Final thoughts: (must be completed to receive credit)
This post will be your opportunity to comment about what you have gained from this workshop. Please be sure to look back at the original post and review the objectives to see if you gained new knowledge based on the objectives. It would also be nice if you could comment on others posts as well before finishing the course. (You have until Saturday 11/07)If you wouldn't mind breaking your final post into two parts: What have you learned and final reflection, you can do them within the same comment. YOU DO NOT HAVE TO ANSWER ALL THE QUESTIONS BELOW, Pick the ones that you feel best to answer.
Here are some questions to guide you in your final post on WHAT HAVE YOU LEARNED:
- What conceptual understanding of base ten does a student need in order to solve operational problems?
- What instructional strategies would you use to reach students at various levels of mathematical ability?
- What opportunities should students be given to assist with building their conceptual understanding of numbers and operations?
- What model do you find most beneficial in building understanding?
Questions based on the objectives of this workshop for your FINAL REFLECTION:
- What type of FOCUS do you need in your grade level to help a student be successful with numbers and operations?
- How can you work together within AND across grade levels to ensure COHERENCE?
- How do you maintain proper RIGOR in your instruction; including conceptual understanding, fluency and application?
A final survey will be sent from the Teacher Center in order to receive your completion certficates
I have learned that students needs to have an understanding of place value knowledge and a grasp on bundling tens to reach a common understanding of the base ten system. This learning begins in Kindergarten and each grade level builds upon number sense. I have learned that the common core is trying to teach students to be thinkers and problem solvers rather than be able to rattle of rote memory facts and how to arrive at answers more quickly. If students have a deeper understanding, they will be able to solve higher order thinking related problems. Watching the videos gave me a better understanding on how to model different strategies. In order to strengthen students' understanding they should be taught with concrete manipulatives, visual aides and drawing diagrams. Decomposing numbers is helpful for understanding place value. I also think using number lines for many different concepts is helpful.
ReplyDeleteWhat can help our students be successful amongst the grade level is having a deeper understanding of the common core as teachers first. Once we understand the thought process, it is easier to teach, but it is a process. Constant practice with fact fluency, skip counting, telling time, etc. for a few minutes each day will help increase the rigor within our instruction. Maintaining rigor is something that the common core has embedded within the lessons. They are challenging and require students to understand the number system and be able to apply these skills with flexible thinking.
I learned a lot in this course and will continue watching and searching for videos to help me continue to wrap my mind around the common core. I enjoyed listening to all of your points of view and feedback. The most valuable part of the course was gaining a deeper understanding of the common core to provide me with a better explanation to others regarding the premise behind the "new" math.
Yes, I agree Julie. Students are working to become better thinkers and problem solvers rather than just "memorizers".
DeleteThrough this class, I have gained an understanding of how concepts spiral and build throughout the grade levels. The most important ideas to me involve the students understanding that number and place value can be “packed and unpacked”, “composed and decomposed”, and/or “bundled and unbundled”. They truly need to comprehend more than just quick facts and algorithms…even though those skills are somewhat the end goal in the upper grades. A very simple model I think is important is a basic place value chart. It is helpful when we introduce multiplying and dividing by units of ten and showing how the digits move within the chart. It demonstrates how the value of each digit is perhaps 10 or 100 times greater or 1/10 or 1/00 the value of what it used to be depending on the operation and divisor.
ReplyDeleteCoherence is achieved in our building (grades 3-5) because we have adopted the modules. This has provided consistency throughout the grade levels, and also should equally prepare the students for the following grade level (vertical and horizontal alignment).
We have also adopted the modules in our building Grades 3-5, so we maintain coherence that way as well. We also have weekly math meetings with grades 3-5 (professional learning communities). That gives us a chance to collaborate and discuss math amongst the building.
DeleteCollaboration is a huge part of making the transition to modules a success!
DeleteI feel that I have learned some valuable information in this class in regards to the progression of skills. It is always important to know what is being taught prior to when you are receiving your students. It is important to see how each skill is being developed. Obviously, the overall goal with the modules it to have the students truly understand and conceptualize the math skills before teaching them the “old fashioned” or standard algorithm, which is ultimately the goal. In our district, we have been working with the modules for the past three years. The first year was extremely difficult because it was a huge shift from what the teachers and students were used to seeing. Since then, I have seen a change for the positive. Children are coming to 5th grade with a deeper understanding of place value and have developed number sense. There are many models that I think are super helpful for children to utilize throughout, starting right in kindergarten with dot cards and progressing through into more complex models such as area models. Despite all the focus on developing math thinkers, I think it is still very important for students to master basic facts.
