My "Greatest Math Learning" this Semester

This math course has been valuable to me in many ways and I find if difficult to decide what "greatest math learning" that has occurred for me this semester. As a future teacher what is most important for me in this class is discovering ways to teach student Math is in the most effective way possible. When I think about what "learning" would best help me to achieve this goal, I believe that the most important thing that I've taken away from this math course is the idea that it is endlessly beneficial to math math "real" and meaningful for students. 

So what do I mean when I say it is important to make math "real" for my students. Well to me it means taking a subject that often appears very abstract to students and making it concrete and relatable for them. It means coming away from teaching students that math works "because it works" or that they've come to the right answer because they've remembered all of the right "rules" for solving an equation, and moving toward teaching them why and how it works. 

So how could a teacher go about making math "real" and meaningful for their students, one might ask. Through this course I have learned many ways to do just that:

1. Show students that math is all around them. 

Math is everywhere and we use it everyday. We use it when we go grocery shopping, when we tell time, and even when we decide what clothing we're going to wear for that day. When students are able to see the many ways we use math in their daily lives, they will see the importance of math. Seeing the math all around us makes math real to us. Counting stops just being a serious of words that are "suppose" to go in a certain order, but instead may decide for a child whether they will know if they're getting an equal share of divided candy, or not. 

2. Make math relevant to your students. 

Math will become more concrete to students when the math they're learning is related to a concept they're already familiar with. For example, when teaching students about parameter it is often more valuable to a child to teach them parameter in relation to a fence, which they will already have some knowledge about, rather than a geometric figure that will have very little meaning to the student. 

3. Use manipulatives in math. 

Manipulatives deepen students understanding of a mathematical concept by allowing them to see and touch math. A concept such as a transition of a geometric figure has much more meaning for students when they can move the shape themselves and see and feel the way that the shape moves. Many different manupulatives exist for various math concepts and often a manipulative can be homemade without too much hassle. Manipulatives help to make math real for students by letting them manipulate the math itself. 

4. Show students the connections between mathematics.

Students will gain a deeper over all understanding of math concepts if they are exposed to the ways that math interrelate. The concept of percentages may become much less abstract when it relationship to division is revealed to students. My understanding of many mathematical concepts was enhanced through the few connections I was exposed to in this course over this semester and through observation of my class it was quite easy to see the benefits of doing this for a group of students. (I could see many light bulbs turning on over my peers heads!) This may mean that the teacher will have to research and discover the many connections of mathematics for themselves if they don't already know. 

5. If students ask a question, do not "lie"

Lying to students about concepts in math does nothing but confuse students and makes math harder to grasp for them. If a student has not yet learned about negative numbers but asks about numbers under zero, it is more beneficial for a teacher to answer the student as honestly as possible rather then simply telling the child those numbers "don't exist" just because they don't need to learn them yet. 

6. Do not just teach that math is, but teach why math is. 

Don't just teach math in a "it works because it works" way but show students why it works and help them reach a deeper understanding than memorization of formulas and "rules". 

Math can often be a subject that various students struggle with, and it is one of the subjects that makes me anxious to think about teaching. This mathematics course has made me much more confident in my ability to teach primary/elementary mathematics. The "greatest" learning I have taken away from this course, that will help me be a better math teacher for my students in the future, is the importance of making math meaningful and real for students and how to accomplish this for students in the primary and elementary classroom setting.

K-6 Math Resources

During this weeks class, my class and I were exposed to the math resources that are made available to all teachers teaching in Newfoundland and Labrador. Although I have worked with the mathematics curriculum guide in the past this is my first exposure to resources outside of the math curriculum. I found my encounter with these resources both informative and thought-provoking. 

Many of the resources were very beneficial, particularly the "Big Books" and story books that are available in the primary classroom. These colorful and fun primary math resources make abstracts mathematical concepts more concrete by relating them to real life concepts. For example, one of the primary books was on the concept of money and this book teaches students about money through something which all students will be familiar with - purchasing items. These children math book resources promote problem-based learning through teaching math concepts through finding solutions to real-life problems which promotes deep understanding. Also the "Big Books" are a size that will be fun for children with illustrations and text that is at a level that is appropriate for the students. 

I found these books to be very beneficial resources for primary, but it disappointed me to see these interesting and fun types of resources for students fade away.  It appears as though the general belief is that these students are older and "mature" and thus do not need visually stimulating and appealing resources to learn anymore, that students can just learn through lecture and examples. Learning in a way that is fun and that relates to what students already know is beneficial for students of all ages. As future teachers we must keep in mind that we are not restricted to using only the resources given to us by the Newfoundland and Labrador school board, but that there are many fun and interactive resources available for teachers at stores, online, and at public libraries. As a future teacher, I will bring my own interesting resources into my elementary classroom to make mathematics fun and appealing for my students to support their learning of the math concepts. 

