Spatial complexity facilitates ordinal mapping with a novel symbol set.

The representation of number symbols is assumed to be unique, and not shared with other ordinal sequences. However, little research has examined if this is the case, or whether properties of symbols (such as spatial complexity) affect ordinal learning. Two studies were conducted to investigate if the property of spatial complexity affects learning ordinal sequences.

Enumeration strategy differences revealed by saccade-terminated eye tracking.

Brain regions involved in saccadic eye movements partially overlap with a frontoparietal network implicated in encoding numerosities. Eye movement patterns may plausibly reflect strategic scanning behaviours to resolve the open-ended task of efficiently enumerating visual arrays. If so, these patterns may help explain individual differences in enumeration acuity in terms of well-understood visual attention mechanisms.

The Importance of Ordinal Information in Interpreting Number/Letter Line Data.

The degree to which the ability to mark the location of numbers on a number-to-position (NP) task reflects a mental number line (MNL) representation, or a representation that supports ordered lists more generally, is yet to be resolved. Some argue that findings from linear equation modeling, often used to characterize NP task judgments, support the MNL hypothesis. Others claim that NP task judgments reflect strategic processes; while others suggest the MNL proposition could be extended to include ordered list processing more generally.

Implications of Change/Stability Patterns in Children's Non-symbolic and Symbolic Magnitude Judgment Abilities Over One Year: A Latent Transition Analysis.

Non-symbolic magnitude abilities are often claimed to support the acquisition of symbolic magnitude abilities, which, in turn, are claimed to support emerging math abilities. However, not all studies find links between non-symbolic and symbolic magnitude abilities, or between them and math ability. To investigate possible reasons for these different findings, recent research has analyzed differences in non-symbolic/symbolic magnitude abilities using latent class modeling and has identified four different magnitude ability profiles residing within the general magnitude ability distribution that were differentially related to cognitive and math abilities.

Non-symbolic magnitudes are represented spatially: Evidence from a non-symbolic SNARC task.

A core proposition in numerical cognition is numbers are represented spatially. Evidence for this proposition comes from the "spatial numerical association of response codes" effect (SNARC) in which faster responses are made by the left/right hand judging whether one of a pair of Arabic digits is smaller/larger than the other. Less is known if a similar SNARC effect exists for non-symbolic magnitudes; and research that has been conducted used stimuli which could be translated into symbolic terms.

Variability in Single Digit Addition Problem-Solving Speed Over Time Identifies Typical, Delay and Deficit Math Pathways.

We assessed the degree to which the variability in the time children took to solve single digit addition (SDA) problems longitudinally, predicted their ability to solve more complex mental addition problems. Beginning at 5 years, 164 children completed a 12-item SDA test on four occasions over 6 years. We also assessed their (1) digit span, visuospatial working memory, and non-verbal IQ, and (2) the speed with which they named single numbers and letters, as well the speed enumerating one to three dots as a measure of subitizing ability.

Culture-Independent Prerequisites for Early Arithmetic.

In numerate societies, early arithmetic development is associated with visuospatial working memory, executive functions, nonverbal intelligence, and magnitude-comparison abilities. To what extent do these associations arise from cultural practices or general cognitive prerequisites? Here, we administered tests of these cognitive abilities (Corsi Blocks, Raven's Colored Progressive Matrices, Porteus Maze) to indigenous children in remote northern Australia, whose culture contains few counting words or counting practices, and to nonindigenous children from an Australian city. The indigenous children completed a standard nonverbal addition task; the nonindigenous children completed a comparable single-digit addition task.

TEMA and Dot Enumeration Profiles Predict Mental Addition Problem Solving Speed Longitudinally.

Different math indices can be used to assess math potential at school entry. We evaluated whether standardized math achievement (TEMA-2 performance), core number abilities (dot enumeration, symbolic magnitude comparison), non-verbal intelligence (NVIQ) and visuo-spatial working memory (VSWM), in combination or separately, predicted mental addition problem solving speed over time. We assessed 267 children's TEMA-2, magnitude comparison, dot enumeration, and VSWM abilities at school entry (5 years) and NVIQ at 8 years.

Sustained attention to a predictable, unengaging Go/No-Go task shows ongoing development between 6 and 11 years.

Response time variability (RTV) is a useful measure of sustained attention; however, little is known about developmental changes in RTV at different temporal frequencies. Thirty-five 6-year-olds, 31 8-year-olds, and 37 10-year-olds completed the fixed-sequence Sustained Attention to Response Task on three occasions, six months apart. Fast Fourier Transform and ex-Gaussian analyses of response time (RT) data assessed momentary fluctuations in RT, gradual changes in RT, and very long responses, thought to reflect attentional control fluctuations, slow-shifting arousal, and infrequent lapses in attention, respectively.

Taking a(c)count of eye movements: Multiple mechanisms underlie fixations during enumeration.

We habitually move our eyes when we enumerate sets of objects. It remains unclear whether saccades are directed for numerosity processing as distinct from object-oriented visual processing (e.g.

Evidence of substantial development of inhibitory control and sustained attention between 6 and 8years of age on an unpredictable Go/No-Go task.

Inhibitory control and sustained attention are important cognitive abilities; however, their developmental trajectories remain unclear. In total, 35 6-year-olds, 32 8-year-olds, and 37 10-year-olds performed a Go/No-Go task; this required frequent responding to stimuli with infrequent inhibition to a target that appeared unpredictably. Children performed this task three times over 12months.

