In Response to an Edublogger

Although I am really not a huge fan of blogs, searching for various edubloggers was interesting, because many of them offer interesting and engaging ideas for teaching your subject, or relevant and useful resources for the same thing. The two edublogs I ended up commenting on were based around mathematics instruction. The first discussed a possible solution to the question, "When will we use this in our real lives?" a very real and regular concern of students in mathematics, which we cannot always respond to with an answer that is deemed "good enough" for students or parents. In this blog, the author suggests changing up the way we teach mathematics, even hinting that the Common Core State Standards consider such a revision to their official document.

What the recommended change was was adding coding to regular mathematics curriculum. This was argued, because coding requires the same type of problem solving that we often stress in a mathematics classroom, and no matter what the topic, this skill is what we are attempting to teach our students. I realize sometimes it seems like it, but our goal is not to bore our students with memorization of useless equations, and I think the first blog I read expressed this well. The author made sure to emphasize that this did not necessarily mean teaching a coding language, such as Python or C++, but rather considering things like programming a calculator to automatically perform the quadratic equation, ridding of the burden on students to perform such procedural knowledge. The author provided other examples of how to apply coding in mathematics curriculum, even suggesting that this topic be introduced to students in elementary school!

What I particularly appreciated about this blog post was that the author said all this knowing that not all math teachers necessarily have strong backgrounds in computer science or coding, but suggested that it was something we could easily be trained in to teach. Perhaps this could mean that some computer science course should be required of those who want to obtain a teaching major in mathematics. I asked the author their opinion on this topic.
Coding in Mathematics Education Blog Post

The second edublogger I read and commented on provided this really simple, but useful quiz/game tool to use in the classroom called Kahoot!(https://getkahoot.com/). She briefly explained how the tool worked, and how she used it in her mathematics classes. She also made sure to describe some limitations of the tool, which I found particularly interesting and helpful in her blog post. She talked about how the quiz tool allows you to download the data of your students responses to the quiz questions which acts as a great formative assessment. Another positive aspect of this tool is that students can participate on any apple or android device, or any computer with internet access. I thought this might play well for a situation of BYOT.

When reading this blog, I found that I became very interested in this tool, especially because it was a mathematics teacher discussing how she uses the tool. Before I even finished reading the blog post, I had to check out the tool for myself. And my response to her blog post was basically just my excitement about the tool and appreciation for her description of the tool, because it made it easy to navigate the tool and implement very useful aspects of the technology tool.
Kahoot! in the Classroom Blog

Technology in my Placement

In the Secondary MAC program at the University of Michigan, we were asked to survey our school placements for the use of technology throughout the building. The school I am currently at is considered a high needs school, and is also a charter school, funded by various organizations. Although it is not a public school, the access to technology is fairly limited, which I will explain below. Before actually discussing the availability of technology, I would like to discuss my research process. I would say this began during the professional development at my placement school, when I learned more about the mathematics curriculum, which used computers in the implementation. When the teachers were being trained on implementing the curriculum, we were provided the opportunity to try computer work in one of the high school's two computer labs. There were about 25-30 Apple desktops, which were slow using the internet, and at least 3-4 were not working. Another aspect of my research began even earlier than this.

Before I had actually started my observation at my placement school, I had researched some to try and better understand the environment I was about to enter into for the entire year. I learned that it was a school that valued art, and had heard that there was a particular stress on graphic design, which I thought would require the use of technology. When the school year had started, I found that the two art teachers on my floor (there is one art teacher for each grade level in the high school and middle school), taught mostly with a 2-D medium, such as pencil on paper drawing.I have yet to see students having access to anything other than an Apple computer, usually for research purposes. Perhaps my understanding of graphic design is lacking, but I have only heard rumor of access to tablets for the art classes. Thus, although the school is supposedly known for graphic design, being closely connected to a college specialized in graphic design, the technology available to students is limited.

