My Greatest Learning

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

My greatest learning this semester:

I went into this course expecting to learn everything that I experienced in primary/elementary math class, but from a teacher's perspective. Things such as, ensuring we knew how to do math (multiplication of large numbers, long division, and solving problems with a given formula) or how to develop math tests and assignments. I was completely wrong. 

 I have learned that we do not need to give tests as a way of assessment. Instead, providing students with fun, interactive problems that are opened-ened is suffice. As well, allowing the students to be creative and providing them them with the manipulatives that they need to answer a question will also help. This way, the students are not faced with questions that only have one right answer and one right set to manipulatives to use.

 The math fair was my favourite activity and possibly where my greatest learning came from this semester. From this activity, I realized that I would want my students to take chances and to not be afraid to make mistakes. Also, through this activity, the students are in charge of their learning and helping others learn new problems. 

Most importantly, I have learned that discussions, which never happened in my previous math classes, should occur after every lesson. Its a way that the students can bring all of their ideas together to see what they realized about a particular problem. One fantastic thing about group discussions is the fact that the students can share different ways of approaching the same problem and seeing the problem from a different point of view. 

Implementing what I have learned into my future classrooms:

In my first blog I said, "I don't have any "best" memories surrounding mathematics in primary/elementary...However, I can tell you about my worst memory." A common statement that has been and will continue to be used by students unless I take what have learned through this course and change the mathematical experiences for my future students. 

My thinking about math has shifted as I learned what math truly is, read recent research, and looked at different math resources. I do not want them to have negative experiences because the learning was too difficult, not fun, not motivating. I will be sure to take what my greatest learning from this semester and implement this into my future classrooms. Evident from this class, I am capable of teaching mathematics and I am continually learning mathematical concepts, ideas, and activities to use in my future classrooms. I will take what I have learned from this course and ensure that my future students will enjoy mathematics in primary/elementary the way that I never experienced until now.

K-6 Mathematics Resources

On Tuesday, February 25th, our Math Education class perused the resources for K-6 students and teachers in Newfoundland and Labrador. Luckily, our table got to start with kindergarden and work our way around the classroom until we got to grade six. As in our textbook on the section about Stations, this was a easy way to manage the materials. The materials stayed in one spot and we move to them. There was also enough resources on each table for each person to have their own individual text to look at.

The one thing that really surprised me was that there was such a dramatic change in these resources as the grade level increased. Kindergarden was filled with bright, colourful picture storybooks (some of which were actually around the size of a young child). The font was large and limited. As the grades progressed, the font got smaller, the text became complicated, and the colours vanished. The older students now have to use a textbook filled with samples on how to do a question, then a long list of practice questions. In chapter four of our text, Planning in the Problem-Based Classroom, the authors describe the process of drill and practice. From what I seen in these resources, there was a combination of both of these. However, teachers should take the time to review all the resources for a particular grade to integrate more practice, problem-solving than the disliked drilling of procedures. It makes learning more fun for the students.

What I like about the resources in all grades was the potential for the students to participate in problem solving. For instance, it might have been in a grade four teacher's guide, where I seen a worksheet that the students can complete. On the page, the students had the chance to create their very own problem and then solve it using number sentences. This would be a great way for the students to be in charge of their own learning.

Teachers should be reminded that textbooks, curriculum, and other resources are just guides. Its up to the teacher to develop good problem-based mathematics classes for the students to have a beneficial math experience. It is our goal to determine the task we want to present to the children and develop a sufficient lesson plan that accommodates the needs of all students and then reflect on this approach. In chapter four of our text, there are 10 steps that teachers should implement into the development of their lesson plans. 

Text: Elementary and Middle School Mathematics: Teaching Developmentally by: Van de Walle, Folk, Karp, and Bay-Williams (2011).

YouCubed

                            © YouCubed

YouCubed is a non-profit organization that offers free online mathematic resource for K-12 students and their teachers and parents. Jo Boaler, math specialist and leader of this site wants everyone to know of the "mathematical revolution." Through the use of this site, teachers will be able to reinsure that their students are engaged in fun, inquiry based learning in mathematics with the use of various lesson plans, games, and up-to-date research articles and news.

I did not know about this website until recently. I perused the site, read-up on recent studies, games, lesson plans for the teachers, and resources for the parents. I like the idea that students should be learning about real world mathematics in a fun way. As we have learned, deep learning happens when children are interested in what they do.

