Visible Learning for Mathematics, Grades K-12 by John A. (Allan) Hattie & Douglas Fisher & Nancy Frey & Linda M. Gojak & Sara Delano Moore & William Mellman

Author:John A. (Allan) Hattie & Douglas Fisher & Nancy Frey & Linda M. Gojak & Sara Delano Moore & William Mellman
Language: eng
Format: epub
Publisher: SAGE Publications
Published: 2016-10-06T13:30:45.791203+00:00

Figure 4.9 Horacio’s Word Card

Understanding place value in our number system is one of the most foundational ideas for elementary children to understand. A full comprehension of place value includes understanding the relationship between the place each digit holds in a multidigit number and the value of that place. For example, in the number 3456, the digit 3 actually represents three thousands, whereas in the number 2453, the digit 3 represents three ones. Without this understanding, students cannot compare or order numbers, and they have great difficulty developing strategies for whole-number operations.

There are many place value tools, such as arrow cards, expanded notation, and base ten blocks, but Mr. Martin’s favorite are coffee stirrers and small rubber bands or twist-ties. He begins by having each first grader make his or her own place value mat (Figure 4.10), and students begin to count with the straws. However, as soon as they get ten ones, they put a rubber band around the straws and the ten becomes a new unit with its own place on the place value chart. Students build numbers up to ninety-nine. They compare the models on their place value chart with numbers on the hundreds chart that hangs in the classroom. They write the numerals under their models and compare their number with the numbers that others in their group have modeled. As students begin to add (put together) two-digit and one-digit numbers, they physically put ten ones together and move that bundle to the tens place before they ever write an equation. In Grade 2, Mrs. Sofal continues to build on previous experiences as students extend their place value chart to the hundreds place and continue to regroup in addition and subtraction. This provides students with the opportunity to make sense of place value in a very physical way, thus building the surface learning that will become deep learning as they apply this knowledge to develop algorithmic procedures.

Figure 4.10 Manipulatives on a Place Value Mat

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