## Saturday, August 23, 2014

### Math Books That Will Change Your Teaching!

Today I am teaming up with some of the best math bloggers out there to bring you 12 different math books that will change your teaching!  Each blogger has chosen a different book to tell you about and will be giving away a copy of that book on their blog.  Check out this great group of blog hop participants!

I spend a lot of my time reading math and teaching professional development books.  I always get some good information out of the books I read but only a handful of them get a special spot on my shelf as the books that I will recommend over and over again to other teachers.  Today I want to tell you about one of those books.

#### A Focus on Fractions: Bringing Research to the Classroom

I first read this book when it came out in 2010 and it completely changed the way I teach fractions.  The authors of this book read all of the research on how kids learn fractions and present it in an easy to read format.

Chapter 1: Modeling and Developing Understanding of Fractions
What kinds of models does your math program use?  Do you know there are three different kinds of models that kids need to interact with as they are developing and understanding of fractions?  I certainly did not!  This chapter will walk you through area, set and linear models and give you some ideas for incorporating more modeling into your classroom.  I found linear models completely lacking from my math program when I first read this book.  As I gradually addressed these changes and added more modeling into our program, I noticed a big difference in kids' understanding and ability to use models to solve problems.

Chapter 2: Inappropriate Use of Whole Number Reasoning
Have you ever had a kid tell you 1/4 is bigger than 1/3 because 4 is bigger than 3?  This is just one example of inappropriate whole number reasoning.  This chapter also gets into some detailed ways that teachers actually TEACH kids to use inappropriate whole number reasoning during their early fraction instruction.  This is a huge eye opener to most teachers, especially those who teach first and second grade.  I had to tweak some of the wording I use with kids when I teach first and second grade fractions.

Chapter 3: What is the Whole?
This chapter helped me push students conceptual understanding of fractions much deeper.  It made me realize that all the questions I was asking involved giving the students the whole and asking them to find a part.  I never thought of asking kids to find a whole when given a part.  An example of this would be showing kids what half of the candy bar looks like and asking them what the whole would be.  These problems seem so awkward at first when you are not used to asking them but quickly become part of your repertoire and really help push kids' thinking to the next level.

Chapter 4: Partitioning
This chapter made a huge difference in how I use models with kids and how I teach them to use models as well.  This breaks down the difference types of partitioning and shows you how to move kids from halving to more complex fractions.  Good drawing of models has gone a long way in helping my kids construct all kinds of algorithms and notice many patterns in their fraction understanding.  Think about how you would teach kids to draw eighths or fifths or twelfths.  Check out this chapter for more help!

Chapter 5: Comparing and Ordering Fractions
Before you read on, think about how many strategies there are for comparing fractions.  I could think of one and only one before reading this book.  The common denominator.  Well I was VERY wrong about that.  Now I listen to my students very carefully when giving them comparing fraction type problems.  I also am much more intentional in which fractions I ask them to compare so that I can elicit some of the different strategies.  This chapter outlines five different strategies for comparing fractions and your students WILL invent these on  their own if given the right fractions.  This chapter gives teachers lots of aha moments!

Chapter 6: Number Lines and Fractions
I am a bit embarrassed to admit that before reading this book, I did little to no work with linear or number line models for fractions.  Fraction number lines barely made an appearance in our state standards and showed up very inconsistently in our math program.  After reading this book, I discovered the power of the number line and now my number line lessons are some of my favorite ways to elicit the big ideas of fractions and to help kids make connections between fractions, decimals and percents.

Chapter 7: The Density of Fractions
This is about really getting at the big idea of infinity and more specifically that there are an infinite number of fractions between any two whole numbers.   The number line model really supports this big idea!  Think about asking your students to name two fractions between one fourth and one half.  Could they do it?  How about naming two fractions between seven eights and a whole?  See how these questions can open up some great discussions?

Chapter 8: Equivalent Fractions and Comparisons
Finding equivalent fractions is such an important skill for kids to have!  It is the gateway to fraction operations and something many MANY kids need more work with.

Chapter 9: Addition and Subtraction of Fractions
Now that my district follows the Common Core State Standards, we do a lot more with fraction addition and subtraction in grades 4 and 5.  Most of this work used to be done in grade 6.  The biggest aha I got from this chapter is that just because a kid can follow the common denominator procedure to add or subtract fractions does not mean they have any understanding of the quantities.  There is an example in the book that asks kids which number the sum of two fractions is closest to and a kid does a great job showing fraction addition with common denominators, gets a fraction like 19/20 and then says the sum is closest to 20!

Chapter 10: Multiplication and Division of Fractions
This chapter is chuck full of great ideas for fraction multiplication and division which has always been something I had struggled to teach in a conceptual way.  This is where I first thought about using the area model for fraction multiplication.

If you teach fractions, this is definitely a book that could change your teaching!  It is loaded with examples of real student work and will open your eyes to some new ideas for teaching fractions.  It also is a great example of using formative assessment to inform your instruction.

Go grab this book now or enter below for your chance to win a FREE COPY!  This giveaway is open to folks living in the US or Canada!  At the bottom of this page you can head over to the next stop on this blog hop!

a Rafflecopter giveaway

1. My kiddos struggle most with understanding multiplying and dividing conceptually. Many of them have been taught the algorithms, but they can not explain what it really means.

1. I agree! I certainly was taught algorthims but could never explain why they work. One day I sat down with my math buddies and figured out why invert and multiply works for division. It took us a few hours but now I know why it works.

2. This looks like an interesting read! My favorite book for developing Fraction Understanding has been Beyond Pizzas and Pies by Julie McNamara.

