Building Mathematical Comprehension- Chapter 9

Second to last post of this book study. Crazy!! Catch up on my old posts by going here:

Chapter 1- Comprehension Strategies for Mathematics

Chapter 2- Recognizing and Understanding Mathematical Vocabulary

Chapter 3- Making Mathematical Connections

Chapter 4- Increasing Comprehension by Asking Questions

Chapters 5 and 6- Visualizing and Inferences & Predictions
 

Chapter 7- Determining Importance

Chapter 8- Synthesizing

Chapter 9-  

Monitoring Mathematical Comprehension

The good news: Many students take part in this mostly subconscious act of self monitoring meaning as they read and do math. 

The bad news: Not ALL students are able to do this on their own.  In fact, in the beginning of the chapter Sammons says that so many children don't expect to understand math. (249) If I don't expect myself to be able to understand, then I'm not going to have much motivation to persevere when it gets hard. It's easy to give up when the expectation isn't there. This really speaks to the importance of building a safe learning environment in our classrooms and having high expectations for ALL students!

This great anchor chart from First Grade Brain Sprinkles can easily be adapted for math.  

The great thing is that this strategy of metacognition encompasses all the other strategies!

Metacognition in math, however, is twofold. First, students must monitor their conceptual understanding (252). Then, students must monitor their understanding of the meaning of the problem (254). Many math students are so engrossed in procedural understanding that conceptual understanding suffers, thus problem solving suffers.

Here's what students need to know about monitoring mathematical comprehension:

1. They are responsible for their own understanding. Students must be aware of times when they don't understand. 

2. Students need to know when they don't understand. 

3. They can pinpoint their misunderstanding. In other words, students know what got them confused in the first place. 

4. Students can use strategies to fix their comprehension. 

5. Strategies should be used flexibly. When one doesn't work, student know to reevaluate and try something new. 

Concrete Example: When a car breaks down, we don't try to keep driving it. We fix it! When our comprehension breaks down, we don't keep working, we stop and fix our comprehension first. (258)

Red Flags Students Should Watch For:

• My internal voice isn't working 
• I can't visualize the problem
• My mind is wandering and I can't focus
• I can't recall the details
• When I ask questions to clarify, I can't come up with an answer (259)

Here are some great thinking stems to assist with metacognition. 

no source for the above Pinterest pin :(

Red Flags Teachers Should Watch For:

• Students who rush through their work
• Students who don't make mathematical connections
• Students who give up easily (260)

Strategies for Monitoring Mathematical Comprehension

Huh?

Have students put a post it with the word "huh" written on it next to the confusing part of the text. If the confusion is cleared up they add a light bulb. The teacher can walk around and see what areas of the text/work should be addressed. (263) 

Ticket Out the Door

This strategy requires students to solve a problem, rate their understanding, or show their understanding in some other way before leaving the class. The teacher then uses that formative assessment when planning the next day's lesson. (264)

 

(Ticket Out The Door poster from Teach-A-Roo)

Color-Code Math Stretch

Similar to the Ticket Out the Door, students rate their understanding of the day's lesson on color coded sticky notes. Green if they understood it well, yellow for moderate understanding, and orange for very confused. On the note students write a quick statement about the concept. (266)

Here's a bit of a spin on this math stretch from Timeouts and Tootsie Rolls.  

So, so, so much to take in. After giving your brain a little break you can check out these other links too! 

Building Mathematical Comprehension- Chapter 8

 

Only two more chapters to go. That just reminds me that summer is coming to an end. Bummer! But the journey to the end has been filled with a lot of interesting math info. You can find little recaps of each chapter by visiting the links below:

Chapter 1- Comprehension Strategies for Mathematics

Chapter 2- Recognizing and Understanding Mathematical Vocabulary

Chapter 3- Making Mathematical Connections

Chapter 4- Increasing Comprehension by Asking Questions

Chapters 5 and 6- Visualizing and Inferences & Predictions

Chapter 7- Determining Importance

Chapter 8- Synthesizing Information 

Students should be synthesizing during and after their reading and math work.

But what does synthesizing mean for students? It means that they take the information they know about a topic and merge it with the new information they are learning to create a completely new idea or way of thinking about that topic. (227)

What should students know about synthesizing?