When I was actually observing in my placement school, there were some other aspects of technology that I noticed as well, such as the spotty internet, and the very restricted WiFi for the school itself. My mentor teacher informed me that although the school had its own internet signal, the free guest signal from the building above the school actually worked better, and that is what I use when I need internet at my placement school. On top of the limited access to technology though, I also had the privilege of being around while a new tech person was hired for the school. Trying to talk to this individual was extremely difficult, because they were constantly running around trying to fix a printer on the second floor, or a projector on the fourth. He was attempting to share his knowledge of technology, while learning about the building he was working in, which is not an easy task.

Although technology is limited, in terms of what is available to students, I was surprised how much the teachers are provided. I guess I am unsure of what is considered normal for secondary education, but each teacher at my placement school received a Mac Pro laptop, as well as an iPhone, that was meant solely for school calls. On top of this, each classroom has its own projector and screen, as well as a classroom telephone for contacting teachers during class. This was interesting to me, because the way the school was built, there was no speaker or P.A. system set up for the classrooms, so individual phone calls is the only way to contact people around the building.

One thing I found particularly interesting was how the mathematics curriculum chosen for the high school relied heavily on the use of computers, as well as having reliable internet access. Technically, the curriculum calls for 60% of the classroom time spent in the classroom, in lecture, while the other 40% is meant for using the online modules to practice skills and deepen their understanding of concepts. I have not been provided the chance to watch students work on the computers, but I know the program is fairly straightforward, and I had heard students were not a fan of the computer work this previous year.

Tech Tools in Use

Last week, we learned about the tech tool VoiceThread. This was an interesting tool, which allowed one person to post images, or a Powerpoint online, and once posted, collaborators could post various forms of comments on the uploaded material, which would then play like a video with the original material playing, while the comments play through. This tech tool was very simple to use, and I thought it was pretty self-explanatory, which the presenters must have recognized as well, since they did not spend a lot of time explaining how to use their tool. The simplicity of this online tool is great for a classroom, because it means as a teacher, you can spend less time explaining how to use the tool and more time having students actually engage with the program. Also, because I would not need to spend as much time on instructing the students how to use the tool, I think the students may remember more about using the tool, since it is something they could figure out on their, almost like inquiry-based learning...but not really.

When first being introduced to it, I found this to be an interesting tool, but was skeptical about how relevant it would be across the disciplines. The presentation definitely made me think about how this tool could be used, especially since the presenters planned a group activity where we had to create a VoiceThread for our content area. After the presentation, I thought that VoiceThread may be good for recording a teacher's voice over Powerpoint slides, and have students comment on the presentation if they have any questions about specific material being presented. This could be useful in any subject area, with this specific use in mind.

Focusing on math, I figured it might be a great presentation tool for a more visual topic, like geometry or trigonometry. When I was working with the math group, we decided  to make a VoiceThread based on teaching students about polygons. This VoiceThread began with introducing some shapes that would be considered regular polygons. It then progresses through a variety of pictures, asking students to leave comments, in whatever format they choose, commenting on any polygons (no matter how abstract) that they identified in the images. Some images were patterns, or signs, and the final image that we had was one of a tiny piglet, which required students to be a little more creative with finding polygons.

One major problem with this tool is that you would need to pay for a subscription if you want to save anymore than 5 presentations, which would definitely be a problem for me if I were using this as a teacher. I would want to have these presentations available to my students throughout the year, for their midterms and finals, as well as for myself just to have a record for reflection on my students' past work.

Another problem that I am still wondering about is how easy it is to moderate the comments on the presentation. Does the person who created the VoiceThread have the ability to delete any comments, or block certain people from commenting on the presentation? When working with technology, I would readily worry about students abusing the tool, but I do not want this fear holding me back from using technology with my future students when it is appropriate.

