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.