Educational Philosophy/Model Integration

              As I approach the end of my second week of CPII, I have thought a lot about my philosophy of teaching and how I can best help my students effectively learn and be able to “do” mathematics. It has been a struggle, so far, to have a cohesive unit of 32+ students engaging in effective dialogue that promotes the Socratic method of learning that I wish to employ in my classroom. But I realize that this type of classroom cannot form out of mid-air. Thus, I will not allow myself to get too distracted by this challenge. And after the past couple semesters in the credential program here at CSUSM, I have learned that to transform education into more student-centered and socially just environment, I must be professional, reflective, as well as innovative in my practices.

              This semester I have many students whom “shut off” their learning caps when they themselves are not talking or being talked to the teacher.  It seems like I need to be their sole source of assurance that they understand something, instead of self-checking, asking peers for their thoughts, or speaking when I encourage whole-class discussion. This problem is compounded when their “shut off” routine leads to talking to their neighbors about something other than the subject of the class’s lesson. In order to counter this effect, I need to plan lessons that prevent student “shut off” mechanisms. In my 531 class this semester, I got in-depth looks into different models of teaching that are out there. To help me with my teaching and to meet the needs of my students, I find the inductive thinking and memorization models to be important models that fit well with my philosophy.

Inductive Thinking

              As human beings, my students are natural conceptualizers. Comparing and contrasting is something we do with every aspect of our lives. I love lessons that make the students inquire, sift through information, and eventually construct their own knowledge based off of their experiences. I recently tried to have my students “construct” the formulas for the lengths of the sides of special right triangles (30-60-90 and 45-45-90 triangles) I spent the night previous drawing different sized triangles of this category and cutting them out. During class, I had the students pick up a couple different sized triangles and trace them onto their paper. After measuring their lengths, I recorded their data in a table on the white board in the front. I thought the lesson would be a great way to see the relationship between the lengths of the sides of these triangles. Unfortunately, I feel like I rushed this phase where students examine and enumerate the data. My rushing led to a superficial inquiry of the data, something I regret now that I reflect on it. I feel I lead the students toward the formulas more so than I wanted to. In any case, I am happy I tried to get my students to create their knowledge of these triangles, instead of “spoon-feeding” them the formulas, something I see too often in classrooms these days. To be honest, I find this is the reason why online resources like the Khan Academy have gained popularity; because if all the teacher is going to do is lecture about formulas and examples you can find in a textbook, then you don’t need the teacher after all. But I disagree that this is the best way to teach; because the world we live in is a mathematics textbook, all our students need is a guiding hand in the conceptualization processes.

Note: This triangle lesson went superb in regards to student engagement. I had much less of my normal percentage of students shutting off during the activity, and felt like the students liked the hands-on approach. I have ideas on how to make it better and feel inspired to do so.

Memorization

I will not spend too much time on this, because I don’t think much time in the classroom should be spent on memorization. But it does have its place in the mathematics classroom, as much as my philosophy says otherwise. I think memorization should be taught after the learning of concepts has occurred. For example, in my high school calculus class, I learned the song, “low d high, minus high d low, square the bottom and do see do,” to help me memorize the formula for taking the derivative of a function that has an expression in the numerator and the denominator (I hope I’m not losing you with all my math talk about triangles and derivatives). This memorization did not take the place of my learning of how and why this formula works, but it was a supplement of my teacher’s lesson to help the concept stick. I haven’t forgotten this song, but thankfully I don’t rely on the song, or memorization techniques in general, for my source of knowledge. If needed, I could prove to you that the formula works, and this is because of the excellent way my teacher presented the material before giving us the nifty song.

Journal: What are my biases?

What are your biases and how do you mitigate your behavior when working with students?

This journal is long overdue. I had some great dialogue with my classmates on the CSUSM Grouply site on the matter, and was unaware of this journal being separate of that assignment for some time.

One of the biases I have with teaching math is that many students don’t have an imagination. By the time many of these students reach my high school class, they have been taught procedural information without connecting it to anything relevant in their lives.

