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The Pursuit of Place Value Understanding, Part III

§ September 23rd, 2011§ 4 Comments- Add yours§ Filed under Teaching Math§ Tagged 3rd grade math, addition, App, base ten blocks, conceptual understanding, elementary school mathematics, iPad, itunes store, Joe Scrivens, manipulatives, Maryscott Glasgow, MontessoriTech, place value, PlaceValue, reforms math, subtraction, traditional math

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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The First Steps in Developing Conceptual Understanding of Place Value

§ June 27th, 2011§ 2 Comments- Add yours§ Filed under Teaching Math§ Tagged conceptual understanding, counting, manipulatives, Maryscott Glasgow, place value

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…