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).

Dave Burgess Video

Stephanie from Third Grade Thoughts shared this YouTube video about Dave Burgess.

I know many have mentioned how awesome it would be to watch Dave Burgess in action. Although he isn't in front of a classroom you definitely get to see his dynamic personality. You even get to experience a magic trick.

My Two Cents

When we started brainstorming for our My Two Cents series, we knew we wanted to make activities that were meaningful, engaging, and teacher friendly. To make them meaningful we made sure they supported the common core standards while giving the students time to be creative critical thinkers. To make them teacher friendly we included everything we thought a teacher would need in a snappy little foldable booklet, as well as providing anchor posters and graphic organizers for expository writing. As we know, certain topics can produce a teacher-induced, glazed over, semi-hypnotic state faster than others. While an interesting topic can produce an engaged and motivated audience. In sixth grade, if you are teaching about Egypt and you start talking about mummies- postures straighten and eyes widen.  They're all ears.


Of course, we can't always be teaching the cool stuff...but then again- why not?

You can check out our first My Two Cents by clicking on the pic.

Teach Like A Pirate - Chapter 16

Do you want to be a great teacher?

As you ponder that- I can absolutely, positively answer yes. I think any teacher in this book study or reading this blog already knows the answer to that question. That's why we are spending our summer reading, learning, blogging, etc. I know I do this to become a better (the best) teacher and to stay motivated and inspired.

I have read quite a few self help books in my day and this chapter reads as that. A self help chapter to let teachers (me) know that it is not silly or egotistical to strive for greatness, it is essential to our profession. 

It is 12:40 a.m. and I am so pumped to be a teacher- what a journey it has been and will continue to be. Teach Like a Pirate helped remind of that.

Jennifer from Rowdy in First Grade shared a great quote from the book. I decided it needed to be framed- it's so great.

Building Mathematical Comprehension Chapter 7

Determining Importance

I found this chapter to be dense with Amazing information. The focus of this chapter is helping students identify relevant information. This will help them not get sidetracked with all the facts and details of a math problem.

Sammons refers to levels of determining importance:

1. Word Level- math vocabulary, bold print, italics, highlighted words, etc.
2. Sentence Level- typically most important information is found in the middle of a math problem. Knowing structure of mathematical word problems is helpful.
3. Idea Level- the Big idea. Students will benefit by practicing how to identify the overall meaning of word problems. Word level and sentence level help get to idea level.

Sammons share several strategies to teach determining importance. Here are three:

• Overviewing- students skim over text and try to find important words, sentences, and ideas
• Highlighting- students decide what is worthy of highlighting
• Read a Little, Think a Little- students read one sentence at a time to find important information

Like I said, it was a dense chapter and I want to focus on a bit at a time. Take highlighting for instance. Put a highlighter in the hands of my students and they will highlight just about everything on the page. I need to explicitly teach them how to distinguish between interesting information and what is important information. After reading this chapter I know have better tools on how to do this. I created a chart that will help me focus on what is interesting information and what is important information and one that will limit the amount of irrelevant highlighting my students are prone to.
Let me know what you think and just click on the pic to download.

It just hit me that I should be compiling a list of children's books that supports each strategy. For determining importance these books will help.

Caps for Sale
The Grapes of Math
Mind-Stretching Math Riddles

Teaching my students to recognize information that is important and useful is essential for them to understand mathematical concepts and problems in deeper way. This is the road to becoming a critical thinker.

Classroom Cutouts

Wendie and I were guests at the gypsy teacher and we shared how to put these fun cut outs together. We think they will make our classrooms look bright and cheery, plus we prefer DIY versus purchasing. Here are my finished buggies.

Don't you just love how the colors pop? We would love to hear about your classroom decor or inspirations..

Building Mathematical Comprehension Chapter 6

Making Inferences and Predictions

Yet another learning filled chapter. With all this knowledge I am absolutely eager to start teaching math.

I am so thankful that I have been able to see inferring and predicting in a new way. I can see the depth of knowledge I have gained and how my students will benefit.  My hope is that gone are the days that we felt the need to rush through standards in order to expose our students to everything we were suppose to cover. As Sammons mentions these strategies require time for students to understand and begin using on their own. If I expect my students to give me reasonable and justifiable inferences, I need to be ready for it to take awhile. 

Sammons mentions one-to one conferenences often and I so guilty of not doing this during math. I went into last school year hoping to make this happen and I failed. But I have to say after reading this book I have a clearer picture of what I need to do to reinforce learning one to one or in a small group. Thank you Laney Sammons!

This chapter was filled with such valuable ways to practice inferring and predicting, I had to put it into a tangible way for me to use. I have seen some great freebies created for this chapter that I know I am totally going to use. Just click on the pic to download and please let me know what you think.

Liebster Award Nomination

I just receive an email that Danielle from Busy Little Brainiacs has nominated us for a Liebster Award!  The Liebster Award is a way bloggers spread the word about fellow bloggers whose blogs have fewer than 200 followers.  Once a blogger receives the award, he or she nominates other bloggers. So now it is our turn to nominate other bloggers who will benefit from some exposure.