1. Mathematical thinking changes as new ifnormation is encountered. It's okay to revise our previous thoughts and ideas about a topic in light of new information that we're learning. Reflection is a great way to make that happen! (231)

2. New information should be tied to prior knowledge in order to create meaning. Students need to be sure that there is consistency as they build on their prior knowledge. (231)

3. Synthesis is what you get when you combine information from various sources that you already have experience with and with various new sources of information. (231)

4.  Synthesis changes as we encounter new information. (232)

5. Synthesis helps with mathematical understanding. Discussion is important in helping students see how synthesizing deepens their understanding of math concepts.(232)

Concrete Examples to Teach Synthesis

Nesting Dolls- Just like nesting dolls, larger ideas can be made up of smaller details, ideas, and concepts. All the little pieces and parts work to build the big concept. (236)

Baking a Cake- Separate ingredients are used to make a cake. Separate ideas can all contribute to one overarching concept. (236)

Conjectures

One of the most effective ways to promote rigorous thinking in students is to have them make conjectures, or educated guesses or predictions. (237)

Boy is Sammons right when she says that teachers struggle with this idea. Well, this teacher does anyways. It's much easier in my mind to teach math the "traditional" way. I teach the concept, kids practice the concept, I test if they've learned the concept.

But deeper understanding is gained when students have to do the hard work themselves to arrive at the big concept. Teaching math concepts through problem solving is key. Not my natural tendency let me tell you. Another reason I'm glad to be a part of this study. Push  myself a little a guess :)

As always Sammons suggest Math Stretches as a way to implement this strategy. This time, however, she suggests taking a backward approach. Give the synthesis, have students provide the details. For example, asking students to Support or Disprove This Conjecture helps them come up with the proof. (240)

I love one thought she includes at the end of the chapter: "Students deserve the opportunity to delve more deeply into the discipline of mathematics, to become more than procedurally proficient." (246)

WOW!

Students deserve that opportunity. Far be it from me to take that opportunity away from my students! I've got some work to do when it comes to teaching math, but as always I'm up for the challenge and can't wait to get out on that limb!   

I'm a 3rd Grade Blogger

I have been trying so hard to get the blogs I follow organized on Bloglovin. I specifically have been trying to get all the 3rd grade blogs into one group. As much as I love reading ALL the blogs I follow, sometimes activities and such aren't quite appropriate for 3rd grade. Sometimes I don't have time to browse, I just need to get to what is more specific to my grade level. 

Mandy over at Caffeine and Lesson Plans has a solution! Check out the top of her blog for the Blogs By Grade tab. You'll find links to all the blogs in your grade level. Sweeeet!!

I'm proud to link up with the rest of my 3rd grade gals...or at the risk of possibly leaving someone out...3rd grade gals and guys...
 

 

If you're a blogger be sure to grab the button for you sidebar and link up with Mandy. If you're a reader, bookmark her page so you can quickly get to your grade level blogs. Thanks Mandy for the link-up! Maybe now I won't spend a gazillion hours on the computer....eh, doubt it. Oh well, it was worth a shot.  

Building Mathematical Comprehension- Chapter 7

I'm so sad about missing this week's Throwback Thursday with The First Grade Pararde, but I'm determined to not get behind again on my book study posts. Since chapter 8 starts tomorrow, I have to squeeze this bad boy in today!

So here we go...Chapter 7: Determining Importance

Apparently some young adults (and probably full blown adults) still don't have this skill down, because as Sammons touches upon later in the chapter, you often find college students who highlight every last sentence on their page in a zillion different colors just hoping that the important stuff is going to stick. What they get is just a really colorful, very expensive textbook. 

 (picture from the Sharpie blog)

The strategy of determining importance can be taught by reminding students that:

1. Determining importance happens at the word, sentence, and idea level.

• At the word level students need to be aware of mathematical vocabulary and their meaning as related to the task/topic. (200)

• At the sentence level students understand that important words often mean important sentence. (200)

• At the idea level students are guided through navigation of details so they can hone in on the significant idea. (201)

2. Determining what is important is will be based on-

• the purpose and/or goal of the task at hand
• the student's background knowledge 
• the student's knowledge of word problem structure
• the ideas shared during discussion and collaboration

3. Mathematicians are able to explain their reasoning when deciding on important information. (204)

4. Mathematicians evaluate the validity of text and information as they determine importance. (205)

• This is developed as students discuss, examine, and interpret data with others. 

