Teaching Children Mathematics

What was your greatest 'learning' this semester with regard to teaching children mathematics? How has your thinking shifted?
There are so many great things I have learned this semester with regard to teaching children mathematics. Growing up, I was always taught there was one right answer in Math, although there may have been many ways to go about it. I realize now, thanks to this course, that this "correct answer" thinking can really damage children and their view on Mathematics. As students, we always look to the teacher for the right answer and we never question their solutions, especially in Math.
This semester, I have learned that it is important to ask open-ended questions and let students figure the answers out for themselves. We never really think for ourselves anymore, and I think this frame of mind has a lot to do with that. As I have mentioned before, I was always good at math in school and I was always confident enough in myself to answer the teacher's questions, but I have realized that there are a lot of students who fear speaking out in class because they are afraid of being wrong. During our team teaching, myself and Abby presented the problem and asked the "students" to quietly work either by themselves or with a partner to find a solution. When we were asked if they were right, we asked them what they thought. Then we would ask them what they did to get the answer and asked them if this obeyed the restrictions we had given them. Not directly saying "yes, you're right" or "no, that's wrong" really frustrated some people - because we are used to being one or the other. It is important to teach children how to think for themselves and to be confident enough to argue that the answer they have is valid because of the way they approached the problem.
I have also learned that math can be so much more than a textbook or a worksheet, thanks to the Math Fair. There are SO many fun activities for children that involve many of the math outcomes in the curriculum guide. These "games" would be a great way to engage all children in learning math since they don't actually see it as learning, but having fun instead. Plus, hands-on learning is great for students who have trouble reading or writing, or both!
I will most definitely be using open-ended questions, shying away from "correct answers", and games in my classroom in the future when teaching my students Math!  This course has enhanced my love for Math and I am more confident now than ever that I will be able to teach the subject, thanks to Dr. Mary Stordy and Education 3940 :)

And of course, you know I can't do a final blog post without some hilarious math jokes! Hope you have enjoyed reading my Math Blog as much as I have enjoyed blogging about Math <3

(Hint: The square root of a negative number is "i")

Classroom Resources

Last Tuesday, our class had the opportunity to check out the resources from Kindergarten up to and including Grade 6 for the Mathematics curriculum in Newfoundland and Labrador.  I honestly did not know there were so many!!  I have been in various classrooms during my observation days and have always seen Math in the classrooms, but I have never really thought about the resources or how many there were for each grade.  What sparked my interest the most was the fact that K-2 have the most beautiful little picture books that deal with math but it breaks my heart to know that the colourful happiness ends there.  Starting with the third grade, they only have text books and workbooks, which are very dull I might add.  I can completely understand why children begin to shy away from math at young ages. 
In my experiences with tutoring Mathematics, children of any age enjoy when you give them things to do "outside" the curriculum.  For example, I would use games for my students so that they were not always just reading and solving the same types of problems over and over.  Some children benefit more from games than we realize because not only are the games very engaging for them, but they are also a fun distraction from the math that is involved.  I also think that students from the ages of 5 to 8 benefit from the math picture books shown in class because they are used to reading these in class and they probably do not realize just how much math they are learning while reading them.  I also do not agree with having these resources for 3 years then taking them out and using only a text book.  It would be like letting small children draw using markers and crayons and then all of a sudden giving them just pencils - it is a huge change that takes away much of the excitement and motivation. 
In the same breath, I am not saying that I think all grades should have these picture books because I understand that as the children get older and learn more, they will be given harder concepts with more thinking involved, but I believe they should have the bright illustrations in their workbooks as well.  When reflecting on going around to the different tables, I had the most fun at the Kindergarten through second grade tables because there was so much more to look at because I was most intrigued by what was inside these little books than I was when I looked at the workbooks and texts - it all appeared to blend together.
Chapter 4 of our textbook deals with planning for a problem-based classroom and there is a section that really got me thinking about the resources that I have seen in the past week.  The section deals with planning for all learners and how to differentiate instruction to fit every student's needs.  Not all students will be able to turn their textbooks to lesson 6 and complete the problems that are presented.  Some students find it easier to learn when there are pictures or graphs or some other kind of visual aid that allows them see exactly what the problem is asking.  I believe that the picture book resources would be great for these students.  Just because the students have outgrown reading simple picture books does not mean they are the only reasonable resources out there.  Take for the example the book that we were shown in class called Math Curse.  This would be a great book for students both younger and older, and there are many more that could be used, we just have to go looking for them! Here are a few I found by simply searching "Math books for children over the age of 7".  I hope to be able to provide my students with a resource-rich mathematics classroom in the future by using some of these books.

