We made it through the school year! I'm pretty sure it was the longest school year ever! We added days to our calendar and lost some precious vacation time. Either way, summer vacation has arrived for us Zones Math ladies and we are truly grateful for it! I don't know about you but I really need these summer weeks to do the 3 R's, relax, revive and refresh! It makes me a better teacher, mother and wife when August hits and it's time to get back to business.
If you are just starting your summer vacation or it is so close you can almost taste it, you might be doing some reflecting on your school year. Did you implement Zones Math? How did it go? I hope you loved it like we do. If you are not in the reflecting state of mind try reading Olivia's blog post that might help you connect with how awesome of a teacher you truly are!
Maybe you thought about doing Zones Math and you just weren't sure if it was for you. Read Meghan's blog post! It will help you make that decision!
Or did you just stumble upon us and now you are wondering what in the world Zones Math even is? Read this for a great explanation!
Whatever state of mind you are in this summer I hope you have time to enjoy the 3 R's (relax, revive, refresh)! Stop back to see us at anytime! We are always here to help you along your math journey!
Until next time,
Here in 5th grade we are working with fractions (yay!). Many of our students still lack a foundational understanding of fractions, so that is where we started. We gave students a TON of opportunities to work with maniuplatives, use fraction tiles, and make discoveries and connections.
A few weeks ago we were working on making equivalent fractions. In order to ensure that students had a solid foundation, we did not introduce the "math way" yet. Students were working with maniuplatives and drawings in order to internalize the meaning of equivalent fractions.
During his work in the Explore zone, one student made an important discovery. I'll let him speak for himself:
This led to a great conversation about the "math way" and co-constructing the algorithm for equivalent fractions.
This is just one reason why we love the Explore zone, and the fact that we have the freedom to conference with students where they are at and catch these important conversations.
What has been your biggest aha moment this year?
I just love the feeling I get when the skills that I have taught my students transfer over to a different content area or a new environment. It solidifies that I have taught them more than just a concept, but a life-long skill that they are indeed putting into practice. The skill I have noticed lately is perseverance.
I really love how ZONES cultivates perseverance with students. Perseverance in mathematics has become quite a hot topic/buzz word lately. I have also seen it being discussed as a "growth mindset". When students persevere through a posed mathematical problem they must see themselves as capable of and effective at learning and doing the mathematical concepts both with skill set and effort.
Perseverance is also viewed as an essential piece of mathematic proficiency. In a National Research Council report, Adding It Up: How Children Learn Mathematics (Kilpatrick, Swafford, & Findell,2001), highlights “productive disposition” [perseverance] as one of five key “strands” of what it takes to be mathematically proficient. They explain that “productive disposition” [perseverance] is interdependent with four other “strands of mathematical proficiency: conceptual understanding, procedural fluency, strategic competence, and adaptive reasoning.”
Perseverance is a very interesting skill. Research suggests that students’ out-of-school experiences influence their perseverance with mathematical tasks. Tasks that have a familiar or real-life context are more meaningful. Because students are able to draw on their everyday experience to solve these kinds of tasks, they are more motivated to stick with the task (Taylor, 2015).
However, what if the students have little academic background knowledge to draw from? The students in my school are highly at risk due to multiple factors such as poverty, family instability and dysfunction, school environment and community resources, English as a second language, and minority youth. They have very little academic background knowledge to pull from when tackling a math problem.
Perseverance is also influenced by the norms of the classroom, particularly a student’s perception about her mathematical ability relative to other members of the class. “Students compare themselves against the norms of mathematical competence in their class[es], construct sets of ‘stories’ that define their own proclivities and handicaps, and use these stories to help them decide when and to what extent they will engage in the social activity of doing mathematics” (Middleton, Tallman, Hatfield, & Davis , 2015). They often think that perseverance is something that some students are skilled at rather than a behavior that everyone can develop. However, as students get older, they begin to have a self perception of their math ability. In my math class in particular, we group our students. My group consists of students at a below grade ability level. By fifth grade, these students have already experienced failure, lack of support, and the awareness that peers are "better" at math.
Perseverance is at the root of the ZONES framework as it is the first Common Core Mathematical Practice Standard (which are the building blocks of ZONES). And even more inspiring, perseverance CAN BE TAUGHT!
I will go into detail in my next post how we go about explicitly teaching it. AND IT WORKS! Recently my students had to take the dreaded State Standardized test. During this test I saw how my ZONES students persevered beyond their peers. I saw them try strategy after strategy to try to determine the answer. This was with mastered skills as well as with new foreign skills. I was so proud of my students during this difficult testing time. I know that state government puts a lot of emphasis and pressure on students' final scores on this test. However, I was just so proud of their effort and perseverance. The fact that they tried and kept trying is a skill I have seen develop over the last 8 months of school. It is also a life skill that they will use in varying situations throughout their lives, both academic and realistic.
