Mother of all blogs (not really)

Looking over all my posts, I realize that I haven't answered all my questions but i've learned more than I could have ever imagined. As challenging as I thought this course, because I'm not a math major, I still managed to learn alot about how to teach math with applications in other subjects. The Inspire Math Academy was a nice touch, I cherished the opportunity to observe the interaction of students and volunteer teachers and the feedback was very useful. We got the chance to try out all the stuff we learned in class. When I saw how it worked out, I was even more convinced that i could and should use this in my classroom.
The big mountain for me was task creation. The information shared was tremendous, but when I sat down to actually create a task from scratch that was culturally relevant and cognitively demanding plus mathematically rich, I just wanted to hide under the bed.

i'm not sure how beneficial it was for me (not a math major) to take this course before taking math content courses. I know that I have a responsibility to catch up and don't mind, but the time constraints with deadlines for graded assignments made the extra work I had to put in a yeoman task. My thing is, don't you have to know something pretty well before you can teach it effectively?

That said, I have a healthy respect for this revolutionary idea of culturally relevant constructivist teaching. Letting go and letting students DO mathematics (or any other subject), strategic questioning to make students think, reflect and refine. There were many epiphany-like moments when someting that I heard a thousand times suddenly made crystal clear sense when we discussed it in class. For example - I never realized how ineffective lecturing was as a major form of instruction in the classroom.

Some of the things I will take back with me: the real purpose of the big ideas and what it actually is, thinking about students and what that means, how a lesson is supposed to flow and the types of questions that should be asked to move students toward sophistication of strategies and ideas.

These are some of the thoughts that I thought when I reviewed my posts to date.

(P.S. - Dr. Matthews, please don't ask me to do anything else... my brain is fried!)

reflections lesson 1

Reflections on the first lesson experience from my perspective. .

I always cherish the opportunity to sit in a classroom taking notes while another teacher is teaching. I get to do so much introspection. I like to look at the different styles.

teaching sixth grade students eighth grade stuff

Reflect on your expectations and opinions about going to Sandtown Middle School and teaching sixth grade students in the INSPIRE ACADEMY.

I look forward to this exercise or any exercise that allows me to refine my practice. I am not yet a math teacher and I am glad that I am the recorder/observer for the group so that I can watch and learn from my peers. In this profession, constructivism is good for teacher learning/training too, so I appreciate the opportunity. I am at present, a 6th grade science teacher so I'm anxious to see how these 6th grade-to-be students would respond to the 8th grade material. Then I could apply the same principle to science, hopefully. I'm going in with high expectations for the teachers AND the students.

teaching and learning math

I don't know about the rest of you but I am having a tough time with these tasks (geometry and algebra) . It seems like some math content (courses) would have been good to have under my belt before I could submit something I really feel good about being graded. Especially as my background is not math. Don't you have to know something before you can teach it effectively? Either that, or you must spend some time studying the content (difficult to accomplish with deadlines).

comments on first lesson plan

Discuss your ideas about your first lesson plan and the comments you received. Where there any surprises in the feedback? Were they already in line with your thinking? How does your current philosophy of lesson planning and teaching compare with what you wrote on you first lesson? What changes will you consider?

The comments I received on my first plan made many things "dawn" on me. I have come to realize the value of the big idea - its purpose in the lesson. My view of the big idea has now changed forever. This will definitely make write future lesson plans much easier. With respect to thinking about students - not just what background information they need but taking into consideration what they bring to the table as far as their informal experiencesith the subject matter thus far outside the classroom.
I have a better understanding now of what the During and After phases should look like - the types of questions that should be asked to get student to reveal their ideas, reflect and then refine them. The goal being sophistication. Wow. I never thought of the whole process holistically like that.

relevant tasks

In class we raised the idea that good problems/tasks should be relevant to the lives of students. What has your experiences regarding the mathematics tasks that you experienced as a student? What about a as a teacher? Do you see relevance as a valid focus for the midddle grades mathematics teacher?

Tasks I experienced as a student have not been relevant. No effort was made to make them relevant. You either got or you didn't, you were interested or you weren't. I'm not a math teacher but i see relevance as a valid focus for math teachers because it could mean all the difference especilly with struggling students. When tasks are relevant syudents begin to realize "ok, so this is why this is important.." or "now this makes sense to me" Students can relate becasue the scenario is familiar and they can focus on the real question. Maybe mountains can become molehills.

