1. Peters, Lien., Op de Beeck, Hans. and De Smedt, Bert."Neural correlates of representing number in different formats (digits, dot patterns, number words) during calculation in children" Paper presented at the annual meeting of the SRCD Biennial Meeting, Pennsylvania Convention Center and the Philadelphia Marriott Downtown Hotel, Philadelphia, PA, Mar 19, 2015 <Not Available>. 2019-07-18 <http://citation.allacademic.com/meta/p960109_index.html>

Publication Type: Individual Poster Review Method: Peer Reviewed Abstract: One intriguing question with clear educational relevance deals with revealing the neural mechanisms that underlie number processing in children. Evidence suggests that children's ability to process number in different formats (digits, dot patterns) is associated with their mathematics achievement (De Smedt et al., 2013 for a review). It remains, however, unclear if and how presentation format during calculation affects brain activity. We therefore aimed to investigate this issue in the current study.

We conducted an fMRI study in 25 typically developing children aged 9 to 12 (M = 10.71, SD = 0.79). Children had to subtract numbers up to ten and compare the result to a reference number (four or five). Numbers were presented as dot patterns, Arabic digits and number words.

Behavioral results are shown in Table 1. There was a main effect of format on accuracy (F(1,24) = 44.84, p < .001) and reaction time data (F(1,24) = 29.25, p < .001). There were no differences in accuracy between the digits and number words conditions (p = .14), but children performed significantly less accurate during the dot condition compared to other conditions (ps < .001). Turning to the response latencies, we found that children were faster in calculating with digits than with number words (p < .001), and faster with number words than with dots (p < .001).
In our analysis of the neuroimaging data, we computed all pairwise contrasts between the three conditions at group level (threshold of p < .01 after family-wise error correction for the whole brain). We first looked at contrasts between the symbolic stimuli, i.e. [Digits – Words] and [Words – Digits]. There were no activation differences between these formats, except for differences around primary visual cortex, which are explained by the fact that more visual information was present in the number words condition. Second, we analyzed activation differences between digits and dot patterns. Angular and superior temporal gyrus showed more activity during calculation with digits than with dots patterns (Figure 1a). On the other hand, dot patterns activated more strongly a widespread fronto-parietal network, in particular the superior parietal lobule (Figure 1b). Finally, activation differences between number words and dot patterns were highly similar to differences observed between digits and dot patterns.

These findings suggest that similar brain networks are recruited during calculation with symbolic magnitudes, i.e. digits and number words. On the other hand, there are clear differences between calculating with symbolic and non-symbolic formats. These differences might be explained by differences in the strategies used to solve these calculation problems. Specifically, symbolic problems might have been solved using fact retrieval, for which angular and superior temporal gyrus have been suggested to be key regions (Grabner et al., 2009). On the other hand, the fronto-parietal network that emerged whilst solving non-symbolic exercises might reflect the involvement of working memory and attentional resources, as well as increased reliance on numerical magnitude processing (see also De Smedt et al., 2011). This might reflect an increased use of procedural strategies whilst solving non-symbolic calculation problems.

2005 - North American Chapter of the International Group for the Psychology of Mathematics Education

2. Sirotic, Natasa. and Zazkis, Rina."Locating Irrational Numbers on the Number Line" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Hosted by Virginia Tech University Hotel Roanoke & Conference Center, Roanoke, VA, Oct 20, 2005 Online <APPLICATION/PDF>. 2019-07-18 <http://citation.allacademic.com/meta/p24561_index.html>

Publication Type: Conference Paper/Unpublished Manuscript Abstract: This report is part of ongoing investigation on understanding irrational number by prospective secondary school teachers. It focuses of representation of irrational numbers as points on a number line. In a written questionnaire, followed by a clinical interview, the participants were asked to indicate the exact location of the square root of 5 on a number line. The results suggest confusion between irrational numbers and their decimal approximation and overwhelming reliance on the latter. Pedagogical suggestions are discussed.

2009 - North American Chapter of the International Group for the Psychology of Mathematics Education

3. Thanheiser, Eva. and Rhoads, Kathryn."Exploring Preservice Teachers Conceptions of Numbers via the Mayan Number System." Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, OMNI Hotel, Atlanta, GA, Sep 23, 2009 Online <PDF>. 2019-07-18 <http://citation.allacademic.com/meta/p369758_index.html>

Publication Type: Brief Research Report Review Method: Peer Reviewed Abstract: Preservice elementary school teachers (PSTs) struggle to understand numbers in our base-10 number system, but uncovering their base-10 conceptions is difficult because the underlying mathematical structure is masked by language and prior experience operating on numbers in base-10. PSTs conceptions of numbers were explored through work on identifying numerals in the Mayan number system (base twenty) during which PSTs drew on their base-10 conceptions. Of 24 participants only 6 could identify a 3-digit and a 7-digit Mayan numeral correctly. Both those numerals were the digit equivalent to 1 with 2 and 6 zeros, respectively, attached. The PSTs answers are categorized and explained. Implications for mathematics education are discussed.

