Connections Between Mathematics and Computational Thinking: Kindergarten Students\u27 Demonstration of Mathematics Knowledge in a Computational Thinking Assessment

Research shows that computational thinking can be used with kindergarten mathematics instruction, however we still do not know much about how specific math knowledge is related to computational thinking and if (and if so, how) children\u27s mathematical knowledge is related to students\u27 performance on computational thinking assessments. This student fills this knowledge gap by examining the following research questions: (1) How are kindergarten students\u27 mathematical knowledge (MK) and computational thinking (CT)MK and CT operationalized during a CT assessment? In what ways, if any, do MK and CT co-occur, and (2) How do students\u27 mathematical knowledge and co-occurring mathematical knowledge and computational thinking relate to their performance on individual assessment items? To answer these questions, I analyzed video data that was originally collected for a larger research study (NSF project award #DRL-1842116), which showed 60 kindergarten students taking an interview-based, computational thinking assessment. I coded and notated the data to describe how students demonstrate their mathematical knowledge and computational thinking, then analyzed the coded data to identify how students\u27 mathematical knowledge and computational thinking co-occurred. Lastly, I described how, for four assessment items, students\u27 co-occurring knowledge related to their assessment item performance. The results show that students demonstrated different levels of mathematical knowledge and computational thinking through their gestures, language, and interactions with the assessment materials. Students\u27 spatial and unit measurement knowledge most frequently co-occurred with computational thinking, and most often when students built and read/enacted programs. I categorized the co-occurrences as independent or dependent, depending on if the co-occurrence related to the students\u27 correct or incorrect response to the assessment items. These findings show that mathematical knowledge and computational thinking are strongly connected, and that students\u27 mathematical knowledge is related to how they performed on the assessment. These findings have implications for computational thinking curriculum and assessment design, mathematics curriculum design, and theory. Based on the results of this present study, I recommend that mathematics curriculum developers take advantage of the particularly strong connections of spatial and unit measurement knowledge with computational thinking to design experiences for children develop their spatial reasoning and measurement knowledge

Using the learning study grounded on the variation theory to improve students’ mathematical understanding

Topic Study Group 37: New trends in mathematics education researchThis paper illustrates how teachers make use of a learning theory, the variation theory, as well as their own professional expertise and collaboration to help students improve their mathematical understanding. A learning study (cf. Pang & Marton, 2003) involves a group of teachers who undertake theoretically grounded collaborative action research on their own practice. Unlike design experiments, a learning study emphasises teachers’ involvement in and ownership of the innovative practices that echo the spirit of the lesson study. The primary role of the researcher(s) in a learning study is to have a professional dialogue with the teachers and to provide professional support when necessary. Furthermore, the major focus of a learning study is on the objects of learning, i.e., on what students are expected to learn, rather than on the teaching arrangements. According to the variation theory, to help students appropriate certain objects of learning, certain patterns of variation and invariance that are co-constituted by the learners and the teacher are necessary. To exemplify this, this paper presents two learning studies conducted in mathematics in Hong Kong. The results show that there was a marked improvement in students’ mathematical understanding after learning studies grounded in the variation theory were introduced.postprintThe 11th International Congress on Mathematical Education (ICME) 2008, Monterrey, Mexico, 6-13 July 2008

Theoretical Model Construction of Deformation-Force for Soft Grippers Part II: Displacement Control Based Intrinsic Force Sensing

Force-aware grasping is an essential capability for most robots in practical applications. Especially for compliant grippers, such as Fin-Ray grippers, it still remains challenging to build a bidirectional mathematical model that mutually maps the shape deformation and contact force. Part I of this article has constructed the force-displacement relationship for design optimization through the co-rotational theory. In Part II, we further devise a displacement-force mathematical model, enabling the compliant gripper to precisely estimate contact force from deformations sensor-free. The presented displacement-force model elaborately investigates contact forces and provides force feedback for a force control system of a gripper, where deformation appears as displacements in contact points. Afterward, simulation experiments are conducted to evaluate the performance of the proposed model through comparisons with the finite-element analysis (FEA) in Ansys. Simulation results reveal that the proposed model accurately estimates contact force, with an average error of around 3% and 4% for single or multiple node cases, respectively, regardless of various design parameters (Part I of this article is released in Arxiv1

