Building Mathematical Comprehension Chapter 3: Making Connections (FREEBIES!)

Today I will be one of your hosts for the fabulous Building Mathematical Comprehension Book Study!  I am really getting into this book :o)  It's only the third chapter and I already have so many ideas flowing through my head.  I had to get a journal just to write them all down so I wouldn't forget!  This chapter was all about making connections as good mathematicians.

As good readers, we always talk about text-to-self, text-to-text, or text-to-world connections.  Before, during, and after reading.  Why not the same for math???  Throughout our lessons we might hit upon some schema that the students should know, but what if they don't remember (I know... that NEVER happens, lol) or what if they didn't really understand it, or what if they remember it WRONG?!  As I started reading the chapter these are some of the quotes that really hit home and opened my eyes to the way we teach math.    Now these are not things we didn't already know but it really drove home the need to discuss their prior knowledge as a whole more before, during, and after the lesson.  I am a firm believer in that students learn so much from each other so why not have them share their background knowledge with each other?

"What students already know about the content is one of the strongest indicators of how well they will learn new information relative to the content."

 

"When students begin to recognize the mathematical connections not only within the discipline, but also to their lives and to other content areas, their understanding becomes deeper."

Prior knowledge can be grouped into three categories: attitudes, experiences, and knowledge.

Attitudes

Have a class discussion at the beginning of the school year about math: your student's thoughts and feelings on the subject.  What have they liked and disliked about the subject?  What would they like to see added to their math block?  Most students have a fear or anxiety about math and this would be a great way to alleviate that.

 

Experiences

Have you ever seen that Disney movie Donald in Mathematician Land?  My students watch it every year and they are always so surprised by how math can connect to everyday life!  I think the biggest "aha moment" for them is when Donald shows them how they can play pool like a professional just by knowing angles, lol.  Have students look for math outside of just their math block.  Use a Math Log (similar to a reading log) to see what they can find at home or help your parents get involved with a Math Newsletter.  I've attached an editable PowerPoint of a sample math newsletter that you can send home to help parents have a better understanding of what is being asked of their kids.  (Print it as a PDF and "Scale to Fit" to get rid of the white sides)

 

 Knowledge

Like I said before, kids are going to have different experiences but why not let them learn from each other?  Let them make the actual connection from the new concept or procedure they are learning about to the things they already know.  "If student's have nothing on which to hook new information, it is very difficult for them to construct new meaning."

Kinds of Mathematical Connections:  Look familiar???

Math-to-Self: Even though you know that your students have a wealth of knowledge in their brain, especially about math, they might not understand how to pull it out and use it to their advantage all the time.  As the teacher, you will need to explicitly teach and model to students how to make the math to self connection.  Whether it be with numbers (7 is my age, how much I get a week for allowance, 7-11, etc.) or skills (percentages: coupons, sales, interest rates, tracking my data, etc.)  The more this is done, you will gradually release the responsibility of this strategy onto your students and soon they will independently be doing it on their own!

Math-to-Math: When students create links between their present and past math learning, they are enhancing their ability to solve problems and construct new mathematical understanding.  Just think about it.  Without know multiplication, you wouldn't be able to do division as easily.  Then think of all the different ways students divide.  No more just long division!  They are using all of their mathematical background knowledge to figure out what works best for them: long division, adding and adding and adding some more (I hate that one!), groupings, arrays, the list could go on.  And you didn't necessarily teach them all of those ways but they created that link on their own.

Math-to-World: The more students are exposed to math, the deeper their understanding.  In a previous post I discussed a newsletter with parents, but you can also challenge them by asking them to do a Math Hunt: find math in everyday life.  The weather, movies, elections, sports, newspaper, etc.  Math is not only found in math.  Math is found in Science, Reading, Social Studies, Art, Music, P.E..  When making your lessons, try and think of ways to incorporate the "math angle" so your students can see that math is everywhere!