Another limitation of this tool, as is the same with many of the other tools we have been introduced to this semester, is that it is dependent on having access to computers, as well as a connection to internet. At my current placement school, I know that students do not have the best access to computers. There are two computers labs for the entire high school, and only around 15-20 of the computers in each lab actually works. On top of this, WiFi in the school is very spotty, so  a student's ability to connect to VoiceThread would be uncertain. Thus, in order to use the tool, students would probably require that students work at home, which would require the assumption that students have computer and internet access at home, which I am uncomfortable with.

Although I think VoiceThread is an interesting and easy to use application, my use of the tool would be very much supplementary to my instruction. I may be willing to use it for student projects perhaps, or for introducing a lesson, just to introduce students to various tech tools, and to keep their instruction interesting and hopefully more engaging. It is still not something I plan on using regularly, but of course I am open to changing my mind about it with more teaching experience.

Exploring Creative Mathematics Lessons Online

On October 16th, 2014, Tom Ward, a Secondary MAC graduate and current high school math teacher at Greenhills in Ann Arbor, visited our classroom to share some of his ideas and strategies for creating engaging lessons. As a future high school math educator, I found this presentation to be the most interesting, because it had been so math focused. Actually, the first example he presented was to help students learn about quadratic equations, which is the next chapter my placement classroom will be covering! This lesson involved watching a video of a basketball practice, where fellow peers were shooting baskets. I thought it was such a great example, where students can see the parabolic shape of the position of the basketball as it is being shot, and with the right video tools, students could spend various lessons trying to calculate the trajectory of the ball, and whether it would go into the hoop.

Although Mr. Ward shared plenty of lesson examples, such as the basketball trajectory, a Mario Jump example, and a Vine example (not directly related to mathematics), what I appreciated most, was that he didn't just present ideas, but he shared how we could find creative ideas for lessons ourselves. He shared some of his favorite teaching blogs, such as Dan Meyer, Sam Shah, Fawn Nguyen, and Kate Nowak, and also provided us with websites (now linked on CTools), which were some more resources for us to check out. I thought this information was much more useful than just giving us three bloggers to follow.

I really enjoyed this presentation, and although Mr. Ward may not have been as enthusiastic as our first guest speaker, it was really interesting seeing a Secondary MAC alum, and hear about his success as a teacher. I also appreciated that he had taught in different states and different types of schools as well, which suggested to me that he would have various perspectives on teaching. Another aspect of Mr. Ward's presentation that not all of our other guest speakers did was that he provided his information so that we could contact him, as well as a list of his favorite resources.

For me, this presentation was very encouraging. I have worried about my ability to be creative, and make each of my lessons interesting and engaging for students. It is nice to know and be reminded how great of a resource the internet can be, and how it can act as an inspiration for many lesson ideas. I thought that Mr. Ward's presentation supplemented this Teaching with Technology class very well, and it will only help us as novice teachers discover all sorts of interesting and engaging lesson ideas!

Connections Across The Disciplines: Understanding the Historical Context of the Odyssey

When first approaching this lesson plan, I did not know what to expect, because I knew that the content areas of the authors was varied between English and Social Studies. I thought that their topic, which included a combination of the literary piece The Odyssey and the history and culture surrounding the piece, was appropriate for their subject areas, and thought it provided an interesting and engaging way for students to form connections with the text. Reading through their lesson plan, I thought the objective was clearly stated, and that the final assessment was well aligned with their objective. I also found that the progression of the lesson was logical and seemed to flow well from activity to activity.

One aspect of their lesson plan that I found particularly interesting was how much they were able to integrate technology throughout their entire lesson. They also made sure to mention BYOD, and how this would work well in areas with fewer resources available to their students. The material appeared accessible to students on laptops, tablets, as well as smart phones, which could be brought to class without too much trouble. I was also impressed with their planning to use technology in the classroom in various ways. They had videos for the first half of the period for students to watch and discuss periodically, followed by a map activity, where students make connections between travel in the epic poem to current day locations on a map. I thought both activities allow for sufficient interaction and engagement of the students. By breaking up the video into segments, I think this would better allow for students to comment and connect with the material being shared.

