with Ms. Murphy & Ms. Thorne

Jessica Murphy/Rebecca Thorne 

Team Teaching Education 3943 - March 26/13

Grade Level: 2

Subjects incorporated: Math & Physical Education

Materials: Number cards, sufficient classroom space for movement and computer/internet for extended practice of concepts

Activity:

Introductory Task:	1. Students will be divided into groups 2. Each group will be given numbered cards 3. Each student will pull two cards and lay them face down 4. Once everyone has two cards, students will flip the cards over and add the sum of their two cards 5. Whoever has the highest sum wins the round
Main Activity:	1. Number cards will be spread out on an area of the floor 2. Students will collect two cards of their choice and instantly find a partner 3. Each student will add the sum of his/her two cards and as a pair, they will perform an action corresponding to the summations (Ex: 6+2=8… Hop on one leg 8 times). 4. Each pair will trade one card and will proceed to find a new partner 5. Repeat step #3 with a variety of actions (Ex: Skip, jump, twirl, clap, etc.)
Extended Practice:	-> To reinforce addition concepts, students will be introduced to an interactive online website where they may practice single digit addition    -> http://www.free-training-tutorial.com/addition-games.html <

Related Mathematics: 
The important math concept this lesson focuses on is addition of 1-digit numbers – a fundamental skill to function in the real world.

Assessing Understanding: 
Teacher observation and peer assessment during activity, and reflection statements regarding what they learned.

Curriculum Connections: 
Demonstrate an understanding of addition (limited to 1- digit numerals) using: communications, connections, mental mathematics, problem solving, reasoning, and visualization.

Extended for Diversity: 
This activity can be extended for diversity by changing the focus from single digit to double digit numbers, increasing the level of difficulty. Also, it could be used for concepts outside of addition (subtraction, multiplication, division). Thus, students with differing skill levels could be given numbers that best suit their abilities.

References:

• http://www.ed.gov.nl.ca/edu/k12/curriculum/guides/mathematics/gr2_math_guide.pdf
• Inspired by www.youtube.com/watch?v=4Bttp1_ejKc

Math Resources...

I'm not going to lie, I'm a little skeptical about using textbooks to teach or learn. Through my entire schooling (including university), textbooks were far too heavily relied on. Don't get me wrong, there have been phenomenal textbooks with important and beneficial information, but I don't think they were used adequately, or to serve the greatest purpose. In terms of resources in mathematics, I think there are many resources, outside of textbooks, that are available to provide better stimulation and motivation in a generation that functions almost electronically. The textbooks should almost be used as a back up plan, or to provide teachers with sample ideas of what could be taught in their classroom. Maybe I'm biased, but as a person who grew up being assigned questions in textbooks almost every single math class, I like the idea of authentic, hands-on learning, or practicing math using interactive math games online that reinforce important math concepts.

On the other side of it, I was happy to see that within the resources there was plenty of organization/connection between grades. For instance, if patterns was the first chapter in grade one, it would be the first chapter in grade two, or three. As a teacher, I think this feature and consistency would be quite useful.

Something else I noticed, along with my classmates, was the immense difference between the appearance of the textbooks in primary grades versus elementary grades. In the primary grades, the textbooks were bursting with colorful images, pictures, stories, and so on. As the grades increased, the textbooks became black and white, and almost boring. When we get older, do we not like color anymore? If I don't find the elementary textbooks to be very engaging, how are students going to find it engaging?

Bring on the color!          http://www.youtube.com/watch?v=4fCMTQXzoXo 

Overall, I have mixed emotions about the textbooks. I'm glad that they are available to use, but at the same time I think there may be more beneficial ways to teach without them... ways that are more meaningful and interactive.

For example...

Math Curriculum - Front Matter

After reading through the front matter in the Newfoundland and Labrador Mathematics Curriculum Guide, the first thing that stuck in my head was the reoccurring element of making mathematical experiences in education relevant and connected. The theme of connections, as well as reference to the NCTM's other process standards, arose quite often in the front matter. I think this was a positive attribute.