The fact of the matter is that mathematics can explain why the world we live in works. Newer technologies today can make exploring the outdoors more of chore than a privilege, something I find extremely disturbing. This disconnect is only becoming more extreme, and it is leaving our students less engaged with the real world (yet more engaged in virtual realities that are visually, not physically, stimulating).

To mitigate my behavior when working with students of limited imagination/creativity, I will remain calm with my students and give positive encouragement for them to be more fanciful. I have found my free-writing/poetry sessions in Jannis’ class to be some of my most memorable mind-opening experiences in a classroom (along with some great synectics sessions). Oh ya, and that reminds me; I am going to try to stimulate my students’ creativity by trying out some synectics sessions in my own classroom. Therefore, my bias in this regard is only fuel for my fire to inspire.

I also have biases that resemble stereotypes(i.e. Asians are good at math, African Americans are good athletes, Jewish people are frugal with their money, etc.). I do my best to not let those biases affect me when I am presented with a situation involving persons or things that fit certain stereotypes. I bring this mentality to my classroom persona. As a teacher, I have the responsibility to teach my content, but also to prepare students to be effective citizens in a Democracy, which is a privilege I take seriously. Teaching critical thinking skills and the ability to make judgements based from experiences, and not from external factors such as the media, is my main philosophy on the matter.

Are Grades Necessary for Learning?

Some words on the Use of Grades these days...Inspired from the video segments found on Larry Ferlazzo's blog


After watching the first excerpt from The Daniel Pink interview, I felt I could totally relate to Pink's beliefs about how grades end up being the reason for going to school. He got straight A's in his 6 years of learning the French Language, but he admitted his inability to speak French today. I had only 3 years of Spanish classes, but I too can say I have little knowledge on how to speak the language. I agree that grades are a form of performance expectations that, if met, do not necessarily relate to the meeting learning expectations.

If we took grades out of the equation I totally feel that students would be better off. I would expect that students would learn more as well. The stress of grades, on BOTH students and teachers, make the learning process harder than it needs to be.

Pink also says on the second chopped YouTube video that he feels that Science (and I'm assuming Math too!) is too much presented as a bunch of facts rather than being built around inquiry. This hit to the core of me and to what I have been thinking about recently as I approach the end of my schooling to become a mathematics teacher. I think about how all the content of our math and science textbooks came to be known. I think about how many generations of curious humans were out there when they thought about and wondered why the world we live in works. People have the brain capacity for wonder and empathy. We as teachers need to foster these abilities in our kids. The way I think about it, the ones who didn't have the textbook growing up were the lucky ones. The Newtons, the Einsteins, the Pythagoreans, the Aristotles (I can go on forever) of the world were the lucky ones. Because they all experienced "Ah-Ha!" moments in their lives. Its a shame to have our kids learn these beautiful subjects without letting them experience "Ah-Ha!" moments. We don't have to have them invent crazy math formulas for this to happen either. Just a little bit of time for student-centered exploration will do the trick.

News of the Day: Reflection

This blog is supposed to describe my usage of Twitter as a search engine for my news, as well as my brief thoughts on what I read today in San Diego UT's front page story on Gary Stein, Marine Sargent from Temecula, CA. He has been identified as the Marine whom started a Tea Party FaceBook group and recently posted hateful and defiant speech towards the President of the United States, Barack Obama. I saw the article in the UT while eating a slice of pizza at Allen's in Carlsbad. I felt the urge to talk about it so I gave the paper over to the gentleman near me eating, told him this was a good, but sad read. I wanted to talk about it some more, so I looked up articles on the matter by searching "Stein Military" in my mobile TweetDeck App. and was directed to articles from Yahoo, Huffington Post, and a newspaper co. site. The UT quoted what Stein said on FB, which was in regards to his thoughts on disciplinary actions possibly happening to those whom were involved in the recent Koran burnings in Afghanistan. I will not repeat the quote, as many other news articles have refrained as well, and the latter story is another conversation in itself. I at the moment I am sickened, and scared, of people like Gary Stein.

