Weekly Report and Reflection Week #4

Hello again blogger friends, today I would like to continue our conversation on education and mathematics. I'm sure that everybody reading this post have studied some form of mathematics at one point or another in their lifetime. Due to this, I'm sure everyone has experienced first hand that different people learn mathematics differently. This is not an abnormality, and in my opinion is almost better than if everyone learned the same way. The important thing is that everyone is able to understand the concept and solve the problems given to them. Having different methods to solve a single problem opens opportunities for deeper understandings.

Applying this idea into an educational setting, we cannot force everybody to learn in the same manner. The problem isn't that different people learn in different ways, but how do we teach many people who learn in different ways? This method is called differentiated learning, and is not a new concept to education.

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 Differentiated learning is the philosophy of providing different students different methods of learning. Some examples of different and effective teaching strategies are:

-Specialization/Generalization
-Guess and Check
-Use of visual aids (Diagrams, charts, etc.)
-Use of manipulatives
-Instrumental vs. Relational learning
-Logical Reasoning
-Working Backwards

I myself experienced how to apply differential instruction within a recent class that I attended. I was given a math problem and told to explain and solve it in more than one way. The math problem itself was that I was given a rubix cube with undefined size. How many blocks of the cube had 1 face showing from the outside, 2 faces showing from the outside, etc. It proved to be more difficult to find more than one way of solving this problem than solving the problem itself. In the end, It turned out that many of the strategies listed above could be applied to this problem. One example is that you could use guess and check as well as visual aids to make a chart describing different sizes cubes and their corresponding number of blocks with 0,1,2, or 3 faces showing. Another method is using our knowledge of cubes (how many vertices, faces, sides) to deduct formulas describing the number of blocks with 0,1,2, or 3 faces given any sized cube.

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 Applying differentiated instruction to your own classroom may seem difficult, especially considering the fact that the teacher himself/herself has a preferred method of instruction. Luckily, you are not in this alone. There are an abundance of resources available for your use, all you have to do is access them. One example of these resources, and maybe the most important resource, is your peers. No matter what situation or difficulties that you are having in your classroom. There is always somebody who has faced this difficulty before you. There is a decent chance that you will not be the only math teacher at your school, and it is not a sign of weakness to ask others for help. Discussing lesson plans, teaching methods, and behavioral strategies with other teachers can be beneficial towards your own classroom. Another resource which is easily accessible is the internet. If you are unable to find the answer you are searching for from your peers, there are many forums, blogs, and websites which exist for the use of all teachers. One example of this is http://teachers.net/ . This website contains multiple resources which aid all educators such as lesson plans, job postings, chat rooms, and forums. You can post any issue which you may have on the forum and the community will come together to brainstorm a solution for you. There are many other sites similar to this which offer important resources for educators in need.

Weekly Report and Reflection Week #3

This week I had the opportunity to explore the use of technology within mathematics. In general, technology is becoming more widely used within the education system in a large variety of ways and subjects. More schools are investing in smart boards, which give teachers more options on teaching styles and methods. I have even seen schools implement students' cell phones into the class by having them text their answers to a certain number which reads and displays the results. The reason for this is that many educators have decided that it is easier to use cell phones to their advantage than to work so hard to keep them out of the classroom. The technology that I used this week in school was a graphing calculator as well as a device which measures the distance an object is away. By using these together I was able to plot on the calculator a graph which displays distance over time. We were given time in class to experiment with this technology and attempt to recreate preset graphs which were given to us. This use of technology was effective because it helped direct the class without strenuous effort from the teacher and kept us on task, as well as engaged.

In general, I think that technology is an amazing resource that all educators should consider. Using it correctly can create an engaging and fun classroom. This is particularly useful in mathematics, considering how often times it can be difficult to make a math classroom engaging. That being said, often times technology can have the opposite effect within a classroom. If not used correctly, students can take advantage of the manipulative you are using and get off topic. Some examples of this happening are students using their phones for games or texting instead of work, or using the graphing calculators to draw pictures. This is why its important for teachers to account for these possibilities and take appropriate precautions. This includes tactics like banning internet or specific websites from students access, or even checking regularly to make sure that students are on task and using their technology appropriately.

