Final Blog :)

What was your greatest 'learning' this semester with regard to teaching children mathematics? How has your thinking shifted?

I enjoyed going to math class all semester, and how could I not? It was a great, easy-going environment which was evident in the conversations that we had... it was one of the classes this semester where we didn't just say what the prof wanted to hear. It was an awesome experience!

Some of the things that I learned this semester that will stay with me and influence my future teaching are:

- I think that it important to teach children the 'whys' of mathematics. Teachers should not just fill children's heads with specific ways to solve questions or one certain method of getting a correct answer. Students should learn about mathematical relationships and reasoning for all of the concepts that they have to learn. It provides them with background information and reasons for why they're doing what they're doing.

- Children are all not the same. Duh. Teachers need to find many different teaching methods since their students all learn and figuring things out in many ways. Children need concepts explained in ways that contrast from one another, since several of them will have a different thought processes. It is important to provide them with the tools that they will need to be able to do things their way.

- Having a math fair is an amazing idea! Students have the chance to feel confident in presenting their problem to their peers. This is a good opportunity for children to realize that there may be more than one answer to a math problem, or that although there is one answer, there is more than one way of solving it.

- Finally, from reading other final blog posts, the majority of you still don't feel 100% confident in teaching mathematics to children. While this is understandable, since we do not have much/any experience in doing so, I think that it is dangerous to walk into a classroom feeling as if you have mastered the material completely anyways. Children will constantly surprise you with questions that will stump you and will introduce you to things that you did not know yourself! A little bit of uncertainty leaves room for you to grow and it's not only our students who are supposed to be learning new things!

This course was an awesome learning experience. Thanks for everything Mary, best wishes!

                                       
                        Not quite how I actually see math word problems, but it make me laugh :)

K-6 Mathematics Resources

On Tuesday's math class, we had the opportunity to look at the resources that are provided to teachers who are in kindergarten to grade six. I was surprised at the amount of materials that was available for each grade. I was not expecting to see a big binder of teacher guides, filled with in depth material on each chapter. There were example problems, explanations, student workbooks, and other resources to aid learning.

I was shocked at the number of picture books that were available in kindergarten, grade one, and grade two. Having children read about mathematics is a great way for them to be introduced to math concepts and foundational problems. They would also get used to seeing important terminology that will be important to know for the future.

One of the downfalls that I noticed when going around to the different tables and checking out these resources is that when we reached grade three the materials were much less 'kiddie'and colorful, and there were not any pictures books for the children to read. I thought that this was a little strange since grade three is still a primary grade and that children that age still need to motivated. If I were teaching this grade I would bring other resources into the classroom that are more stimulating to children in grade three.

Since these resources are only to be used as a guide, the classroom teacher can chose which parts of the resource to use and where to bring in additional resources that would be beneficial in learning the required material. For a young teacher, it may take a while before being comfortable enough to bring in resources that might work in the classroom. I think that math lessons should not always be text oriented, but it is definitely comforting to have something to use as a guide especially in the first few years teaching or when in a unfamiliar grade.

I found it interesting to see many problem-solving questions in the text books with other equation-like problems. My own experiences with problem-solving was that it was separate from other mathematics (for the most part), so it was nice to see how the mathematics resources has changed.  

YouCubed for Future Success!

The essence of mathematics is not to make simple thing complicated, but to make complicated things simple.  - S. Gudder

I am so glad that I was presented with the opportunity to explore this website and get familiar with it! Jo Boaler should be praised for the work that she has put into this movement. She is the driving force behind math change in the United States and is leading the YouCubed project. 

My first impression of this website was that it had a cool layout that was easy to navigate. When I examined the different aspects of the site, I realized that it outlined great inquiry-based, meaningful learning teaching methods. These methods would certainly make teaching mathematics more interesting and it would make learning it much more appealing to children.

While searching throughout YouCubed I read the article Unlocking Children's Math Potential: 5 Research Results to Transform Math Learning. I was completely absorbed in the article and thought that it was fascinating how the brain can acquire information when appropriately stimulated and when children are motivated. I wholeheartedly agree with the five points that are made in this article, especially with the research provided to back it up. I love how, at the end of the article, Jo draws attention to a certain term that Gloria Ladson Billings uses to describe teachers. She calls them "dream-keepers" as if to draw attention to "the opportunities that teachers have to help students achieve their dreams". To a teacher in training, this is can be a very overwhelming feeling, to have that much influence on the outcome of a child's dreams... but it is also very motivating!

As I continued browsing I noticed all of the units and lesson plans that were made available.. and they actually look like children would enjoy them! The elementary lesson plan example involves a hands on situation with objects that are larger than the manipulatives that they have probably grown accustomed to using during mathematics. These glow sticks (cool, right?) and styrofoam balls are bound to be effective in keeping children's attention focused on the lesson.   

The middle and high school lesson plans incorporate questions about math that students are supposed to reflect on and think about the different processes used to solve certain math problems. This encourages students to think about their thinking - metacognition. There is time allotted for students to work both individually and in groups.

One of the most appealing aspects of this website is that there is a section for parents. There are games available for home use so that children can continue learning at home and parents can be involved. There are also pointers on subtle ways to make math more fun. My favorite at home game that is on the site is "Race to One Hundred". I think that it is an excellent way to get children motivated to do math. 

