Benchmark-based strategies in whole number line estimation.

In this study, we used verbal protocols to identify whether adults spontaneously apply quartile-based strategies or whether they need additional external support to use these strategies when solving a 0-1,000 number line estimation (NLE) task. Participants were assigned to one of three conditions based on the number of external benchmarks provided on the number line. In the bounded condition only the origin and endpoint were indicated, the mid-point condition included an additional external benchmark at 50%, and in the quartile condition three additional external benchmarks at 25%, 50%, and 75% were specified.

The Development of Symbolic and Non-Symbolic Number Line Estimations: Three Developmental Accounts Contrasted Within Cross-Sectional and Longitudinal Data.

Three theoretical accounts have been put forward for the development of children's response patterns on number line estimation tasks: the log-to-linear representational shift, the two-linear-to-linear transformation and the proportion judgment account. These three accounts have not been contrasted, however, within one study, using one single criterion to determine which model provides the best fit. The present study contrasted these three accounts by examining first, second and sixth graders with a symbolic and non-symbolic number line estimation task (Experiment 1).

Number sense in the transition from natural to rational numbers.

Background: Rational numbers are of critical importance both in mathematics and in other fields of science. However, they form a stumbling block for learners. One widely known source of the difficulty learners have with rational numbers is the natural number bias, that is the tendency to (inappropriately) apply natural number properties in rational number tasks.

Children's understanding of the addition/subtraction complement principle.

Background: In the last decades, children's understanding of mathematical principles has become an important research topic. Different from the commutativity and inversion principles, only few studies have focused on children's understanding of the addition/subtraction complement principle (if a - b = c, then c + b = a), mainly relying on verbal techniques.

Aim: This contribution aimed at deepening our understanding of children's knowledge of the addition/subtraction complement principle, combining verbal and non-verbal techniques.

Experts' Misinterpretation of Box Plots - a Dual Processing Approach.

Recent studies have shown that students often misinterpret the area of the box in box plots as representing the frequency or proportion of observations in that interval, while it actually represents density. This misinterpretation has been shown to be based on the saliency of this area and can be explained by heuristic reasoning as defined by dual process theories. In this study we tested whether expert users of box plots also display this misinterpretation and show signs of the same heuristic reasoning as found in students.

Children's use of addition to solve two-digit subtraction problems.

Subtraction problems of the type M - S = ? can be solved with various mental calculation strategies. We investigated fourth- to sixth-graders' use of the subtraction by addition strategy, first by fitting regression models to the reaction times of 32 two-digit subtractions. These models represented three different strategy use patterns: the use of direct subtraction, subtraction by addition, and switching between the two strategies based on the magnitude of the subtrahend.

Task complexity, student perceptions of vocabulary learning in EFL, and task performance.

Background: The study deepened our understanding of how students' self-efficacy beliefs contribute to the context of teaching English as a foreign language in the framework of cognitive mediational paradigm at a fine-tuned task-specific level.

Aim: The aim was to examine the relationship among task complexity, self-efficacy beliefs, domain-related prior knowledge, learning strategy use, and task performance as they were applied to English vocabulary learning from reading tasks.

Sample: Participants were 120 second-year university students (mean age 21) from a Chinese university.

Adults' use of subtraction by addition.

The present study investigates adults' use of addition to solve two-digit subtractions. Inspired by research on single-digit arithmetic, we first examined regression models in which different problem characteristics predicted participants' reaction times. Second, we compared performance on two-digit subtractions presented in 2 presentation formats, i.

Using addition to solve large subtractions in the number domain up to 20.

This study examined 25 university students' use of addition to solve large single-digit subtractions by contrasting performance in the standard subtraction format (12-9=.) and in the addition format (9+.=12).