Although the elementary resources did not include interesting resources for the students, the resources provided were still very beneficial for teachers. Many of the activities, in the teacher's guide and the math textbooks that I read were activities which promoted group work and problems solving techniques that require students to think critically. Although I believe the activities in the Math book were very useful and beneficial, the text books were often written in a way that I believe would be above many students reading level in each grade. The way that the problems in the book are written appeared to be confusing, even for me. As a future teacher, although I will use these resources to find ideas to use in lesson plans to teach math concepts, I will not expect my students to learn any concepts directly from the math book. The students in my class will be at various different developmental levels and not all students will be able to learn the way the lessons are taught in the text book. I will take activities out of the resources that I am provided and I will modify these activities to fit the students in my classroom.

As future teachers it is always reassuring to be exposed to the resources that we will have at our disposal when teaching different subjects. At times it feels overwhelming to think that as a future teacher we must create lesson plans for every subject, every day of the school year, from scratch. Being exposed to the math resources reminds me that I am not expected to come up with ideas to meet the objectives all on my own. I will be given resources, and I will have access to many more resources, to aid me in creating the lesson plans in my primary/elementary classrooms. 

Do Schools Kill Creativity?

When I attended primary/elementary school, there was little room for creativity.

Instead, my teachers concentrated on processes such as memorization. On many of my tests teachers have written that the answer that I had given was "technically correct" but was not the answer they had given us to give back to them. What they would have preferred was to have me regurgitate the exact information they had given me in previous classes.

 Why was creativity not seen as more important? In Sir Ken Robinson's TED talk titled "Do Schools Kill Creativity?" Sir Ken Robinson explores this question and gives his take on the subject. He believes that children as a whole have an extraordinary ability to be creative, and that through going through our education system this ability is stripped from them. Ken gives many reasons for why he believes this to be the case.

Sir Ken Robinson believes that the ultimate goal of the school system is to create students prepared to enter university. The subjects valued in university are subjects such as math, science, and literature. Subjects in the arts, that revolve around creativity, are seen as much less valuable by our society. Students who excel in the arts are often to feel as if they are stupid because they do not do well in the subjects that are seen as important, and they're not given the opportunity to work with what they are good at. These students are taught that what they're passionate about, or good with, is insignificant and the child abandons their talent and struggles with what the education system has deemed as important.

In the TED talk video, Sir Ken Robinson talks about a particular case of a young girl who is a dancer. The child is hyper and fidgety in class, and doesn't excel at the core subjects, so the parents and her teacher assume that the child has something "wrong" with her. Luckily, the doctor she was taken to realized that her talent laid in her ability with movement, and she was able to attend dance school. This is an important lesson to me as a future teacher. If a child is struggling in the "core" subjects than instead of assuming the student is effected by a learning disability, I will attempt to find where this child's intelligence lies. If a child is hyper, I will find out if the child works well with movement, rather than giving them a diagnoses of a hyperactive disorder.

Sir Ken Robinson talks about the diverse and dynamic nature of intelligence. Although we're aware as educators that these different intelligence exist, we're often guilty of not putting this theory into practice. As a future teacher I will do my best to support all of my students talents to the best of my ability in the rigid school setting I will be working in. I will try to teach in a way that is valuable to all types of learners, and I will support my students in the pursuit of doing what they love to do, and exploring where their talents lie.

YouCubed - Revolutionizing Mathematics

YouCubed is a non-profit, web-based website that offers mathematics resources for both educators and parents. YouCubed revolutionized approach to mathematics attempts to offer research based resources to help teachers and parents excite students and promote a deep understanding of mathematics - and ultimately to transform the way that students think about math. YouCubed promotes the idea that all students can learn and achieve high levels in mathematics equally if given equal opportunities and exposure. The YouCubed organization also promotes learning mathematics in innovative ways that introduce students to the ways that math is used to solve problems in their lives and possible future careers. 

YouCubed is an excellent resource for my future career in teaching mathematics in the primary/elementary classroom setting. This website, once it is fully operating, will offer an abundance of beneficial resources such as lesson plans, and research articles, that will assist me in creating a classroom that fosters excitement and deep understanding of mathematics in my students. The website has already offered me some insight into the organizations revolutionary approach to teaching mathematics in the articles featured in the big ideas portion of the website Big Ideas titled "Unlocking Children's Math Potential". This article dispelled the myth that only some students can do well in math through explanations of the areas of knowledge that address the myth. This article began my initial excitement about this website as a beneficial resource to use in my future teaching. 

The website YouCubed also offers teachers some excellent and thorough lesson plan ideas that utilize these revolutionary ways of  thinking about teaching mathematics, such as "Crazy 8's Club: Glow in the Dark Geometry" - a innovative lesson plan for elementary-aged school children. These lesson plans are great for teachers because they show teachers what a lesson plan that uses this revolutionary approach to mathematics may manifest itself in the classroom. These lesson plans also cover all of the necessary aspects of a well thought out lesson plan such as the necessary background knowledge, materials needed, and the objectives that the lesson plan is teaching toward. 