The video "Window into the Classroom" features children working on mathematics. They use the words creative, game, and story to describe the different ways that a person can interpret math. It is refreshing to hear children talking that way about mathematics and to know that there is hope that more and more students will adopt this point of view. At the end of the video one child said "you can use anything for math", which sounded backwards to me. I am used to hearing the phrase "you can use math for anything". But, it makes complete sense that these children are adopting that attitude about mathematics with the approach to teaching that is being used with them.

I think that this is a great website that could be an excellent resource for the classroom and at home. I am looking forward to seeing this site being fully operational and the effects that it will have since it is available to everyone! 

Mathematics?

Typically, when the subject math is brought up, I think about numbers and solving equations. After these superficial thoughts pass, I'm left thinking how math can mean problem solving and how that can be applied to many different situations in life.

After some research I have discovered that over the years the term mathematics has come to mean different things to different people and there is no universal definition. Most definitions classify mathematics as a science.

One of the more interesting findings that I found was from a mathematics professor at Fordham University. Dr. Lewis stated that "mathematics is not about answers, it's about process". This surprised me a little because I pretty much had the exact opposite thoughts about math. I thought that when it came to math that the answer was the most important thing.. that's what you were doing all of the work for! But, upon reflection, during my time in the school system, having the right workings but the wrong answer did get you some marks. I feel that by thinking the same way that Dr. Lewis does about math makes the process a lot more appealing.

While doing research on the definition of mathematics I found this silly, but interesting video on math, which questions if it was discovered or created, if there is a math 'truth', or if math even exists. If you haven't been confused yet today.. here's your chance!

Do Schools Kill Creativity?

Listening to Ken Robinson in class was such an enlightening experience. The way he spoke about creativity in the educational system was refreshing. I feel that it would be beneficial for teachers and schools to adopt Ken's attitude about creativity and how it should be embraced rather than pushed aside and labeled 'wrong'. I think that we should not suppress children's preferred outlets, but try our best to put children in situations where they do their best learning as much as we can.   

While listening to Ken it was interesting to realize how people react so strongly when education is brought up in a conversation. For all of the good memories that people have about their time in school, it is often the unpleasant memories that stand out. This was also evident in our class discussion. To be spoken down to or to be made to feel like it is your fault for not learning course material is very belittling and would definitely have an impact on your views on a certain teacher, subject, and your own abilities.

I also found it interesting how it was pointed out that we teach children in hopes that they will thrive in the future when we really have no idea what that future will look like...making education more like a guessing game than anything else.
                                           
Although I was aware of this since the beginning of my own educational experience, it was unsettling to hear it directly stated that mistakes are discouraged in schools. Since making mistakes shows original thought and is a way of producing new ideas, it is odd to hear it being argued against. It seems as if school systems had one desired outcome for students and that uniqueness has been crushed. As Ken said, students are being "educated out of creativity".
                                             

It was troubling to realize how medication is now often used to deal with hyperactivity that may be a overshadowing a talent that a child possesses. The famous Gillian Lynne would probably not have been able to explore all of her talents if she just so happened to see another doctor who was more likely to prescribe medication. It is saddening to know that some other children are not so lucky as to escape that route.

Not all people learn by the way of traditional mathematics, and teachers need to try to incorporate different learning techniques into the math classroom. Also, it is important for them not to expect every student to be a mathematician, but to encourage them to work to the best of their capabilities.  

My Mathematical Autobiography

When reflecting back on the mathematics education that I received from kindergarten to grade six, I realized that I only remember being taught in one specific way. I remember each of my teachers teaching new concepts to the class, followed by some modeling with class participation. We were then sent to work solving the assigned problems from our text books. I do not recall learning mathematics through play or in any other way than how I described. I do not have a specific best or worst memory in relation to mathematics in the primary/elementary grades, but have always had a positive experience with it. I did not have to work too hard to be successful learning the concepts that were introduced in class. I also had a strong support system at home to help me with any problems that may have come up. I was considered "good" at math because I received nineties and hundreds on most of my tests and completed most of my seat work and home work correctly.

I feel that if any of my math teachers had any negative feelings towards math that they disguised them well enough so that I did not catch on to their dislike of the subject. I think that this is an important aspect of teaching to encourage children to learn things that will be important to them. Teachers should not let their personal feelings on such subjects influence how children feel about it. The teachers that I had all assessed in a similar way. They would correct seat work, home work, and work sheets and give tests.

In high school math was still taught in the same manner, by teaching the new concepts by building on what we know, teacher modeling, and student practice. I did not achieve top marks at the beginning of high school but they got better in the later years due to better concentration and different teachers. In high school, I liked the idea of how math had a definite answer, but while doing tests it caused me to have a lot of anxiety because for the most part, I was either going to be right or wrong. Since starting university I have taken a course on finite mathematics and algebra and trigonometry, the latter being my favorite.

I feel that although I engage with mathematics in my life, it is in a subtle way. I do not think of it as doing math, I think of it as banking and shopping list estimates. Mathematics has found a way into my life in a useful, noninvasive way. Since having a mathematical background helps me with my daily life, I definitely feel like it is necessary for children to acquire math skills to better their futures!

Welcome!

Hi! This blog will be used to share my personal thoughts on different aspects of Ed 3940. I will reflect on the discussions that will take place in class and contribute any information that I think may be useful. Enjoy :)