I was also impressed with how precise timings were marked out in this lesson plan, but wonder about the details of the discussions following each of the videos. Although I am sure the individuals who wrote the lesson have discussion questions in mind for each of the video segments, I am interested in knowing what these questions were, and what they wanted their students to obtain from each of the segments. Another aspect that I was interested in was who this lesson was aimed towards. I noticed that the students were expected to have recently read The Odyssey in their lesson planning process, but it was not quite clear what level the students would be at when being given this lesson.

Another thing that could make the goals of this lesson plan more clear would be to include the purpose of each activity. They provided plenty of time for discussion throughout the video portion of their lesson, but it is unclear whether there will be time provided to discuss the map activity. I thought this was an interesting and engaging activity for students to work together on, but I think by having a more explicit discussion session on what the students gained from the activity, students will have a better understanding of why they are participating in such activities and what your goals are as their teacher.

After having read through each section of their lesson plan, as well as their discussion of BYOD and their lesson planning process, I am now thinking about all the possibilities after this lesson plan. I wish I could find activities and assignments where students could go from making connections between the text and the historical context, to somehow bringing in a part of themselves to the discussion, so that they are looking for connections between them, the text, and the historical context. Unfortunately, I have not read the texts discussed in this lesson, but I think there are plenty of branches to build on from this lesson. That being said, I found this lesson to be interesting and its incorporation of various school subjects made it so. It seems that students would be able to gain a lot from this lesson, and I think the time for discussion will especially encourage this growth of knowledge for the students.

An Experience with Evernote

For our final summer class, we were each required to research a certain program that helps organize your life, the assignment being called "Organizing Your Online Life". I was assigned the program Evernote. I had heard great things about this program before beginning this assignment, but never had any hands on experience with it. I was a little unprepared to look at it from a teaching perspective, because I had only ever seen it used as a note-taking program, which is more closely associated with the student role.

My experience with researching was pretty basic. For learning to use any technological program, I find it easiest to find a YouTube video explaining in detail with visuals. I was actually able to find a 40 minute video going through all of the basics and all of the possibilities with just a basic Google search. (Video at: Evernote 2014 Tutorial --If you're at all interested) I was able to learn very quickly some of the tricks people had found with using this program, as well as the basic functions that most people use it for.

After having done the research, I found that Evernote seemed to be more of an organizational tool, rather than a hands on classroom tool for students. One major drawback I noticed with Evernote in comparison to Google Drive, was that there is no function for collaborative work, unless you buy a Premium subscription, which has a monthly or an annual fee attached to it. I think if Evernote itself could offer all of the perks of the Premium membership, I would be fully on board to use it in my classroom. You can share all different forms of documents with students, like webpages with and without images/ads, documents, lists, presentations, images, edited images, sound clips,...it's amazing. But the application seems much more geared towards individual organization rather than collaborative work, which I really enjoy about google docs.

Not to say that the basic application does not come with its perks! You can get a browser add-on which allows you, like I mentioned before, to clip web pages with and without pictures or ads, so it's easy to save any web pages of interest in one, organized place, separated into folders and neatly stored. Also, because Evernote is an online program and is compatible with basically any device, you can access your saved documents on any device you may have!

I really would watch the tutorial video, to see how Evernote could help you organize your own personal life, but as far as use in the classroom goes, I think it may just create more work for you as a teacher, and as Kaitlynn had mentioned, it becomes exhausting trying to spread yourself out across so many different online applications. When do the use of programs like this become counterproductive??

Video Games: Thoughts from a Different Perspective

This is an interesting topic for me, which makes this assignment really exciting! This past year, I've had many conversations about all the benefits to be had through playing video games. I cannot claim to be much of a game player myself, but I have learned a lot about them through the eyes of others.

