How I ended up with less: Strategies in simple subtraction.
Nicole D. Robert and Jo-Anne LeFevre, ÐÓ°ÉÔ­´´ University

Are They Married? The Representation of Magnitude and Polarity Information of Positive and Negative Numbers.
Geoffrey Barnum and Jo-Anne LeFevre, ÐÓ°ÉÔ­´´ University

(Back Row) Geoffrey Barnum, Jo-Anne LeFevre, Thomas Faulkenberry- Texas A & M University, Jamie Campbell- University of Saskatchewan, (Front Row) Joanne Lee- Wilfrid Laurier University, Nicole Robert

Posters:

• Fixation Patterns in Single-Digit Multiplication.
  Evan T. Curtis and Jo-Anne LeFevre, ÐÓ°ÉÔ­´´ University
• Extended Training Biases Judgments of Grammaticality Towards Exemplar Similarity.
  Evan T. Curtis1 and Randall K. Jamieson2, 1ÐÓ°ÉÔ­´´ University, 2University of Manitoba
• Cultural differences in computational estimation.
  Chang Xu, Jo-Anne LeFevre, and Emma Wells, ÐÓ°ÉÔ­´´ University
• Cultural Differences in Computational Estimation: Efficiency and Adaptivity.
  Emma Wells, Chang Xu, and Jo-Anne LeFevre, ÐÓ°ÉÔ­´´ University
• One, 2, Thrie: Effects of Surface Format on the Intentional and Unintentional Activation of Quantity.
  Geoffrey Barnum and Jo-Anne LeFevre, ÐÓ°ÉÔ­´´ University
• Mental additions with and without carrying in children: How is working memory involved?
  Sara Caviola, Irene Cristina Mammarella, Cesare Cornoldi, and Daniela Lucangeli, University of Padova

Counting Ability in Preschool Children
Kristina Dunbar, Ozlem Cankaya, Jo-Anne LeFevre

The present study assessed the effectiveness of numerical board games on preschool children’s early numeracy skills. Fifty participants (M = 3:8 years) were assigned to one of three intervention groups: a linear condition, a row condition with numbers grouped by decade, and a control colour condition. For counters who could count to 12 or less (less- proficient counters), the row condition was the most beneficial in improving rote counting ability and number recognition. The intervention methods were no more effective at improving the counting ability or number recognition performance of counters who could count to 13 or more than the control condition. These findings suggest two main ideas: (1) preschool children benefit most from an intervention method that extends well beyond their pre-testing counting ability and number recognition ability and (2) an intervention method organized by decade into rows can further assist the numeracy skills of children.

Formal and informal numeracy activities in the home: Predictorsof children’s early numeracy outcomes
Mamy Kalambay, Carla Sowinski, Jo-Anne LeFevre

The present study was designed to explore the relation between home numeracy activities and children’s mathematical performance in preschool. A total of 32 parent-child dyads from six different day care centers in Ottawa participated in the study. Parents were asked to complete a questionnaire that included demographic questions, the frequency of involvement in home learning activities, and familiarity with a list of commercially available games suitable for preschool-age children as a measure of shared number game play. The children were visited in their daycares; during the visits, trained research assistants administered measures of spatial attention, vocabulary, abstract counting, number recognition, numeration and non-symbolic arithmetic. It was hypothesized that home numeracy activities could predict the mathematics performance of children. In addition it was expected that formal and informal numeracy activities would differentially predict children’s early numeracy outcomes. Consistent with these hypotheses, home numeracy experiences were related to children’s outcomes and different types of home numeracy activities had different relations with the math and number outcomes.

Kristina Dunbar presenting her poster. Winner of the People’s Choice Award.

Mamy Kalambay presenting her poster.

For more information on PURE 2012 click to go to the Department of Psychology’s webpage.

