Final thoughts:
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 Sunday 08/16)
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 fractions does a student need in order to solve fractional 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 fractions?
- 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 fractions?
- 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?
What have I learned?
ReplyDeleteI have learned about the importance of instilling a really good conceptual foundation of fractions in my third grade students! I really understand now the importance of the concept of the Unit Fraction and Comparing using Equal Wholes. I think third graders need to have many opportunities to work with concrete materials to illustrate unit fractions and compare fractions. I really like bar (tape) diagrams the best, but I now understand even more the importance of the area models and the number lines and will continue to teach these with enthusiasm. :) I still feel confident in teaching several ways to draw and represent fractions to "prove" an answer to a fraction problem and encouraging students to use the method they feel communicates their answer in the most effective way. I also feel like the idea that there are "many ways to solve a math problem" was communicated through this class, which is a concept that I love to instill in the students.
Final Reflection
This class opened my eyes to the coherence of instruction across grade levels. I was excited to see what strategies elementary students are using to solve problems with whole numbers. When I first started teaching using the modules 2 years ago, it seemed as though all of the tape diagrams, number lines, break apart strategies, were new to the kids and they were still focused on solving problems using a preset set of rules (algorithm). Now I am encouraged that students will start coming into third grade with a deeper understanding of representing math with pictures and explaining why math works. I also see the importance of my job in third grade to make sure I thoroughly teach all the standards because the 4th grade teachers are counting on me! One comment I do want to make about how the modules are set up is that the pacing is so rigorous! If you do not follow the pacing guide and get a few days behind, you are scrambling to catch up. For the past two years, we have been scrambling to catch up during fractions, right before the state exam. Fractions seems like the last place we would want to scramble because the concepts are all such a base for the 4th and 5th grade curriculum.
One last comment... The videos were so helpful! I think every school should make time for their teachers to watch these CCLS videos about how the standards are being taught in the previous grade level and the grade level above which you are teaching. It was a real eye opener!
I really enjoyed the class and thank you to all the participants for the helpful comments and strategies!
Lori: Great final reflection, i couldnt agree more. I LOVED the studio talks and agree more teachers would benefit from watching them. My goal this year is to try and get more teachers to step outside their own classroom and see math in other grade levels to enhance their instruction.
Delete
ReplyDeleteWHAT HAVE YOU LEARNED:
- What instructional strategies would you use to reach students at various levels of mathematical ability?
I loved the use of the number line. Students can use this in earlier grades and continue to use it later. When they are confused with fractions they can refer back to the whole numbers on the number line.
I also like the use of area models and bar graphs. These actually show what it taking place in the equation.
I think that real life models should also be included in any of these strategies.
The instructional videos were excellent in my own understanding.
FINAL REFLECTION:
- How can you work together within AND across grade levels to ensure COHERENCE?
I would make use of the Progression Chart we were shown on day one. I am a checklist sort of person, and can see how everything fits together in the chart.
I do think that grade level and multiple grade level meetings need to be held in order to ensure coherence among grade levels.
Great!!!
DeleteWhat conceptual understanding of fractions does a student need in order to solve fractional problems?
ReplyDeleteI think, as the document and videos showed, that students need to see that fractions are not so totally different than the whole numbers they have already been working with. There is a certain intimidation factor that comes with fractions when they are formally worked with in the upper elementary grades, even though they have been cutting things in half and so on from their earliest memories. Using the number lines, unit fractions, part-whole understandings, area models, etc. extensively and thoughtfully can help demystify fractions and set students up for success. As for instructional strategies to use for students of varying abilities, I think the progression document and videos gave a fair number of tools we can use to help most, if not all, students build better understandings.
Final reflection:
Like Jen wrote, I think some across grade level meetings can help ensure coherence. I think we need much more collaboration among teachers with what works - we need to talk about it, and we also need to see it in action (videos, peer observations, interactive workshops, etc.). As much as we are often driven by a particular series, what really works is not always a part of the series being taught as scripted. Hearing how other professionals have "bought time" and deepened understanding through other more powerful/effective means would benefit both students and teachers.
Thank you to each person who has contributed their thoughts, experiences, and encouragements to this course. I am confident that I will be using some of the tools (videos, website recommendations, etc.) and some of your reflections as I move forward from here...
I agree Dana! The first few years out everyone was focused on learning their own material, now we need to spend time learning why were teaching what we are teaching and see the coherence of it all!
DeleteWhat have I learned.
ReplyDeleteThe role of concrete and pictorial steps in learning have been highlighted for me. I now plan on including more hands on experiences for my third graders this year. In the past I had an array station at my centers. Using a work tray, students would build arrays for each math fact with fun manipulatives. Then they would place their name card on the tray and take a picture of their model with the Ipad. At the end of the day I would scroll through the pictures on the Ipad and record their completed work on my grade sheet. I am going to use this same strategy for fraction work. I will have them use plastic fraction tiles at the center station to practice modeling different fraction tape diagram problems. I can't wait to see all their recorded work on the Ipads!
