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Saturday, December 20, 2014

Children's Mathematics Book Study: Part 3

Welcome to week 3 of our book study on Children's Mathematics.  I was so excited to dig into the chapter on base 10 concepts after last week's reading.  I also really liked all the strategies shared in chapter 7 and I love watching videos of kids solving problems.   If you missed this week's Monday Math Literature post, you might want to check it out.  I took one of the questions from last week's chapter about writing story problems based on a children's book and applied it to The Mitten.  You can check out my process and grab the set of problems I wrote.

If you are just joining us, it is not to late to join our book study.  Grab a copy of the book and maybe a friend or two and jump in when you are ready.  Also, if this December is just to hectic for you, I will be starting another book study the second week in January.  Read more details about both book studies here.  

Here is the posting schedule for Children's Mathematics:
December 7: Chapters 1- 3
December 14: Chapters 4 & 5
December 21: Chapters 6 & 7
December 28: Chapters 8 - 10
January 4: Chapters 11 - 13

I will post each Sunday morning and share it on my Facebook page.  Please join in by leaving a comment on my blog post or Facebook page.  If you have your own blog and want to write a post about the book that works too!  Add your link in the comments section here.  Thank you to all who shared last week!

Chapter 6: Base-Ten Number Concepts

After being introduced to the idea last week of the importance of exposing kids to multiplication and measurement division problems I was very excited to explore this chapter in more detail.  There are some excellent videos to watch and some great examples of problems that get kids thinking in tens.  I love the range of problems presented in this chapter and the examples really got me thinking about how I can ask more base ten multiplication and measurement division problems of kids at all grade levels.

Teaching Concepts versus Teaching Procedures

I have seen time and time again how powerful it can be for students to construct their own knowledge and I love how the paragraph as the top of page 91 supports this idea.  It is so tempting to teach kids a procedure or a rule and tie it into a cute jingle because then it seems like they "get it" right away.  It is also the way most teachers were taught themselves and the only way most adults have ever experienced learning.  As someone who works with kids over a span of 7 years, I have seen first hand how these rules don't hold up over time.  It certainly takes longer to let kids develop a good conceptual understanding of math concepts, but it pays off big time later when they can add to their knowledge rather than throwing out old rules and learning new ones.  

Number Words

When I first started teaching math at the primary level, I remember feeling very frustrated by the lack of understanding in reading and writing numbers.  Even very small numbers seemed to be super challenging for some kids to read and write.  It just seemed like such an easy skill to me because I had been doing it for so long.  "As adults, we have used number words and pace value for so long that we no longer pause to think about the fact that there is a difference between spoken number words and written numerals or that the same symbol can have many different values depending on where it is placed in a numeral."  After I took some time to stop and think about all the nuances of place value and of the English language, I realized why my students were struggling with this so much.  I have to say that arrow cards have really changed the way I teach number words and can make a huge difference for your students.  

Chapter 7: Children's Strategies for Solving Multidigit Problems 

This chapter opens with this statement: "Problems with two- and three-digit numbers actually provide a context for children to develop an understanding of base-ten number concepts.  As children solve and discuss these problems, their understanding of base-ten number concepts increases concurrently with an understanding of how to apply this knowledge to solve problems."  I love this statement and think it sets a great tone for the chapter.  I have spent a great deal of time developing better ways guide my students through multidigit problems over the last 3 years.  When I first started my blog, I wrote this post about how I presented a group of second graders with a problem that involved them solving 1000-668 without ever having "taught" them how to do it.  I was so impressed at the time with how well my students did with this and how many strategies they had.  Now I do these types of problems a lot more with kids.  It really helps them cement their place value understanding while building their own strategies for multidigit computation.  

There are so many excellent examples and videos in this chapter that I could spend a full week talking about all the great ideas.  Similar to the earlier chapters, it is important to remember that kids move from direct modeling to more efficient methods over time.  If you change the numbers or the context of the problem, they might revert back to direct modeling.  It is not a linear progression where kids graduate from one type of problem solving and never use it again.  They will move up and down in terms of efficiency based on the problem type, the numbers and the language in the problem.  

What are your thoughts on this week's reading?  Please respond in the comments below or head over to Facebook and leave your thought there! 

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