What We Learned This Semester

It is the final week of classes so it is my turn to write the blog post—unfortunately it will be the last post until January 2014.  I will continue this blog the next time the course is offered.

This is the first time that I have taught this course by myself.  Recently someone said that a teacher should ask “what have they learned?” rather than “what have I taught?”  This class is definitely a good class to ask the first question since I don’t think that I have really taught my students anything.  However, I am fairly certain that they have learned lots of things.  So, with their permission, here are their answers to the question, “what have they learned in Math 371?”

From Leanne Holdorf:

Of all my classes this semester, Math 371 is by far my favorite. I was able to dabble in technology that I didn't think I'd have access to for a while. We explored different programs and applications that will help me as a teacher. And I really started to understand why technology is so important. It captivated me and made me excited to learn more. That's what technology is meant to do in a classroom. It is not simply there to make life a little easier but to also engage students in new and different ways.

From Kaitlin Ward:

I have learned how to use Ipads effectively in the classroom. I have learned what apps I might use in my classroom, and what apps I know I won't use because I didn't find them very useful. In addition, I have learned more about what different schools are going one to one. I have learned how to create videos that I could use if I choose to do flipped instruction. I have learned how to use programs like Voice Thread to help make my lessons more engaging. Overall, I feel like I have a better grasp on different programs and apps that I can use to help engage my students in the classroom.

From Jackie Currier:

     In math 371 I have learned how to use different technology in ways that apply to the classroom. We learned how to use a ti-nspire, using it in a classroom activity so all students can follow along, how to connect it to the smart board, and how to export the calculator work and print it to use in your class. We learned how to use an iPad mini in many different classroom settings, from homework and class work management software to in class activities we won't over dozens of different ways to use the iPads. We also learned how to make an online survey, since you showed us making the app rubric.

     We also learned some probability and statistics, since that is what content we used to make all these technological activities. Though we may have skimmed the statistics part and stuck to the probability part. However we became much more familiar with the standards for probability and statistics for both middle school and high school.

From Dillon Johnson:

I'm not sure if I can state exactly what I've learned, but I do know that much of what I learned came from our discussions.  I think hearing other students’ perspectives on apps or different technologies and their reasoning gave me my best learning as they look at things much differently than I do. 

So, what have I learned as the instructor of the course?  I have learned:

·         Lacking a detailed plan doesn’t mean that learning won’t occur.

·         Classroom discussions are a meaningful instruction method.

·         It is okay to get off topic once in a while.

·         Direct instruction is my least favorite teaching technique.

·         My students probably taught me more than I taught them.

This class has been a lot of fun and I am already thinking of changes to make the next time I teach it!

Joining the Network

As I sit here typing on the mini iPad provided by the math department for the semester, I have begun to realize just how easy it is to join the network with one tap by my finger. Of course, the World Wide Web is not my only network. As teachers, we are privy to an incredible amount of resources by just being who we are! From having classes with peers in the same education program to being members of national clubs such as the National Education Association, we have a network more valuable than many of us really understand until much later in our careers.

To really put this into perspective, a few weeks ago on an online program, I was able to have a conversation about flipped instruction, one-to-one schools, and Common Core with a high school math teacher in California. As a soon to be teacher, I was eager to hear what he had to share about his many years of teaching. Not only did I learn from him but he learned from me! The network and flow of information does not only go from older to younger teachers, but useful information can come from either direction. Yet another example is my brother. He is finishing his first year of teaching high school math in Nebraska. On many occasions, he has asked for my opinions on certain lessons, and I know that some time in the future, I will ask him questions. In this sense, my network is close to home. But we have to remember that as teachers, we have more than just family that might be teachers. We have more than those people we spent hours studying with to pass a final in the education program. We have more than our advisors who have shown us what we need to know. We have more than the other teachers in our school (or district). We have every teacher in the state or the country or even the world that is willing to share their knowledge. And in my experience (however limited), teachers are almost always willing to pass information. After all, our job is to inform.