One game, which I have learned a great deal about these past couple years, is called Starcraft 2: Heart of the Swarm (SC2), which is a real-time strategy game, where you can play as a single player through a story line, but I believe it is best known for its multi-player game play. Here's a short preview video of just a cinematic that was released just before the game itself.

Starcraft 2: Heart of the Swarm Cinematic Preview

Basically, in the multi-player mode, you play as one of three races, Protoss (aliens), Terran (humans), or Zerg (bugs), each with various units, technology, and strategies. In the video above, Blizzard Entertainment created animations of a Terran vs. Zerg battle, which is personally my favorite match-up to watch. Each player is responsible to build buildings, which allow for the creation of units, which they want to make a particular composition in order to defeat their opponent. Along with creating an army, in order to be effective, a player wants to scout their opponent to properly attack and defend against them. This game requires macro play, which consists of building technology, collecting an income in minerals and gas, and constantly creating units, as well as micro play, which involves moving your units, usually your army to most effectively attack your opponent, or to avoid certain attacks, you need to move your army a certain way. 

This game can range from fairly simple, to extremely complicated, meaning that there are professional Korean players making millions each year practicing and playing competitively...they're really really impressive. This is one of the games taken very seriously in South Korea, to a point where people will live in a gaming house, sometimes practicing upwards of 14 hours a day. You can watch their streams on twitch.tv and also watch tournaments of the game too. (There will actually be a tournament in Detroit this August!) Anyways...

Because of this huge range of skill sets, I will try to narrow down my discussion to focusing on the Terran race, which I am most familiar with, in terms of the James Paul Gee article "Good Video Games and Good Learning," which we read for class. 

1. Identity: Players create a username under which they play other players around the world. They are matched up against players with a similar skill level, and can play games from 1v1 all the way to 4v4, where you have four players against four. Players usually in it the game for the long haul as they "ladder," which means they play game after game, trying to beat their opponents to gain points and move from the Bronze league all the way to the Grandmaster league (which is the top tier players in the region).

2. Interaction: After each game, each player will see a screen such as the one below, which shows their stats in comparison to their teammates and opponents. The graphic below shows a 2v2 game of the amount of resources collected throughout the game by each each player.

This feedback allows for players to see specifically where they could use improvement, whether it be income use, army size, APM (actions per minute), or the order they created their buildings and units. Players also have the opportunity to watch replays of the games, where they can see the perspectives of all players to better understand what occurred throughout the game, and what they may have missed.

3. Production: As was discussed above, players are responsible for creating tech/buildings as well as units to create an effective army.

4. Risk Taking: Because you're playing a live opponent usually, often there is a lot of risk taking involved. The point system makes it a challenge, as you want to gain more points by beating your opponent, but if you lose, you only lose so many points and you can re-queue a game to try again. As I said before, you want to scout your opponent to know what they are up to, but this is not always possible, and when attacking blindly, you are taking a huge risk. But, once again, you learn from the risks you take. One even more important aspect of risk taking in this game has to do with the economic efficiency you reach for while playing. Each game, with the requirement to collect and spend resources, you want to effectively spend, which requires knowing what buildings, tech, and units to spend resources on, which resources to collect and how much at each base, and when to spend you resources collected. As you can tell, it gets complicated really quickly, and there's a lot to think about while playing in real-time (as it is an RTS). It's so complicated, that I know I'm not properly explaining it all, even with all the time in the world...

5. Customization: The game play is set into different leagues, so when you first start playing, you begin in Bronze league, and as you gain more points, by beating your opponents, you can move up into Silver league, then Gold, then Platinum, then Diamond, then Masters, and for those elite player, then Grandmasters. This allows for players to play at their level and progress at their own pace. 

6. Agency: In this game, you are totally responsible for what occurs, and have the power to be in total control of your units. One example of this is the micro mechanics involved in using your army at the top levels. Below is a video of MarineKingPrime, the person (who introduced this game to and explained everything to me)'s favorite player, microing his Terran (blue) units against a larger Zerg (red) army, in order to survive an insane engagement against one of the best Zerg players, Startale Life.

