The Benefits of an Interdisciplinary Approach to Mathematics Education on Issues Around Computation in School.

We present arguments in favor of an interdisciplinary approach in mathematics education. As an instance, we briefly recall how cognitive neuropsychologists promoted intense finger gnosis acquisition, i.e.

Finger gnosis predicts a unique but small part of variance in initial arithmetic performance.

Recent studies indicated that finger gnosis (i.e., the ability to perceive and differentiate one's own fingers) is associated reliably with basic numerical competencies.

Natural frequencies improve Bayesian reasoning in simple and complex inference tasks.

Representing statistical information in terms of natural frequencies rather than probabilities improves performance in Bayesian inference tasks. This beneficial effect of natural frequencies has been demonstrated in a variety of applied domains such as medicine, law, and education. Yet all the research and applications so far have been limited to situations where one dichotomous cue is used to infer which of two hypotheses is true.

Children's sequential information search is sensitive to environmental probabilities.

We investigated 4th-grade children's search strategies on sequential search tasks in which the goal is to identify an unknown target object by asking yes-no questions about its features. We used exhaustive search to identify the most efficient question strategies and evaluated the usefulness of children's questions accordingly. Results show that children have good intuitions regarding questions' usefulness and search adaptively, relative to the statistical structure of the task environment.

Effects of finger counting on numerical development - the opposing views of neurocognition and mathematics education.

Children typically learn basic numerical and arithmetic principles using finger-based representations. However, whether or not reliance on finger-based representations is beneficial or detrimental is the subject of an ongoing debate between researchers in neurocognition and mathematics education. From the neurocognitive perspective, finger counting provides multisensory input, which conveys both cardinal and ordinal aspects of numbers.

Transparency in risk communication: graphical and analog tools.

Why is it that the public can read and write but only a few understand statistical information? Why are elementary distinctions, such as that between absolute and relative risks, not better known? In the absence of statistical literacy, key democratic ideals, such as informed consent and shared decision making in health care, will remain science fiction. In this chapter, we deal with tools for transparency in risk communication. The focus is on graphical and analog representations of risk.

Detection of syntonies between multiple spike trains using a coarse-grain binarization of spike count distributions.

At very short timescales neuronal spike trains may be compared to binary streams where each neuron gives at most one spike per bin and therefore its state can be described by a binary variable. Time-averaged activity like the mean firing rate can be generally used on longer timescales to describe the dynamics; nevertheless, enlarging the space of the possible states up to the continuum may seriously bias the true statistics if the sampling is not accurate. We propose a simple transformation on binary variables which allows us to fix the dimensionality of the space to sample and to vary the temporal resolution of the analysis.

Use of simple heuristics to target macrolide prescription in children with community-acquired pneumonia.

Background: Macrolides are the first-line antibiotic treatment of community-acquired pneumonia (CAP). Owing to alarming resistance rates among invasive Streptococcus pneumoniae isolates, particularly in young children, macrolide use should be restricted to patients infected with susceptible pathogens, eg, Mycoplasma pneumoniae.

Objective: To develop a simple clinical prediction rule for identifying M pneumoniae as the cause of CAP in children.

Representation facilitates reasoning: what natural frequencies are and what they are not.

A good representation can be crucial for finding the solution to a problem. Gigerenzer and Hoffrage (Psychol. Rev.