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Association: Name: North American Chapter of the International Group for the Psychology of Mathematics Education URL: http://www.pmena.org
Citation: URL: http://www.allacademic.com/meta/p117533_index.html Direct Link: HTML Code:

McCarthy, Peter. "Investigating Teaching and Learning Subtraction that Involves Renaming using Base Complement Additions." Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada, Oct 21, 2004 <Not Available>. 2009-05-26 <http://www.allacademic.com/meta/p117533_index.html>

McCarthy, P. -. , 2004-10-21 "Investigating Teaching and Learning Subtraction that Involves Renaming using Base Complement Additions." Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada Online <.PDF>. 2009-05-26 from http://www.allacademic.com/meta/p117533_index.html

Publication Type: Conference Paper/Unpublished Manuscript Review Method: Peer Reviewed Abstract: This study investigates the teaching and learning of subtraction by using base complement additions (BCA). The BCA is a derivative of equal additions (EA) algorithm, which was intensively used in the US a generation ago, and its (BCA) rationale is based on compensation. Like the EA, the BCA is a rule of procedure for solving compound subtraction problems by changing both the minuend and the subtrahend. The BCA procedure transforms compound subtraction into simple subtraction by way of base complement(s). By base complement of a number s relative to the base b, we mean the positive number that should be added to s to obtain b. In other words c is the base complement of s if s + c = b, where b is the base. This research is a qualitative study, which describes two students’ (in grades 4 & 5) learning of the base complement additions method for compound subtraction of whole numbers. The purpose of the study is to learn more about children’s ways of doing subtraction that involve renaming. The study is an attempt to throw some light on the teaching and learning of compound subtraction by BCA. It is also an attempt to determine whether the teaching of compound subtraction by the method of BCA compares favorably with the method of D in terms of skill development if manipulatives are used to teach both algorithms. In particular the research addresses the questions: 1. How does BCA compare to D, as an algorithm for teaching/learning compound subtraction, in terms of skill development? 2. Which method do students choose to use when subtracting? Why do they say they chose the method? 3. In what ways does the learning of both methods increase students’ arithmetic competence? The study offers pupils an additional tool for their mathematical toolkit- to extend the knowledge base (of learners) to improve upon their learning. For teachers the study has the potential to inform them about an alternative procedure for subtraction that involves renaming. The data collection covered the period of November 2000 to January 2001. Pre-intervention, intervention and post-intervention design was used and computational tests and interviews were two main evaluation instruments used for the study. Results of the study indicate that participants were more confident with base complement additions than with decomposition, that students made fewer errors, recognized errors in worked examples, and chose base complement additions over decomposition as their method for compound subtraction.

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