Thank you Danielle. This is a great way to keep us newbies motivated and not to get discouraged.
 

To accept the nomination, I need to do the following:

1. I'm linking back to Danielle at Busy Little Braniacs.
2. I'm nominating 5 more blogs that have fewer than 200 followers. 
3. I'm answering 11 questions created by Danielle.
4. I'm listing 11 random facts about myself.
5. I'm creating 11 questions for my nominees to answer. 

I'm nominating these lovely blogs for Liebster Awards. If you have already been nominated, I apologize and know that I found your blog worthy of repeating this award. 

Erin at The Wright Stuff by Valery
Erin at Inspired Elementary
Marie at Beach Lovin' Teach
Amanda at A Traveled Teacher
Kathy at Kathy's First Grade Adventure

Danielle's Questions

1. What is your favorite subject to teach? 

I love to teach reading. I love to read and enjoy transferring that love for reading to my students.
2. What is your favorite book?

My all time favorite book is Watership Down.
3. If you could live in any country, which one would you live in? 

I think Norway looks like a beautiful place. Plus, I love their sense of style in home decor. 
4. Do you have any pets? If so what kind and what are their names?

Martha- I have three dogs (Lefty, LuLu, and Little Guy) and three house rabbits (Molly, Harley, and Quinn)

Wendie- has five dogs (Tess, Bandito, Mr. Darcey, Oliver, Sophie) and three of the cutest goats you have ever seen (Emmie, Trixie, and Janie). 
5. What was your first job?

My first job was working at a retail store when I was 16. But my first "real" job was teaching. 
6. What's the best advice you ever got? 

The best advice has been to have a tough skin but a soft heart.
7. What is the most played song on your iTunes?

I have been trying to motivate myself to exercise so I have been listening to a lot of Britney Spears songs. Don't judge me :)
8. Who is your role model or what inspires you? 

My role models are definitely my parents. They have an amazing work ethic that would inspire anyone.
9. What is your favorite part about back to school?

My favorite part of is decorating my classroom.
10. What is your dream vacation? 

My dream vacation would be to Italy.
11. If you weren't a teacher, what would you be?

Easy, working with animals in any capacity.

11 Random things about us (1-6 Martha and 7-11 Wendie)

Martha- 

1. I started teaching at the age of 21.

2. I love animals- especially dogs.

3. My husband is a teacher.

4. My husband and I met at the school we teach in. 

5. I am bilingual. I speak Spanish and English.

6. I have two older sister that are also teachers.

Wendie-

7. I am an author.

8. I have been a resource teacher.

9. My husband has an amazing "green thumb."  

10. I have a son and a daughter

11. I use to have horses.

Questions to my nominees:

1. What do you enjoy most about teaching?

2. What is the last movie you saw in the movie theater?

3. Do you have any pets? If so what kind and what are their names?

4. What is your favorite book?

5. What's the best advice you ever got?

6. If you could keep just three possessions (besides your family and pets), what would they be?

7. Do you have a piece of clothing or an accessory you can't live without?

8. Do you have a hobby? If so, what is it?

9. What is one teaching supply you could not live without?

10. Where is your favorite vacation spot?

11. What is your favorite color? 

 

Teach Like a Pirate Chapters 13-15

Stand and Deliver

What? Teachers are professional speakers? Come to think of it, we are. I find it fascinating that I can be so at ease in front of a big group of students and then terrified when speaking to a small group of adults. Now, over the years I have become more comfortable with the latter, but it took me some time and practice. Which is how I see integrating hooks into my lessons. I know it is not the quantity of hooks I use, but using just the right hook at the right time and lesson can have a profound affect on my students learning. And at the same time allowing their excitement and motivation about learning to sky rocket.

The six Stand and Deliver hooks are honed in to bring out that inner presenter and draw students in.

Advanced Tactics

Advanced tactics are just that- tools to enhance what we are teaching but not replacing the interaction between students and teacher. Burgess brings up a great point with the use of technology. As educators, we should definitely be exposing our students to the amazing technology that is available and incorporating that technology into our practice, but not allow that technology to facilitate as the teacher. It is that interaction between teacher and students that is the "magic." It's this interaction that helps create those Aha! moments for students.

Around the Edges

These hooks sound like a fun experience for the students and the teacher as well :) Yet, they go beyond that to the kind of environment we create in our classrooms. I have focused on this area in my teaching for some time. Challenging myself to create an environment that is welcoming, safe, and collaborative. The hooks Burgess presents here, will enhance my current practice. One of the hooks I am looking forward to using is the Contest Hook. I think it will help to build community and a healthy sense of competition.

Wow! I cannot wait to get started. How about you?

I have completed my project of bringing you an easy, go to place where you can find the hooks presented by Burgess. They will be more meaningful if you have read the book and Burgess's examples. Really, his examples brought each hook to life. Don't miss out on that.
I did not laminate mine because I want to be able to jot down my own examples. I hope you find them useful.  Here what they look like.

