How do you teach students a conceptual understanding of Place Value?
This is a question that regularly puzzles parents and teachers alike. How do you teach students proper place value when you have been through all the correct maths curriculum the way it was laid out, and still they don't know how to add tens and hundreds correctly?
I'll tell you a story:
The little girl sits puzzling over the problem on the page. She’s only in grade two, but the stress of high performance expectations is already in place. Here’s the problem she needs to solve:
500 – 78
The little girl remembers that she needs to cross out the five and make it a four. She also knows that one of the zeros becomes a nine and the other one becomes a ten, but she just can’t remember which is which, and it’s so frustrating! Finally, she has an idea. She tries different values and adds 78 to each of them until she comes up with:
422 + 78 = 500
She writes 422 as the answer and receives that coveted gold star on her paper. No one knows that she doesn’t understand how to complete this type of subtraction with regrouping (or “borrowing,” as it was called in her day).
Why do students find Place Value hard?
Throughout primary and high schools across Australia, I have seen the same issue happening time and time again. The little girl did exactly what most students continue to do well after the Place Value lesson has been taught to them.
So what is the issue? It isn’t a faulty memory or that the concept is particularly difficult.
It's what happens when a student is taught only an algorithm and a formula for maths and is not given any conceptual understanding of the role of place value.
Teaching Place Value in a hands-on, foundational way is essential
The definition of place value is rather simple. Place value is the position of a number that tells what value it is assigned, and is vital in our communication of maths as a universal language.
Here at Maths Australia we often say place value is as simple as the knowing that "every value has a place". The place tells us “what kind”, the value tells us “how many.”
For example, in the number 246, the digit 4 indicates there are four (how many) tens (what kind).
Despite its simple definition, place value can be a challenging concept for a young child to grasp. Regardless of whether dad is in the kitchen, the living room, or the garage, he is still dad, but if the digit 3 is in different locations (tens or hundreds place, for example), it means something different. In the Math-U-See curriculum, place value is first introduced in the Primer level through using "Decimal Street". Each of the houses on Decimal Street represents a separate place value. This is reiterated in the Alpha level and again in Beta.
Here's a rough drawing of what I'm talking about:
See how you can see that there are two units in the "units house," three tens in the "tens house" and one hundred in the "hundreds house"?
Therefore, the number would be 132.
And that is correct.
If your student can use the manipulatives and see, touch and feel where the each number goes, they're successfully learning Place Value! They are also engaging their multi-sensory senses and gaining not only a strong understanding of this basic maths concept, but a knowledge that they will retain (and use) for life.
According to Sherman, Richardson, and Yard, “Place value is perhaps the most fundamental concept embedded in the elementary and middle school mathematics curriculum.”
Place value provides the foundation for regrouping, multiple-digit multiplication, and more in the decimal system, as well as a starting point for the understanding of other base systems. Place value allows your 12-year-old son to understand the difference between the $50 he received for his birthday and the $500 price tag on the iPad he’s saving for. Place value allows the student learning scientific notation to understand why 54,800,000 can be represented as 5.48 X 10.
Almost all mathematical concepts build on the understanding of place value.
That's why it's so important.
“Place value is perhaps the most fundamental concept embedded in the elementary and middle school mathematics curriculum.”
Studies have shown that place value understanding has a positive correlation with overall mathematics achievement. For the grade 2 student described above, place value would have helped her understand that when she crossed out the 5 in 500, she was really decomposing 1 hundred into 10 tens, of which 1 needed to go to the ones or units place to allow her to subtract, leaving 9 to go to the tens place. There would have been no need to memorise (and forget) an algorithm!
What does research say about teaching Place Value using multisensory methods?
The way Place Value is taught to your student is essential. Research has shown a correlation between using manipulative representations of numbers (as opposed to one-to-one representations e.g numbers drawn on paper) is huge in the understanding of place value. In other words, representing the number 24 with two 10 blocks and four units rather than writing down "24" or showing 24 units (without showing that the tens and hundreds are distinctly different from the units) correlates with a better understanding of place value. The Math-U-See presentation of place value using Decimal Street and our color-coded pieces for units, tens, and hundreds supports this research-based hands-on and multisensory representation.
Additionally, studies have shown that the way numbers are verbalised by English-language speakers may negatively influence the way students think about and represent numbers in comparison to Asian-language speakers. Math-U-See provides some alternate number naming strategies to help bridge this gap and promote better understanding of base ten.
You can watch the video presentation on place value here and see how the Math-U-See program can help your students gain a better understanding of this foundational concept.
If you were wondering if your student can really understand place value, you can check their understanding of place value (and other maths topics from basic addition to algebra) by using our free Online Placement Tests.
These diagnostic tests are easy to use and the results are automatically calculated to show where you student is at, and what you can do to help them.
You can take the Online Placement Test here:
Let us know how you go,
The Team at Maths Australia
1. Kouba, V. L., Brown, C. A., Carpenter, T. P., Lindquist, M. M., Silver, E. A., & Swafford, J. O. (1988). Results of the fourth NAEP assessment of mathematics: Number, operations, and word problems. Arithmetic Teacher, 35(8), 14-19.
2. Miura, I. T., & Okamoto, Y. (1989). Comparisons of U.S. and Japanese first graders’ cognitive representation of number and understanding of place value. Journal of Educational Psychology,81(1), 109-114.
3. Miura, I. T., Okamoto, Y., Kim, C. C., Steere, M., & Fayol, M. (1993). Cross-national comparisons: France, Japan, Korea, Sweden, and the United States. Journal of Educational Psychology,85(1), 24-30.
4. Sherman, H. J., Richardson, L. I., & Yard, G. J. (2014). The impact of place value on mathematics. Retrieived January 13, 2017, from http://www.education.com/reference/article/impact-place-value-mathematics/.