YouCubed

Yesterday I was introduced to a whole new Mathematics world - YouCubed! For those of you who are questioning what YouCubed is, it is an amazing resource for both teachers and parents to use with students in Kindergarten through to Grade 12. It is described as "a non-profit organization offering free K-12 Mathematics resources for educators and parents" by the site's leader, Jo Boaler. She is a Math Specialist at Stanford University who has become a driving force behind math change around the world. 

Although the site is not completely finished yet, I would still recommend that it be visited by educators and parents involved in Math. There are games for students so that they are not bored with the same everyday routine of "take out your textbook and turn to page 146. Do problems 1-9." There are more than ten games listed, with very detailed instructions - so detailed that a teacher could use them for a lesson plan for a change one day. There are also Apps listed that can be downloaded to a computer or mobile device for children to "play" around with. I think the idea of Math games are amazing. When children are playing them, they think it's just for fun and that there is no learning involved. When I have tutored in previous years, I would always "treat" my students with a game for doing so well. They would be so happy to have "free time to play" that they would completely forget they were being tutored! Little did they know, they were learning so much from these games. 

I have read a few articles associated with the YouCubed website and I have come across some very important information that has really opened my eyes. Some of this information includes the fact that each and every student has the potential to be good at Mathematics - we just need to teach it the right way. Math should be open and broad and we should be teaching various concepts that match the learning style of the student. There is also a huge difference in the Math we need in our everyday lives and what is being taught in classrooms today. In the article "The Stereotypes That Distort how Americans Teach and Learn Math" Boaler says "Students in the Common Core will spend less time practicing isolated methods and more time solving applied problems that involve connecting different methods, using technology, understanding multiple representations of ideas, and justifying their thinking." We should be teaching students not only how to do the problems in their book, but how to get to the answer, apply what they have learned, and justify their thinking or they will struggle with Math later in their lives. Another point that was made in this article that I view as important is the fact that we should not be pressuring children to get their Math done quickly - this will only promote anxiety. Allowing students time to think will do wonders for their minds.

For those of you who would like to check out this website, click here.  I can guarantee I will be a regular visitor and I cannot wait for the site to be complete.  I will most definitely be using it as a resource when I get out into the classroom and I will start telling every teacher I know about it!  I believe teaching Mathematics is very important and I think educators everywhere should have access to this free website!  I hope you enjoy it as much as I did :) ! 

What IS Mathematics?

After thinking, researching, and listening in class on Tuesday, I believe Math is the study of various concepts, such as addition, subtraction, division, multiplication, fractions, decimals, lines, graphs, patterns, theories, algorithms, and so much more.  It involves numbers, symbols, shapes, letters, measurements, problem-solving, word problems, and so on.  Math has been around for centuries and as time passes, more concepts and algorithms are added.  Math is not gender specific, though when asked to think of a famous female mathematician, I could not.  

To do mathematics means to solve problems using a specific set of steps which are learned through the knowledge of another person, generally a teacher. You can solve problems in many ways, including (but not limited to) mentally, using manipulatives, with a calculator, etc.  If you follow the set of steps with which you are provided, you may not always find the correct answer, but you generally have workings to reinforce your answer.

When you are thinking mathematically, you are thinking with numbers, logic and reasoning.  You are often using the knowledge you have learned about the various concepts of Math to figure out a problem.  Thinking mathematically requires you to think in steps or in a specific sequence and you are generalizing your answer.  Since math is a science, when you are thinking mathematically, you are thinking scientifically!

Photo from: http://www.mycutegraphics.com/graphics/school/school-kids/math-center.html

Do Schools Kill Creativity?

Sir Ken Robinson's 2006 TED Talk made me seriously think about how schools and teachers can kill the creative minds of children. Some of the things that Robinson said that I found very interesting were that creativity is as important as literacy and we should treat them both as equals. We, as teachers, are caught up in teaching children Math, Science, and Language Arts first and we let the rest fill in when possible. Not all students will be good at these subjects - is it fair that they should suffer through them and put their interests in other subjects on the back burner? I certainly do not think so. Another thing I found interesting was when he said children are not frightened of being wrong. I have realized that adults make them feel that way, especially in schools. We are always looking for the right answers and look down on the wrong ones. We are teaching kids not to take chances and not go to outside of their comfort zone. After watching this video, I have discovered that we all think this way and we prevent children from being original. This both surprises me and troubles me all at once.