The next thing that I noticed about the NL Curriculum Guide was how similar it was to the WNCP curriculum framework. They're almost identical in some ways. My concern with this is that Western and Northern Canada possess vast differences, so is it appropriate that we're all using the same curriculum framework? I'm also going to note that the publish date on the WNCP is May 2006. It's March 2013... If our NL curriculum is based upon this protocol, are we really up to date?     A lot has changed since 2006.

Now, to steer away from the negative, something I did find particularly useful in the guide was the timeline that was organized into units/topics. I think as a beginning teacher, I would find this to be quite helpful in terms of planning and time management. On the other hand, I don't think teachers should live by the guide, however they should use it simply as guidance. There are going to be students with different interests, backgrounds, exceptionalities, abilities, cultures, etc., and there are many things in the guide that are going to have to be adjusted to meet the needs of differences that exist.

So What? - Based on the first week in February

In a world that's constantly changing, the way we teach needs to adapt to fit the needs of this 21st century generation. It's a classic case of out with the old and in with the new. Chapter one focuses on this aspect and offers a current perspective of what should be happening in mathematics. For example, successful mathematics education requires equity, a well articulated curriculum, technology, useful assessment, and teaching and learning experiences that are relevant, current, and meaningful.

In terms of equity in mathematics education, chapter one emphasizes that in order to achieve success in math, there must be high expectations and strong support for all students. Personally, I grew up in a time where if you weren't one of the strongest math students in class then you faded off into the background. It's called the Matthew Effect, which simply stresses the concept of: 'the rich get richer and the poor get poorer'. Those who were good at math would complete worksheet after worksheet because they grasped the way they were being taught. Those who struggled and needed alternate, more meaningful learning experiences developed an anxiety about math. The equity principle calls for equal opportunities and supports for all students, not just the math experts (2). 

The NCTM declares that "In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures" (1). This is why it's so important for teachers and students to care about mathematics. It's a competitive world and it's becoming more and more difficult to attain successful employment... mathematics can help with this problem. I know for a fact there were certain careers that I dreamed about that I didn't make an attempt at because I thought they would involve mathematics, an area to which I held no confidence. Hopefully this flaw in mathematics education can be improved or eliminated, and students can begin to live up to their full potential.

So far in this math education course, I have learned that the best way to develop excellence in math is to follow the five process standards. For example, when working with various math problems in class, the professor is constantly providing the time and opportunity for solutions to be solved without the answer being given. In these situations, we have covered problem solving, reasoning and proof, communication, connections, and representations. So, if I learn best this way, why not teach younger students this way? They might not be university students but they're a lot more intelligent than they're given credit for. If we provide them with meaningful math experiences, who knows what they could achieve?

Class Video

Do Schools kill creativity?

Although carried out in a humorous and witty manner, the suggestions and points made by Sir Ken Robinson in the above video are both compelling and relevant to those involved in the education system. Robinson brought ideas to my attention that I hadn't thought about or considered. I love when people can make me think. 

"The most useful subjects for work are at the top. So, you were probably streered benignly away from things at school when you were a kid - things that you liked... on the grounds that you would never get a job doing that, is that right? Don't do music, you won't be a musician. Don't do art, you won't be an artist"

This part of Robinson's speech resonated to me because of the truth it holds. I vividly remember teachers and adults guiding me away from my interests and towards what they held as "important" in school - math and language. I always considered myself as a person who had little to no creativity, but I'm beginning to reconsider this notion. I don't think I had the opportunity to explore my creativity.

"Stop humming"
"Put that drawing away"
"Times New Roman, size 12 font, white paper, essay format"
"Stay inside the lines"

Sound familiar? Robinson notes that "We are educating people out of their creative capacities". I have to agree with this concept, as I grew up in an education system where creativity wasn't valued. Why wasn't it valued? If more time and effort was put into encouraging creativity, I feel as though I would be much more passionate in areas of life that I ignored, or put to the side.

