As educators, we need to see the greater picture: How will our students be able to apply the concepts in the future? Surely, they will remember a jingle that may teach how to properly regroup in subtraction so that they can get the correct answer. However eights years from now, the jingle will not be of importance. Rather, knowing how to utilize the skills will.
I enjoyed studying the standards between grade levels to see how they built upon each other. I'm sure there are resources already available showing these spiraling trends, but I found a simple resource by the University of Arizona explaining how each grade level builds upon a certain standard, hence the link: http://ime.math.arizona.edu/progressions/
Because each grade level builds upon the previous and now holds great accountability through the CCSS, it is important that students are able to understand and explain the conceptual processes of mathematics. As I prepare each lesson and/or unit for my students, I find myself reflecting on how I learned a mathematical concept (i.e., division) and begin understanding why in division, we need to divide, multiply, subtract, and break down. This concept makes sense now because I know understand the conceptual background between this shortcut. Hopefully one day in class, I can begin to show our cohort why all these shortcuts we learn work. Eventually by dissecting these shortcuts, we will be able to teach our students the conceptual understanding behind mathematics.
Therefore, it is important for quality articulation between grade levels so that teachers can collaborate and share how to understand and teach a certain concept. Hopefully through multiple grade levels, a certain mathematical process can be utilized to teach the methods in which students will practice over 2-3 years. Last week, we had Chinese students and teachers visit and attend our school for several days. I conversed with the Chinese teacher while I was teaching division, and the teacher told me her students learn division starting in first grade using base-ten blocks and continue to practice their division in second grade. In third and fourth grade, students practice the algorithm behind division, which means these Chinese students have been learning and practicing division for 4 years. No wonder they think like super computers! Jokes aside, we cannot limit our students saying that they are unable to learn a certain concept. Instead, we have to present a lesson with careful scaffolding so that students are able to grasp the content.
I think grade level articulation is paramount to establishing the development of best practices and strategies for improved instruction. However, "vertical " dialogue and knowledge between grade levels, below and above, are particularly powerful and critical to understanding the "whole picture" of where are students are coming from academically, and where they will be going up to, "the next rung of the ladder"
ReplyDeletethe following school year. Math is very sequential. Teacher knowledge of the sequential nature of mathematics is important to understanding where we pick up from an instructional level,and where and how we need to take our students to the next level. Collaboration, knowledge, dialogue, and articulation about best practices are powerful tools to guide meaningful instruction.
It's interesting that you mention that through teaching you have learned the conceptual reason behind why the methods (strategies/tricks) we learned in mathematics, growing up, worked; because I have found myself making some of those same discoveries, as I work to develop a conceptual understanding of mathematics within my students.
ReplyDeleteI think that this idea of what we grew up learning mathematics is also plays a role in teacher's reticence to change from skills based to concept based teaching, especially if they don't feel that math is a strong subject for them. It's much easier to show students the tricks than to have them explore and make their own conclusions.
I enjoyed studying the standards and being able to view what knowledge my students are coming to me with, what I have to teach them to contribute to their math progression, and what they will learn next year. I feel that it is crucial for math instructors to be able to collaborate in order to make common core work. It will definitely be a challenge to get students using the academic language and then having them articulate concepts on CCSS test.
ReplyDeleteCurrently at my school, one of the main goals is to reward students for using the academic language, even if they use it incorrectly. When this happens we see if another student can help their classmate correctly use the academic language.