5. Students use their important information to solve problems. 

• Remember, the goal is increased understanding, not expertise and using the Determining Importance strategy itself. 

How To:
Here's what we all really want to know. How to teach this strategy. Here are some ideas from Sammons.

Overviewing
Teach students to skim over text before reading. Locate the important words and the question first so students have an idea of what to expect. (207)

Highlighting
Students need to be taught how to highlight. Don't just hand them highlighters and let them go at it. Remember those rainbow textbooks I mentioned at the beginning...yah...we don't want those. Be sure to model highlighting!! (208)

Read a Little, Think a Little
Break the mathematical text into chunks. In a word problem this means going sentence by sentence. Pause after each chunk to carefully consider the text. Have students put the chunks into their own words. This make retrieval later much easier! (209)

Build on the Concrete
Sammons gave a great concrete example for determining importance from the book Comprehension Connections by Tammy McGregor. You use a strainer and a pot with water and spaghetti to show how your brain lets the less important things fall through only to catch the really important stuff. Life in 4B has some great pictures and an anchor chart. Click a pic to be taken to her fab post. 

Math Stretches
No chapter would be complete without some math stretch ideas. This one is the "What's Most Important About _____?"

Students add what they think is most important about that topic. Once everyone has responded you can discuss with the whole group. This would be when you clear up any misconceptions and make confirmations as to the important details of that topic.  

Brenda over at Primary Inspired talked about this pin that she had found when covering chapter 6.

 

I loved the idea and I think it could work for this stretch too. I'm thinking of making some Velcro titles so that I can change the response questions. Pictures of that coming soon hopefully. 


Problem Solving
Make sure students are familiar with the structure of word problems.

Usually the first sentence sets the context...
The second sentence gives the facts...
The last sentence asks the question...

Be sure students understand this is a guideline and that some word problems will be structured differently.   

Whew! Glad to be caught up. Hopefully I'll stay on track and see you next week for another chapter and a throwback on Thursday. Maybe even for my first Monday Made It of the summer! That's so embarrassing to admit...I can't believe it!

Goin' on a Blog Hunt....I'm Not Scared!

Time for a Blog Hunt! Find a treasures worth of blogs for teachers, by teachers. Don't be scared...

Laura Candler from Corkboard Connections is hosting this hunt after the closing of Google Reader. If you didn't import your blogs into a new reader, you're probably scouring the internet as we speak to find those faves again. Scour no more!

Let the hunt begin!

If you're a teacher with a blog you'll want to head over to Corkboard Connections and download her guidelines first. Create your post and then link up. If you're a teacher with a blog that means you are more than likely a reader of teacher blogs so keep reading below...

If you're a reader of teacher blogs you'll want to start an account with a feed reader so you can keep track of the blogs you follow all in one place. There are a ton of readers to choose from. I chose Bloglovin' because, well, let's face it...how appropriate is a feed reader named Bloglovin'! As my mom would say...I lovers it!  Once you have your account ready you can go to Corkboard Connections or to the bottom of this post and start browsing for amazing blogs to follow. You'll want to look for a button that might look like this:

PS. This button above will allow you to follow ME on bloglovin'!

You might find a ton of cutesy buttons like this...

 

...but they'll all essentially be asking you to follow the blog with Bloglovin'. I think I better get me one of those cutesy buttons!

Why Bloglovin'?
Of course there are other reasons why I like Bloglovin' besides its adorable name. Each feed includes a little picture from the post which helps things stay purty...see...

I can also "like" a post by clicking the word like with the little heart at the bottom. This helps me out because sometimes I want to come back to a post later. I can see all of my "liked" posts all in one place...see, like this...   

And another fav feature is putting my blogs in groups. I teach 3rd grade so every time I come across a 3rd grade blog I can put it into my special 3rd Grade group.

Of course I can follow a blog as an email subscriber, but then my email gets clogged up and it's easier to manage everything when it's all in one place (That's for you Mrs. K! Smooches and Hugs!!).

Hope to see you all on Bloglovin' and happy hunting!