## Strategy use and basic arithmetic cognition in adults

##### Date

2010-10##### Author

Metcalfe, Arron

##### Type

Thesis##### Degree Level

Doctoral##### Abstract

Arithmetic cognition research was at one time concerned mostly with the representation and retrieval of arithmetic facts in memory. More recently it was found that memory retrieval does not account for all single digit arithmetic performance. For example, Canadian university students solve up to 40% of basic addition problems using procedural strategies (e.g. 5 + 3 = 5 + 1 + 1 + 1). Given that procedures are less efficient than direct memory retrieval it is important to understand why procedure use is high, even for relatively skilled adults. My dissertation, therefore, sought to expand understanding of strategy choice for adults’ basic arithmetic. Background on this topic and supporting knowledge germane to the topic are provided in Chapter 1.
Chapter 2 focused on a well-known, but unexplained, finding: A written word problem (six + seven) results in much greater reported use of procedures (e.g., counting) than the same problem in digits (6 + 7). I hypothesized that this could be the result of a metacognitive effect whereby the low surface familiarity for word problems discourages retrieval. This was tested by familiarizing participants with a subset of the written word stimuli (e.g. three + four = ?, six + nine= ?) and then testing them on unpractised problems comprised of practiced components (four + six = ?). The result was increased retrieval reported for unpractised problems with practiced components. This indicates that surface familiarity contributes to strategy choice.
Chapter 3 focused on another classic phenomenon in the arithmetic cognition literature, the problem size effect: Response time, error, and procedure rates increase as a function of problem size. A previous study reported a reduced problem size effect for auditory multiplication problems compared to digit problems. I hypothesized that if this reduction was due to problem encoding processes rather than an effect on calculation per se, then a similar pattern would be observed for addition. Instead, I found that the size effect for addition was larger. I concluded that the auditory format promotes procedures for addition, but promotes retrieval for multiplication.
Chapters 4 and 5 were concerned with a well-known methodological issue in the strategy literature, subjectivity of self-reports: Some claim self-reports are more like opinions than objective measures. Thevenot, Fanget, and Fayol (2007) ostensibly solved this problem by probing problem memory subsequent to participants providing an answer. They reasoned that after a more complex procedure, the memory for the original problem would become degraded. The result would be better memory for problems answered by retrieval instead of by procedure. I hypothesized that their interpretation of their findings was conflated with the effect of switching tasks from arithmetic to number memory. I demonstrated that their new method for measuring strategy choice was contaminated by task switching costs, which compromises its application as a measure of strategy choice (Chapter 4). In a subsequent project (Chapter 5), I tested the sensitivity of this new method to detect the effects of factors known in the literature to affect strategy choice. The results indicated that Thevenot et al.’s new method was insensitive to at least one of these factors. Thus, attempts to control for the confounding effects of task switching described in Chapter 4, in order to implement this new measure, are not warranted.
The current dissertation expanded understanding of strategy choice in four directions by 1) demonstrating that metacognitive factors cause increases in procedure strategies, 2) by demonstrating that the process of strategy selection is affected differentially by digit and auditory-verbal input, 3) by investigating the validity of an alternative measure of strategy use in experimental paradigms, and 4) by discovering a critical failure in the sensitivity of this new measure to measure the effects of factors known to influence strategy use. General conclusions are discussed in Chapter 6.

##### Degree

Doctor of Philosophy (Ph.D.)##### Department

Psychology##### Program

Psychology##### Supervisor

Campbell, Jamie I. D.##### Committee

Borowsky, Ronald; Thompson, Valerie A.; LeFevre, Jo-Anne; Murphy, M. Shaun; Kalynchuk, Lisa##### Copyright Date

October 2010##### Subject

Cognitive science

Arithmetic cognition

Basic arithmetic

Skilled performance

Strategy use