During this visit, we observed the morning math block again. Ms. H had the students review their math homework from the previous night, which was on multiplication and estimation. The objective of the lesson was to try to get students to approach the same problem with multiple methods, and to understand the underlying concept behind how multiplication works. The teacher explained to us that it is important that students are not just simply going through the steps of an algorithm to solve a multiplication problem, because when they get to higher level problems (with two or three digit factors) they will be lost without having a solid foundation in the fundamentals.
In order to achieve this understanding, the teacher modeled several different methods - traditional algorithm (multiplying each column, carrying over, and adding), estimation (rounding a two-digit number to the nearest ten), using place value blocks, and using graph paper to draw grids and arrays. This was done mostly through direct instruction, the teacher explained each method and allowed for guided practice, then independent practice (during which she circulated around the room and helped out struggling students).
I felt this approach was very effective, especially in the discipline of math where students need a solid understanding of basic concepts and skills before they can move on to higher-level operations and functions. In providing so many means of accessing one particular skill, the teacher is opening up multiple points of access for students with different learning styles. Her way of differentiating instruction allowed for visual/kinesthetic learners (place value blocks), logical/visual learners (graph paper arrays); analytical learners (algorithm method) all reach the same goal and understanding through different means. Also, the blend of group instruction, individual practice, and small group practice allowed each student to learn in an environment that best suited their individual learning needs.
At the end of the lesson, the teacher remarked to us that she did not get as far as she had hoped to; some students seemed to be still struggling with grasping the basics, so she would have to extend the lesson until the next class. She felt that they were not yet ready to complete the homework she intended to give out that day, so she was going to hold it off until she thought it would serve as a good review/reinforcement for the students. I really gained a lot from the teacher's insight and reflection, as well as her ability and willingness to be flexible and sensitive to how students were responding to instruction. It is so tempting to have too much rigidity and structure in the classroom, so I feel that I can learn a lot from observing and reflecting on this experience.
Sunday, November 11, 2007
Monday, November 5, 2007
Field Visit 4
Once again, we observed instruction during the morning math and problem solving lesson. This week we focused on student participation, specifically charting each student's participation throughout the lesson.
The class began with a "Multiplication madness" challenge, where the teacher gave each student a different problem and asked them to solve it using multiple methods. This was to test their understanding of how multiplication works, since many students seemed to be going through the steps blindly without really understanding how they reached the answer. The algorithm the teacher wanted them to understand looks like this:
Problem: 64 x 7 = ?
Solution: 60 x 7 + 4 x 7 = 420 + 28 = 448
The students also used estimation to check their answers using estimation (multiplying 60 x 7, which is 420, and understanding that the actual answer must be bigger, since we rounded down when estimating).
In the process of helping students attain an understanding of these concepts, the teacher used practice problems and examples with the whole class, asking such questions as, "Tell me what you did. Walk me through the steps." This forces the students to use metacognition and become more aware of their own thinking processes. The following diagram shows the frequency of participation of each student, by seating arrangement:
The participation was fairly well distributed, with most students contributing 2-3 responses or comments during the 1-hour math block. One student only participated once; he seemed to be struggling with understanding the concepts and was looking down at his own worksheet rather than attending to group instruction. Another student participated four times, he also seemed to be struggling but was more willing to talk through his thought processes and be corrected and guided in front of the whole class. This may be due to a difference in learning styles or personalities, some students are more willing make mistakes in front of their classmates, while others feel that learning is a more independent endeavor. The teacher did well in recognizing and differentiating to these different learning profiles, she does not push any student to participate beyond what they are comfortable with, and she also offers extra help or individual tutoring sessions to students who need one-on-one work. I felt these options were appropriate and effective for the class and the group of students she was teaching.
The class began with a "Multiplication madness" challenge, where the teacher gave each student a different problem and asked them to solve it using multiple methods. This was to test their understanding of how multiplication works, since many students seemed to be going through the steps blindly without really understanding how they reached the answer. The algorithm the teacher wanted them to understand looks like this:
Problem: 64 x 7 = ?
Solution: 60 x 7 + 4 x 7 = 420 + 28 = 448
The students also used estimation to check their answers using estimation (multiplying 60 x 7, which is 420, and understanding that the actual answer must be bigger, since we rounded down when estimating).
In the process of helping students attain an understanding of these concepts, the teacher used practice problems and examples with the whole class, asking such questions as, "Tell me what you did. Walk me through the steps." This forces the students to use metacognition and become more aware of their own thinking processes. The following diagram shows the frequency of participation of each student, by seating arrangement:
The participation was fairly well distributed, with most students contributing 2-3 responses or comments during the 1-hour math block. One student only participated once; he seemed to be struggling with understanding the concepts and was looking down at his own worksheet rather than attending to group instruction. Another student participated four times, he also seemed to be struggling but was more willing to talk through his thought processes and be corrected and guided in front of the whole class. This may be due to a difference in learning styles or personalities, some students are more willing make mistakes in front of their classmates, while others feel that learning is a more independent endeavor. The teacher did well in recognizing and differentiating to these different learning profiles, she does not push any student to participate beyond what they are comfortable with, and she also offers extra help or individual tutoring sessions to students who need one-on-one work. I felt these options were appropriate and effective for the class and the group of students she was teaching.
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