Another point discussed by Robinson that stood out to me was the following:
"In the next thirty years more people worldwide will be graduating through education since the beginning of history. / Suddenly, degrees aren't worth anything. / Now, kids with degrees are heading home to carry on playing video games." 

One of my biggest phobias has always been the fear of dedicating years of my life in order accomplish a piece of paper (University degree), only to return home and live in the basement of my parent's house. I have friends who have completed their degrees and they are literally (like Robinson says) sitting home and playing video games, or working a minimum wage job. After plugging in the time, the effort, and the money, one would expect to gain employment after finishing University. Unfortunately, this is not necessarily the case anymore. With times changing, we have to adjust. With such competition, we need to educate children to  reach their full potential and creative capacities in order for them to succeed. Step one could be the aim for more compassionate teachers and doctors, such as those experienced by Jillian Lane in Robinson's speech. 

Math Autobiography

     Outside of the basic math concepts (addition, subtraction, multiplication, and division), I feel like my math career has been a lot of short term learning. I remember learning topics in math, doing well on the tests, then forgetting most of what I learned. In younger grades, I was one of the best in my class at math. I would fly through math worksheets and ace tests. As I reached higher grades, math became much more difficult. In particular, I struggled with problem solving, which was practiced in almost every math class. This was peculiar because I was a good reader and loved words. Language Arts was my specialty, but something about the combination of generating an equation or formula from a confusing riddle was frustrating. Somehow, I still managed to do well and keep A's and B's throughout my whole math career. Unfortunately, I know it's because I was memorizing... not understanding. 

     As the years progressed, my confidence in math dwindled. In younger grades, math was fun - bright, colorful, and full of fun materials. I mean, we played math games, built towers, used various math materials such as geometric shapes, and so on. It was noticeable that my math teachers in younger grades put effort into making math interesting and stimulating. In higher grades, there was no concern for this. Math became dull and repetitive. The concepts became more challenging and the teachers were less patient and understanding. If you weren't a top math student in the class, it was almost as if teachers cared less about you. I can even remember pretending to complete assigned math work and lying about being finished - praying that the teacher wouldn't call on me to answer a question out loud. I think this was mainly due to pressure from the math teachers and peers in class. Those who weren't experts at math were terrified to be humiliated - both by the teacher and students. For this reason, I think it's important that math class offers a safe and comfortable working environment. 

     When I look back at my math career, one thing I'm thankful for is the fact that I had parents at home who could help me learn math concepts before tests and complete math homework. If it wasn't for this privilege, I would not have been nearly as successful in math. It was not enough for me to be given a math problem on the board in class and be expected to master it. I needed to practice concepts at home. The sad reality is that there's an abundance of students who don't have the help they need outside of school. Because of this, I would like to be able to offer some sort of after school math help for my students in the future. 

     After high school, I completed math 1090 and math 1000 in Grenfell in Corner Brook. As I did 1090 first, I was not required to write a math placement test upon my entry into Grenfell (this was why I did 1090 first). Those who immediately entered math 1000 had to do the placement test - I had way too much anxiety about the test to even consider this route. I did fairly well in both math courses, scoring above 75, which I was happy with considering math was not my forte. I have heard that math courses in St. John's were much more difficult than those in Corner Brook. My professor in Grenfell was phenomenal. She sort of spoon fed us, giving us which problems would be on the tests and teaching concepts step by step so those having difficulty could follow along and understand. This was the type of instruction I needed in order to be successful in university math. 

  

     Currently, my feelings about math are pretty neutral. I have had good experiences and bad experiences. The bad experiences have made me want to be a more caring and considerate math teacher. I have been bartending downtown in St. John's for a number of years and calculating tabs, sales, and change has been the only math that I have seen in the past 3 years. I am looking forward to getting back into the math groove and revisiting many of the math concepts that I have forgotten many years ago.