I also found the story about Gillian Lynne to be extremely amazing. To think that she could have been put on medication to "calm her down" seems wildly outrageous to me. It is quite possible that we have already done this to many children. It would be very comforting to think that there are more people out there like her childhood specialist who, instead of diagnosing and labeling her, was able to let her talents flourish by suggesting her mother take her to a dance school. If there is one thing that educators take from this video, I hope that it is the realization that not all students who are distracted or not paying attention have a disability but may need to "move to think", as Robinson says.

Two things surprised me during this TED Talk. One was the fact that we get educated out of creativity rather than growing out of it. Once we go to school, our capacity to be creative diminishes and when it is not used, it is lost. The other thing that made me really think was the fact that every education system around the world uses the same hierarchy or subjects, in that Math, Science and Languages come first and the Arts come last. I have never thought about this before and I can now see how true that really is. This is outrageous to me, since not all children have an interest in these three subjects.

It is very troubling to me that teachers help to squander the talents of young children. Going back to the case of Gillian Lynne - her amazing talents could have went unrecognized if it was never brought forth that she needed to move to think. Isn't it our job, as educators, to bring out the very best in children and not to put them down in any way? I believe it is important to get to know each child in your classroom for this reason. It is also important to take into consideration Gardiner's Multiple Intelligence Theory when teaching, since not all students will learn the same way. I believe we were shown this video in class for this reason - so that we come to realize and hopefully prevent a student's creativity from being diminished because of school.

Math Autobiography

Photo from: http://www.uniqueteachingresources.com/image-files/caterpillarnumberlinestraightexample.jpg

I attended Cabot Academy in Western Bay, NL from Kindergarten to Grade 9.  I am currently doing my observation days here with the same teachers (for the most part) that taught me.  I loved the school growing up, and continued to tutor there from Grade 10 to 12.  I feel very honored to be placed at Cabot Academy and I am learning lots from my former teachers! :)

Growing up I absolutely loved Math and that continues today.  It was a subject I was always good at and I can remember my teachers encouraging me to help my classmates when they were busy with other students.  I always felt completely comfortable with until I completed some courses here at Memorial.  Though I may have had a hard time with some of the university Math, I still love the subject!

Though I don't remember much about Math in Kindergarten, Grade 1 or 2, I can remember it being a huge part of our curriculum from Grade 3 onward.  We had Math every single day and we had tests after every unit.  If some units were longer, it would be broken up in to two sections and we would have a test on each section.  In Grade 3, we had multiplication tables on the walls and one inside our exercise book and we were tested on them frequently.  In Grade 4, we used a burgundy book but I cannot for the life of me remember the title of these books.  I'm thinking that the books for Grades 5 and 6 were blue and green but I could be totally wrong.  I can remember posters with the addition, subtraction, multiplication, and division signs on them and a brief description of each of them in one of the Grades, but I'm not sure exactly which one it was. 

I can honestly say I have had great experiences with Math in Primary and Elementary grades.  My Grade 3 teacher would sit us all on the floor at the front of the room in a circle and play "Brain Quest" with us.  This was a question and answer game that she would put us in small groups for and I remember a fair component of it being Math.  Our class really enjoyed this game and it enhanced our Math skills.  In Grade 3 I can also remember my teacher assigning me problems from the Grade 4 text, and my teachers continued to challenge me in Math throughout the grades.  I had excellent teachers who provided a Math-rich classroom for us, so I don't exactly have any "bad" memories regarding the subject.  Because of this, I believe that my teachers had a passion for Math as well which has most likely influenced me in a way.  I truly hope that I can be as good of a Math teacher as they were.

In high school, I took Advanced Math and loved every minute of it.  I was always encouraged in school to do Math in university, so when I had to complete a focus area, I knew right away it would be in Math.  I have completed Math 1050, 1090, 2050, 2320, 3240 and Stats 2500 in university. 

I believe Math is a subject you use everyday and is essential for this reason.  I frequently use Math at work, since I work at a convenience store.  I use it when I am shopping to calculate my total before I get to the cashier.  We all use Math frequently throughout the day - counting money, estimating the time it takes to get to and from school, making supper with different amounts of things, and so on.

Photo from: http://www.featurepics.com/FI/Thumb300/20100305/Love-Math-1477252.jpg

Welcome :)

Hi everyone! 
Welcome to my Math blog.  Forgive me in advance but I loooove Math! 

The purpose of this blog is to share my experiences and ideas surrounding the subject, and to read others' opinions and get a sense of how their Math teachers helped shape these opinions.  I hope to gain a better sense of how to be a good Math teacher by reading about my classmates' experiences in Primary/Elementary School.

I look forward to reading your blogs :)