Keep trying out there! We teachers need to persevere during these last few months of the school year too!
Hyman Bass and Deborah Loewenberg Ball. (April 2015) Beyond "You Can Do It!" Developing Mathematical Perseverance in Elementary School. University of Michigan http://www.spencer.org/sites/default/files/pdfs/bass_ball_mip_0415.pdf (April 27, 2017)
http://www.corestandards.org/Math/Practice/ (April 27, 2017)
https://en.wikipedia.org/wiki/At-risk_students (April 27, 2017)
http://www.ascd.org/publications/books/104017/chapters/The-Importance-of-Background-Knowledge.aspx (April 27, 2017)
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: How children learn mathematics. National Research Council, National Academies Press.
Middleton, J. A., Tallman, M. A., Hatfield, N., & Davis, O. (2015, April). Taking the severe out of perseverance: Strategies for building mathematical determination (White paper). Chicago, IL: Spencer Foundation. Retrieved from http://hub.mspnet.org/index.cfm/28128
Pasquale, Marian. (2015) Productive Struggle in Mathematics. Research Brief. Interactive Studies in STEM Teaching and Learning. Education Development Center, Inc. http://interactivestem.org/wp-content/uploads/2015/08/EDC-RPC-Brief-Productive-Struggle.pdf (April 27, 2017)
Taylor, E. V. (2015, April). Cultural considerations in support of mathematical perseverance: The role of context activation (White paper). Chicago, IL: Spencer Foundation. Retrieved from http://hub.mspnet.org/index.cfm/28130
Happy spring everyone!!
I feel like it's at this point in the school year when we are feeling drained, tired, and pretty uninspired. Often times our students are feeling the same way. And yet, we still have content to cover, ideas to explore, and concepts to master.
Sometimes we just need a fresh view on something or an idea to get us going. In that spirit, I present to you some of our favorite websites for lessons and inspiration:
And, of course, don't forget all the resources we have curated for you right here on our website! The Resources page has all of our go-to resources, organized by zone! Check out and find something you love!
I hope you find some inspiration here! And don't hesitate to contact us if you need more ideas!
Looking forward to summer,
It's Meghan, back this week with another (hopefully) awesome idea. If you don't remember, or are new to our blog, I teach 1st grade. I love math and technology.
One of the questions we often get is how we create math groups during the guided math portion of ZONES. Math groups for me are fluid, based on the standard we are working on and each student's proficiency. I use technology, specifically Seesaw, to streamline my data collection. This is something you can do with a little or a lot of tech in your classroom. It works on any device or computer.
So today . . . Seesaw and exit tickets! Whatever the exit ticket is that I am using to gauge understanding, I have my students take a picture or screen shot of it and turn it in to our exit ticket folder on Seesaw. I can then see how my students are doing (without sifting through a pile of papers) and easily give feedback that my students can see, and that parents have access to as well.
Here are a couple examples . . .
Exit Ticket in Pieces Basic
Pieces Basic is a free app on our iPads. The students had to build the number 45, screen shot it and turn it in on Seesaw. I saw how each student was doing and gave them immediate feedback, either affirming their work or correcting their mistakes. You can see in the comment below the picture, I told the student what needed to be changed. On the picture, I edited their work using the drawing tool to show the student the correct way to build the number. From this exit ticket, I was able to create a group of students that needed to be pulled for additional instruction.
Paper Exit Ticket
Here is an example of an exit ticket from our math curriculum (Engage NY). The student completed the exit ticket and took a picture in Seesaw. To give feedback on this exit ticket, the draw, label and text features we all used. Again, the student has immediate access to this, as do parents.
In the paid version of Seesaw, you have access to 'skills'. These are areas you are working on that you want to assess the students on. Think standards, but less formal. The goal of this feature is to give you a quick view of how students are doing with a concept. When a student turns an item in, you quickly mark their understanding on a 4 point scale. Then in the 'skills' view, you have a visual of how the students are doing. You can pull a red (does not understand), yellow, light green group, or green group (ready for extensions). So easy! No lists of student, no piling paper together. All of this is hidden from students and parents. It is only for you and your instructional purposes.
While Seesaw Plus/For Schools is paid, it is not that expensive. If it looks interesting to you, you should look into it.
In summation, use exit tickets/quick checks to build small groups. And then, use technology to streamline that process so you have more time to spend with your students during the guided math portion of ZONES.
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