Block Puzzle Research Articles

Construction Tasks for Children With Blindness: Analyzing the Completion Ratio of Six Puzzles

Introduction: There are major differences when children with blindness perform construction tasks using haptics, without relying on sight, compared to when children with typical vision perform them through sight. When using sight, in all of the processes, the overall image can be grasped simultaneously while executing the task. When using haptics, the construction must be made by touching each piece sequentially and successively. In this study, framed block puzzle construction tasks that can be implemented by haptic means are developed with the objective of considering the order of difficulty of the task. Methods: In all, six framed block puzzle construction tasks were performed by 39 children with blindness, and the analysis was conducted from the perspective of the task-completion ratio. These six tasks were established on the basis of factors such as wood panel division and dimension, symmetry and asymmetry, and the number of block patterns. Results: A significant difference was observed in the completion ratio between one- and two-dimensional tasks, between two-dimensional symmetrical and asymmetrical tasks, and between two-dimensional asymmetrical tasks with multiple and single correct patterns. Discussion: This study clarified that the task order of difficulty is influenced by the factors of division and dimension, symmetry and asymmetry, and number of block patterns. Thus, we identified a task order wherein difficulty increases in the order of one- and two-dimensional symmetrical tasks and two-dimensional asymmetrical tasks with multiple and single correct patterns. Implications for Practitioners: Based on these hypotheses, providing instructions to children with blindness, in the order of simple to difficult tasks, is vital after ascertaining each child's level of capacity for spatial cognition.

Intergenerational or intragenerational learning? The relationship between interpersonal neural synchrony and older adult's learning acquisition

ObjectivesLifelong learning facilitates active ageing, and intragenerational learning—the process by which older adults learn from their peers—is an effective means of achieving this goal. The present research aims to elucidate the mechanisms and differences between intergenerational and intragenerational learning models for older adults as evidenced by brain-to-brain synchrony. MethodsFifty-six instructor-learner dyads completed a study comparing intergenerational and intragenerational learning models, as well as task difficulty. The study utilized a block puzzle task and functional near-infrared spectroscopy (fNIRS) for hyperscanning. ResultsThe instructor-learner dyads showed greater interpersonal neural synchrony (INS) and learning acquisition in the intragenerational learning model in the difficult task condition (t (54) = 3.49, p < 0.01), whereas the two learning models yielded similar results in the easy condition (t (54) = 1.96, p = 0.06). In addition, INS and self-efficacy mediated the association between learning models and learning acquisition in older adults (b = 0.14, SEM = 0.04, 95 % CI [0.01 0.16]). DiscussionThis study is the first to provide evidence of interbrain synchrony in an investigation of the intragenerational learning model in older adults. Our findings suggest that intra-learning is as effective as traditional inter-learning and may be more effective in certain contexts, such as difficult tasks. Encouraging intra-learning in community service or educational activities can effectively mitigate the challenge of limited volunteers and enhance learning acquisition among older adults.

The 5-puzzle doubly covers the soccer ball

This paper studies a sliding block puzzle defined on the two by three grid, which we call the 5-puzzle. Our main aim in this paper is to show a fine geometric property of the graph representing the transitions of the positions of the 5-puzzle. We show that by identifying every position with its 180° rotation and applying path contractions, the soccer ball graph is obtained.

The construction of geometric mental relationships in a pattern block puzzle activity at age four

Using constructivist scholar Constance Kamii’s perspective on autonomy, physical, social, and logico-Mathematical knowledge, this research investigates a curriculum method developed to engage young children in the construction of geometric knowledge. To study this method, I designed a seven-week pattern block puzzle intervention with four-year-old children in a constructivist classroom. All children were considered at-risk for school failure. The investigation is rooted in my unsatisfying experiences with pattern blocks in my preschool classrooms. Data were obtained from pre and posttests assessment administered to ascertain effects of the intervention on all children and from observations of children’s behavior as they engaged in the pattern block activity. Piaget’s (1936/1952), Piaget and Inhelder, 1948/1956) theory of knowledge and intelligence was the framework for detailed qualitative analysis of one exemplar’s progress during the intervention. Results of pre and posttests and microanalysis indicate children made significant progress in their construction of geometric knowledge. Children learned to match shapes with corresponding spaces and distinguish among and coordinate the sizes of angles and spaces. I describe using a series of detailed drawings, one exemplar’s actions during the activity. I conclude with suggestions for further research and educational implications.

Artificial intelligence: Deep neural reasoning.

The human brain can solve highly abstract reasoning problems using a neural network that is entirely physical. The underlying mechanisms are only partially understood, but an artificial network provides valuable insight. See Article p.471 Conventional computer algorithms can process extremely large and complex data structures such as the worldwide web or social networks, but they must be programmed manually by humans. Neural networks can learn from examples to recognize complex patterns, but they cannot easily parse and organize complex data structures. Now Alex Graves, Greg Wayne and colleagues have developed a hybrid learning machine, called a differentiable neural computer (DNC), that is composed of a neural network that can read from and write to an external memory structure analogous to the random-access memory in a conventional computer. The DNC can thus learn to plan routes on the London Underground, and to achieve goals in a block puzzle, merely by trial and error—without prior knowledge or ad hoc programming for such tasks.

Give me a hand: Differential effects of gesture type in guiding young children's problem-solving.