2012 - The Mathematical Association of America MathFest

4. Lang, Julie. and Thacker, Lindzey."Graphs with equal domination number and identification number" Paper presented at the annual meeting of the The Mathematical Association of America MathFest, Monona Terrace Convention Center, Madison, WI, Aug 02, 2012 <Not Available>. 2019-07-18 <http://citation.allacademic.com/meta/p600820_index.html>

Publication Type: Student Paper Review Method: Peer Reviewed Abstract: The domination number of a graph is the minimum cardinality of a subset of vertices $S$ such that all vertices are either in $S$ or adjacent to a vertex in $S$. The identification number is the minimum cardinality such that the intersection of $S$ with the closed neighborhood of each vertex is distinct. This presentation will discuss instances in which the domination number and the identification number are the same as well as a method of constructing such graphs.

5. Mazzocco, Michele., Chan, Jenny Yun-Chen. and Praus, Taylor."Children’s Judgments of Numbers in Context Reveal Their Emerging Number Concepts" Paper presented at the annual meeting of the SRCD Biennial Meeting, Pennsylvania Convention Center and the Philadelphia Marriott Downtown Hotel, Philadelphia, PA, Mar 19, 2015 <Not Available>. 2019-07-18 <http://citation.allacademic.com/meta/p956664_index.html>

Publication Type: Individual Poster Review Method: Peer Reviewed Abstract: Efforts to delineate distinct aspects of “number sense” are needed to identify sources of individual differences in early mathematical thinking. Here we propose that children's response to numbers in context may reveal important but subtle differences in their early number concepts. Specifically, we consider the ambiguity of number words (e.g., 3 apples, 3 boxes of apples, 3 o’clock, 3 years old, 3 Maple Avenue) and the limited knowledge about how children extract number word meaning across these contexts. Accordingly, we developed a storybook-based task, the Numerical Ambiguity Interpretation Task (NAIT), to measure children’s interpretation of number words in various contexts. We aim to identify how developmental and individual differences in children's responses to “numerical ambiguity” reflect the nature of their early number concepts.
We individually administered the NAIT to 4-, 5-, 6-, and 7-year-olds, following a warm up task to determine their vocabulary and counting knowledge. Each experimental story passage concerned two main characters, and was followed by a prompt to select the larger of two numerical sets (e.g., Who has more, Tara or Abe?). Children could reply that either Tara or Abe had more items, or that there was insufficient information on which to base a comparison (such as by reporting, "I don't know (who has more)"). Across passages, the degree of numerical ambiguity was manipulated, either by presenting useful illustrations that clearly depicted quantities (unambiguous condition), by presenting uninformative illustrations in which quantities could not be discerned (mildly ambiguous condition), or by asking children to compare either misaligned sets (moderately ambiguous condition), or sets that were misaligned with the prompt query (most ambiguous condition). A "filler" condition was used to provide non-numerical prompts, in order to add variety to the task and evaluate children's attention and engagement.

Data collection for one cohort of 69 participants is complete at the time of this submission. The responses to "filler" questions indicate that the children were engaged in the task, and their numerical comparisons were at ceiling under the unambiguous condition. Our main variable of interest was the frequency with which children recognized numerical ambiguity, across age groups and conditions. A repeated measures ANOVA revealed main effects of Condition, p<.001, ŋ2 = .689, and Age, p=.021, ŋ2 = .139; and an Age × Condition interaction, p=.003, ŋ2 = .142. Four-year-olds were generally less likely than 7 year olds to report, “I don’t know” under ambiguous number comparison conditions; but even older children rarely reported, “ I don't know” (accurately identified ambiguity) in the moderately ambiguous condition. Although some children in each age group seemed to recognize grossly ambiguous number comparisons, many 4 year olds did not. Thus, despite being near or at ceiling under unambiguous number comparison conditions, there were individual and developmental differences under ambiguous conditions. We propose that these may reveal important variation in emerging number concepts.

The 69 participants in our first cohort had above-average vocabulary scores, so we are collecting data from a more diverse sample.