Building Mathematical Comprehension Chapter 10

Guided Math Classroom

Last summer I read Laney Sammons's Guided Math book. I was so eager to get started and hopeful to implement in my classroom. Unfortunately, I was not quite prepared and did not fully see the whole picture. Now that I see the light, and am more fully prepared with effective tools I am so excited to get started.

I so appreciate how flexible the instructional framework for Guided Math is. There are specific components but within each component there is lots of flexibility. The components include:

1. A Classroom Environment of Numeracy- (daily) a classroom filled with numeracy provides students with lots of opportunities to engage with math. Students are encouraged to use manipulative, talk, problem solve, question, generate ideas, etc.
2. Math Stretches and Calendar- (daily) "warm-up" math activities provide students with a preview of future math concepts or a review of what has been learned. Math Stretches allow students the opportunity to use the 7 strategies they have been taught (the ones in this book ;). The Math Huddle is a great idea. Students can share their thoughts and engage in a mathematical discussion. How awesome is that?! The Calendar provides so many opportunities to preview and practice skills that have been learned. 
3. Whole -Class Instruction- (your choice) My inner voice keeps saying Modeling and Think Alouds. Good, it has been engrained in my brain.
4. Small-Group Instruction- (your choice) make groups homogeneous yet flexible to change. Here is where strategies are reinforced and individual student's needs are met. 
5. Math Workshop- (your choice) students can work alone, in pairs, or in groups. Teachers provide anchor charts, organizers, and feedback. Students responsibility is to complete tasks and demonstrate their mathematical understanding.
6. Conferencing-(daily) one-on-one conferences are brief conversations that assess students understanding and guide their thinking. 
7. Assessment- (daily) use formative and summative assessments. This can be done by observation, students can share orally or in writing.

Along side this framework a teacher must motivate and encourage students to "become mathematicians." Sammons shares what "becoming a mathematician" looks like and how teachers can create an environment where this is possible.

Within each component of the framework there is flexibility and structure. I think that allows for teachers to be creative and resourceful in the use of materials they have. For instance, Wendie has been working diligently to create our "Critical Crumbs." -->Critical Crumbs are individual math tasks that focus on the four critical areas of third grade math in the common core standards, namely:

• multiplication/division relationships
• unit fractions
• area of two-dimensional regions
• properties of two-dimensional shapes 

Critical Crumbs provide a daily practice and warm-up activity that focuses on these four critical areas. I can see how they can fit in during Math Stretches or Math Workshop. Here is an example of our Critical Crumbs.

 Also, our Math Anchors and Math Jumbles could work nicely as Math Workshop activities. Check them out and let us know what you think. 

 

 

Masterpiece Frames

Wendie and I really wanted to be able to showcase student work that is creative and demonstrates critical thinking. A while back we found these cool frames at Michaels and decided that they would make awesome frames to showcase our students "Masterpiece." That is what our header will be for these frames. Look how great they turned out!

Freebie!

We wanted to share our My Two Cents series with our blog friends- so we have a freebie for you. Who doesn't love a freebie!? Please let us know what you think.

Just click on the pic.

Building Mathematical Comprehension Chapter 9

Monitoring Mathematical Comprehension

How will our students monitor their comprehension?  They need to have a wide variety of comprehension strategies in their tool belt in order to do this. All the strategies we have been reading about will come into play when students are monitoring their comprehension.

First step: Conceptual Understanding

Students need to become active, engaged participants in their thinking. Yes- they need to "think about their thinking." Sammons provides for us great "Fix-Up" strategies that become the students responsibility to use when they do not understand. It is important for students to be responsible for this process. Only they know when their understanding breaks down. Explicit questions to pose: 

1. How do you know whether or not you understand?
2. What do you do if you are confused?

Second Step: Problem Solving
Have you ever had a student who would start a problem and attempt just about everything, but never really stop to understand what the problem was about? I have. This is often true of our struggling readers who focus on a word or two and start trying to problem solve. Sammons emphasized the importance of spending time helping students to look at how to find the "overall meaning" to problems.

Then, students need to develop a plan of attack. They need to be aware of connections between things and how to link it to the unknown data. So, they need to understand the problem and how the mathematical concepts are related.

Sammons shared a "Comprehension Checklist" that will help students monitor their comprehension.
I took it and made it my own, but it is all Sammons. Click pic to download.

Here are some signs that students should be aware of to help them know that their comprehension has broken down.

• Your internal voice interacting with math concept or problem
• You are unable to visualize math concept or problem
• Your mind wanders away from work at hand
• You are unable to recall details of math idea or problem
• You cannot find answers to questions asked to clarify meaning

I had to create something handy dandy to keep these close and readily accessible

Sammons suggests that students brainstorm "Fix-Up" strategies and create a chart they can refer to. She also provides lots of suggestions. Click pic to download.

I am so thankful that now I have additional resources to help my students who struggle. The result of modeling this strategy and doing think alouds consistently will be that they now have resources that will allow them to be successful.
Other suggestions to continually have students monitor their comprehension are:

• Ticket out the Door- students can explain their understanding and also rate their understanding
• Comprehension Constructor- provides scaffolding for students fix-up strategy and overall plan
• Color-Coded Metacognition Math Stretches- students reflect on a word or concept and use a color to represent their understanding

Amazing strategies for our students to surpass those "comprehension roadblocks."

Teach Like a Pirate Final Chapter

Whew! What a book- it was full of inspiration and useful ideas. Truly, one of the best feelings was having a group of people to share reflections, fears, and empowering moments with. Thank you! I hope that we will revisit from time to time how the "hooks" are working for us and especially the impact it is having on our students learning.

Since we completed our book study I thought how fun to start our own TLP crew to continue supporting one another through our teaching adventure. I kind of feel like we are members of something special - I'm sure you do too.

Just for fun!

Building Mathematical Comprehension Chapter 8

Holy Moly! Synthesizing.

This chapter on synthesizing was a toughie. Mainly, in the sense that it is difficult to come up with a way for my students to think about their process of putting together new mathematical ideas, previous learning, and reformulations.

Synthesizing is definitely one of the more challenging strategies to teach. It requires lots of think alouds and teacher modeling. The ability to synthesize first requires teachers to begin with the concrete models (nesting dolls and baking a cake) and then to move to the process of synthesizing.

The process is where it gets tricky. One way to do this is by making conjectures. Conjectures are described as informed guesses and predictions. Students can make conjectures by being given open number sentences where they have to decide if they are true or false and explain why.

In order for our students to practice synthesizing, the problems we choose need to allow students to find patterns and relationships, have more than one solution, and allow for questions (the what ifs).
I honestly had such a difficult time with, how do I help my students "see" their thinking process? I put together an organizer I am going to try out this year. I want to share it with you, but please know it is a work in progress. Click pic to download.

Teach Like a Pirate Chapter 18

Finding a Crew

What a gift to find a positive, student focused person or group to work with. I think this is essential to our growth as teachers and as people. I consider myself an introvert, that enjoys working on my own. But  I have been amazed at how much I have learned and enjoyed working collaboratively with Wendie on our blog and our TPT store. I am truly learning more and enjoying myself more having a partner in the process.

This blog and other blogs that I enjoy, have been such a positive addition to my teaching life. In the blog world I can share my highs and lows, and always find other teachers that will encourage and motivate me. 

Visual reminders, like photographs, notes, cards, etc. are always helpful to me when I have had a challenging day. I love Nikki's art work from Melonheadz, they make for a great reminder of "my crew" who offer encouragement and love (my hubby, my special pets, two of my sisters who are also teachers, and a teacher friend that inspires me to be a better person).