This post is part of my Guided Math Book Study. I will discuss each chapter in two sections: an overview of the chapter and my learning/wonderings and how this learning will affect my mathematics instruction. You can read the entire series of posts by clicking here. (Graphics for this post provided by Scrappin' Doodles.)
Chapter Two is all about Numeracy. Numeracy includes being able to see, use and understand math and mathematics concepts. I myself nodding when Sammons pointed out that when you walk into an elementary classroom--no matter whose it is--you are pretty confident in knowing that language arts are taught in that classroom. The same isn't as true with math. Sammons asserts that we MUST provide this same framework and foundation for teaching math.
She identifies Seven Foundational Principles of Math:
1. All students can learn mathematics
2. A numeracy-rich environment promotes mathematical learning by students
3. Learning at its best is a social process
4. Learning mathematics is a constructive process
5. An organized classroom environment supports the learning process
6. Modeling and think-alouds create a learning environment in which students' mathematical understanding grows
7. Ultimately, students are responsible for their learning.
(Sammons, 2010, pg 37)
I especially love number 7. I think that all too often we are told it is OUR responsibility to ensure students are learning and while it is, it is also the students' responsibility to understand they won't learn it if they don't own it.
Sammons talks at length in this chapter about building a classroom learning community. We all know this is important overall but her explanations of how it pertains to math is rock solid, especially when she points out how NCTM standards dictate that students be able to problem solve, provide reasoning and proof and make connections. Students won't be as comfortable doing that if they don't feel a part of a learning community.
It is important to understand that Sammons models much of her thinking after a Guided Reading model, just shifting it to apply to mathematics instruction. Therefore each area of the classroom is given some thought as it pertains to exactly how to set up a classroom for guided math. If you already have a whole group area, a small group area and an area for workshop materials for reading/writing, you are well on your way to being able to transition into a math workshop framework as well because they are practically identical. To me the most important part is having an area for whole group--I have found this to be important even with older students. I have always had my 4th and 5th graders gather on the floor for certain aspects of our day. I do this partly to keep them all close to me but also to increase the sense of community in the classroom. A small group area can be as simple as a stretch of carpet you meet on with your groups. One year my room wasn't big enough for two separate areas so I took out my U-shaped table and met with my small groups on the floor where our large group area was and it worked out just fine.
The best part of this chapter, in terms of my learning, was the section providing more information about how to set up a Numeracy-Rich environment. It should include some (or best of all, ALL) of the following components:
--Manipulatives (these can be hand-made and sometimes STUDENT made such as flip books for reference)
--Problems of the Day/Week
--Graphic Organizers (I especially like the modified Frayer model!)
--Class Made Charts
--Tools for Measuring
--Literature related to math (both commercially produced and student-created)
*I went to a 3-part math workshop this year and we talked at length about how neglected math is on a word wall. My binder for that workshop is at school but there is an amazing article in there that talks a lot about how we can easily integrate math vocabulary onto our already existing (and often mandated!) word walls. I will try to remember to grab it when I go back to my classroom and add it to this post. It's worth reading!
**Math Journals is a concept I definitely love after experiencing some of the changes our district math coordinator put in place at the end of the year. I have found over the years that my students can perform a math equation or concept but they really don't own it or get it. They can't explain how they know. To me, that means they really don't understand the concept--they just know the steps to follow to get the right answer. Using math journals will provide me with a weekly look at my students' thinking in terms of HOW they process math and allow me to guide them if they are having a lot of misconceptions.
I loved this entire chapter, mostly because it validated everything I've been feeling about my math instruction! I was browsing along the web earlier this week and came across Calendar Math by Stephanie at Teaching in Room 6. I don't know if I was living under a rock but WOW. The brief encouragement that Sammons provides and Stephanie's fabulous resources (which you better believe I WILL be purchasing) make this a reality for me. Someone else did the work and I just have to implement it. No excuses there!!
I also plan to really make sure that my students have access to manipulatives. It is so easy to write it off with the older kids because of time constraints BUT it is important for them to understand that these manipulatives have a purpose. I definitely want to make sure my "big kids" know and understand ten-frames as well as base-10 because I know that numbers and operations tends to be very low across our school. They just don't have a good number sense and I need to change that.
I will definitely be using the math vocabulary/word wall. Last year I covered my shelves with posterboard but never really did much with that space. This year I will use that space as a math word wall. It will be perfect. I also definitely want to incorporate the Frayer model. Students often confuse math terms and I hope by implementing that frame with some of the more confusing words that my students will be able to enrich their vocabulary and not stumble when they come across the words in math problems which then result in them not knowing what they should do.
Stay tuned for my thoughts and reflections on Chapter 3: Using Math Warm-ups in Guided Math on July 10!