Why Do Students Struggle with Place Value?
Misunderstanding and errors are evident in student work when place value concepts and procedures are learned in isolation from previous knowledge and with little meaning (Baroody, 1990). For example, not remembering from which direction to count over the number of places when multiplying decimals can be a result of not understanding why the decimal point is placed in a specific spot in the product.
Conceptual and Procedural Errors
In general, conceptual misunderstandings occur when students lack fundamental understanding and experience with positional systems (Kamii, 1986). Learners struggle with trading groups for collections of groups, such as regrouping 10 tens for 1 hundred. There is a lack of understanding of the place value structure, that is, multiplying each place value position to the left of a number by the base (such as 10) and dividing each place to the right of the decimal point by the base.
If students’ errors are conceptual in nature, remediation begins with using manipulative materials. These might include place value blocks, counters of any type, and place value charts. Use of more than print-based activity is critical for students needing less-traditional approaches (Clausen-May, 2005). When errors are more procedural in nature, students forget rules and algorithmic steps but do understand how the system works. Remediation activities do not necessarily have to involve manipulative materials in those cases. Lessons are focused on drawing and/or representing objects and then connecting numerals to those figures or making notations as reminders. For example, when subtracting, students can draw an arrow over the “2” if that helps them remember where to start. Or, pupils could circle the ones column in each example, prior to computing, in order to remember to regroup that place and not the tens place.
Common Errors Related to Place Value
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