ENTRY 4: PRIME TIME UNIT PLAN
Description of Entry:
This was the unit plan I used to teach my three regular sixth grade math classes and one honors class. It is entitled Prime Time, and is part of the Seattle School District’s newly adopted curriculum, the Connected Mathematics Project (CMP). The overall goal of the CMP is for students to develop conceptual understandings of mathematical ideas. Students work through investigations to learn these mathematical concepts and answer reflection questions to communicate what they have learned. This unit focuses on basic number theory, such as factors, multiples, prime and composite numbers, even and odd numbers, square numbers, greatest common factors, and least common multiples.
Program Goals and Targets:
In this unit plan, I demonstrate my ability to plan over an extended period of time (1C). The unit plan covers the entire Prime Time book, which turned out to be 28 school days. However, I still remained flexible enough to modify the lessons when there was need. I also show my ability to use and understand instructional strategies (1B). I do this by planning various kinds of activities to reach all learners, such as the Product Game, problems of the day, tiles to model factor pairs, and reflection questions. By designing the unit around the key concepts and using inquiry strategies in developing my curriculum, I also demonstrate my subject matter knowledge (1A).
Reflection:
This was the third CMP unit that I had taught, and I believe that I have learned a lot along the way. I really like the way that the curriculum is set up. Each unit contains four to seven investigations. In these investigations, concepts are explored in-depth with a goal of deep understanding. Each investigation is followed by a set of reflection questions, in which students articulate their understanding. There is a significant push for student reasoning in the CMP. Students are asked to reason with information represented in various ways (pictures, graphs, symbols, and written words) and to move among them flexibly. The material is challenging because of the amount of reasoning they are asked to do, and the depth of explanations they are asked to make.
One of the biggest debates in mathematics education is what it means to learn and understand math. Traditionalists would argue that learning comes by listening carefully to what the teacher says. From this standpoint, a teacher’s job is to give students the important information, demonstrate the procedures, and then have the students practice what they just saw. Understanding would then consist of computational proficiency in the algorithms learned.
However, constructivists would argue that students only learn meaningfully when they construct their own knowledge. From this standpoint, a teacher’s job is to facilitate students’ cognitive development, not to transmit information. Then, students are considered to have understood something if they saw how it was related to what they already knew. The CMP, like most standards-based curriculum, takes this perspective.
One of the biggest downfalls of standards-based curriculum is the amount of time required to complete the units. This was one of my initial worries during the use of the CMP. The unit entitled Data About Us was a 25 to 30 day unit on the mean, median, and mode. How could I justify spending five to six weeks on a topic that was traditionally covered in five to six days? But as my students and I went through the material, I saw that they were developing a much deeper understanding. They were not simply memorizing formulas, but discovering what those mathematical terms were. They worked through problems that conflicted with their previous understanding, forcing them to revise their prior knowledge. Their level of understanding had to be high, because of the constant explanations and reflections they were asked to make.
Over the past few decades, the education field has realized the importance of conceptual understanding in the mastery of math. Whereas traditional math educators saw factual knowledge and procedural facility as mathematical proficiency, today’s educators see conceptual understanding as a huge component as well. As the National Council of Teachers of Mathematics (2000) state, “Change is a ubiquitous feature of contemporary life, so learning with understanding is essential to enable students to use what they learn to solve the new kinds of problems they will inevitably face in the future” (pp. 20-21). For these reasons, there has been a trend to move away from curriculum focused on rote memorization and algorithms, and more towards those focused on learning with understanding. While this process may take more time than the traditional method of teaching, I believe that it is well worth it.
Return to Portfolio