Reading direction and spatial effects in parity and arithmetic tasks.

This study investigated the relationship between numerical and spatial processing and reading direction, conducting conceptual replications of the Shaki et al. (Psychonomic Bulletin & Review 16(2): 328-331, 2009) parity task and the Mathieu et al. (Cognition 146: 229-239, 2016, Experiment 1) simple addition (e.

What is learned in procedural learning? The case of alphabet arithmetic.

This research pursued a fine-grained analysis of the acquisition of a procedural skill. In two experiments ( = 29 and = 27), adults practiced 12 alphabet arithmetic problems (e.g.

Evidence for a retrieval over a sum counting theory of adults' simple addition.

Researchers have recently proposed that educated adults solve the simplest addition problems (e.g., 3 + 2) by an automatic counting procedure, challenging the long-held view that educated adults solve small additions by associative memory retrieval.

Does the min-counting strategy for simple addition become automatized in educated adults? A behavioural and ERP study of the size congruency effect.

Recent studies have proposed that the sum-counting strategy for simple addition (i.e., count up of the summed value of the two operands one by one) used at early age becomes automatized in adults, challenging the long held view that skilled adults solve simple addition problems by fact retrieval.

"Compacted" procedures for adults' simple addition: A review and critique of the evidence.

We review recent empirical findings and arguments proffered as evidence that educated adults solve elementary addition problems (3 + 2, 4 + 1) using so-called compacted procedures (e.g., unconscious, automatic counting); a conclusion that could have significant pedagogical implications.

Transfer of training in simple addition.

In recent years, several researchers have proposed that skilled adults may solve single-digit addition problems (e.g., 3 + 1 = 4, 4 + 3 = 7) using a fast counting procedure.

Transfer of training in alphabet arithmetic.

In recent years, several researchers have proposed that skilled adults may solve single-digit addition problems (e.g., 3 + 1 = 4, 4 + 3 = 7) using a fast counting procedure.

Operator priming and generalization of practice in adults' simple arithmetic.

There is a renewed debate about whether educated adults solve simple addition problems (e.g., 2 + 3) by direct fact retrieval or by fast, automatic counting-based procedures.

Language, visual working memory, and dot subtraction: What counts?

To investigate cognitive factors affecting subtraction of visual objects, we adapted the dot subtraction task developed by Pica, Lemer, Izard, and Dehaene (2004), who used it to investigate calculation by the Mundurukú, an indigene group in Brazil that has a limited number word vocabulary. In the dot subtraction task, briefly displayed arrays of moving dots are used to represent the quantities for subtraction. We tested 40 Canadian university students' dot enumeration, Arabic digit subtraction, visual working memory, and performance on the dot subtraction task with dot display durations of 2, 1.

Language-specific memory for everyday arithmetic facts in Chinese-English bilinguals.

The role of language in memory for arithmetic facts remains controversial. Here, we examined transfer of memory training for evidence that bilinguals may acquire language-specific memory stores for everyday arithmetic facts. Chinese-English bilingual adults (n = 32) were trained on different subsets of simple addition and multiplication problems.

Retrieval-induced forgetting of multiplication facts and identity rule.

This research investigated retrieval-induced interference between counterpart multiplication (2 × 3 = 6) and addition facts (2 + 3 = 5). Adults (N =72) repeatedly solved either a set of simple addition (0 + 2, 1 + 5, 2 + 3) or multiplication problems (0 × 2, 1 × 5, 2 × 3) during a practice phase and then switched operations during a test phase that included counterparts to the practiced problems and control problems. The paradigm afforded measurement in response time both of inter-operation retrieval-induced forgetting (RIF) and generalization of practice across different problems within operations.

Generalization effects in Canadian and Chinese adults' simple addition.

Recent studies proposed that skilled adults solve simple addition problems (e.g., 2 + 3 = 5) by automatic counting procedures rather than fact retrieval for memory.

Effects of pitch on auditory number comparisons.

Three experiments investigated interactions between auditory pitch and the numerical quantities represented by spoken English number words. In Experiment 1, participants heard a pair of sequential auditory numbers in the range zero to ten. They pressed a left-side or right-side key to indicate if the second number was lower or higher in numerical value.