ReplyDeleteI agree with your statement, "despite all the focus on developing math thinkers...it is still very important for students to master basic facts." Students that have that basic skill are more proficient in math and ultimately do better. I strongly believe that not knowing math facts slows down student progress. I also think that algorithms should be included with the shifts toward conceptual understanding. It was mentioned over and over again that a variety of models and methods be provided to students so they could solve problems different ways. So why isn’t algorithms one of the methods of choice?
DeleteTina...I have some third graders that are ready to use and understand an algorithm with a model. When doing a 3 digit subtraction problem last week, we drew place value blocks as our model, but I had the algorithm written next to the model. Everytime we completed a step by adjusting our PVB, we showed how the algorithm was adjusted. Some students are ready for that, so I feel it is important to help them see the connection between the model and the algorithm.
DeleteI have learned a great deal from this online course. I knew very little about the Common Core math standards before this course and now I feel like I have a much better understanding of how the common core is aligned and the coherence from one grade level to the next. It’s great how everything comes together with a systematic and logical connection by 5th grade. One concept that kept coming through was the importance of understanding the progression of numbers and operations in base ten. This is a new concept for me and it was interesting to watch the videos and actually see examples. Using models and pictures seem helpful and provide meaning to the concepts being taught. I liked the number line for addition and fractions (with the fraction bar). I also liked the hundreds grid. I’m not yet sold on the area grid, but maybe I’ll feel more comfortable with it after more practice.
ReplyDeleteI think the biggest thing I have learned through completing this workshop is how important the modeling is for all of the students, no matter what the grade. I never knew the algorithm was put on the back burner on purpose, and the modeling is what should be the main focus of the math experiences. Just last week, my third graders were solving word problems involving measurement using subtraction of 3 digit numbers. This year (thanks to this course), I did not worry if the students knew how to do the algorithm. Instead, we discussed some drawings and pictures we could use to help us solve the 3 digit subtraction problems. Once I started drawing pictures of place value blocks, several students seemed to breathe a sigh of relief and said, "I remember using those last year." With that being said, I don't think one particular model is effective for all learners. Using the count forward method with or without a number line (http://youtu.be/U4cwKsM_Mv8) is a good strategy as well. When it comes to mathematics, being able to think about and understand the concept of what is happening is much more important than solving an algorithm. That was my "ahha" moment.
ReplyDeleteFinal Thoughts: I feel very fortunate to work on the grade level team that I do. We talk about our math lessons everyday. I have even shared some ideas that I have gotten from this course to help other teachers not be as stressed about teaching certain lessons. As our third grade teachers begin to see more and more classes come through from our K-2 building with Common Core math module experience, I feel the conceptual thinking and learning will get easier for everyone, even parents. Teachers and students are more on board with Common Core math. I think it is time to provide some quality inservice to parents.
What have I learned? A lot! I chose to answer the question what model do I find most beneficial in building understanding? I would have to say unifix cubes. I am a big fan of the old saying "students learn best when they are actively involved in the lesson." One of the reasons I like the cubes the best is that they can be used with so many math topics (counting, patterns, basic operations, probability, graphing, sorting, measurement, etc...). The new series we are using this year has an awesome manipulatives kit included and I like them all but the cubes are my favorite:)
ReplyDeleteI believe the best way to ensure coherence is working together. If the teachers have a common planning time during the day - bonus! But If not, it is so beneficial to still find some planning time. Not only is horizontal time important but also vertical. It is so much easier for the kids if all grades are using common language/vocabulary. It is also easier for the kids if the teachers make the manipulatives available each year. We all received the same kit so that helps with consistency. Some kids will not need the manipulatives after a while but some will always feel more comfortable with them or at least having them as an option.
I've learned in this course how important modeling is to developing math sense, no matter what grade level you work with. Secondly, but no less important, is the spiral concept, that topics are revisited each year with additional layers of complexity added onto them. As a veteran teacher, I learned that there was one "right way" to solve problems growing up. Now, multiple methods are encouraged and celebrated. I also never knew about the math videos on EngageNY .... I will be looking for more videos on the 6-8 curriculum for tips and hints.
ReplyDeleteTo answer a second question .... what opportunities should be available for kids? I think that the models (both paper and drawing) should ALWAYS be available to kids. I am hoping that as kids grow through this curriculum, they will become more comfortable with manipulatives and reach for them to solve more and more complex problems.
Coherence is a really important concept to me. I like to know what skills my kids are coming to me with from sixth grade and below. Teaching seventh and eighth grades, I feel comfortable with those curriculums. Having a high school son has been an eye opener for me as far as the direction my kids head into when they leave me. One of my next steps will be to chat with the high school algebra 1 and pre-algebra teachers to find out what they would like us to focus on more at the middle level.