The following is a great question from a reader and my attempt to answer it. Join the conversation by email (abfosEd@gmail.com) or on Twitter (@AbfosEd)!
I have been reading everything I can get my hands on that has CCSS stamped on it. I have an aggravating issue that I just can’t find guidelines for. Regarding the written sequence of the math domain Numbers and Operations in Base Ten, was there a rationale for the sequence in which they are listed? More importantly, what is your professional recommendation for the order in which they should be taught? I’m trying to make sense of my district’s rationale for sequencing the “powers of ten, multiplying and dividing whole numbers” standards during first quarter and the “read, write, compare, and round decimals to thousandths” in the 3rd quarter. From your perspective as a classroom teacher, would you have concerns with that particular sequence? I appreciate kindly your reply.
Thanks for your question and for engaging in the conversation on commoncorestandards.com! Like you, I am learning and studying to make the standards practical. Let me address your questions to the best of my ability in several parts.
- What is the rationale for the sequence in which the standards are listed?
My understanding of the sequencing of the CCSS-Mathematics comes from the CCSS document itself as well as some training I recently participated in through MC² and New Mexico State University.
In theory, the standards were designed so that they could be engaged by teachers and students in their current sequence and would lead to deep understanding of the concepts in a logical progression.
However, the CCSS authors recognized that learning is fluid and may not always follow those theoretical lines of progression. See the introduction to the CCSS-M. The rationale for the listed sequence is also contained in those introductory paragraphs.
- What is your professional recommendation for the order in which they should be taught?
In my view, the CCSS-M represent an excellent outline of the skills and concepts that should be mastered, mostly in order, at each grade level. However, I envision many situations in which a teacher will make informed decisions about changes that should be made in sequence or depth of instruction based on the needs and prior knowledge of students in the classroom. It is very likely that two or more standards should be taught and uncovered simultaneously. For example, standards 5.NBT.1 and 2 (Recognizing computational patterns in multiplying or dividing by powers of 10) really MUST be taught together in order to achieve meaningful depth. This is where the instructional shifts come into play. Each grade level has particular focus areas that encompass several clusters or standards. An excellent resource on the idea of FOCUS and overlapping standards in major, supporting, and additional roles can be found at engageNY.org. Here is a link to the document, then scroll down to your desired grade level. I would recommend that the CCSS-M should be an important guide when considering scope and sequence of instruction, but it should not be set in stone.
- Would you, as a classroom teacher, have concerns with the particular sequence prescribed by my district for 5th grade Numbers & Operations?
In a word, “yes”. It seems to be the nature of district curriculum maps to attempt to make standards better, or more practical, or more “user-friendly” by changing the sequence of adopted standards to match the textbook or the way things have been done in the past. I think I see that your district curriculum map is trying to separate the learning of whole number operations from the work of decimal operations, but I think this is a mistake. I believe students would be much better served with a complete understanding of place value with whole numbers and with decimals before they begin working on the operations. This gets to the heart of the instructional shifts and how we must in many cases change not WHAT math concepts we teach, but HOW they are taught and presented. Your district sequencing of these vital 5th grade Math standards suggests a focus on algorithmic process instead of deep conceptual understanding. Do we want to simply teach 5th graders what to do when they see decimal operations, or do we want them to truly understand decimals and make good mathematical decisions about how to use decimals and know that their work makes sense? I would encourage you to begin the professional conversation that many of us are having across the country about how to stay true to the CCSS-M while allowing for individual teaching styles and rich educational experiences. But stand your ground and remind colleagues and administrators that the goal is mastery of the standards, not just coverage.
If all else fails, remember: We don’t teach the curriculum map (or the CCSS), we teach students!
Thanks again for your question, RJ, and for indulging a lengthy reply. I hope it is helpful.