The Teaching Laboratory Data Management (TLDM) System

In the teaching laboratory, students generate large amounts of data and often struggle with the subsequent calculations for results. Grading the substantial amounts of results and calculations from a large class is very taxing for teachers, who are left with less time to interact with students. The TLDM system aims to resolve the primary challenge associated with laboratory experimental calculations: while the numerical operations for a given experiment are expected to be the same, the correct numerical results vary based on the unique raw data collected by each student. The system provides scalable instructional scaffolding to guide students through their own calculations. The system also works to generate custom marking keys unique to each student’s raw data to assist teachers in grading the numerical component of reports, leaving them with more time to provide feedback in other areas.

Numerical operations in living cells by programmable RNA devices

Integrated bioengineering systems can make executable decisions according to the cell state. To sense the state, multiple biomarkers are detected and processed via logic gates with synthetic biological devices. However, numerical operations have not been achieved. Here, we show a design principle for messenger RNA (mRNA) devices that recapitulates intracellular information by multivariate calculations in single living cells. On the basis of this principle and the collected profiles of multiple microRNA activities, we demonstrate that rationally programmed mRNA sets classify living human cells and track their change during differentiation. Our mRNA devices automatically perform multivariate calculation and function as a decision-maker in response to dynamic intracellular changes in living cells.

Mapping numerical perception and operations in relation to functional and anatomical landmarks of human parietal cortex

Human functional imaging has identified the middle part of the intraparietal sulcus (IPS) as an important brain substrate for different types of numerical tasks. This area is often equated with the macaque ventral intraparietal area (VIP) where neuronal selectivity for non-symbolic numbers is found. However, the low spatial resolution and whole-brain averaging analysis performed in most fMRI studies limit the extent to which an exact correspondence of activation in different numerical tasks with specific sub-regions of the IPS can be established. Here we disentangled the functional neuroanatomy of numerical perception and operations (comparison and calculation) by acquiring high-resolution 7T fMRI data in a group of human adults, and relating the activations in different numerical contrasts to anatomical and functional landmarks on the cortical surface. Our results reveal a functional heterogeneity within human intraparietal cortex where the visual field map representations in superior/medial parts of IPS and superior parietal gyrus are involved predominantly in numerosity perception, whereas numerical operations predominantly recruit lateral/inferior parts of IPS. Since calculation and comparison-related activity fell mainly outside the field map representations considered the functional equivalent of the monkey VIP/LIP complex, the areas most activated during such numerical operations in humans are likely different from VIP.

Parallel individuation supports numerical comparisons in preschoolers

While the approximate number system (ANS) has been shown to represent relations between numerosities starting in infancy, little is known about whether parallel individuation – a system dedicated to representing objects in small collections – can also be used to represent numerical relations between collections. To test this, we asked preschoolers between the ages of 2 ½ and 4 ½ to compare two arrays of figures that either included exclusively small numerosities (< 4) or exclusively large numerosities (> 4). The ratios of the comparisons were the same in both small and large numerosity conditions. Experiment 1 used a between-subject design, with different groups of preschoolers comparing small and large numerosities, and found that small numerosities are easier to compare than large ones. Experiment 2 replicated this finding with a wider range of set sizes. Experiment 3 further replicated the small-large difference in a within-subject design. We also report tentative evidence that non- and 1-knowers perform better on comparing small numerosities than large numerosities. These results suggest that preschoolers can use parallel individuation to compare numerosities, possibly prior to the onset of number word learning, and thus support previous proposals that there are numerical operations defined over parallel individuation (e.g., Feigenson & Carey, 2003; https://doi.org/10.1111/1467-7687.00313).