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As a future educator, I hope that I can accomplish this goal of implementing technology into my classroom. Just as well, I have to be prepared to run a classroom without the use of technology. Even though this resource can be very useful, technology can also be expensive. Due to this, many schools and educational settings cannot afford devices such as computers or smart boards. Since I do not know which school I will be working in or where it will be, I cannot always expect to have this resource available to me. Even without technology, there are other ways of engaging a classroom and teaching them the curriculum effectively. In the end, I must understand how to use technology and utilize it in a classroom, but be prepared to not have it at all.

Weekly Report and Reflection Week #2

Hello friends, today I wanted to talk about relational and instrumental understanding. These are two different ways of perceiving information, and in my opinion they are both equally valuable. To start off our conversation I will go over both teaching methods quickly in case you do not know the difference. Instrumental learning is most commonly seen in high school mathematics. Students are given a rule, an algorithm, or a function which they are to memorize and accept to be true. They then utilize this instrument to solve the math problem which will be provided soon after. Relational instruction works a little differently. Every function, algorithm, and rule that has been taught in the curriculum has a background (whether extensive or short) of mathematical reasoning which makes it legitimate and useful. If one understands how a mathematical concept or equation is derived, they no longer have to memorize it. Within mathematics, relational instruction is often seen in the form of proofs. Relational instruction within math is more commonly seen in a post secondary setting.

http://www.slideshare.net/mrspal/number-sense-8855176

The main question that I wanted to discuss within this blog is: which is better, relational or instrumental instruction? The answer that I as well as many others in education believe to be true is that they are both equally important.  Both forms of instruction have their pros and cons which can be utilized. In a hypothetical scenario where the educator is teaching students of an important equation such as the quadratic equation, relational instruction gives a student a deeper understanding of the mathematical concept. By understanding the derivation, they will be able to apply the the quadratic equation to other problems and areas of mathematics easily. Just as well, students will gain a further understanding of the implications that this equation has in a real world scenario. On the other hand, relational instruction is a much slower process, which is to be expected. Within the classroom, the teacher cannot simply hand their student the equation and tell them to apply it to the problem, but they have to explain why that equation is applicable. Outside of the classroom, students will have to derive the quadratic equation every time they plan to use it because they have not memorized it. Instrumental learning, however, is much more efficient. Students will be able to call upon the quadratic equation immediately and apply it to the problem because they have memorized it. Unfortunately, students will also have a very narrow minded idea of the quadratic equation and its implications. They will be able to solve the problem, but not necessarily understand how that solution affects them. Put simply, the difference between relational and instrumental instruction is a trade off between efficiency and deeper understanding.

Calvin and Hobbes explains the necessity for relational instruction better than I ever could.
http://www.gocomics.com/calvinandhobbes/2011/03/09 

Ideally after an educator is finished teaching a unit students will both have a deep understanding of its concepts as well as be efficient in applying them. Achieving this has to be possible, right? I believe that it is our goal as educators to achieve the perfect balance of relational and instrumental instruction so that we can create a classroom environment where this happens.

Math Anxiety and Me

Hello again friends! As mentioned earlier, the purpose of this blog is for one of my university courses. This same course recently required me to read an article on how people almost brag about how bad they are at math. I will provide a link to the article here:

Hollywood's Math Problem

Now before I get started on deconstructing this article I want to make a quick point. It is rare that I thoroughly read an article or text that is provided to me in class. Despite this, I couldn't help myself from genuinely being interested in this article and reading it to the end (which is an accomplishment in itself). Given that it can't be longer than 750 words. my accomplishment isn't much to brag about, but it has to count for something, right? The point is if you haven't opened the link and read the article yet, I strongly recommend you do it now. Why do I think this article is so important? The whole time I was reading it I could not help but think to myself how true it is. I could call upon countless situations where acquaintances of mine have made jokes at their own expense about how they are incapable of doing any form of math. At this point the majority of people nearby agree, so we all hold hands and sing kumbaya because none of us can count past 10.