1. I have not read that one but it looks good! The title of that reminds me that I also learned from this book how much my program over relied on circle models for fraction concept development. The research shows that the circle model is harder to generalize than some of the other area models.

3. The most challenging thing about teaching fractions is adding fractions with like denominators. The kids want to add both the numerator & the denominator instead of keeping denominator same.
chief9937@Yahoo.com

1. That shows they don't have conceptual understanding of fractions!

4. You definitely peaked my interest in the book. I am looking forward to reading this book and enhancing my teaching of math to my first graders. My most challenging concept is definitely fractions.

1. It is a great book for first grade teachers! I know there are chapters on fraction operations but serious fraction understanding starts in first grade and you don't want to be one of those teachers who is teaching misconceptions!

5. Students have a hard time realizing it's just division. Transitioning to generalization to see that fractions are all around them is very difficult.

6. While I LOVE teaching math and fractions, I find that my struggling second graders have the hardest time understanding 1/3 is more than 1/4. Like you stated, that denominator needs to be understood better! This sounds like an awesome book for me! I would love to win it and read it now for back to school! Thanks, kath. ThePaperPumpkin@aol.com

1. Improper whole number reasoning is huge in second grade!

7. Teaching fractions is not in my 1st grade curriculum, but I tutor 3rd & 4th graders so this book will be helpful.

1. It is a super helpful book!

8. I want a copy of this one! I have always loved teaching fractions and making them "make sense" to students. I used lots of models with my kids when I taught fifth grade, and it made all the difference. Thanks so much for sharing this one--it's new to me. Wish me luck! :0) Enjoyed reading your thoughtful post...

Smiles,
Sarah

9. my students always struggle with fractions so this could be very helpful!
- Ashton

10. This is a new book to me! I can't wait for it to arrive so that I can read it! Thanks!

Jamie aka MissMathDork!

11. I was taught fractions with the traditional procedural model. It is difficult sometimes for me to not rush ahead to the procedures before students have a solid conceptual understanding.

12. This book seems great. We covered some of these concepts during the Math Endorsement class I am taking. Don't be embarressed about the number lines. I've been there too! I think I want a copy of this one!

Greg
Mr Elementary Math Blog

13. What I find challenging about teaching fractions is EVERYTHING! I have moved this year from teaching kindergarten to 3rd grade, which I have never taught...so everything is tougher because it's above the number 20! LOL! But I am trying very hard to make sure the students are getting the material needed and using INB's.

14. This comment has been removed by the author.

15. I would love some inspiration on teaching fractions. I am tired of pizza and brownies for fractions and I am always looking for new ways to teach my 4th grade students a deeper understanding of fraction concepts.

16. I LOVE teaching fractions--there is so much we can do to help students develop their number sense for those "numbers between the whole numbers"!

17. I think the most challenging part of teaching fractions is making sure they understand that the when you are talking about a unit fraction - thebigger the denominator, the smaller the piece.

18. Fractions can be so difficult for teachers and learners. I would love to share this resource with teachers at my school!

19. I have always tried to teach fractions with hands-on activities, but your post has made me realize there's more to consider. I have to read this book!
Brandi
The Research Based Classroom

20. I have a hard time getting the students to know when to multiply and when to divide fractions in word problems.

21. Fractions are always challenging for my students. I think this is because the whole concept is very abstract to them. This book could really help my fraction instruction! Thanks for the giveaway :)

22. Differentiating how I teach fractions is the largest challenge to my instruction. Thank you for the recommendation of this resource!

23. I recently moved to an intervention position where I'm teaching fractions to 5th graders for the first time. This book looks like a fantastic resource!

24. My biggest challenge when teaching fractions is fractions as a part of a group, such as 1 flower is white and 3 are pink. As a 1st grade teacher, you've made me wonder if I'm teaching the wrong way--I NEED this book! :-)

25. Fractions is my biggest challenge due to fact that the students have so many misconceptions. Once those misconceptions are formed, it is difficult to break through. Hopefully, this book will give me a few more tools to break those darn misconceptions.

1. This book does a great job of showing what misconceptions kids have and what formative assessment prompts to give to elicit these misconceptions and how to help kids get over them!

26. I would like more real fraction connections. Many fraction problems or activities are not something we really think of in fractions so they seem fake when you use the problems. I would really like to learn more about teaching without misconceptions.

27. Division & multiplication of fractions is the hardest for my students to understand. Lots of modeling and picture drawing. :)

28. Fractions in general are very hard!

29. As a math coach I am always seeking out information that will benefit my teachers!

30. I found it tough to get students to understand that 1/2 doesn't always equal to another 1/2, it all depends on the whole! I finally found a great hands-on activity that works - but it's so hard to explain, I'd have to take pictures (hmmm.. future blog post!)

Thanks,
Linda
The Purple Teacher

31. When I taught fractions I found that students did not understand why during division that a reciprocal was taken of one fraction then they could multiply across. This year I anticipate my students struggling with the concept of what a fraction actually is.

32. I teach basic skills math to 1-3 graders. No matter what I do I can't get them to remember the meaning of the numerator and denominator!

33. Seems like a great resource. I teach 6th grade and they still struggle with understanding fractions...often they can do the work, but have no idea why the answer is correct conceptually.
I Have 2 Questions

34. This looks interesting as fractions have been a hot topic lately since so many children and adults have trouble with them.

35. The toughest part for me is balancing time spent helping my older students really understand how fraction operations work, with learning efficient algorithms (and practicing them) so that they can use fractions fluently as one of many mathematical tools at their disposal.