I don't care about the story from a political standpoint. As a supporter of Barack Obama, some may feel I am mad at him because he doesn't support my views politically. But the way he spoke about the president was vulgar and disrespectful to the point that it made me upset. He and many Tea Partiers have been distasteful, hateful, and racist at times (See Part 2 of the video here). Coming from the standpoint that Nazis used hate to create political momentum, I feel that this is the most "nazi"-istic party America has ever bred.

Every person entering the U.S. military repeats an oath swearing to support and defend the U.S. Constitution and "that I will obey the orders of the President of the United States and the orders of the officers appointed over me." This an oath to good maintaining good form, supporting the republic for which its stands; it is also an oath of not supporting unethical behavior, like the burning of the Koran or urinating on dead Afghan civilians.

It's time to Learn Outside

This post is in response to my reading from a Tweeted link It's Time to Learn Outside.

As a future math teacher, it is a huge goal of mine to instill respect and understanding, if not love, for nature. Mathematics is a very effective way to understand the world in which we live in, and beyond! I have seen that textbooks have noticed this correlation, but there is something lost in translation when a teacher explains nature to a class reading from a textbook. Unnatural, is my pun-intended way of thinking about it. Your simply not going to get an enriching experience in understanding nature unless their is the physical presence of nature in your curriculum.

Now there is a small amount of this "learning outdoors" happening in public high schools today. For example, in learning trigonometry, many teachers send their students out in pairs with a clinometer to measure the angle of elevation of a tree or some other tall object. Then, by using the angle and the distance they are standing from the object, they can employ trig formulas involving right triangles in order to find out the height of the object. This is fun and all, but it doesn't teach the concepts; it just allows us a simplistic way to use the concepts.

In his blog, William Sterrett writes, "We'll need leaders who understand how the natural world works and how humans are a part of nature." No better place to foster this understanding than outside.

Learning in New Media Environments

After watching the TED video of Mike Wesch, I had some revelations about how media affects societies. Mike's stories about his experiences in Papa New Guinea were able to open my eyes about how this happens. I realized that when media changes, relationships change too. Mike said "media mediates relationships," and it can be positive or negative in its effectiveness. For example, I have found that my words can be misinterpreted a lot easier over a text message than when I am physically sitting next to a person at a coffee shop. Media can make you detached if misused.

As a educator, it is my responsibility to make sure the use of technology and various medias are used in a way that make the best of our innovations, rather than let the innovations get the best of us (through eliminating individuality and critical thinking abilities). For example, I see students in math classes using a calculator without being able to explain their procedures and their answers. Whats the use of using a $100 calculator to calculate an integral of a function if there's no connection for the student?!

I need to teach students to foster their creative minds to "analyze, criticize, see new information, create new connections, and ultimately create information." Our technology had made being knowledgeable unimportant. The ability to be able to use the knowledge technology provides us in a productive manner is what I see my role as an educator to be today.

Disrupting Class - Reflection on how disruptive innovation will change the way the world learns

Chapter 1: Why Schools Struggle to Teach Differently when each Student Learns Differently

1. Explain the difference between interdependence and modularity.  How is education currently organized?  



   - We have an interdependent architecture in our schools today. The curriculum is rather similar no matter where you are or who you are teaching because there is mandated standardization, and trying to change one part of the school system causes a change from another part and so on. On the other hand, "[m]odularity allows for customization" (Christenson, 2011, pg. 23). Modularity will allow us to teach students differently because we know they learn differently. In addition, students need to build knowledge off experiences. Different students have different experiences, and thus our teaching toward them should be different as well.