And they lived happily ever

Except that nobody lived happily ever after, because there are a couple things really wrong with this picture, the first of which is that almost everybody is capable of doing basic math. So why are we both lying and bragging about the fact that we can't do so? The second is that whether you like it or not, having a basic understanding of math is essential in day to day life. Society isn't asking you to calculate the probability that Jimmy pulls the ace of spades from a deck then successfully does a back flip, we just want you to know how to correctly tip your waitress so that everyone can leave the restaurant happy.

Now the biggest question about this anomaly is why? Why are people proud of the fact that they "can't" do basic math, and furthermore making jokes about it? In my opinion, the center of this problem is math anxiety. Math anxiety is a feeling of tension, apprehension, or fear that interferes with math performance. Put simply, math can be intimidating. If you don't understand a concept, it can be very overwhelming and this causes students to be anxious. What happens when students become anxious? Their performance is hindered, they are unable to focus and from here math becomes increasingly overwhelming. From here we continue to stumble down the dark spiral that is math anxiety.

And the next thing you know you're four years into your math degree and regretting every life decision you ever made

Math anxiety is often times why people cut themselves off from mathematics. This is where you start hearing things like "Math just isn't for me", or "I'll never understand math, so why bother putting the effort in?". I believe that this is the foundation that causes people to avoid any form of math within society, and simply boast to others about how you can't do math instead of trying to solve a problem. It is easier to avoid a problem than be embarrassed failing to solve it. Although I have never suffered from math anxiety, I understand where people who suffer from it are coming from. I am drop dead awful at soccer, you will never see me kick a ball because I have no motor control of my feet. If you ask me why, I guarentee you that I'll laugh it off and state that I just cant do it because that's how I am. Have I ever put the effort forward to try and learn how to play soccer? Never, because I would rather avoid the whole situation than have others see me try and embarrass myself. I'm not trying to organize a pity party based on my lack of athleticism, I'm just wanted to make an analogy which would express how math anxiety works and how it relates to the issues covered in this article.

Math anxiety is becoming an increasingly larger issue in society. The people who have the largest affect on this problem are those who teach it. Math anxiety is a serious issue and it is one that I plan to address within my classroom. Now I could spout off poetry about how my future classroom is going to be perfect, how I will diminish math anxiety with my magical engaging lesson plans, proceeded by a herd of unicorns waiting outside my door to escort students to their next class.

In a perfect world

Unfortunately it's not that easy. I don't know how I will tackle an issue such as this within my classroom. Fortunately I have plenty of time to figure it out. If we're lucky I'll be able to make another post about my progress with math anxiety.

Until next time.

Introduction

Hello friends!

My name is Mark, and this is my blog. This is where I will be talking about math, hence the name of the blog itself. I am working on this as a project for one of my university courses, but I am looking forward to posting regularly and sharing my ideas with you. More specifically, this blog will be an opportunity for me to explore my own ideals and findings with relation to math in the education system.

Before we get started on the mathematics aspect, I should probably tell you a little more about myself. My career goal is to become a high school math teacher. I know that for many people this sounds like the least interesting goal ever, but part of the reason I am looking forward to this blog is to show you that its not.

I want to work towards ending the stigma that math is dull and difficult.

Because when some people think of math this comes to mind

 With the right motivation, engagement, and a little bit of hard work, math can be extremely interesting and rewarding. I know this because I have experienced it first hand. I hope to one day become a math teacher that can engage his class in math and destroy this stigma one student at a time. I hope that the same class I am writing this blog for will teach me different techniques and ideas to help me accomplish my goal.

Such ends my first blog about math with Mark. I look forward to sharing ideas with you and learning more about math! Until next time.