I would like to comment and reflect on what I have read in some articles that I found interesting and surprising. Firstly, in Twelve Steps to Increase Your Child's Math Achievement and Make Math Fun we learn that we should not call a child "smart." Wow, I have never thought about this previously. "You're smart!" is usually spoken as a positive comment. However, after reading this article, it can actually dampen a child's spirit if they happen to fail. Be reassuring that everyone makes mistakes and that we learn from these times. Also, we have reflected on our "worst" moments in math, but it should not be discussed with your students. In Unlocking Children's Math Potential: 5 Research Results to Transform Math Learning I read that we should not make the children work faster during mathematics because it causes anxiety. Almost everyone can remember this aspect of their schooling experience, including myself. As a future teacher, I will incorporate this practice into my classroom to make sure that math is not a hurry-up-and-get-the-answer type of subject, as what I had experienced.

The most important aspect of this site is the parents ability to access new materials that they could use at home with their children. What they learned years before (or happened to forget) could be completely different than how their children approach solving a problem or learning a new concept. As the mathematics teacher, you should also review this site with the parents and students to ensure that they understand how to use the site.

Overall, I think that this site is well organized and is easily accessible to teachers, students, and parents. Learning should be authentic, meaningful, and motivating. It is our job to unlock our students' mathematical potential  Hopefully more people will learn about this site (not yet fully operational) and join YouCubed's mathematical revolution to ensure all students are achieving to their fullest potential. I signed up to join the revolution so that I will be updated on the resources and content that is added to the site. YOU should too.

What IS Mathematics?

After being subjected to mathematics for practically my entire life, I have never actually thought about, "What IS mathematics?" ...Uh, a subject with numbers and stuff? (Jokes).

Off the top of my head, I would define it as an important subject that involves numbers and practiced equations that we can use to benefit our daily lives. To be honest, I could not think of a good, elaborate answer to this question on my own. Therefore, I done some research to expand my knowledge on mathematics. I know that Wikipedia is considered a "non-creditable source" in university, but I seriously love Wikipedia. So, the various users have defined Math as, "the abstract study of topics, such as quantity (numbers), structure, space, and change" (Wikipedia, 20 January 2014). After hundreds of years of theories and practice, mathematicians have created what we know as math today. We have been learning bits and pieces of math since that first day of Kindergarten (and maybe even before that, learning the concepts of numbers at home with your parents/guardians).

So, what does it mean to do mathematics? It involves a wide variety of mental skills and abilities. It's not just putting that pencil to paper to answer a multiplication question or plugging in some numbers on your calculator. We actually reflect on what we have previously experienced and think about how we can apply that knowledge. Within our course textbook, the authors (Van de Wall, J., Folk, S., Karp, K., Bay-Williams, J., p. 11) say that to do mathematics, it involves a number of verbs to understand the task at hand. The list is as follows:

explore            represent          explain

investigate      formulate          predict

conjecture        discover           develop

    solve              construct        describe

justify                verify                  use

Each one of us remembers using at least some of this actions to "do" our math at some point. I have used 14/15 verbs that I can remember, for sure.

If a person is thinking mathematically, I think that they are using their mathematical/logical intelligence described by Howard Gardner (1983). We use our knowledge about numbers and try to get an answer based on our mathematical skills. For instance, when I go to the grocery store and compare the price of two items of different weights to see what the best deal is, I'm thinking mathematically. When I count the hours of sleep I will get every night if I went to bed at a certain time or when figure out what bus I need to take to school to make sure I get to my classes on time (given that the buses are usually running late or that there may be traffic), I am thinking mathematically. I believe that every person thinks mathematically to some degree. If we were not exposed to math throughout our lives, then we would not possess this ability. Therefore, it is important for our future students to "do" math and learn different ways to get their answer to be successful members of our society. MATH IS EVERYWHERE.

After our class today (January 23rd), we shared our ideas about mathematics. In our group, we summed up what we learned in the following web:

It may be hard to see, but we said that it is human created, an art, misunderstood, and abstract. Even though we had plenty of similarities, it was nice to see how everyone else in my class viewed mathematics. This activity helped me realize that we all have some idea of what math is, what it means to do math, and think mathematically. Hopefully by the end of this course, we will all have a good understanding of mathematics and how to use this knowledge to teach our prospective students.

Sir Ken Robinson - Do Schools Kill Creativity?