Chapter 2: Making the Shift:  Schools meet Society’s need

2. Explain the disruptive innovation theory.  What does this have to do with schools?


   - Chapter 2 describes two types of innovations that are visible in any industry. The first, there are the type of innovations that improve and sustain an existing industry. In Disrupting Class, the authors write about how "[a]irplanes that fly farther, computers that process faster, cellular phone batteries that last longer, and televisions with clearer images are all sustaining innovations. On the other hand, disruptive innovation is the phenomenon of products entering a market that are not labeled as "breakthrough improvements," like the improvement of high definition TVs. A disruptive innovation benefits people who had been unable to consume the oft-expensive product that the sustaining industry offers. In the text, the authors explain how the personal computer is a great example of a disruptive innovation. Successful disruption changes the market; everyone (almost everyone) has a personal computer, and I have never even heard of minicomputers.
   What does this have to do with schools? Well, the the problem with the public education system is that it is basically a monopoly. In addition, everyone uses it (kids/adolescents basically have a requirement to be educated). This means that it is basically impossible for the new business models that disruptive innovation theory creates to be allowed to develop on their own and mature naturally. 
   Our schools need to improve by embracing disruptive theories within existing schools, a task not yet done successfully in a private industry (yet there is hope, as schools have proven to be able to assimilate to disruptive redefinitions of performance in past).


Chapter 3: Crammed Classroom Computers

3.  Why doesn’t cramming computers in schools work?  Explain this in terms of the lessons from Rachmaninoff (what does it mean to compete against nonconsumption?)


   - We have implemented computers in school by "cramming" them into the existing teaching and classroom models that were in place before they arrived. We have yet to let them disrupt the old methods to improve and transform the way we teach and learn, with the idea to become a more modularly framed school system. 
   We have been trying to implement computers into a classroom in such a way that would be analogous to selling tickets to people expecting to see Rachmaninoff play his second piano concerto, but instead having Rachmaninoff push the play button on a phonograph recording of himself. It would seem ridiculous. The phonograph did not get popular by replacing live music, but by providing music to those whom could not be at a concert when they wished to hear music. Disruptive innovations originate and mature by competing first with nonconsumption. For example, the personal computer originated by providing a computer to those whom did not want to put a gigantic and expensive minicomputer in their garage. 


Chapter 4: Disruptively Deploying Computers

4. Explain the pattern of disruption. 


   - The pattern of disruption, where new substitutes for the old, almost always follows an S-curve when measuring the percentage of the market using the new approach over time. "[T]he initial substitution pace is slow; then it steepens dramatically; and finally, it asymptotically approaches 100% of the market" (Christenson, 2011, pg. 97). 



5. Explain the trap of monolithic instruction.  How does student-centric learning help this problem?


   - The trap of monolithic instruction is that teachers in this model teach in a way that benefits very few types of learning intelligences. With limited time to instruct, the teacher can't possibly cater to all learning styles for each bit of content students are to learn. "As the monolithic system of instruction shifts to a learning environment powered by student-centered technology, teachers' roles will gradually shift over time." With student-centered technologies, teachers will be able to "coach" students to fit their unique style. 


Chapter 5: The System for Student-Centric Learning

6. Explain public education’s commercial system.  What does it mean to say it is a value-chain business?  How does this affect student-centric learning?


   - Public Education's system operates like a value-adding process (VAP) business. A VAP business "brings input materials into one end of their premises, transform them by adding value, and deliver higher-value products...at the other end" (Christenson, 2011, pg. 126). Using this definition, students in a school are the input materials, and they are the educated material output the other end. 
   The public education's current commercial system hinders student-centric learning. Textbooks are predominantly geared toward the dominant learning style of the authors whom create them, which are geared toward the style of the standardized assessment given at the end of the term that checks for understanding. The current business model could be more student-centric; but, if publishers were to create "different books for each type of intelligence, their volume per title-and their profitability-would decline markedly" (pg. 129). The text goes on to say that a new facilitated network, rather than a VAP business, needs to emerge to provide student-centric products for students in our public school system.


Note: I found the question about value-chain business to be synonymous with VAP business. If you feel I am incorrect here, please comment.