Letting go

The term Letting Go has been used by Van de Walle and in our classrooms to represent how teachers teach THROUGH problems. Where are you on this at this point? Examing the teaching stations, and your own ideas. Key- When should the mathematics teacher let go and when do you believe it is best to do otherwise?

I agree that for students to truly understand mathematics, they must spend a considerable amount of time doing mathematics. By doing math, students can observe relationships and make conjectures and even begin to ask why. Students can begin to make logical arguments for why the things they observe to be true are in fact true.

By letting go, teachers allow students to construct their own ideas. The teacher, however, should provide suitable tasks that challenge students and encourage thought. Students learn better this way versus when things are explained to them by the teacher. They learn from each other.

The teacher guides through strategic questioning and monitoring. S/he should not let go all the time - there are times when the teacher could review, pull ideas together in a way that makes sense, present a mini-lecture on a topic or an overview, help students organize their thoughts.

Most importantly, by letting go, teachers can show students that there may be more than one way to look at a thing and there may be more than one way to arrive at a correct answer.

How is mathematics used by those in the pubic domain?

How is mathematics used by those in the pubic domain? To address this question, explore the news or print media in the next few days to get an idea of its power to decide. What does this imply for the teaching of mathematics, constructivism, and who can do mathematics?

There's a broad spectrum of uses for mathematics in the public domain. One example is the use of statistics to influence decisions. The validity of research and studies on which many arguments and theories are based depends on the statistical analysis of data generated by experiments, surveys, polls etc. In sports, statistics could determine the value of an athlete.

Meteorologists depend on mathematical models to predict the weather. If the price of oil per barrel increases significantly, it would raise the price at the pump, which in turn could affect consumer spending and the economy. If a particular stock goes up or down by a certain percentage, stock holders would be affected.

Implications for the teaching of mathematics: the teaching of mathematics must prepare students for the real-life tasks that await them, and understanding the world around them. Teachers need to draw more on these examples for use in their classrooms to make math more relevant. By implementng constructivist strategies, the math makes sense and becomes 'doable' for everyone.

"limitations" to the student-centered teaching of mathematics?

Constraints are issues that can be overcome. Limitations make one think of reasons why something cannot be achieved. Some "limitations" of student-centered learning:1) fear of loss of control by teachers; 2) lack of classroom culture necessaryfor student-centered learning to occur; 3) lack of knowledge on teacher's part on how to manage/facilitate/monitor activities in such a classroom.

My current thinking is that studen-centered teaching is a good idea - students construct their own ideas and learning takes place - is is the number 1 goal. When students are learning, discipline problems decrease and classes can be fun.

Renee's blog on constructivism in classrooms

Prior to this course, I thought that students should be able to see problem worked out on the board by the teacher, and be able to reproduce it in their practice problems - like I did when I was in school. I took his notion with me to the classroom as a teacher. I would explain something in detail on the board, then I wondered why didn't they just reproduce what I did to get the answer?
From these theories and perspectives of constructivism I have learned :
1) that students learn in different ways
2) the brain should be actively engaged in learning
3) The value of social interaction in learning
4) The value in letting students come up with their own ways to solve problems that makes sense to them
Implications: Many teachers (including me) have to change their whole paradigm from teacher-centered to student-centered instruction in classrooms. Let go of the reigns - not altogether, but enough to let the student develop naturally.
The classroom will look like students running the show, with the teacher facilitating, monitoring and guiding the discussions. Students must be taught the rules for discussion and constructivism classroom culture.

ReneeBlog

I have had to teach math concepts in my science class this past year, specifically measurement. I couldn't figure out why it was so difficult for the students for the most part to grasp it, much less retain it. What I said in class today about teaching mathematics was how I thought it could be better taught, realizing that I have to rethink the way I teach math. I have realized even while I was teaching, that the person that does the most work (i.e. the teacher) is the one who learns the most. I often felt the need to explain, demonstrate and model and that took up alot of time.

So I said that math is about strategy and solving real problems. However, I feel as though I understand this better in theory than in practice.