In this hilarious, yet very informative TED Talks video, Sir Ken Robinson explains to his viewers how schools are killing the creativity of their students. I whole-heartedly agree with his point of view. What I found interesting from his lecture was the fact that we are all born with creativity. However, we are not encouraged to pursue these skills. Instead, core subjects like Mathematics and Language Arts take up the majority of the teaching time. As prospective educators, we can change this. Well, maybe not change the standards, but we can integrate the arts into these core subjects to allow students to use or find their talents.

Primary/Elementary teachers should always keep in mind that all students are unique and learn differently. We can help our students in their daily math classes by integrating creativity through the use of the arts. Students of all grades can use their imagination to expand their knowledge in this subject. For instance, they can create and develop questions/answers, design graphs, or explore using manipulatives to name a few. As teachers, we do not need to only make these learning experiences for our students efferent, but make them aesthetic. Our mathematics lessons should be interesting, fun, and memorable for our students.

Creativity is important. Let's encourage it, not fight it.

I hope you enjoy this video as much as I did. 

Math Autobiography

To begin a new course about teaching students math education, I must first reflect on my past and current schooling experiences involving mathematics and input my thoughts and ideas about what I had encountered.

Mathematics in my primary/elementary classrooms was pretty average (no pun intended). We had our textbooks, multiplication and division facts posted on the walls, and we usually sat in groups to do our seat work. The teachers would show us something new, then we would do our assigned work. We got to use manipulatives, like the geometric or base ten blocks, which always made class more fun.  

I don't have any "best" memories surrounding mathematics in primary/elementary. Overall, class was usually good. However, I can tell you about my worst memory. In grade four we were introduced to rounding and I could not wrap my head around that concept. So, when the teacher called on individual students to recite their answer to the questions, my answers were always wrong. I got additional help to learn how to round, but sadly it was not from my teacher. I also remember being given multiplication sheets to complete as a race with our classmates. You would think that since I can only recall bad memories that nowadays I might not like math. However, I am the complete opposite. As I got older, I became more motivated and had better teachers as the years progressed. I have learned from some of my teachers on how I should and should not teach my future students. Math shouldn't be a competition because that discourages students and causes them to become unmotivated. As well, teachers, no matter what subject they are teaching should always offer additional help if necessary. Even if it is a simple topic, such as rounding.

During my primary/elementary years, I was good at math. I just did not have the motivation to do my school work. I usually understood the concepts fairly well and done my work in class. However, I would never do homework, which I now realize is important to further our understandings.

I am sure my teachers felt that mathematics was an important subject (and it sure is). They were always prepared for class, offered varied instructions, then would walk around the class to monitor our progress.

The assessment my teachers used to ensure we achieved the outcomes was usually in the form of unit tests and assignments. They probably used anecdotal records or checklists, but I cannot remember. I believe that all forms of assessment should be use to ensure the students have achieved the mathematics outcomes and can provide the students' parents/guardians with a multitude of evidence on their child's success or struggles.

Once I got into high school, math became much more interesting to me. I was enrolled in academic math and in grade twelve I was in both academic and advanced math classes. I think high school math was a better experience for me because my math teachers wanted to be math teachers. It is what they spent their entire life focusing on, therefore they knew the best way to teach a concept. My teachers would even offer additional tutoring, especially around finals/publics. Also, SMART boards and the use of technology was integrated more into the classroom by those years, which made math more interesting and fun. To add, I was also a Mathlete. I worked with a few other students in my class and the grade below us in math competitions in different districts across Newfoundland. This is surprising, right? I went from a student who was not motivated to do her homework, to a person who had an extracurricular activity in mathematics! 

In my past four years in university, I have only taken two math courses thus far. Math 1090 and Stats 2500.

This time last year I was enrolled in Education 2900, which is an distance statistics course that I took for my Education elective.

Mathematics is everywhere in my daily life. One instance would be that I am the Treasurer of the 2013-2014 Primary/Elementary Education Society, therefore I collect, count, and record all funds for our upcoming events. Its a very important duty that requires mathematical and organization skills.

Nowadays, I really do enjoy mathematics. I no longer find it hard and enjoy learning new mathematical concepts.

I am excited to see what Education 3940 has to offer me and I am sure it will aid in my future teaching ability as a primary/elementary mathematics educator.

Welcome!

Welcome to my Education 3940 blog. The purpose of this blog to to integrate mathematics and technology and to post my knowledge and understanding towards math education as I learn new things to apply to my future primary/elementary classrooms.