MarineKingPrime vs. StarTale Life

7. Well-Order Problems: Because the players move up through the leagues, they are allowed to learn gradually the skills needed to play at the top leagues, and the game-play is tailored to their needs and skills.

8. Challenge and Consolidation: Similar to 7.

9. "Just in Time" and "On Demand": Although players cannot demand which league to be in, they are placed based on win rates and points, and can play against the computer at whatever level they may choose.

10. Situated Meanings: The game is learned through playing and watching others. So any actions or instructions are usually accompanied by images or run throughs.

I think from just these 10 aspects of video games you can see the relevance SC2 has, and there is a lot to figure out while playing and a lot to learn. This game is based on a lot of risk/reward quick decision making, and is extremely difficult, because of the multi-tasking involved while trying to make these decisions. I believe there really is a lot to learn from such a complicated game as this, and when you take the time to understand the economic ideals, and the mathematics behind cost/benefit decisions, this could be a tool used to gain knowledge and learn to apply some aspects from school to the game. 

I know I just attempted to share a lot of information that may have been confusing. So if you have any questions, feel free to leave them and I'll do my best to answer! 

The Question of Assessment...in particular The Smarter Balance Assessment

We had been discussing this idea of student assessment, as well as teacher assessment and evaluation a lot this week, and it has been difficult to understand where my beliefs lie in terms of these various forms of testing for both students and teachers. I suppose this post is supposed to focus on student assessment though, so let me begin there...

In terms of The Smarter Balance Assessment, I enjoyed taking it, but can see areas in which students may struggle. We had discussed, as a group, our problems when being given the test in class. One comment was that the preparation involved for taking the test was confusing and overwhelming and I would agree. Nobody needs to begin their test having to go through a list like this...

...without fully understanding what these options change. Perhaps, if students were able to mess around with these options before taking the actual test, this would allow them to truly find the best settings that fit their needs. I understand that allowing students to choose the settings that best fit their preferences is meant to reduce discrepancies based on overall preference and comfort with certain looks of the text, but this can easily be seen as too much to decide somewhat blindly.

Another concern was that the questions were so disorganized in terms of how to answer and/or respond to the problem posed. Although, I enjoyed answering these questions, as a future math teacher, I understand why a student, who is not prepared for a test of this format, would be easily thrown off and perform below their actual understanding of material on this assessment. Going into this activity, we were not prompted with much, other than to log in and pick a grade and topic...then try out a few of the questions. I found the questions quite interesting, and I think they may more accurately test the students' understanding of the material they were supposed to have been taught. I think with proper preparation and framing by the teacher, students would not be so thrown by the varying types of questions, because I believe that being able to switch from one format of question to another is a skill that can and ought to be developed. I just wonder how much time we, as teachers, have to spend on trying to prepare students for this type of test format, and whether we even want to be teaching in response to this particular test.

Just going through the 9th Grade math portion of the test, one thing I was concerned about was question 2 shown below:
It's difficult to read the question here, but it ask students to find possible centers for a tangent circle to the original circle, and asks students to show their work in the box designed for paragraph writing. If you're unfamiliar with the work involved with mathematics problems (especially geometry questions), which I doubt you are, you would recognize how difficult it can be to explain in words how you solved a problem. For me, the process of solving this problem required diagrams, equations, and drawing/erasing lines and values. How do I write all of my steps in one word processing box, especially under the pressure of a time constraint, and knowing that this is the 2nd of who knows how many questions...?

The last confusing aspect of this exam that I remember from class is the issues with navigation throughout the text. The arrow navigation buttons would not allow you to move onto the next problem without having entered some answer to the current problem, which I would think most students are not used to, having taken the ACT and GRE myself, knowing that this is not the case for those tests. I wish I had gotten to try out this function myself more, as I think I was too focused on answering the problems...but this would also require some preparation for students in order to efficiently navigate the test.