Queens University

Posters:

The Role of Working Memory and the Language Effect for the Bilingual-Chinese in Complex Mental Multiplication
Chang Xu, Ineke Imbo, Chris M. Herdman, Jo-Anne LeFevre; ÐÓ°ÉÔ­´´ University, Universiteit Gent, Belgium

The purpose of the present study was to examine whether the role of working memory in complex multiplication for the Chinese differs when responding in first and second language. Participants solved multiplication problems (13 x 6) in two languages under working memory loads. The results showed that participants were faster and more accurate when responding in Chinese than in English. Furthermore, they were more likely to rely on phonological working memory for horizontally presented problems, and visual working memory for vertically presented problems. The results will be discussed in relation to current models of numerical representations and working memory.

Counting Ability in Preschool Children
Kristina Dunbar, Ozlem Cankaya, Jo-Anne LeFevre, Carla Sowinski; ÐÓ°ÉÔ­´´ University

Does playing numerical board games enhance preschool children’s numeracy skills? Fifty children (M = 45 months) played either a linear game, a row game where numbers were grouped by decade, or a colour game. Compared to the colour game, children in the number game conditions showed improved rote counting and number recognition. The row game was most beneficial. Children who could already count past 12 did not show improvements. These findings suggest that the game context must engage children beyond their existing counting ability, and that a game focusing on decade organization can further develop numeracy skills.

Subitizing Latency—But Not Approximate Number System Acuity— Correlates With Arithmetic Fluency In Adults
Carla C. Sowinski, Jo-Anne LeFevre; ÐÓ°ÉÔ­´´ University

We examined relations among approximate number system (ANS) acuity, subitizing latency and measures of addition, subtraction and multiplication fluency in adults (N = 109). The ability to quickly and accurately name small quantities (subitizing speed) was associated with simple symbolic arithmetic performance. However, the ability to accurately compare large quantities (e.g., ANS acuity) was not significantly correlated with arithmetic performance; this finding is counter to recent findings by Lyons and Beilock (2011). Approximate and exact quantity processing in relation to math skill development will be discussed.

Eye Movement Differences between Retrieval and Procedures in Simple Subtraction
Evan T Curtis, Corrie Bouskill, Jo-Anne LeFevre; ÐÓ°ÉÔ­´´ University

Participants (N = 30) solved subtraction problems while their eye
movements were recorded. Participants solved small problems (e.g., 6 – 3) faster and more accurately than large problems (e.g., 17 – 5). Participants also made more fixations and recorded longer gaze duration on large problems than on small problems. On small problems participants looked most often at the center of the screen, consistent with previous research examining eye movements during multiplication. However, on large problems participants looked most often at the operands. The difference in fixation patterns is argued to reflect the use of procedural strategies rather than fact retrieval.

The relationship between direct retrieval and mental and calculator-based computation in arithmetic: Implications for the Testing Effect
Aryn Pyke, Gary Bourque, Jo-Anne LeFevre; Carnegie Mellon University, ÐÓ°ÉÔ­´´ University

The testing effect suggests that attempting to directly retrieve answers during learning improves subsequent recall. The current study further explores whether or not direct retrieval processes tend to proceed in series or in parallel with computation processes in simple arithmetic. If in parallel (race model), might ‘testing effect’ benefits accrue even when answers are computed, either mentally or with a calculator? We also explored whether retrieval attempts might (or might not) be obligatory but instead determined by factors like the degree to which the computation process is inconvenient (e.g., calculator with scrambled keys). Results and implications are discussed.

Evan Curtis, Ozlem Cankaya & Aryn Pyke

Claire’s Poster at the Poster Session

University of Alberta

Posters:

Home Numeracy Activities and Children’s Numerical and Arithmetic Outcomes: A Longitudinal Perspective
Sowinski, Carla; LeFevre, Jo-Anne; Skwarchuk, Sheri-Lynn; Smith-Chant, Brenda; Kamawar, Deepthi; Bisanz, Jeffrey