Have y'all ever heard of DynaMath?  I LOVE it!  It's a Scholastic Magazine they publish each month or so and it is all about math in the real world.  They talk about movies, current events, books, tie it into science and social studies, etc.!  Each article is geared towards a specific math topic and there are problem solving questions at the end of each article that require you to practice said skill and have read the article to get your answers correctly!  Have I mentioned that I love it???  We use it for one of our math stations as enrichment but if you find a specific article that is gear toward what you are teaching you could always photocopy it and do it whole group :o)  There are also extra practice sheets and quizzes online for teachers to reproduce if you wish.  It is a GREAT way to tie in math and real world connections.  Click on the image below to check it out.  You can even look at a digital issue (the whole magazine) for free online.  If your schools doesn't have the funds to get a class set then this is another option.

*No, Scholastic did not pay or bribe me to say all of that, I, and my kiddos, just REALLY enjoy this magazine*
 

Now the question is, how to do all this?  When you are planning your math lesson it can be difficult to just "wing it" when coming up with connections on the spot.  As you are deciding on your think-aloud, make sure you can come up with connections that are authentic and ones that you'll be able to use sentence stems with that your students can become familiar with and use when they are independently making connections.

1. You want to make sure your students know what schema is and how to build it!  I love the schema roller technique.  Choose a math topic and write down all your schema based on that topic.  Tear apart everything you wrote down and lay it on a desk.  Take a sticky lint roller (that's your brain) and roll it over the desk.  This shows the kids that everything you've ever learned is now stuck in your brain, you just have to find it :o)
2. Daily math stretches - these should be brief and each student will be complete one discrete part of the stretch, and then the class will meet together to discuss the task.  The students should be the primary contributors to the discussion, you facilitate.  I know, I know it's difficult, but we have to let go y'all :o)  Another good idea was the "How did my family use math last night."  This really gets them thinking about their math-to-world connections!
3. Use anchor charts that they can refer back to!
4. Current events (discussed above) and children's literature can be an essential tool to making connections!  In every chapter so far they have mentioned how important children's literature is and I cannot agree more!  I like that for this chapter though it was not necessarily math picture books that they discussed.  Any book that you read you can find math connections in it!
5. My final point that I found very important was that this is a strategy... NOT THE LESSON.  Although this strategy is important and will be very helpful, do not spend a lot of time on it.  It is not your main lesson (usually).

I hope y'all are enjoying the book as much as I am and I can't wait to see what everyone else thinks!  Don't forget to head over to Brenda (Primary Inspired) and Beth's (Thinking of Teaching) blogs and link up what you thought of this week's chapter!

BMC Chapter 2: Recognizing and Understanding Mathematical Vocabulary

Just as it states in the blog post, chapter 2 is all about vocabulary!  I was very excited to read this chapter since my other book study is on becoming a "word nerd."  Even though I am reading Word Nerds and it has great ideas I have never taught math (I will be next year though) so some of the ideas from this chapter were really enlightening and I plan on using them in my classroom.

When the author wrote that every student is a Mathematical Language Learner I could not have agreed more!  Just thinking about all the different activities and accommodations I make for my ELL kiddos, that's exactly what I should do for my math group!  They need multiple exposures, visual representations, etc.  Math is like a whole new language if you think about it!  Add on that some of our math vocabulary has multiple meanings, but if the kids try to use their prior knowledge to decode the words they will get so confused.  Two examples: feet and yard.  When kids hear those words they think of a body part or their "front/back yard," not twelve inches and 36 inches.  So what can we do to help them learn this "new language" you might ask?

The first thing you need to do is compile a list of your math vocabulary.  Now I'm not just talking about what the chapter tells you in bold words.  Look at your state standards or the Common Core practices, look at the word problems and find words that kids will need to know to become successful mathematicians.  The textbook can be very helpful but it is not the end all be all and you want to make sure you're words align with your standards.  This would be great to do with your team during a PLC (does anyone else have those???).

Once you have your list of vocabulary words there are many different ways the author gives you to help promote their vocabulary fluency inside and outside of the classroom!

1. Letter to parents asking for their support at home with the new words.  I really like this idea because as much as we might complain about parent involvement sometimes, most of them really do want to be helpful they just don't know how or what we are learning about.  By sending a letter home for every unit and telling them the words and how they can incorporate it at home can be huge to our student's learning!  You can even include a challenge (Math Hunt) and have them find these words/examples in the real world and bring them in for extra credit on the test or make a big collage for your classroom.

2. Math Word Wall - I love this idea but I think I would want it to look a little different from our regular word wall.  This one would have pictures and examples, etc. but I just can't think of how I would want it to look, especially with the limited space...  Anyone else do this?  What does your Math Word Wall look like?

