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Summary of Reference

Author:
Fuson, Karen, C and Briars, Diane, J

Title:
Using a Base-Ten Blocks Learning/Teaching Approach for First- and Second-Grade Place-Value and Multidigit Addition and Subtraction

Bibliographic data:
Fuson, K. C. & Briars, D. J. (1990). Using a base-ten blocks learning/teaching approach for first- and second-grade place-value and multidigit addition and subtraction. Journal for Research in Mathematics Education, 21 (3), 180-206.

Summary: 
The English language constructs its spoken system of number words differently from its written multidigit number marks. The spoken system explicitly identifies the value of the number (five thousand three hundred) whereas the written marks derive their value from their position within the number. Children must, therefore, construct named-value and positional base-ten conceptual structures for the words and marks and relate these conceptual structures to each other and to the words and marks.

English has several irregularities in the words for two-digit numbers and are not named-value. This is in contrast to the way several Asian languages use words and make it more difficult for English speaking children to construct named-value meaning for multi-digit numbers. The lack of verbal support for named-value or base-ten concepts of ten makes it particularly important that support for constructing such ten-structured conceptions be provided in other ways to English speaking children.

This paper describes two teaching case studies using a learning/teaching approach with base-ten blocks to embody the English named-value system of number words and digit cards to embody the positional base ten system of numeration. It reports on extensions to earlier studies by Fuson in which practical tests of how children learn addition and subtraction have been made and analyses its results in respect to three goals:

  • understanding multidigit addition and subtraction and justifying procedures with named-value/base-ten concepts
  • understanding place value concepts
  • being able to add and subtract multidigit numbers of several places, including subtraction problems with zeros in the top number.

    The paper shows that second grade students receiving the instruction outperformed third grade students’ results as reported in the literature.