Strategy Switch Costs in Arithmetic Problem Solving

By Lemaire, Patrick; Lecacheur, Mireille | Memory & Cognition, April 2010 | Go to article overview

Strategy Switch Costs in Arithmetic Problem Solving


Lemaire, Patrick, Lecacheur, Mireille, Memory & Cognition


Three experiments tested whether switching between strategies involves a cost. In three experiments, participants had to give approximate products to two-digit multiplication problems (e.g., 47 × 76). They were told which strategy to use (Experiments 1 and 2) or could choose among strategies (Experiment 3). The participants showed poorer performance when they used different strategies on two consecutive trials than when they used the same strategy. They also used the same strategy over two consecutive problems more often than they used different strategies. These effects, termed strategy switch costs, were found when the participants executed the easiest strategy and when they solved easy problems. We discuss possible processes underlying these strategy switch costs and the implications of these strategy switch costs for models of strategy choices.

One of the hallmarks of human cognition is that participants use several strategies when they accomplish cognitive tasks (Siegler, 2007). This multiple-strategy use permits one to alternate flexibly between different strategies and to adapt to the demands of problems and situations. Two central issues with regard to cognitive strategies concern how we choose among strategies for solving each problem and how we execute a strategy once it has been selected. The present study contributes to these issues by showing that participants obtain poorer performance when they use different strategies on two consecutive trials than when they use the same strategy and tend to repeat the same strategy over successive problems.

Previous findings on cognitive strategies showed that both strategy choices and strategy execution are influenced by problem and strategy characteristics, as well as by participants' skills, working memory capacities, and age. For example, in arithmetic, participants tend to retrieve correct solutions to problems like 3 × 4 directly from memory when retrieval is accurate and fast and to use counting on problems like 7 × 8 when retrieval is not accurate (e.g., Campbell & Xue, 2001; LeFevre, Bisanz, Daley, Buffone, & Sadesky, 1996). As another example, in episodic memory, participants tend to use mental imagery more often to memorize concrete words and mental rehearsal to store more abstract words (e.g., Dunlosky & Hertzog, 2001).

Computational models of strategy choices (e.g., Lovett & Anderson's [1996] ACT-R model; Lovett & Schunn's [1999] RCCL model; Payne, Bettman, & Johnson's [1993] adaptive decision maker model; Rieskamp & Otto's [2006] SSL model; and Siegler & Arraya's [2005] SCADS* model) share several core assumptions regarding how we choose among strategies. All these models propose that choosing among multiple strategies crucially involves associative mechanisms such as activating the relative costs/ benefits of each strategy and selecting the strategy that works best for a given problem on the basis of problem and strategy characteristics. All models also assume that strategies including fewer and/or simpler procedures (e.g., retrieving the correct solution of arithmetic problems like 3 × 4 directly from memory) are easier to execute than strategies including more and/or more complex procedures (e.g., adding 3 four times). These assumptions have proven sufficient to account for most findings on strategy choices and strategy execution.

However, several strategy phenomena are not accounted for by models of strategy choices. For example, it is unknown why some groups of participants, such as older adults (see, e.g., Lemaire & Arnaud, 2008), sometimes use fewer strategies even when they know and can use all available strategies. Also, it is unknown why problem features and relative strategy efficacy together never fully account for strategy choices or why participants are sometimes biased in strategy choices (i.e., they continue to use a strategy when an alternative is faster and/or more accurate; e. …

The rest of this article is only available to active members of Questia

Sign up now for a free, 1-day trial and receive full access to:

  • Questia's entire collection
  • Automatic bibliography creation
  • More helpful research tools like notes, citations, and highlights
  • Ad-free environment

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this article

This article has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this article

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited article

Strategy Switch Costs in Arithmetic Problem Solving
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Full screen

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited passage

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.