No generalization of practice for nonzero simple addition.

Several types of converging evidence have suggested recently that skilled adults solve very simple addition problems (e.g., 2 + 1, 4 + 2) using a fast, unconscious counting algorithm.

Failures to replicate hyper-retrieval-induced forgetting in arithmetic memory.

Campbell and Phenix (2009) observed retrieval-induced forgetting (slower response time) for simple addition facts (e.g., 3 + 4) immediately following 40 retrieval-practice blocks of their multiplication counterparts (3 × 4 = ?).

The N3 is sensitive to odd-even congruency information in arithmetic fact retrieval.

This study investigated the behavioral and electrophysiological effects elicited by adults' simple addition verification when false answers agree or disagree with the odd-even status of the correct sum (parity congruency vs. parity incongruency), while they are near or far from correct (small vs. large splits).

Interoperation transfer in Chinese-English bilinguals' arithmetic.

We examined interoperation transfer of practice in adult Chinese-English bilinguals' memory for simple multiplication (6 × 8 = 48) and addition (6 + 8 = 14) facts. The purpose was to determine whether they possessed distinct number-fact representations in both Chinese (L1) and English (L2). Participants repeatedly practiced multiplication problems (e.

Operand-operator compatibility in cognitive arithmetic.

Adults' simple addition performance (e.g., 3 + 4 = ?) is faster, more accurate, and more often based on direct memory retrieval (rather than a procedural method, such as counting) when problems are presented in digit format (3 + 4) than written-word format (three + four).

MorePower 6.0 for ANOVA with relational confidence intervals and Bayesian analysis.

MorePower 6.0 is a flexible freeware statistical calculator that computes sample size, effect size, and power statistics for factorial ANOVA designs. It also calculates relational confidence intervals for ANOVA effects based on formulas from Jarmasz and Hollands (Canadian Journal of Experimental Psychology 63:124-138, 2009), as well as Bayesian posterior probabilities for the null and alternative hypotheses based on formulas in Masson (Behavior Research Methods 43:679-690, 2011).

Retrieval-induced forgetting of arithmetic facts.

Retrieval-induced forgetting (RIF) is a widely studied phenomenon of human memory, but RIF of arithmetic facts remains relatively unexplored. In 2 experiments, we investigated RIF of simple addition facts (2 + 3 = 5) from practice of their multiplication counterparts (2 × 3 = 6). In both experiments, robust RIF expressed in response times occurred only for high-strength small-number addition facts with sums ≤ 10, indicating that RIF from multiplication practice was interference dependent.

Semantic priming with product verification but not production.

Campbell and Reynvoet (2009) found that time to name a single-digit target was about 8 ms faster if preceded by a near prime (±1) compared to a far prime (at least ±3) when prime-digit pairs were interleaved with number comparisons (9↑3; name larger) and not when they were interleaved with multiplication problems (9×3; state product). This is consistent with the claim by previous researchers that magnitude comparison can enable a semantic pathway for digit naming whereas number-fact retrieval can inhibit it. To pursue this, the current study compared priming in the context of multiplication production (9×3=?) versus multiplication verification (e.

Semantic alignment and number comparison.

Are the quantity representations activated by Arabic digits influenced by semantic context? We developed a novel paradigm to examine semantic alignment effects (e.g., Bassok et al.

Neighborhood consistency and memory for number facts.

Verguts and Fias (Memory & Cognition 33:1-16, 2005a) proposed a new model of memory for simple multiplication facts (2 x 3 = 6; 8 x 7 =56) in which learning and performance is governed by the consistency of a problem's correct product with neighboring products in the times table. In the present study, to directly investigate effects of neighborhood consistency, participants memorized a set of 16 novel "pound" arithmetic equations. The pound arithmetic table included eight tie equations with repeated operands (e.

Adults' strategies for simple addition and multiplication: verbal self-reports and the operand recognition paradigm.

Accurate measurement of cognitive strategies is important in diverse areas of psychological research. Strategy self-reports are a common measure, but C. Thevenot, M.