I cannot begin to describe just how many people I have met or become friends with in my professional network. Honestly, I am constantly surprised by how many people I have available to talk to about my future career. Better yet, I know that my network of support will forever increase as long as I am a teacher. That is such a comforting feeling to know that no matter the problem, I will always have a pluthera of people to talk to about it. So remember that you will always have someone to discuss with. Luckily, social networks like Facebook, Google Plus, Linked In, and others are always at the touch of our fingertips.

Society's view on math

I read the article “Mathematics Education: A Way Forward” by David Wees, ,http://www.edutopia.org/blog/mathematics-real-world-curriculum-david-wees

and it started with the equation:

 Population × Bad curriculum ^{Multiple generations} = Functionally innumerate population.

Which is such a true statement, that we don’t always think about. The adult population, of American as well as Canada, has a generally bad experience with math. Not only was it a boring subject in school, they were also told by their parents that it is okay to hate math. I believe that it is critical that we realize that as a society Americans don’t like math, as future and current math teachers we need to foster an environment where it is easy to like math. Though this article is about Canadian math education, I think it applies to American math education as well. This article focuses on three ways to make math more enjoyable and beneficial to society. The three ways are: changing the curriculum to real-life problem solving situations, making the material relevant, and boosting engagement.

            The first way, changing the curriculum, is currently being partially done for us. With the common core standards going into effect students are seeing many more problem solving style questions and being asked to explain their reasoning for their work. In this way we are already addressing the first problem. The second part of this, however, is to do problem solving in our classrooms. Whether it’s projects, homework questions, or our lectures, we can incorporate problem solving skills into our classroom.

            The second way is making the material relevant. To me this is the reason most students begin to not like math, they are not shown any uses for it and cannot find any themselves. A feeble application of mathematics is almost worse than none at all because it is seen as a confirmation that there are no uses for math; that the teacher is grasping at straws to come up with an application for the math they are learning. Honestly some students will never use calculus or trigonometry, but some students also won’t use poetry. It isn’t showing that all math can be used by everyone, the important thing is showing that all math has a use or purpose other than “it’s on the test”.

            The final way is boosting engagement, this ties in with making the material relevant. By making the content relate to the students you greatly increase their interest, and their desire to learn. Even little things, like using students’ names in problems engage that student more. But bigger things, like relating the material to their hobbies or making fun activities that use the material, can have a huge effect on a student’s desire to learn. When a student wants to learn, they can move mountains; when they do not want to learn you cannot make them.

            I see these three things as highly important to us changing society’s view on math, one student at a time. I would like to eventually have a society where it isn’t okay to hate math the way that it isn’t okay to hate English, the way that it isn’t okay to dislike grocery stores. Many other teachers and I would like to have a culture where math is just another tool in our tool belt that we can use to solve daily problems. This is the change in society that I would like to see.

Because the Math Gods Say It Is So!

     So often, students evaluate problems by following the steps their secondary Math teachers told them to follow, but never actually realize why they are doing it. I am guilty of doing this. Last week, I was tutoring a student on factoring by grouping, and I just realized what we are really doing when we factor. For example, when you are given the following equation:

We look at the first two terms and factor out the GCF (greatest common factor). Then we do the same process for the last two terms. Now, the (x+2) becomes a factor and then the remaining terms become the other factor of (3x^2+4). That is how we got the last line, but what I realized last week was that we actually factor out the GCF again. This time the GCF is (x+2) and then (3x^2+4) is what is left after you factor out the GCF, and this is how you get your two factors by grouping. I never realized that we were actually just factoring out the GCF again. I just always thought if the two ( ) were the same then they became one and then the remaining terms created the other factor. 

   This happens all the time in Math. The students follow a process, but they don't actually understand why they are doing it. Their secondary Math teachers just told them that it was done this way because they said so, or because that is how the book says to do it. As educators, we need to have our students discover processes of solving problems on their own. By doing so, they will be able to observe the steps in a more in depth manner, and they will be able to understand the why rather than just the process. I hope that as a future educator, I will be able to help my students make these connections and help them create a more conceptual understanding.