Biology and personality: a mathematical approach to the body-mind problem

[EN] Purpose ¿ The purpose of this paper is to investigate the body-mind problem from a mathematical invariance principle in relation to personality dynamics in the psychological and the biological levels of description. Design/methodology/approach ¿ The relationship between the two mentioned levels of description is provided by two mathematical models as follows: the response model and the bridge model. The response model (an integro-differential equation) is capable to reproduce the personality dynamics as a consequence of a determined stimulus. The invariance principle asserts that the response model can reproduce personality dynamics at the two levels of description. The bridge model (a second-order partial differential equation) can be deduced as a consequence of this principle: it provides the co-evolution of the general factor of personality (GFP) (mind), the it is an immediate early gene (c-fos) and D3 dopamine receptor gene (DRD3) gens and the glutamate neurotransmitter (body). Findings ¿ An application case is presented by setting up two experimental designs: a previous pilot AB pseudo-experimental design (AB) pseudo-experimental design with one subject and a subsequent ABC experimental design (ABC) experimental design with another subject. The stimulus used is the stimulant drug methylphenidate. The response and bridge models are validated with the outcomes of these experiments. Originality/value ¿ The mathematical approach here presented is based on a holistic personality model developed in the past few years: the unique trait personality theory, which claims for a single personality trait to understand the overall human personality: the GFP. Keywords Integro-differential equation, Body-mind problem, Bridge model, General factor of personality, Response model, Second-order partial differential equation, c-fos, DRD3, Glutamate, Methylphenidate Paper type Research paperMicó, JC.; Amigó, S.; Caselles, A.; Romero, PD. (2021). Biology and personality: a mathematical approach to the body-mind problem. Kybernetes. 50(5):1566-1587. https://doi.org/10.1108/K-03-2020-0138S1566158750

Co-design of Hardware and Algorithms for Real-time Optimization

It is difficult or impossible to separate the performance of an optimization solver from the architecture of the computing system on which the algorithm is implemented. This is particularly true if measurements from a physical system are used to update and solve a sequence of mathematical optimization problems in real-time, such as in control, automation, signal processing and machine learning. In these real-time optimization applications the designer has to trade off computing time, space and energy against each other, while satisfying constraints on the performance and robustness of the resulting cyber-physical system. This paper is an informal introduction to the issues involved when designing the computing hardware and a real-time optimization algorithm at the same time, which can result in systems with efficiencies and performances that are unachievable when designing the sub-systems independently. The co-design process can, in principle, be formulated as a sequence of uncertain and non-smooth optimization problems. In other words, optimizers might be used to design optimizers. Before this can become a reality, new systems theory and numerical methods will have to be developed to solve these co-design problems effectively and reliably

Theoretical Model Construction of Deformation-Force for Soft Grippers Part I: Co-rotational Modeling and Force Control for Design Optimization

Compliant grippers, owing to adaptivity and safety, have attracted considerable attention for unstructured grasping in real applications, such as industrial or logistic scenarios. However, accurately modeling the bidirectional relationship between shape deformation and contact force for such grippers, the Fin-Ray grippers as an example, remains stagnant to date. To address this research gap, this article devises, presents, and experimentally validates a universal bidirectional force-displacement mathematical model for compliant grippers based on the co-rotational concept, which endows such grippers with an intrinsic force sensing capability and offers a better insight into the design optimization. In Part I of the article, we introduce the fundamental theory of the co-rotational approach, where arbitrary large deformation of beam elements can be modeled. Its intrinsic principle allows taking materials with varying stiffness, various connection types, and key design parameters into consideration with few assumptions. Further, the force-displacement relationship is numerically derived, providing accurate displacement estimations of the gripper under external forces with minor computational loads. The performance of the proposed method is experimentally verified through comparison with Finite Element Analysis (FEA) in simulation, obtaining a fair degree of accuracy (6%), and design optimization of Fin-Ray grippers is systematically investigated. Part II of this article demonstrating the force sensing capabilities and the effects of representative co-rotational modeling parameters on model accuracy is released in Arxiv

Stiffness and Compliance of Kinematic Chains in Motion

The main aim of this thesis is the analysis of bioinspired kinematic chains controllable both in position and compliance (or stiffness) from a static and a dynamic point of view. In motion control theory, the redundancy of muscles, with respect to the number of degrees of freedom in a typical biomechanical system, permits the formulation of several control strategies. In this work the Feldman quadratic muscular model, proposing a direct connection between the magnitude and the frequency of sub-cortical electrical stimuli and muscular co-activation, is adopted. Two new indicators, the Dynamic Stiffness and Compliance Operators, are defined in a mathematical way by the use of functional analysis. These new indicators allow a theoretical and practical study of the performance of a chain during collisions or under external perturbations. The Dynamic Stiffness Operators can be useful in the treatment of many mechanical problems, as, for example, the estimation of the force generated by the system when it commits an error in terms of its trajectory, fundamental in breakable object manipulation. Instead, the Dynamic Compliance Operator, measuring the deviation from a given trajectory in presence of external perturbations, is defined as the inverse of the Stiffness Operator and is very more complex to calculate explicitly. In order to perform this calculation many mathematical instruments are used. Finally the mathematical theory developed in the thesis is applied to the design of electroactive polymer fiber bundles driven by bioinspired control variables to implement pseudomuscular actuators devoted to the realization of biomimetic movements