Week Three - Reaction to the Private Universe Project Video - Workshop 3: Inventing Notations

One thing that I thought was very interesting in the video was the high level of support that the Englewood teachers’ received. It is not uncommon in the field of education for teachers to be required to attend a workshop that is labeled as professional development and then not receive any further professional development on the topic discussed in the workshop. While teachers are obviously expected to implement new ideas that they learn in a workshop, they are often not given any support from facilitators coming to their classrooms or meeting with them after school. Thus, the end result is often that when a teacher gets frustrated he or she often gives up because there is nobody with whom to discuss the situation that he or she has encountered. As a result, continuous professional development is the most effective way to get teachers to learn and implement new things. Fortunately, for the Englewood Public School System, the teachers did, in fact, receive continuous professional development. As a result, the ideas seemed to be implemented in classrooms effectively.

On a different note, I particularly liked that the students in the video were given the opportunities to share their ideas. This is the best way for students to learn from one another. I found it interesting that students came up with vastly different strategies for solving problems. For example, some students made lists, other students created diagrams, and some students made tables. Allowing students to create their own representations of their solutions provides a teacher with the ability to see how students “see” problems. In essence, by allowing students to share their solutions, a teacher can learn how students think about a problem and how they go about solving it. This is very valuable information that is not always easy to acquire.

One must remember that a student’s level of interest generally correlates with his or her level of engagement. Thus, I particularly liked the decision that the teacher from Redshaw Elementary School in New Brunswick, New Jersey made, which was to allow students to work on problems that interested them. The video informs the viewers that the students were not interested in solving for the number of possible combinations of two different colored blocks to form five-block towers and six-block towers. However, the students were interested in the number of combinations of four-block towers that could be made from three and four different colors. Thus, choosing to use the pizza problem was a great decision because it is similar to the type of problem that the students wanted to solve. This demonstrates a teaching strategy that is flexible and adaptable to student interests. Students are more likely to learn when they enjoy what they are doing. Thus, this method of teaching is admirable because it is more likely to be effective. As a teacher of science, I try to choose topics that interest my students to teach them the major themes of biology. For example, we are currently learning about cell division, and several students have asked questions about cancer. While cancer is only a subtopic of the unit on cell division, I will now spend additional time discussing cancer its relationship to cell division because the students are interested in it. In essence, I can use the students’ interest in cancer to get them to learn the information about cell division that is required by the New Jersey Core Curriculum Content Standards. Thus, when I become a mathematics teacher I hope to incorporate this strategy of teaching into my teaching of the new subject matter.

I was really surprised by one Conover Roads Elementary School fourth grade student’s method of solving the pizza problem. The student was able to use a system of binary numbers to come up with the solution. I felt that it was a better strategy than the ones that I used to solve this problem on the first day of class. The student’s method was very efficient, and I think I could have solved the problem faster had I used his strategy. In addition, his chart made it much easier to determine if there were any duplicate solutions. My own realization that I learned from this elementary student provides me with additional motivation to include the sharing of ideas in as many mathematics lessons that I teach as possible. This way the students can learn from one another.

Also, the discussion between Amy Martino and this same student from Conover Roads Elementary School demonstrated that students will not necessarily notice isomorphisms unless one actually encourages them to think critically and creatively about two problems that are basically the same. This type of activity where students are forced to think critically and creatively is so important at a young age. All too often, students struggle with being able to come up with original ideas. They want to be told what to do and how to do it. By encouraging students to think critically and creatively in elementary school, students will be more capable of dealing with high level thinking questions in high school and in college.

On a sad note, I agree with the narrator that the world is full of “Brandons”. What she meant by this is that there are many very intelligent students who “slip through the cracks”. In my opinion, these students are capable of thinking critically and creatively; however, they do not fit the mold of a typical “smart” child. In other words, they may not do well on standardized tests or some performance-based assessments. However, when these students are given free reign to solve a problem in their own way they can be impressive. I have seen this time and time again in my biology classes. For example, some students who rarely do well on tests, quizzes, and labs shine when I assign my Cell Parts Project. Basically, I require the students to teach the class about a cell part in any way that they see fit. Many students use PowerPoint Presentations. Other students create songs, games, or movies. However, my point is that some students who fail assessment after assessment are capable of demonstrating a high level of understanding in an assignment like this. Thus, we must give students the opportunity to think about problems in their own way. This will allow students the opportunity to make the material make sense to them. I plan on incorporating these ideas into my teaching when I become a math teacher.

In conclusion, I felt that the video made several important points. Students should be given the opportunity to think critically and creatively in mathematics class. Also, at least at first, they should be given free reign to determine what notation to use and how to use it. In addition, students should be able to convince someone that their answer is correct. Lastly, students should share their ideas with their classmates, so that they can learn from one another. In my opinion, anyone who incorporates these ideas into their teaching of mathematics is likely to be more effective.