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Week 13 Summary: New ideas (April 9 - 15)

The semester is nearing its end! To celebrate the course, we will have a few Summary tasks. This should feel like looking down from a tall summit - at all the paths, valleys, slopes, and climbing walls that led up there.

During the course, you frequently said, "I never knew this idea existed" - for example, about ethnomathematics.


  1. Name five or so ideas, big and small, that you discovered for yourself in relation to this course.
  2. Define each idea your name - or the aspects of it relevant to what you do and where you are going, personally and professionally. You can use your own or found pictures, videos or interactives to illustrate your definitions, if you would like to add illustrations.
  3. Explain why you love or hate the idea, or your other feelings about it.

Diskutera uppgift

  • Carolyn   21 april 2012 21:49

    4. Math is fun/creative

    Again, I have always thought math was fun, well except for calculus. I enjoy finding patterns and different ways to find the same answer. That is probably my favorite thing about math, the fact that even though there may be one answer there can be many ways of finding that answer. Anyway, this course has just reinforced the fact that math can be fun and creative. I have learned so many different activities especially through blogs. The many answer to one problem has only been reinforced by these blogs that give so many activitues for learning thing. I can definitely say that I am walking away from this course with many great resources for making math fun for all.

    5. Learning and Play

    Once again learning through play is something I support in every subject. I believe play lends to self discovery, where kids can find out things on their own. I think not eveything needs to be learned in a classroom through direct instruction, there should be time for play and indirect learning. However with that said I think incorporating play into instruction is also important. Bringing in math games, or for that matter and subject, is essential. I will definitely be incorporating games and play into my future classroom

  • Carolyn   21 april 2012 21:37

    1. Math is Art, Art is Math

    Before this class I never really thought about Math as art, unless of course you count making Mickey Mouse using my high school graphing calculator and I even needed an app for that. However the more and more we began thinking about Math as art I started recalling how much art had been incorporated into my math education. Tesselations, graphing, and almost anything in geometry I had used to make art. I have also always considered myself a "math person" and not an "art person," nothing about me si artistic, but I have learned from this class that this may not be true. 

    2. Patterns are and issue?

    Who would've thought? I LOVE patterns and think that they are an essential part of math. Moreover there are patterns everywhere. I never would have thought that math educators were in such a dispute over patterns. I am all for them and again, think they are an essential part of math and teaching math. As I had said in the beginning of this class, I love looking for patterns and attribute them to my sucess as a student in math. Maybe it's just me but I am for patterns and plan on using them as a tool to help my students understand and learn math.

    3. I am not that "tech-savy"

    This isn't really anything about math directly, but I have learned so much about blogs and webinars and even twiitter from this class. I have never taken an online course before and I wasn't sure what to expect. Even more so, I would have never expected to learn so much more than math from this course. Coming into the course I always thought I was tech savy, but really I can just use my computer for Facebook and checking my e-mail. The world of blogs never interested me, basically because I never took the time to look at any of them. However this course, for lack of a better word, forced me into blogs and I couldn't be more grateful. I have really began reading different blogs, not all related to math, but I am appreciative for this new world this course has opened up for me. 

  • Laura Haeberle   15 april 2012 23:32

    Teaching Patterns in Math

    Firstly, I had no idea there was such a controversy about this! I never realized that teachers would be against teaching patterns in math. Granted, patterns and math are very closely intertwined, and I can see why some teachers believe that it doesn't translate to real life. But, math is everywhere, and patterns are a core aspect of math. In my own classroom, I want my students to naturally recognize the patterns of the world around them. I want them to embrace the Fibonnacci sequence with every pine cone they pick up! I want patterns to matter in their worlds, because I know that the simply discovery and critical thinking helps their math skills and their observation skills.

    Using Online Resources

    I never would have imagined how many teacher resources are available online! I always assumed there would be lesson plans and maybe articles, but there are multiple live, thinking communities of math teachers out there! This group on P2PU is one such example. When math teachers and experts get together, the results are fantastic. Interacting with some of the math professionals over this semester has made me think critically about various topics, and gave me a taste of online networking. Now, if I'm struggling with teaching a concept in math, I know there are supportive communities online! These same communities will let me know when new, important things are happening in the math world. 