Ultimately, I think the Smarter Balance Test, at least the math section, can be an effective tool for measuring a student's mastery of certain grade level's math content. My only concern is that it would require a lot of preparation, in order to get students comfortable with the changing format of the test, and the ways in which to navigate the test.
I'm wondering whether those of you who took the English portions of the exam experienced similar issues as those of us who took the math portion.

Understanding Education Through the Eyes of John Dewey

In John Dewey's piece entitled My Pedagogic Creed, one is quick to notice the direction of his attention in terms of education. I found it interesting how he believes that education begins almost at birth, and I would agree. As humans, it is in our nature to constantly be taking in tons of information from our environment. From there, our brains make sense of this information and turn it into useful pieces of knowledge, understanding, or awareness. It's important to me to recognize everyone as a learner, no matter where their skill set may lie, and I think Dewey clearly points this out in the first section of his text. We are natural learners, eager to take in and make sense of information, but how do educators fit into this learning process?

Dewey continues on to say "...the only true education comes through the stimulation of the child's powers by the demands of the social situations in which he finds himself." Here, I believe he is referring to the difference between passive and more active learning, or at least my understanding of both types. At birth, the way we are acting as learners is more passive, more innate, while in social situations, we must consciously assess the situations, or pay close attention to details expressed, and learn to act accordingly, often in a way that is deemed "acceptable" by the society that we are in. Dewey describes these two different sides of the "educational process" as the psychological (basic learning from your environment) and the sociological sides. This sociological side incorporates how the child, as an individual, works with and among those in their society in order to increase social welfare. One thing I never thought about, was how these two sides were dependent on each other. For example, the individual must have some understanding of their surroundings in order to learn to function in a social situation with others. In other words, in order to learn to function with others in a society, the individual must have certain actions developed in response to the constant intake of knowledge of their environment and themselves, for others to respond to, and for the individual to learn from those responses. It actually seems like a somewhat circular model of learning.

In the next section of his piece, he explains that schools and educators act as a social institution, which sets the stage for the "social situations" mentioned in the quote above. This is where the teacher fits into the equation, and I believe that my current teaching philosophy follows fairly closely with Dewey's. He states "...that education which does not occur through forms of life...is always a poor substitute for the genuine reality..." For me, this means that we must incorporate and use the knowledge and information around us in order to really teach and learn. As stated before, we are constantly accepting information from around us, and I believe in order to educate, it is our job as teachers to make our content relevant to students. When content is relevant, students will connect with it, forming some deeper understanding being able to form a relationship between the information provided and how it affects them, as well as how they can use it in their daily lives. As a math teacher, it may  not be that students will need to be able to pull the pythagorean theorem out at the grocery store, but they could recognize the appearance and usefulness of triangles in the structure of the store, or the effectiveness of wet floor signs to remain standing. Being able to see the pervasiveness of mathematics in their current and active lives, they will be able to interact with the subject as if it were a social situation, in which it is in action throughout their day, changing the way they see the world and how they interact with the world.

As a side note: I've noticed that I've been using knowledge and information interchangeably, and that makes me want to define them more precisely. I never considered myself talented in the art of defining words...but here's my attempt. The difference between knowledge and information is the way it is compartmentalized. Knowledge is acquired with more cognition than information perhaps? Or maybe knowledge is gained from information?
I wonder...what is the difference in your opinion between knowledge and information?

This reading really helps to support my motivation in finding ways to relate math to everything in my students' lives. Whatever they may be interested in, there is a way to connect math, and I believe that if students and people can recognize this, they would understand the importance of mathematics and the beauty of understanding it. Just as reading and writing allow you to connect with others and reflect on your experiences, mathematics allows you to connect and understand your world. My goal as a teacher is to present this idea to students in a meaningful and relevant way...