First lesson experiences from my perspective

The students were confused at the beginning. Then they begin using trail and error. Students began making progress when they started working together. As time passed, students continued being engaged in the problem. They became excited once they found the value of a variable. They really worked well together, and students who finished first begin assisting other students. During the final class discussion, students were able to explain how and why they had their answers.

Expectations about going to Sandtown Middle School

I honestly do not know what to expect. This will be my first time seeing an entire lesson done by problem based teaching with middle school students. Although the task is an algebra task, I feel the 6th graders will have access to the problem based on our group planning. I am looking forward to this lesson.

I also believe it may be a challenge because we do not know these students. We don’t know their ability level. Although I understand all lessons do not go as planned, I believe we as teachers are better prepared when we know our students and their learning styles.

Teaching without Procedure?

I understand the importance of students constructing knowledge. I also understand that problems/tasks should be relevant to the lives of students. But how who I teach order of operations, without giving rules. I think this is a topic that will have to be taught through procedure. Another topic is slope, a student can understand the concept of slope, but without giving the student the formula m=y2-y1/x2-x1. How will students solve a problem?

Importance of Relevant Task

Problems that are relevant to the lives of students are interesting because it is something to relate to. Middle school students need to be engaged to learn. By having good problems/tasks that students can relate to, we should be able to assist student in learning and making connections to what they already know.

First Lesson Plan

One major change made to my lesson plan was the big idea. The new big ideas were a bigger picture of what the lesson plan was about. Big ideas are important because they identify what is require to be learn by the end of the lesson. I also had to make changes in the before stage.
The first lesson plan was mostly teacher-center. The opening started with the word “fraction” on the board and students were to individually write a definition for the word, using pictures, diagrams, words, etc. Students would then label all known parts of the fraction: fraction bar, numerator, and denominator. Next they would answer a series of questions, including what does numerator mean? What does it stand for? What does denominator? Again this process was teacher-centered and depending on previous lessons taught by the teacher, not constructed knowledge. There was also no clear task, students were asked to compare fractions 1/10, 2/5, and 4/10. This was not a clear problem-based task. As a result the task was changed to
There are eighteen pencils on the table. Ten of the pencils are sharp. What fractions of pencils are sharp? What fractions of the pencils are not sharp? Are there more pencils sharp or not sharp?
This task is more student center. Teacher would monitor student’s progress.

Letting Go.

To me letting go means avoiding direct instruction. Letting go allows students to think for themselves and allow conversation among students. This allows students to utilize and sharpen their thinking skills. Letting go, may be difficult because it is a new concept to us. We want to teach the way we were taught. But in order to teach what needs to be taught by the new Performance Standards, we may need to try constructivism as the new deliver of mathematic concept. I am willing and definitely will try these new concepts in my classroom. However, I know I will definitely need to work my questioning technique. Again, as a new concept, it may seem hard. Only because it is different, it is not what we are use to doing. But I believe it is doable.

Math in the Real World

Math is used all the time. We use math in our personal lives to balance our checking accounts, to calculate or estimate our groceries bills, to set monthly budgets, just to name a few. A sales company may use math to budget expenses, make sales predictions, interpreting graphs and charts and analyzing data. A mortgage company uses math to calculate monthly payments for loans depending on the amount borrowed, the interest rate and the time period of the loan. Tire shops use the circumference and area of a tire and/or rim to determine if it will fix on a specific car.

Math is all around us. Math teachers should use this to our advantage. We should find information and problems that are relative to experiences of our students. By using relative information and problems, the students are more likely to retain information.

June 19 - Limitations

Letting go is definitely a major limitation to student-centered teaching in mathematics. As teachers, we tend to teach the way we were taught which is traditional the teacher-centered model. Teacher’s attitude toward the concept is another limitation. Teachers are already responsible for covering a certain amount of content within a year and may feel pressured. Some moving out of their comfort zone may not be a priority.

Moving toward student-centered teaching methods will be beneficial to the student because it increase student skills, motivate student involvement and participation, as well as, force high level thinking. Student-centered teaching also requires time for planning. Teacher must provide opportunities for students to solve problems, construct examples, answer questions, explain reasoning, and summarize discussion. Teachers must think ahead, we must do less telling and allow students to discover. The ultimate goal is for students to retain knowledge and know why they are doing what they are doing.

June 14 - Reflection

Constructivism and understanding is important when students learn mathematics. In using these theories students will be involved in the problem and will not become bored and possibly cause other problems.
For example with teaching through problem solving, student will have an opportunity to explain why and how they solve the way they did. This gives student the chance to express themselves and builds self-confidence. While working in groups, each member has something unique to bring to the discussion and give them an opportunity to learn from each other through group exploration.

June 12, 2007 - Reflection

My past experiences in learning math has been taking notes and practicing problems working individually. My teaching experience in math has been taking notes, practicing problems, and applying concepts through solving real problems within groups. However, I often find myself using most of the class time lecturing (like I was taught) and realize I (the teacher) am doing most of the work within the classroom. Sometimes it becomes frustrating when the students still do not understand.

I realize that making a connection, helping the students understand why a concept is important is beneficial (ex. solving real world problems). I must now learn to allow the students to do most of the work, by solving, explaining, and using different strategies to solve problems in class.