Please let me know what you think. Just click on the pick to download.

TpT Freebie

Our Very First TpT Freebie

Woo Hoo! Wendie and I have just added our first product to TpT and we are so thrilled. We cannot wait to hear from you to see what you think. We have been working hard to create a product that is easy to incorporate into your daily reading curriculum and that also reinforces the anchor standards for reading. Click on the pic to download.

Teach Like A Pirate Chapter 12

Hooks, hooks, and more hooks!

Setting the Stage...

I think an important aspect of teaching is room environment. Teachers make strategic choices of where to place desks, bulletin boards, charts, classroom libraries, etc. We are constantly asking ourselves if the location works best for students. I bet most of us are thinking about our classroom themes and how we are going to decorate. I, for one, love this part of the beginning of the school year.

Burgess recommends that we think of our rooms as a blank canvas that can and should change to enhance our lessons. He will often change the entire look of his classroom to support his teaching. Burgess has some nifty suggestions in how to do this. Now, I am not sure if I will be able to let go of my most perfect theme, but I know that I do not want my theme to stay stagnant the entire school year and that the room is another tool to enhance learning.

The Board Message Hook is one that encourages students to wonder and be curious of future learning. I like that these hooks peak student's curiosity and create a positive anticipation for lesson to come. I definitely want to use these hooks more. Burgess also mentioned the use of QR codes- now I know what they are, I just haven't used them. I am going to make it a goal to incorporate QR codes into some of my lessons. Does anyone have any suggestions on how to create lessons using QR codes?

Now, on to the costume hook. Wearing costumes can create greater engagement and bring learning to life. Burgess already told me to "get over it" if I am worried about looking silly. So, this will be my work in progress. Don't get me wrong, I am often my most comfortable in front of my students but I have yet to wear a costume.

Additional hooks that I have used and find to be effective are the Props Hook, The Involved Audience Hook, and The Mystery Bag Hook. I am amazed how Burgess uses everything available to help his students learn. He definitely has put much thought into his hooks and better yet he has used them.

There is more treasure in books than in all the pirate's loot on Treasure Island.

-Walt Disney                             

I am finding this to be true in regards to Burgess's book.

Happy 4th of July!

Happy 4th of July! We hope everyone has a fun filled Independence Day.

Building Mathematical Comprehension Chapter 5

The Importance of Visualizing Mathematical Ideas

I have used the visualization strategy for so long and not considered it while teaching math? In such simple, but profound ways Sammons's book is helping me rethink the way I teach math. Sammons shares that cognitively, if deeper learning and understanding is to be made students, they  must be able to process information in two ways. One being linguistically and the other nonlingustically. Combining the two when I teach will increase my student's comprehension. I have to say, when I think about my lessons that went very well I was naturally (intuitively) doing both.

Now, in order to help my students use visualization as a true strategy I need to be systematic and explicit in my teaching they use of the strategy. Sammons suggestions of what mathematicians do with this strategy is beneficial. Mathematicians...

• use their schema to create a mental image- remind students that we all have different schemas and that it is okay if they are unsure. That is common in learning something new.
• are motivated and engaged as they visualize- tell students that combining prior knowledge and new learning is essential to create images.
• revise their mental images as they discover new information- as students receive new information students need to learn how to incorporate that information into their mental images. I love this one! 
• understand the value of sharing their mental images- this not only helps build verbal skills, but it helps students process their own thinking. It will also help them with the revision of their mental images.

Pretty powerful stuff! Another amazing section was how to concretely help students who struggle with visualization. I can definitely visualize myself using this 7-step sequence in a small group. Is everyone as excited as I am?!

 This chapter also reiterates the power of modeling and Think- Alouds. I know that I cannot assume my students will naturally understand visualization on one try. My think-alouds need to go beyond the introduction to my lesson. I need to embed them throughout the lesson; in large group, small groups, with students help, in writing, one-to-one conferences etc.

I cannot do this chapter justice. I created an organizer that I hope will help me be more direct and explicit in teaching students to draw upon what they know and create a mental image. Just click on the pic to download. Let me know what you think.

Teach Like A Pirate Chapters 10 & 11

These could possibly be my favorite hooks. My artistic creativity and ability have definitely improved the more I have practiced and been exposed to new medias. I am also inspired by how amazingly creative my fellow teachers are and definitely by the bloggers I have "met."

Burgess shares that music and art  enhance our lessons, and also allow students to grow in their creativity and recall information taught in a deeper way.

• Music creates a mood. It allows for recalling something memorable.
• Drama and dance allows for movement and the opportunity for students to access information in a different way.

The "What's in it for Me?" hooks provide students freedom, choice,  and a sense of autonomy. I strongly believe, as many of you do, that our students are capable of so much and must be allowed opportunities to demonstrate this. I am still adding hooks...stay tune to download final product.

Love Melonheadz pirate theme