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Misconceptions of Multiplication and Division

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on 24 September 2015

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Transcript of Misconceptions of Multiplication and Division

Misconceptions of Multiplication and Division
Multiplication
Division
 Carry out short division of numbers involving decimals.
Ignore decimal point when calculating, then simply ‘slot back in’. Comes from over generalization of adding decimals.
 Find remainders after division
Lack of understanding of WHAT the remainder actually represents, need to see calculation in concrete way, i.e. cubes left over after division.
 Know and use halving as the inverse of doubling
Children confuse the words ‘halving’ and ‘doubling’.
Lack of understanding that two operations are linked, often taught separately.

Common Errors
Multiplication:
Standard Algorithm ( carried digit )
The small carried digit is often the most difficult, it gets added in before the second multiplication or is forgotten.

Division:
Standard Algorithm ( bring down / long division)
The place value of a middle zero is left out, it gets misplaced with another digit or is forgotten


References:

Chapman Kate, Mathematics Organization: National Centre for Excellence in the Teaching of
Mathematics (2006). https://www.ncetm.org.uk/

Karp,Karen S., and Jennifer M. Bay-Williams. “Chapter 13: Developing Strategies for Multiplication &
Division Computation.

“Elementary and Middle School Mathematics.” By John A. Van De Walle, 8th ed. N.p.: Pearson, 2013
236-57. “The National Strategies”.



Multiply decimals mentally by 10 or 100, and explain the effect.
Misunderstand the concept of making a number 10/100/1000 times bigger.
Know by heart all multiplication facts up to 10x10.
Children not understand the meaning of ‘lots of’ or ‘groups of’. Children see it as a test of their memory, not linking tables facts.
Understand the operation of multiplication as repeated addition or as describing an array.
Children are sometime display arrays of cubes/objects in an unclear pattern and have a hard time figuring out the solution.
Preventing misconceptions/ errors for Multiplication
Area Model: It supports students understanding and reasoning of multiplication
Partial Product: Students record the products and add using column sheets.
Preventing misconceptions/ errors for Division
Division Algorithm: It introduces one digit divisors. Its useful for students who struggle with the basics
The Explicit Trade method and the use of place value columns help with leaving out a middle zero.
Division Algorithm Example:
Explicit trade method example:
Area Model Example:
Partial Product Example:
75 - 5 = 70
12 - 2 = 10
Full transcript