    Using OERs

    Open Education Week really changed my opinion on OERs. Attending webinars was quite beneficial, as I was able to hear a real perspective on the topic of available resources. As a student, I was appalled that the textbook companies made so much money selling material that deserves to be free. As a teacher, I was intrigued by the idea of opening these resources, allowing both students and teachers the opportunity to learn without having monetary limits. It's a shame that the textbook companies have such control over these areas, and that resources are difficult to obtain because of the troublesome middleman.

    Connecting Math and Art

    I am also very interested in the connections between math and art. I knew that there were similarities, but I learned how to make the best of both together. In math, art provides a visual representation of topics, and really reinforces learning. It supplements mathematical concepts and brings information into a more digestible format. In art, math can be used for control and standards. There are many programs that allow students to play around with math concepts online, and test how changing limits and numbers affects what is created. There are so many areas of math and art that intertwine perfectly, and I can definitely use this knowledge to create some engaging lesson plans!

    Math is FUN

    Okay, so growing up I was never the biggest fan of math. I always considered it to be my most challenging subject, and doing it seemed like a daunting task. Through this course, I've learned some secrets to making math even more enjoyable! It all comes down to providing choices for learning a concept (board game? visual representation? neumonic device?), making the lesson engaging, and displaying the connections to real life. If children have a stake in their learning, they will be inspired to achieve. Children can't think of math as a hard subject or a boring subject, or learning will become a chore. Maybe I can even get my kids to learn math without realizing it!

  • Kathy Cianciola   12 april 2012 23:40

    Many Activities

    This course inspired me to see that teaching math should involve more than simply addition, subtraction, multiplication, division and mathematical calculations. Activities such as dance, making patterns, creating art and learning basic computer programming can be effectively used to teach mathematics. 

    Math Is Everywhere

    The course also inspired an awareness that mathematics can be found in many unexpected places, crochet, movies, fun computer games.  As a matter of fact, My son and I had been playing many of these without being consciously aware we were even doing math!  (chocolate-covered broccoli). Math, indeed, is all around us, and is an integral part of everyday life.


    Having a theme that really fit my philosophy, "Letting The Child Lead," helped guide my ideas throughout this course.  I am an Early Childhood/ Special Ed major. Since I'm leaning toward working in the field of Special Education, I know that many of the hands-on, kinesthetic  ideas I've gleaned from other students, and from this course, will help with my work in this field. 


    Although I still don't consider my self a math expert, I feel like I have been given a nudge to learn more.   I really loved Scratch, and I would like to do more with programming (if I could ever find the time).  

    Many Choices

    I really liked having the freedom to explore, and being given choices.  I think this is something that most students appreciate with regard to learning.

  • Carolyn Lesser   12 april 2012 15:37


    Math as art

    I think this was probably one of my most favorite weeks. I, like Sandy, never really thought of math as art. Now I see that math is its own kind of art! As a prospective elementary teacher I will definitely be dealing with math and I will be making art a big part of it. Looking at math from this perspective makes it more interesting and visual which can be very helpful for students and my own learning.  

    Math and computer aids

    This was my first online class so it was very eye opening how much you can do on here! Of course being 20 in this age I use the computer constantly and use it to look up information and do work but I never thought of really creating aids to help in math learning. Scratch was really cool and I think if I practiced more with GeoGebra I could get a lot of use out of that as well. I can definitely see myself using these kinds of sites in my teaching and for my own learning.  


    Again with things on the computer! I really enjoyed participating in webinars and other networking choices. I never used webinars before but I see that they are a great way to communicate new and upcoming ideas and to just staying on top of things. At first I was nervous doing these live chats but after a while I started becoming more comfortable. It is a good way to meet new people as well and to make connections throughout the world. Making these connections give us a much bigger perspective of the world around us which is something that is important to me. I was also introduced to a lot of webinars that deal with education which is great and something I can continue to follow for years!


    I liked the fact that we got to help create a Wikipedia page. In my summer intern I was supposed to help create a page for a company product and I was totally lost but when I go back this summer I will be able to do a much better job. I never got into wiki before this because as a student my teachers said never to use it and that the information isn’t always reliable. This could be true but it is a great starting point to learn basic information. I think as teacher I might be able to create some kind of project for my own students to do which would really help them to see how these kinds of sites work. It would be very informative just like it was for me and with the way our society is going technology is just going to become more important all the time!