Researchers have found that home numeracy experiences predict young children’s numeracy skills but little research has examined the impact of home numeracy experiences over time. We used a longitudinal design to examine links between parents’ home numeracy practices and children’s numeracy skills in Kindergarten, Grade 1, and Grade 2. At the start of the study, parents (n = 104) reported the frequency of home numeracy activities; these activities were separated into direct and indirect practices. Direct numeracy practices involve purposeful teaching of math or number concepts (e.g., learning simple sums), whereas indirect numeracy practices include a numerical component that is not the focus of the activity (e.g., measuring while cooking). Children participated in Kindergarten (n = 104, 49% female), Grade 1 (n = 91, 46% female) and Grade 2 (n = 71, 45% female). Each year, children completed (a) arithmetic tasks (addition in Kindergarten and Grade 1; Woodcock-Johnson calculation in Grades 1 and 2); and (b) number skill measures: KeyMath Numeration, digit recognition and next number tasks (these three were combined to create a composite number skill variable for each grade). Direct home numeracy practices in Kindergarten significantly correlated with children’s number skills and arithmetic performance in Kindergarten, Grade 1 and Grade 2, whereas indirect home numeracy practices were only correlated with calculation in Grade 2. Hierarchical regression analyses examined Kindergarten numeracy practices as a predictor of children’s skills in Grades 1 and 2, controlling for parents’ education and children’s gender, vocabulary, visual-spatial working memory and the previous years’ skill. For Grade 1 number skills, direct home numeracy practices failed to predict unique variance once Kindergarten number skills were included as a predictor. However, in Grade 2, direct home numeracy practices uniquely accounted for 2% of the variance in Grade 2 number skills (p = .059; controlling for Grade 1 number skills). Analyses of calculation skills showed a different pattern. In Kindergarten, direct practices predicted 5% unique variance in addition skills. In Grade 1, direct practices predicted 4% unique variance in calculation (controlling for addition in Kindergarten). However in Grade 2, direct practices did not predict unique variance after controlling for calculation in Grade 1. Instead, indirect practices accounted for 5% of the variance in Grade 2 calculation. Future research should explore whether or not it is simply early exposure to specific numeracy activities, ongoing home learning activities, or both, that account for these findings.

Exploring the Roles of the Number Naming System and Early Experiences in the Development of Numeracy: A Comparison of Chinese- and Turkish-speaking Children
Cankaya, Ozlem; Xu, Chang; LeFevre, Jo-Anne;

Chinese-speaking children learn about number names and counting at younger ages than English-speaking children. One factor may be that the Chinese number naming system is simpler than in English. For example, twelve is named as the equivalent of ten-two and thirty-five is three-ten-five. The Turkish number naming system is similar to Chinese between 11 and 19, but from 20 on resembles English. Given this, one might expect Turkish-speaking children to have some advantages in learning number names from 1 to 20, similar to those shown by Chinese-speaking children. However, educational experiences at home (e.g., the amount of practice) are also relevant. In China, numeracy skills are highly valued and children spend considerable time practicing these skills. In contrast, mathematics education in Turkey is not emphasized to the same degree as it is in China. Thus, a comparison between Turkish and Chinese children may clarify the relative effects of language and children’s home experiences on early numeracy development. Turkish- or Chinese-speaking 3-, 4-, 5-, and 6-year-olds were tested in Ottawa, Canada. Children’s early numeracy skills were explored in Turkish (n = 20) or Chinese (n = 22), and children counted as high as possible in English. Chinese-speaking children’s counting and number system knowledge in Chinese were superior to that of Turkish-speaking children’s knowledge in Turkish whereas children’s spatial span, non-symbolic arithmetic, object counting, and abstract counting in English were not different between language groups. Parents’ attitudes and reported actions differed: Chinese parents attributed more importance to the acquisition of literacy and numeracy skills, and reported that they exposed their children to reading and books more frequently than did the Turkish parents. Parents’ attitudes predicted children’s performance on counting and number system measures, even after group differences were accounted for. However, neither language nor home experiences predicted children’s performance in non-symbolic arithmetic. In conclusion, the regularity of number names did not appear to help Turkish-speaking children learn to count to 20, at least in comparison to Chinese- speaking children. The Chinese number naming system continues to be regular beyond 20, however, and so some of the language-group differences may reflect that continued regularity. Our research suggests that the influence of cultural differences in parents’ attitudes and expectations about early numeracy and literacy skills are as relevant in understanding children’s acquisition of number system knowledge as language- specific effects.

Carla Sowinski at the Poster Session