Adults' gestures support children's learning in problem-solving tasks, but gestures may be differentially useful to children of different ages, and different features of gestures may make them more or less useful to children. The current study investigated parents' use of gestures to support their young children (1.5 - 6 years) in a block puzzle task (N = 126 parent-child dyads), and identified patterns in parents' gesture use indicating different gestural strategies. Further, we examined the effect of child age on both the frequency and types of gestures parents used, and on their usefulness to support children's learning. Children attempted to solve the puzzle independently before and after receiving help from their parent; half of the parents were instructed to sit on their hands while they helped. Parents who could use their hands appear to use gestures in three strategies: orienting the child to the task, providing abstract information, and providing embodied information; further, they adapted their gesturing to their child's age and skill level. Younger children elicited more frequent and more proximal gestures from parents. Despite the greater use of gestures with younger children, it was the oldest group (4.5-6.0 years) who were most affected by parents' gestures. The oldest group was positively affected by the total frequency of parents' gestures, and in particular, parents' use of embodying gestures (indexes that touched their referents, representational demonstrations with object in hand, and physically guiding child's hands). Though parents rarely used the embodying strategy with older children, it was this strategy which most enhanced the problem-solving of children 4.5 - 6 years.

Any Monotone Function Is Realized by Interlocked Polygons

Suppose there is a collection of n simple polygons in the plane, none of which overlap each other. The polygons are interlocked if no subset can be separated arbitrarily far from the rest. It is natural to ask the characterization of the subsets that makes the set of interlocked polygons free (not interlocked). This abstracts the essence of a kind of sliding block puzzle. We show that any monotone Boolean function ƒ on n variables can be described by m = O(n) interlocked polygons. We also show that the decision problem that asks if given polygons are interlocked is PSPACE-complete.

Manipulating Double-Decker Molecules at the Liquid−Solid Interface

We have used a scanning tunneling microscope (STM) to manipulate heteroleptic phthalocyaninato, naphthalocyaninato, and porphyrinato double-decker (DD) molecules at the liquid-solid interface between 1-phenyloctane solvent and graphite. We employed nanografting of phthalocyanines with eight octyl chains to place these molecules into a matrix of heteroleptic DD molecules; the overlayer structure is epitaxial on graphite. We have also used nanografting to place DD molecules in matrices of single-layer phthalocyanines with octyl chains. Rectangular scans with a STM at low bias voltage resulted in the removal of the adsorbed DD molecular layer and substituted the DD molecules with bilayer-stacked phthalocyanines from phenyloctane solution. Single heteroleptic DD molecules with lutetium sandwiched between naphthalocyanine and octaethylporphyrin were decomposed with voltage pulses from the probe tip; the top octaethylporphyrin ligand was removed, and the bottom naphthalocyanine ligand remained on the surface. A domain of decomposed molecules was formed within the DD molecular domain, and the boundary of the decomposed molecular domain self-cured to become rectangular. We demonstrated a molecular "sliding block puzzle" with cascades of DD molecules on the graphite surface.

Shape L'Âne Rouge: Sliding Wavelets for Indexing and Retrieval.

Shape representation and retrieval of stored shape models are becoming increasingly more prominent in fields such as medical imaging, molecular biology and remote sensing. We present a novel framework that directly addresses the necessity for a rich and compressible shape representation, while simultaneously providing an accurate method to index stored shapes. The core idea is to represent point-set shapes as the square root of probability densities expanded in a wavelet basis. We then use this representation to develop a natural similarity metric that respects the geometry of these probability distributions, i.e. under the wavelet expansion, densities are points on a unit hypersphere and the distance between densities is given by the separating arc length. The process uses a linear assignment solver for non-rigid alignment between densities prior to matching; this has the connotation of "sliding" wavelet coefficients akin to the sliding block puzzle L'Âne Rouge. We illustrate the utility of this framework by matching shapes from the MPEG-7 data set and provide comparisons to other similarity measures, such as Euclidean distance shape distributions.

The Late Jurassic to Early Cretaceous sedimentary succession of the Hoherstein-Sandling area (Salzkammergut, Austria) implications for the reconstruction of the block puzzle in the central Northern Calcareous Alps

The Late Jurassic to Early Cretaceous sedimentary succession of the Hoherstein-Sandling area (Salzkammergut, Austria) implications for the reconstruction of the block puzzle in the central Northern Calcareous Alps

Assessing Cognitive Workload Metrics for Evaluating Telecommunication Tasks

Telecommunication technology provides the potential for teamwork across distances. In this way, geographically separated team members can communicate electronically to solve problems. An experiment was conducted to test the sensitivity of three cognitive workload metrics to tasks performed under conditions of telecommunication vs. face-to-face communication. Twenty-three teams participated as subjects. A block puzzle pattern task was tested at four levels of puzzle difficulty under the two communication conditions. Task performance (time to complete and errors), as well as cognitive workload ratings were measured. Three workload metrics [Subjective Workload Assessment Technique (SWAT), NASA-TLX, and Modified Cooper Harper (MCH)] were compared. Each person's spatial ability was assessed using the Cognitive Laterality Battery. Both performance and workload varied as a function of puzzle difficulty. While all workload metrics were able to discriminate amongst some of the puzzle difficulty levels, SWAT had the two advantages of providing the most sensitive measure of difficulty plus a wider range of workload ratings.