[Formula: see text]A longitudinal analysis of the attention networks in 6- to 11-year-old children.

Attention is critical for everyday functioning. Posner and Petersen's model of attention describes three neural networks involved in attention control-the alerting network for arousal, the orienting network for selecting sensory input and reorienting attention, and the executive network for the regulatory control of attention. No longitudinal research has examined relative change in these networks in children.

Cognitive factors affecting children's nonsymbolic and symbolic magnitude judgment abilities: A latent profile analysis.

Early math abilities are claimed to be linked to magnitude representation ability. Some claim that nonsymbolic magnitude abilities scaffold the acquisition of symbolic (Arabic number) magnitude abilities and influence math ability. Others claim that symbolic magnitude abilities, and ipso facto math abilities, are independent of nonsymbolic abilities and instead depend on the ability to process number symbols (e.

Number-specific and general cognitive markers of preschoolers' math ability profiles.

Different number-specific and general cognitive markers have been claimed to underlie preschoolers' math ability. It is unclear, however, whether similar/different cognitive markers, or combinations of them, are associated with different patterns of emerging math abilities (i.e.

Longitudinal changes in young children's 0-100 to 0-1000 number-line error signatures.

We use a latent difference score (LDS) model to examine changes in young children's number-line (NL) error signatures (errors marking numbers on a NL) over 18 months. A LDS model (1) overcomes some of the inference limitations of analytic models used in previous research, and in particular (2) provides a more reliable test of hypotheses about the meaning and significance of changes in NL error signatures over time and task. The NL error signatures of 217 6-year-olds' (on test occasion one) were assessed three times over 18 months, along with their math ability on two occasions.

A combined analysis of the Frost Multidimensional Perfectionism Scale (FMPS), Child and Adolescent Perfectionism Scale (CAPS), and Almost Perfect Scale-Revised (APS-R): Different perfectionist profiles in adolescent high school students.

To investigate differences and similarities in the dimensional constructs of the Frost Multidimensional Perfectionism Scale (FMPS; Frost, Marten, Lahart, & Rosenblate, 1990), Child and Adolescent Perfectionism Scale (CAPS; Flett, Hewitt, Boucher, Davidson, & Munro, 2000), and Almost Perfect Scale-Revised (APS-R; Slaney, Rice, Mobley, Trippi, & Ashby, 2001), 938 high school students completed the 3 perfectionism questionnaires, as well as the Depression Anxiety Stress Scales (DASS; Lovibond & Lovibond, 1995). Preliminary analyses revealed commonly observed factor structures for each perfectionism questionnaire. Exploratory factor analysis of item responses from the questionnaires (combined) yielded a 4-factor solution (factors were labeled High Personal Standards, Concerns, Doubts and Discrepancy, Externally Motivated Perfectionism, and Organization and Order).

Worry and working memory influence each other iteratively over time.

Little research has examined whether the relationship between working memory (WM) and anxiety/worry remains stable or changes over time; and, if changes occur, the factor(s) influencing change. Claims about influence are typically inferred from data collected at a single time point, and may misrepresent the nature of influence. To investigate the iterative influence of WM and Worry and/or vice versa, 133 fourteen-year-olds completed WM and Worry measures several times over the course of a single day as they prepared for a math test.

Cognition-emotion interactions: patterns of change and implications for math problem solving.

Surprisingly little is known about whether relationships between cognitive and emotional states remain stable or change over time, or how different patterns of stability and/or change in the relationships affect problem solving abilities. Nevertheless, cross-sectional studies show that anxiety/worry may reduce working memory (WM) resources, and the ability to minimize the effects anxiety/worry is higher in individuals with greater WM capacity. To investigate the patterns of stability and/or change in cognition-emotion relations over time and their implications for problem solving, 126 14-year-olds' algebraic WM and worry levels were assessed twice in a single day before completing an algebraic math problem solving test.

Preschoolers' dot enumeration abilities are markers of their arithmetic competence.

The abilities to enumerate small sets of items (e.g., dots) and to compare magnitudes are claimed to be indexes of core numerical competences that scaffold early math development.

Working memory, worry, and algebraic ability.

Math anxiety (MA)-working memory (WM) relationships have typically been examined in the context of arithmetic problem solving, and little research has examined the relationship in other math domains (e.g., algebra).

Spatial representations are specific to different domains of knowledge.

There is evidence that many abstract concepts are represented cognitively in a spatial format. However, it is unknown whether similar spatial processes are employed in different knowledge domains, or whether individuals exhibit similar spatial profiles within and across domains. This research investigated similarities in spatial representation in two knowledge domains--mathematics and music.

Patterns of knowledge in children's addition.

Patterns of conceptual and procedural knowledge of addition were examined in 5- to 8-year-olds (N = 80). Conceptual knowledge was measured by assessing children's responses to problems in which addends were reordered or decomposed and recombined. Problems were presented using abstract symbols, numbers, and physical objects.

The Faces Pain Scale for the self-assessment of the severity of pain experienced by children: development, initial validation, and preliminary investigation for ratio scale properties.

Altogether 553 children (195 first graders, mean age 6.8 years, and 358 third graders, mean age 8.7 years) participated in the development of a self-report measure to assess the intensity of children's pain.