    Math and play

    As a young student I remember playing review math games and having fun. However, I don’t really remember any learning math games, they were purely for review. If you didn’t know the material then you really couldn’t participate. From this class I see that you can create the type of games that teach the students as well. Actually the one MIT webinar I watched talked about a game called Lure of the Labyrinth which was a wonderful example of a game that would teach students about working with puzzles and problem solving. Incorporating games and play is fun for all ages and helps to engage students. I think this is the real key to getting kids excited about math!

  • SandyG   11 april 2012 09:08
    1. Math as art

    I love art: the symmetry and use of juxtaposition to convey emotion and create images.  Other than for geometry, I had never seen art used in a classroom in the way that we discussed.  Now, though, I say “of course”!  I think math and art make an obvious team, and I think it’s a great way to reach students.  

      Something beautiful; something mathematical. 


            2. Math can be fun- games

    This was totally a foreign concept to me.  The reason I waited until my final semester to take the one required math course for my program was because I didn’t think was fun, and I had no expectation that I would be able to do well in the class.  I can’t even express my astonishment when I realized a few weeks ago that … I can’t believe I’m saying this… I LIKE this math class.  I really do! It has been so interesting to see how games and art and computers can be used to change up the tried and true rote fashion in which my math classes were taught.  Though I don’t profess to understand mathematical operations any more than I did previously, I can see how math can be fun, and if I happen to teach a special education class in which I must provide some math instruction, I will certainly revisit some of the tools we discussed in this class. The great thing is there are so many free tools to be used on the internet such as


             3. Modern math

    When I first saw that we would be discussing modern math, I was unsure what that meant.  It seemed to me that unlike English that is alive and evolving every year, math seemed unchanged.  After attending #mathchats on Twitter, I see that there is as much debate in the math world as there is in the world of languages.   The ideas aren’t as old as Pythagoras, and they have changed and are changing.  There is active debate over seemingly many issues in the math world, and it seems to be a very active, inspired community.


       4. Digital storytelling in math

    Digital storytelling is an obvious tool for language arts and social science departments, but I would not have thought to use it in a math course.  What a great idea, though!  A math teacher in my building does a project with numbers using video cameras, and I’ve seen the students enjoying the process, but he also does something called “math formals”  twice a year—he wears a tuxedo to school and his students all dress up in their “Sunday best”.  High school boys actually come to school wearing ties!  The whole purpose is to show “math pride” so that when other kids see them, they’ll know “oh… he/she is a math student”, and if they have 100% participation, the class period is treated to fun activities and a snack—with math worked into every part of the time.  When I looked for my required video for the task, I found a story made be students on Youtube, and it was obvious that they were motivated and took the assignment seriously but had fun.  I thought it was fabulous to combine something creative, fun, and digital with math.


              5. Number sense

    I admit that when we had to originally come up with our concepts for our first assignment, I Googled “math concepts” and number sense came up so I listed it.  I had no idea what it was!  I do now, though.  I completely understand the idea of making math relevant and part of the real world.

  • Maria Droujkova   12 april 2012 08:51
    Som Svar På:   SandyG   11 april 2012 09:08

    Sandra, as you can imagine, your response to this task makes me happy. In designing this course, love and beauty of math were main goals. But a professor can't just broadcast beauty or love - they grow through actions of people experiencing them. You worked hard in this course, and your work took you to a happy world - more precicely, your work built a happy world for you - where you now experience playful, beautiful math. What an epic journey! Well done, Sandra!

    There is some unexpected treasure along the path you are taking, by the way. You don't "profess to understand mathematical operations" better than before. You may find yourself - if not now, even though I can point out where you've done high-quality math in course tasks, then later - seeing operations and other formal math in a new light. You will be asking different questions and focusing on different aspects of math - those that make sense and seem beautiful and interesting to you, personally. This layer of personal meaning and significance makes all the difference in the world, for mathematical understanding. Parents and teachers I know tell me so. People who, as adults, begin to see the beauty and fun of math activities, also begin to understand math better - without even trying.

  • SandyG   12 april 2012 17:18
    Som Svar På:   Maria Droujkova   12 april 2012 08:51

    It has been a very suprising journey!