 





3. Graphic Organizers - the same ones you use for your reading vocabulary except now you will use number representations.

Frayer Diagram

Venn Diagram

"These Are.../These Are Not..." Chart

Matrix or Semantic Features

Analysis Grid

Concept Map

 

4. Games and Other Learning Activities - these are what really motivate my kids!  This is also where I see the biggest growth in correct vocabulary use.  Through these activities my kids are showing me that they can use the words correctly (Speaking and Language) and that they can explain or justify their answer by writing in their journals using their new found vocabulary (Writing).  Again, I can only speak from the reading stand point, but if it worked in my reading class why not in my math class?

Vocabulary Charades

Make My Day (Students have answer cards and you call out "If you have 7 + 9, make my day."  The person with 16 will come up and bring you their card.  Continue this until all cards are gone.)

I Have, Who Has

Math Hunt (explain above)

Talk a Mile a Minute (like Taboo or Pyramid but with math terms)

5. Literature Links - you all know how I feel about children's literature in mini-lessons... LOVE!  If you head on back to my post on chapter 1 there is a great link that will take you to a website that has different picture books for each math unit!  One thing I really like about using children's literature in my lessons is that not only can it give the kids a real world application but it gives them a common experience.  Very rarely do they all have the exact same background experiences, but with a read aloud they will and you now can go back and reference the book in small groups and what not.

Whew that was long!  Thanks for sticking with me through that lengthy post :o)  I hope you got some good ideas that will help you embed your math vocabulary into your lessons.  Check back on Friday as I will be hosting Chapter 3 of the Building Mathematical Comprehension Book Study.  It's all about Making Mathematical Connections!

Building Mathematical Comprehension: Chapter 1 Comprehension Strategies for Mathematics

Okay, so I am totally behind on this book study!?  Well, really only a week and to be fair I did read it when I was supposed to, just not write about it when I was supposed to... LOL.  I promise I'll be on the ball when it is my turn to host!  I told you I had two book studies going on this summer and this is my second one: Building Mathematical Comprehension by Laney Sammons with Beth from Thinking of Teaching and Brenda from Primary Inspired. 

Chapter 1 was a big "DUH!  How did I never notice that?" moment for me.  It was all about the reading comprehension strategies you use during your literacy block and using THE SAME ONES in your math block.  We were departmentalized last year and we were forever and always telling the kids, "It's the same thing you do in reading, just do it for math or science," but we never showed them how.  I just expected them to be able to do it, and I was wrong.  Some serious teacher reflecting went on during this chapter folks, let me tell ya.

The author included a chart on how good readers and good mathematicians use the same strategies and how - I LOVED IT!  I was also very intrigued by the idea of  the different types of knowledge the readers draw upon as they are reading their math problem.

• Knowledge about content: background knowledge.  We all know kids absorb more of the lesson if they have a strong foundation and background in that area.  Same goes for numbers!
• Knowledge about structure: loved the idea of word problems as a unique genre!!!
• Pragmatic knowledge: similar to background knowledge but experiences they have had through years of interaction with others.  This reminded me of my childhood.  My dad always did logic puzzles, riddles, or who-dunits with me.  We would always watch mystery movies together and he always got me critically thinking and I think that is a huge reason as to why I enjoy math.  It's a mystery/problem, there is a correct answer and I WILL figure it out, lol.
• Knowledge about the social/situational content: the reason or goal for reading your math problem

You all know how I LOVE children's literature and I adore the idea of incorporating children's literature into my lessons!  Read alouds are something that always stick with my kids for some reason, so why not have read alouds for math to help them remember a concept?  Click on the picture below to take you to another blog with an AMAZING list of children's books based on math concepts!

You see what I mean... all "duh" moments but I just never thought about them in terms of math!

The author goes on to tell about explicit instruction when introducing a new strategy (very CAFE/Daily 5-esque), which strategies to use in the beginning, during, and after reading a math problem, and to remember the four C's when introducing a new concept (conception, connection, construction, and comprehension).  LOTS of great information folks!  I'm very excited because the next chapter is on vocabulary and it's going to go perfectly with my other book study: Words Nerds.  Don't forget to link up your thoughts and read what others have to say!