Final Reflection
- How do you maintain proper RIGOR in your instruction; including conceptual understanding, fluency and application?
Well I am all excited about teaching fractions, but there is that language component that might bring on some challenges. Reading and writing!!! Rigor comes in when that great solution needs to be communicated in writing. Along with all the models, kids need to be taught to use the vocabulary words that will explain work accurately.
Keep me posted Heidi I would love to hear how it goes with Ipads! Thanks for all your insight
DeleteWhat I have learned:
ReplyDeleteI have learned that there a many different ways to teach the concepts. My favorite ways always include manipulatives and giving time for the students to explore meaning with them. Seeing how the Singapore strategies, like bar models, are used to benefit the students just reaffirms that I am teaching the right methods to help our children succeed. I would have a hard time picking just one most beneficial model. I think both the bar models and area models are very beneficial to the students. They are both visual and the students get to do the work themselves which aides in their understanding.
Final reflection:
The focus for the grade 3 will be on understanding breaking a whole into unit fractions. They need to understand that they have to be equal parts and that if they are comparing them to another whole that they wholes must be the same. Unit fractions with larger denominators are getting smaller will be focused on. I will also focus on using many types of hands on activities that the students can use to explore these unit fractions, and then with finding basic equivalent fractions. (number lines, bar models, fraction tiles and games, direct instruction and video clips)
The focus in 4th grade will be equivalent fractions, comparing fractions and adding/subtraction fractions. I will model using the area model for whole numbers and how it relates to using it with fractions. The number lines and bar models will also be used so that the students can show for themselves how they can come up with equivalent fractions. (number lines, bar models, fraction tiles and games, direct instruction and video clips)
Working together with my fellow teachers will be key for coherence. I will be recommending that they seriously think about taking this class in the winter. I will share our initial document on what is to be taught across the grade levels. Making sure to review after the NYS testing is over and exposing the students to what they will be learning in the next grade. My strongest recommendation would be spiraling! Begin each school year by spiraling the concepts were taught the year before so that the students are continually reminded of what they have previously learned.
Great summary!! Spiraling is definitely an important part of every curriculum especially in the younger grades!
DeleteWhat I have leaned:
ReplyDeleteThis online study has certainly reinforced the importance of comparing the size of the wholes before beginning a comparison. I also like the idea of instructing students to compare fractions by using methods that are not solely focused on finding common denominators. Thinking about the "missing piece" and breaking fractions down into their unit fraction before comparing fractions are both excellent opportunities for students to develop their math sense and understanding.
As far as opportunities that students should be given, I think students should be given time to practice and explore as well as the opportunity to use manipulatives in school as well as at home.
Final Reflection:
The sequence of the Envision math program I used while teaching 4th grade placed the study of fractions in the spring. Each year, I felt like I was flying through those units - sometimes combining or glossing over lessons - in an attempt to cover all that was required before the state test in May. I knew at the time this was a disservice to the material but when the pressure is really on, it's difficult to do anything else. This close study of the progression of fraction instruction has reminded me that somehow the appropriate amount of time must be found to explore and teach these concepts fully. In order to ensure coherence across grade levels, it might be beneficial to hold not only grade level meetings but intermediate level meetings as well. One concept that might be discussed at these meetings is the appropriate and consistent use of precise vocabulary. Finally, one take away from this experience that I will strive to internalize is that rigor is not defined as only work done with paper and pencil. Using and creating visual models as well as exploring with manipulatives can also be rigorous and deepen the knowledge and understanding of our students.
I agree with you, Carrie. Sometimes you rush through those lessons in preparation for the NYS tests. I still think they should be given in June so we are not so rushed…but that's another discussion! I have served on the sixth grade math committee for the past three years in our district. We have realigned the Pearson Math Series to better meet the needs of our students. We have grouped the lessons in variety of ways to make it more meaningful. We have also developed and gathered a variety of additional lessons that we felt got the job done better than some of the Pearson lessons.
DeleteOne last thing…because of our math committee meetings we encouraged other grade levels to do the same. We also shared common terminology/vocabulary that we should be using in each grade. As a result, other math committees have been initiated.
DeleteWhat I have learned:
ReplyDeleteI have learned how to be a more informed and better instructor when it comes to teaching computational principles using fractions. I have increased my knowledge base on using the number line and bar diagrams effectively as an additional method. I think the students will enjoy the variety! The videos have also pointed out common misconceptions that students can have and how we as teachers can alert them to these issues.
Final reflection:
I always enjoy taking classes online in the summer. I pick up innovative ideas from my peers as well. These classes prepare you for the upcoming school year and help you reflect on past learning/teaching. All of these classes help us transition in to better meeting the needs of our students while adhering to the Common Core Curriculum. One thing that I keep meaning to mention is that we need to apply the concept of greater rigor to keep current with todays educational needs and demands. I feel many teachers can get stuck in a rut and don't keep current by seeking out new methods for instruction. Congratulations to my fellow peers…we will return to school a better teacher in September!