- Gain an understanding of the Numbers and Operations in Base Ten Progression across Grades K-5, informed by the Progressions for Common Core State Standards in Mathematics.
- Collaborate within and across grades levels to make connections and enhance instruction through the use of Common Core Math Standards coherence.
Things to Consider Throughout the Workshop:
- What type of FOCUS do I need in my grade level to help a student be successful with Numbers and Operations?
- How do we work together within AND across grade levels to ensure COHERENCE?
- How do we maintain proper RIGOR in our instruction including: Conceptual Understanding, Fluency, and Application to help students master the understanding of Numbers?
To Begin:
1. We will be working on dissecting the Numbers and Operations in Base Ten, K-5 Progression Document in order to better understand the coherence of fractions across the grade levels. Please download this document and use it as a working document making your notes, clarifications and new leanings directly on it. (Click below)
Progressions for the Common Core State Standards in Mathematics, Numbers and Operations in Base Ten
** Read Pages 2-4 of this Document to gain an overall understanding of the Overview of this Document
** Read Pages 2-4 of this Document to gain an overall understanding of the Overview of this Document
2. Watch the short video clip of the Numbers and Operations Base Ten Coherence: Click Here
3. After completing 1 and 2, comment below on the following:
- What is the importance of understanding the Progression of Numbers & Operations in Base Ten?
- What is one overall idea that you noticed?
- What is the importance of understanding the Progression of Numbers & Operations in Base Ten?
- What is one overall idea that you noticed?
Understanding the importance of the Progression of Numbers and Operations in Base Ten seems critical with the common core standards. The spiraling effect from grade level to grade level is something that interests me and is the reason I took this course. The overall idea I noticed is that students have to see numbers as more than just “numbers”. They have to see numbers and think about how they can be composed and decomposed in order to perform operations. Having this foundational knowledge is important, however, fluency with number operations is imperative.
ReplyDeleteIt is important to understand the progression of Number and Operations in Base Ten. Knowing what is taught at each grade level, helps you to see how the skills are connected and built upon each year. Students are expected to develop a deeper understanding of numbers. Initially, they will learn how to create models or drawings in a concrete form. Eventually, they need to begin to think more abstractly about their representations. I can see how models will help students to conceptualize what the numbers really mean.
ReplyDeleteIt is imperative to understand the base ten number system in order to be successful with the common core standards. In order to gain a true understanding of numbers, the learning should begin right at the K level with a deeper emphasis on the number system. Students learn how to bundle and decompose numbers to understand operations, rather than just rote memory to learn facts. I notice that in order for this method to be effective, it needs to begin in K and build upon that in the upper grades.
ReplyDeleteI agree that this instruction needs to begin in kindergarten. As a 5th grade teacher, we struggled to implement these ideas the first year because students lacked the foundation. Each year seems to be a bit easier as the students coming up have had more instruction it that area.
DeleteLet me start by saying the reading and the video are very confusing to someone who is in a secondary classroom. The only reason that I can understand what is being discussed is due to a prior training with an E1B math specialist, who showed us how her daughter is learning to add. I do not think the reading allows the reader to grasp the concept unless they already have experience with the topic. I think a you tube video showing what they mean by adding and subtracting with base ten units would have been very helpful in this blog. Now to answer the questions...I think the use of Base Ten helps students truly understand what a number means. By visualizing 500 as 5 100 units, it helps students develop a better understanding of numbers. The one thing that stuck out to me was the use of "algorithms." This may have stuck out to me, because I really don't have a sound understanding of algorithms and never used that term until after graduated from college and became a teacher. It seemed like everything was based upon an algorithm in the text. I really do not feel that the text was written in a way that elementary teachers can understand the reading without being able to collaborate with specialists in the field.
ReplyDeletehttps://www.youtube.com/watch?v=Cgv2qAlOEWE
DeleteSeeing something like in the link above was mind-blowing to all of the math teachers at the high school level. We couldn't believe how drawn out the process of adding had become.
Collaboration is an essential tool. As an elementary teacher, it has been super helpful to work with others to gain a greater understanding of how to teach math in this new way.
DeleteThank you for sharing the video. I was also confused by the text and appreciated the added link to help visual what was being stated.
DeleteThanks for sharing the extra video link. The visuals that teachers provide are meant to help students make a better connections with how the progressions work. It is a very time consuming process; however, I have noticed it helps students become strong problem solvers at the elementary level.
DeleteThanks kyle! Your jumping the gun lol. The rest of the discussions have the videos to watch :)
DeleteThanks kyle! Your jumping the gun lol. The rest of the discussions have the videos to watch :)
DeleteI loved this video - it was very clear that this boy really understood what he was doing, rather than following a set of prescribed rules given to him.
DeleteI think it is very important to have an understanding the progression of numbers & operations in Base 10 for many reasons. Mainly, it is so much easier to grasp the why's and how's down the road if you see where it started. If you can see where your students came from/started, it is easier to make those connections later. You can build on the previous knowledge. One idea I noticed overall is that place value doesn't go away. It grows like a sponge. It spirals from year to year but gains more power each year. This is something I have wished for for years. I wish they would focus on fewer topics and go into more detail (I am tired of mile wide inch deep). Although I feel it's still a little too much content each year...I definitely feel like they build on each topic each year.
ReplyDeleteBeing a special education teacher and not having the math background, I was also confused by the wording in the text. However, the one concept that kept coming through was the importance of understanding the progression of numbers and operations in base ten. I liked the video that Kyle suggested because it helped me to understand how students are now learning to add numbers using base ten. This is a new concept for me and it was interesting to see it in action. For many students, being able to visualize with pictures what is happening with numbers must be helpful and provide meaning to the concept of adding. I also liked the video that showed how the concepts are connected and build on one another from year to year. It seems like a natural progression that will aide in student understanding.
ReplyDeleteI think it is important that there is a a continuous progression that teachers have an opportunity to see and understand. Knowing what a previous grade has done and what a following grade will need to accomplish, helps establish the importance of covering the curriculum efficiently and effectively. I have noticed from implementing the NYS math modules (year 3), students are beginning to arrive in third grade with more academic vocabulary and strategies under their belt.
ReplyDeleteThat is great-that they are arriving more prepared! I really don't object to the standards, but merely the way that they were implemented. It seems that it will work out, but it will take time before our students at the secondary level are truly prepared to write, think, and speak at the common core math level expected of them.
DeleteBeing trained as a special education teacher with a certification from birth through age 21, the courses I took in math instruction were very cursory or focused on adapting traditional math instruction to the needs of learners with special needs. Although the progressions documents are dry, they are very necessary to understanding the driving force behind the core standards. Equally as important is the need for each grade level teacher to know what standards come before and after theirs. Yes, kindergarten teachers should read the Algebra 2/Trig standards as should the Algebra 2/Trig teacher read the kindergarten standards. Having read this progressions document and watched both videos, it is clear that the goal of the number and operations standards are to cycle back upon themselves on a yearly basis and continually add to the knowledge students are building. Developing fluency with basic operations is essential in the elementary grades since in the middle school years, we rely on this fluency being in place while we tackle more complex concepts. Having a solid understanding of the base 10 system is so important - I can't help but wonder and wish that the number system had been taught to me so many years ago in this way, rather than memorizing a set of rules without really understanding them. Maybe fewer people would lament that they "were never good at math....."
ReplyDeleteProgression in Numbers, Operations and Relationships in the Senior Phase
ReplyDeleteis mainly important to understand complex mathematics later on in the
FET phase. How is this aspect primarily achieved in the Senior Phase?