The current YouCubed website also offers an example of the resources the website will offer to help teachers to relate mathematics to real life problems for students through the organizations math and innovation approach. This example provides students with a problem that the Google company had faced recently and how the company used mathematics to solve the problem. I believe this approach is beneficial for students because relating what they're learning about mathematics in their classroom to a real life standing will reinforce their understanding of the math concept and will promote deep levels of understanding for the students. The YouCubed websites provides teachers with real life examples of how to accomplish these connections to real life issues. 

Finally, one of the most exciting aspects of this site for me as a future teacher, is a section where the website provides ideas and resources for parents to use to assist their children with mathematics outside of the classroom setting. I have learned that it is often difficult for teachers to find effective materials for parents to use at home, and I have also heard similar complaints from parents of students who are struggling with math concepts. YouCubed offers parents resources such as YouCubed games, and articles such as "Twelve Step to Increase Your Child's Math Achievement and Make Math Fun" to assist parents in helping their children learn in this revolutionary and innovative way. 

YouCubed is a fantastic, revolutionary, web-based organization that offers free K-12 mathematics resources for teachers and parents, and affordable professional development for educators. I will use this exceptional website resource to assist in my teaching in my future primary/elementary classroom to promote an interest in math and a deeper understanding of the math concepts in my students. I will also recommend this website to the parents of my students who are looking for extra beneficial resources for students to use at home.

What IS mathematics anyway?

When you think of mathematics what do you think of?

When I think of the question "what is mathematics?" I immediately think of concepts such as formulas, problem solving techniques, geometry, numbers and simple equations such as addition and subtraction. I've never truly thought deeply about what math is or how one could define it. After conducting some research I feel I have reached a better understanding about what math is.  

The first idea that became obvious during my research is that there are many different definitions of mathematics. Math is defined in many different ways for many different people. An article called "What is Math?" by Wendy Petti claimed that Bertrand Russell defines math as "the subject in which we never know what we are talking about, nor whether what we are saying is true." I believe that this definition alludes to how little we know about what exactly mathematics is or how to define it. 

It is important for teachers to define what mathematics means to them, so they can decide how to provide their students with the best education in the subject. Like all subjects, a teachers over all plan for a school year will be much more effective, deliberate, and purposeful if the teacher has a clear objective for his/her students, than if a teacher is basing what they teach toward on various opinions and definitions on what math is. 

What are some of the definitions of math?

The online dictionary (dictionary.com) defines mathematics as:

"The systematic treatment of magnitude, relationships between figures and forms, and relations between   quantities expressed symbolically."

This definition is what many people think of when they think of math and covers very important aspects of what Math is, but it is through definitions such as the definition given by  Elaine J. Hom in his online article titled "What is Mathematics?" that we realize that math can be defined as much more than this. Elaine Hom defines Math as:

 "...all around us, in everything we do.'Math' is the building block for everything in our daily lives, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports." 

This definition points out that math is more than just math equations on a worksheet, but math is a gigantic aspect of our daily lives. All of us use math on a day to day basis; when shopping, playing, reading time, through music and counting, in art, and in many other everyday activities. Usually during these daily activities we don't even realize how heavily we're relying on mathematics. 

I made the important realization that math was much more than numbers and formulas but a necessary concept that we use on a daily basis. This realization is important to realize as a future teacher because this shows the possibilities of relating the subject to what is relevant in our students daily lives. This discovery also helps to guide the definition I create for myself as a future primary/elementary mathematics teacher. 

What is mathematical thinking?

 

Mathematical thinking is what students need to perform the math activities they encounter in the classroom and in their daily lives. It is a teachers goal to teach their students to think mathematically, but what does mathematical thinking mean? When I think of mathematical thinking I think of trying to figure out how to approach a problem, and then deciding the steps to take in order to solve a problem. An article by Kaye Stacey titled "What is Mathematical Thinking and Why is it important" states that mathematical thinking includes "components... such as reasoning, modelling and making connections between ideas."

Although its important to teach in a way that recognizes and enhances these processes, it is important to realize that we take part in mathematical thinking often in our daily lives as well. When I decide what time to leave my house to catch the Metrobus in the morning before school I am taking part in mathematical thinking. Because mathematical thinking occurs in our everyday lives, it is possible to teach the skill in a way that is natural for the students. 

Having a better understanding of math has many implications for me as a future teacher. I learned that there is not one specific definition of math and that teachers must create their own definition to create a plan with direction and purpose. I learned that math is defined as more than numbers and formulas, and mathematical thinking is more than processes, but these concepts take place in our day to day lives. I believe that this is important to me as a future teacher because now I will teach to the real life implications of math as well as the "technical" aspects of mathematics. 

Welcome

Welcome to Jody's Mathematics Blog 

Hello and welcome to my Math blog. In this blog I will be discussing and sharing some of the key concepts that are covered in my Education 3940 course. These concepts will surround learning to teach mathematics in the primary/elementary classroom setting. I look forward to viewing and learning from similar blogs available on this topic. I hope you enjoy my blog and that you discover some valuable resources and information valuable to you in your future teaching careers.