Private Universe Project in Mathematics Workshop 1: Following Children's Ideas in Mathematics

The Following Children's Ideas in Mathematics video opens with the following questions: “Are these ideas [the mathematical principles taught in school] extended in subsequent grades? Will the mathematics my students have learned help them in their careers?” These are two very important questions. The first question is based on the fact that students need reinforcement, and thus, it is important that what they learn is used in subsequent grades levels. In addition, what the students use should be expanded upon as they get older. However, it is probably the second question that is more important. It seems to be a question very similar to what Grant Wiggins and Jay McTighe would ask with regards to their Understanding by Design unit planning strategy. Determining if the mathematics being used has a purpose in life is very important because teachers need to be able to identify what concepts students will need to remember five, ten, or even twenty years later.

When watching first half of the video entitled “The Youngest Mathematicians”, I realized that revisiting the same mathematical ideas in subsequent grades was vital to a student’s growth in terms of mathematical thinking. What was most surprising to me was the amount of growth that some students could show in just a few months. For example, the young boy in the video named Michael learned to apply a strategy in third grade that his classmate had applied in second grade. Learning from one’s classmates is something that is typically absent in a traditional math class. Also, the number of students who drew lines to form combinations increased dramatically from second to third grade. This indicates how the degree of mathematical thinking as it pertains to multiplication increases dramatically from second to third grade with the non-traditional style of teaching in the video. In addition, I noticed that the teachers employed a “learning by doing” strategy in the video, which is a lot better than the simple rote memorization strategies that the teachers used to use before the standards movement.

When watching the second part of the video entitled “From Towers to High School”, it made me think about how important it is that we challenge students. When I look in mathematics classes I almost always see the same thing. First, the teacher goes over the homework. Then, the teacher lectures about something new. After that, the students are given some problems to work on that relate to the new learning. Lastly, the students are assigned homework that requires them to practice what they learned in class. There is very little creativity in this style of teaching. Plus, it is too teacher-centered. Students need to learn through inquiry, and this type of teaching does not meet this need. However, the video shows students working with Unix Cubes, which is certainly a student-centered activity. It appears that the students in the video were challenged from a very early age to think critically about problems and develop their mathematical thinking skills. In essence, the video presents a feasible alternative to teaching math using rote memorization and formulas.

The film ends with two questions. “In what ways are the students in the study similar to your students? How are they different?” Personally, I think they are very similar to my students. Just like the students in the video, my students learn best when they are involved in the learning process. Thus, my students learn best by performing labs, building models of cells, DNA, proteins, and other molecules, and participating in their own learning experiences. The students referred to in the video performed better in the non-traditional math classes, but when they were put in a geometry class that was taught in a traditional way they did not learn much. My students are the same way. They do not retain as much from lectures as they do from labs or hands-on activities. The one major difference between the students in the video and my students is that the students in the video worked in an inquiry-based mathematics curriculum from grades two to eight. My students likely did not always have teachers that taught them in this fashion, and thus, I had to train them in how to learn in an inquiry-based setting at the beginning of the year.

In essence, this video points out how important it is for students to be challenged at a young age in mathematics. It is so important for students to begin thinking mathematically as soon as possible. It is also extremely important that students build on the skills that they learn in one grade level in the following grade level. In essence, this film gives me a lot of ideas on how math should be taught.