Cognition, Vol. 1, No. 1

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Notifications View Subscribe. User Username Password Remember me. Posted: More More Announcements Remember me. Edited by: Mojtaba Soltanlou, Krzysztof Cipora In this special issue, we will concentrate on direct and conceptual replications specifically in the field of numerical cognition and mathematics learning. The order of sorting increasing or decreasing angle is determined randomly for each layer. A self-avoiding partial trail can be formed by traversing the dots by their sorted order. Figure 2 illustrates sorting by increasing angle.

Algorithm 1 : The DAC approach. Before connecting the partial trails, a round of checking is performed to ensure that there are no intersections among them Lines In the case when two trails intersect, i. When no intersections are found, all the partial trails are connected together to form a complete trail Lines The choice of pivot dot should guarantee that no intersection will be resulted from joining it and the last dot in the inner layer.

Finally, alphanumerical labels are assigned to the dots based on their order in the complete trail. With the algorithm described above, the DAC approach is able to generate TMT instances that reproduce the two desired spatial characteristics: unwinding clockwise or counter-clockwise and self-avoiding.

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In the following part of this section, we will explain how the design of the DAC approach help to reproduce these characteristics. The DAC approach uses both intra-layer and inter-layer designs to reproduce this characteristic. The intra-layer strategy ensures the partial trails exhibits the desired pattern locally within a layer, while the inter-layer strategy ensures that the pattern is embodied globally by a trail.

Within a layer intra-layer , sorting and connecting the dots according to their angles with respect to the anchor point endows a partial trail with the desired unwinding pattern. As shown in Figure 2 , the dots in a layer can also be viewed in a polar coordinate system with the anchor point as pole.

Visually, it can be viewed as a trail gradually uncoiling from the anchor point. The direction of unwinding can be controlled by the sorting order. If the angles are sorted in ascending order, the partial trail unwinds counter-clockwise. Conversely, the partial trail unwinds clockwise. At the inter-layer level, the definition of the layers help to create a complete trail in the desired unwinding pattern. The layers defined must be nested. This requirement ensures that the area of an inner layer is surrounded by its outer layers.

The trail formed by joining partial trails within nested layers also appears to be nested, which gradually unfolds when traversing from an inner layer to an outer layers. To generate self-avoiding trails, the DAC approach also uses intra- and inter-layer strategies.

The intra-layer strategy ensures each partial trail formed is self-avoiding. The inter-layer strategy generates a self-avoiding trail by connecting the partial trails while avoiding intersections in the connecting process. At the intra-layer level, sorting and connecting dots by angles ensures that the resultant partial trail is self-avoiding. These sectors are contiguous but non-overlapping. Each line segment of a partial trail spans within exactly one of the sectors.

Thus, the line segments have no intersections with each other, except for the joints.

At the inter-layer level, using non-overlapping layers can help to reduce intersections among partial trails in different layers. However, a partial trail formed by traversing the dots within a layer may still cut through other layers. Intersection checking is performed to detect and eliminate intersections in such cases, as described by Algorithm 1 Lines 6 to Moreover, the choice of pivot dot while connecting adjacent trails also avoids creating intersections in the combined trail.

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It maintains the modelling flexibility to accommodate the differences between Parts A and B. The dots in Part A scatter more evenly over the rectangular test region, while the dots in Part B are more skewed towards the rim of the area. There are a number of strategies Table I to manipulate the distribution of the dots to cater to such differences. In the following sections, we will describe how this algorithmic approach can be implemented and built into computerized TMTs.

For the ease of modelling, we used three concentric layers, with each of their centres at the origin. As illustrated in Figure 4 , L 1 is a rectangle, while L 2 and L 3 are hollow rectangles.

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Collectively, the three non-overlapping layers cover the test region exhaustively. The values of d i are presented in Table II. Compared to Part A, Part B has smaller relative density in L 1 and L 2 , but much greater density in L 3 , which is designed in accordance with the observations made from the paper-and-pencil TMT. Comparatively, for Part B, A 1 spans across larger area, while A 2 and A 3 are made smaller so that more dots would be placed near the edge of the test region. Using the aforementioned parameters, we built the test application, iTMT.

It is a touch-screen application that can administer computerized tests on tablets. Instead of using a pencil, the subjects need to connect the dots using their fingers. Test—retest reliability : Whether the test results are consistent across different instances as measured by time to completion and whether there are significant practice effects.


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The study involved ten participants aged from 33 to 84 years, with 8 above 50 and 4 above As age is an important factor which affects cognitive abilities, we recruited participants from a broad age range to include people with different levels of cognitive abilities. Considering that some elderly participants are illiterate or only had limited education, only Part A of TMT was administered.

Each subject was administered three tests consecutively, including one paper-and-pencil test and two computerized tests on a tablet. Before conducting the tests, the participant was shown a sample TMT with eight dots so as to become familiar with the connecting rules and test procedures. Then, the paper-and-pencil test was administered to the participant. The time taken to complete the trail, i. After an interval of 30 s, two computerized tests were administered to the participant consecutively. The test statistics were recorded by iTMT for later analysis.

As proposed in Gaudino et al. Total segment length is defined as the summed length of the shortest line segments connecting successive dots. Visual interference is quantified by summing the number of dots that lie within 3 cm of each line segment. The two metrics of the paper-and-pencil TMT administered in the study were calculated and used as normative values for evaluating the computerized tests.

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The paper-and-pencil TMT has a total segment length of Two t -tests were performed to determine whether the computerized tests generated by iTMT have a similar level of difficulty to the paper-and-pencil test Table III. The test results suggest that there is no significant difference between the computerized tests and the paper-and-pencil test in terms of total segment length and visual interference.

Hence, the results further indicate that, as measured by these two metrics, computerized tests and the paper-and-pencil test can be considered to have a similar level of difficulty. The construct validity of the computerized tests generated by iTMT was measured by correlating the time taken by the same participant to complete a computerized test and the paper-and-pencil test.

The Pearson product-moment correlations between time to completion are shown in Figure 6. When test performance was measured by time to completion, the computerized tests generated by iTMT were able to produce test scores that are highly correlated with the paper-and-pencil test score of the same participant, suggesting high construct validity of the computerized tests. The test-retest reliability of the computerized tests generated by iTMT was calculated by correlating the time taken to complete the first and the second computerized test.

The Pearson product-moment correlation between the time to completion of two computerized tests is shown in Figure 7.

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Moreover, iTMT was found to have almost no discernible practice effects. As shown in Figure 7 , some participants took longer to complete the first test, while others took longer to complete the second test on iTMT. From the first to the second administration, the average time to completion was only reduced by 5.

While the reduction in average time to completion for eTrail Smith, was Comparatively, iTMT was less susceptible to practice effects, providing further evidence to support its high reliability when administered repeatedly. In this paper, we proposed a DAC approach to generate instances of TMT that can be used in longitudinal cognitive assessment. Our proposed approach is able to generated a theoretically unlimited number of different TMT instances which can be used in consecutive test administrations. The preliminary results from the pilot study support the effectiveness of our DAC approach.


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Due to the illiteracy of some participants, only TMT Part A and its computerized versions were tested in this study. This paper argues that both human translators and machine translation systems can greatly benefit from contrastive studies of text structure. Due to the great terminological and definitional confusion regarding structures in texts, the paper first discusses the main viewpoints on these issues and then outlines the two most significant differences between Italian and Danish text structure.

One regards the notion of information density: Italian tends to accumulate the same information in shorter text spans and to include a larger number of Elementary Discourse Units in each sentence than Danish.

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