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The Pursuit of Place Value Understanding, Part III

§ September 23rd, 2011 § 4 Comments- Add yours§ Filed under Teaching Math § Tagged , , , , , , , , , , , , , , , ,

On May 23, 2010 in my very first blog, Teaching Math; It’s All in the Balance, I shared my view that both the traditional and reform camps have something to offer math educators. Basically, traditionalists believe skills should be taught based on algorithms, formulas and step-by-step procedures; reformists support a more inquiry-based approach that emphasizes developing conceptual understanding and problem-solving skills. My contention is that a balanced approach is best.   Also, I am an advocate for using engaging, interactive technology whenever possible to reach and teach this generation.

I shared a conversation I had with Grant, my oldest grandson, about adding two two-digit numbers. During our talk it was obvious his skill for adding single digits was developing nicely, but he lacked an understanding of place value concepts.  Even though he could get the right answers, when I asked him the value of the digits, he had no clue.

In my second blog posted on June 27, The First Steps in Developing Conceptual Understanding of Place Value, I emphasized the importance of developing a foundation of understanding.   I also shared ways to help children understand place value when first learning to count with non-proportional items (straws and money) and with proportional manipulatives (base-ten blocks) when adding and subtracting.

Grant is now in the 3rd grade.  He tells me he “gets” math.  He doesn’t need my help, thank you very much.  That is… until this week. Monday, he called to say he had taken a test last week, and he wasn’t happy with his grade.   “Can I come down, Gigi? Can you help me?”   Smile. Gigi is back in the picture.

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Whole Number Division with Semi-Concrete Base Ten Blocks

§ August 26th, 2011 § 4 Comments- Add yours§ Filed under Teaching Math, Technology in Education § Tagged , , , , , , , , , , ,

Helping children develop conceptual understandings, making math learning relevant, and integrating discovery and skills-based learning are all important.

In the blog post The First Steps in Developing Conceptual Understanding of Place Value I shared my 2nd grade grandson’s experience in learning two and three digit addition and subtraction.  He had been learning to add and subtract digits without any understanding of place value, so I introduced the operations using non-proportional objects to teach re-grouping. § Read the rest of this entry…


Relevance: Discovery, Skills-based, and Manipulatives

§ August 23rd, 2011 § 4 Comments- Add yours§ Filed under Teaching Math § Tagged , , , , , , , , , , , , ,

Recently I penned My Last Math Class and shared how I made math learning real for an unique group of students.  Following on its heels, I shared information on the 3 R’s —Rigor, Relevance, and Relationships— coined in 2010 by The International Center for Leadership in Education.

Now I want to expand this theme into another area of math education and discuss what is more meaningful and effective — discovery learning or skills-based learning.  Much material is available to fuel this debate, but I don’t lean towards one or the other.  I am quite comfortable with my seat on the fence, where I have a vantage point. § Read the rest of this entry…


The First Steps in Developing Conceptual Understanding of Place Value

§ June 27th, 2011 § 2 Comments- Add yours§ Filed under Teaching Math § Tagged , , , ,

Photography by Kathy Cassidy

In an earlier blog I shared my concern about my eight year-old grandson knowing how to calculate the correct answer when adding two-digit numbers without knowing the value of the digits in the addends or sum.  But helping children understand place value is more than telling them which number is in the ones place and which number is in the tens place or even that the 5 in 54 equals 5 tens.    It takes their active involvement to develop conceptual understanding of this key concept.

Think about your own experience, your child’s or grandchild’s experience when learning to count.  I’m pretty sure  those experiences are similar to mine—that it seems intuitive to use one-to-one correspondence with real objects when learning to count.  One, two, three balls.  Four, five, six books.  However, when learning to count to ten and beyond, it seems that imitation and rote memorization are valued.  To illustrate my point, haven’t we all heard a parent claim that their child can count to 20? § Read the rest of this entry…