知识建构:从“儿童化”思维到“数学化”方法——基于“儿童现实”计算教学的思维分析与算法建构

常态的计算教学课堂中所形成的算法,时常以教师“成人化”的认知经验和固有的计算法则直接替代学生的数学思考,抑制了学生“儿童化”思维探索算理的过程,忽略了“数学化”方法的自然建构,丧失了学生“算术”素养的培养和计算技能的形成。因此,数学课堂上“数学化”方法的形成,需要经历学生的“经验现实、认知现实、思维现实”等“儿童现实”的“儿童化”思维的过程,数学思考才能直接抵达学生的已有知识经验、思维起点以及动手操作等儿童认知。如此教学,学生的思维活动才能实现“数学化”的自然“蜕变”,数学知识才能真正实现从“儿童化”思维到“数学化”方法的自然建构。

小学数学运算方法迁移的“现实化”过程

感悟数的运算本质的一致性,不是简单地要求学生在运算中进行计算方法的直接迁移、计算方式的机械模仿或者计算过程的自由尝试,而是需要引领学生经历“零起点”的认知过程、“裸视图”的思维过程和“应变化”的内化过程等“现实化”的儿童认知过程,从而真正感悟数与运算的本质内涵,建立计算算理的本真联系,形成计算方法的本能迁移。

Joint 3D traveltime calculation based on fast marching method and wavefront construction

3D traveltime calculation is widely used in seismic exploration technologies such as seismic migration and tomography. The fast marching method （FMM） is useful for calculating 3D traveltime and has proven to be efficient and stable. However, it has low calculation accuracy near the source, which thus gives it low overall accuracy. This paper proposes a joint traveltime calculation method to solve this problem. The method firstly employs the wavefront construction method （WFC）, which has a higher calculation accuracy than FMM in calculating traveltime in the small area near the source, and secondly adopts FMM to calculate traveltime for the remaining grid nodes. Due to the increase in calculation precision of grid nodes near the source, this new algorithm is shown to have good calculation precision while maintaining the high calculation efficiency of FMM, which is employed in most of the computational area. Results are verified using various numerical models.

指向算理理解的计算教学

在小学数学计算教学中,教师要应用各种方法,促进学生理解算理,进而引导学生建构算法。理法融通,是学生计算学习的最高境界。指向算理理解的计算教学,要依靠学生的经验、依靠学生的操作、依靠直观的图形等。要让学生知算理、晓算法;依算理、明算法;释算理、用算法。还要将算理理解和算法建构统一到学生计算学习之中,使之成为学生计算核心素养的重要组成。

Listless zerotree image compression algorithm

In this paper,an improved zerotree structure and a new coding procedure are adopted,which improve the reconstructed image qualities. Moreover, the lists in SPIHT are replaced by flag maps, and lifting scheme is adopted to realize wavelet transform, which lowers the memory requirements and speeds up the ceding process. Experimental results show that the algorithm is more effective and efficient compared with SPIHT.

Comparison on construction of strut-and-tie models for reinforced concrete deep beams

With consideration of the differences between concrete and steel,three solutions using genetic evolutionary structural optimization algorithm were presented to automatically develop optimal strut-and-tie model for deep beams.In the finite element analysis of the first method,the concrete and steel rebar are modeled by a plane element and a bar element,respectively.In the second method,the concrete and steel are assigned to two different plane elements,whereas in the third method only one kind of plane element is used with no consideration of the differences of the two materials.A simply supported beam under two point loads was presented as an example to verify the validity of the three proposed methods.The results indicates that all the three methods can generate optimal strut-and-tie models and the third algorithm has powerful capability in searching more optimal results with less computational effort.The effectiveness of the proposed algorithm III has also been demonstrated by other two examples.

Shear strengthening of pre-damaged reinforced concrete beams with carbon fiber reinforced polymer sheet strips

This paper presents the results of an experimental investigation on the response of pre-damaged reinforced concrete （RC） beam strengthened in shear using applied-epoxy unidirectional carbon fiber reinforced polymer （CFRP） sheet. The reasearch included four test rectangular simply supported RC beams in shear capacity. One is the control beam, two RC beams are damaged to a predetermined degree from ultimate shear capacity of the control beam, and the last beam is left without pre-damaged and then strengthened with using externally bonded carbon fiber reinforced polymer to upgrade their shear capacity. We focused on the damage degree to beams during strengthening, therefore, only the beams with sidebonded CFRPs strips and horizontal anchored strips were used. The results show the feasibility of using CFRPs to restore or increase the load-carrying capacity in the shear of damaged RC beams. The failure mode of all the CFRP-strengthened beams is debonding of CFRP vertical strips. Two prediction available models in AC1-440 and fib European code were compared with the experimental results.

Construction of a 3D meso-structure and analysis of mechanical properties for deposit body medium

For deposit body medium, the internal structural properties may be the controlling factors for the strength of the material and the mechanical response. Based on the results of soil-rock meso-statistics using digital imaging, a simulated annealing algorithm is adopted to expand the meso-structural features of deposit bodies in 3D. The construction of the 3D meso-structure of a deposit body is achieved, and then the particle flow analysis program PFC3 D is used to simulate the mechanical properties of the deposit body. It is shown that with a combination of the simulated annealing algorithm and the statistical feature functions, the randomness and heterogeneity of the rock distribution in the 3D inner structure of deposit body medium can be realized, and the reconstructed structural features of the deposit medium can match the features of the digital images well. The spatial utilizations and the compacting effects of the body-centered cubic, hexagonal close and face-centered packing models are high, so these structures can be applied in the simulations of the deposit structures. However, the shear features of the deposit medium vary depending on the different model constructive modes. Rocks, which are the backbone of the deposit, are the factors that determine the shear strength and deformation modulus of the deposit body. The modeling method proposed is useful for the construction of 3D meso-scope models from 2D meso-scope statistics and can be used for studying the mechanical properties of mixed media, such as deposit bodies.

Research of CBR, DM and smart algorithms based design methods for high-rise building structure form-selection

First, the high-rise building structure design process is divided into three relevant steps, that is, scheme generation and creation, performance evaluation, and scheme optimization. Then with the application of relational database, the case database of high-rise structures is constructed, the structure form-selection designing methods such as the smart algorithm based on CBR, DM, FINS, NN and GA is presented, and the original forms system of this method and its general structure are given. CBR and DM are used to generate scheme candidates; FINS and NN to evaluate and optimize the scheme performance; GA to create new structure forms. Finally, the application cases are presented, whose results fit in with the real project. It proves by combining and using the expert intelligence, algorithm intelligence and machine intelligence that this method makes good use of not only the engineering project knowledge and expertise but also much deeper knowledge contained in various engineering cases. In other words, it is because the form selection has a strong background support of vast real cases that its results prove more reliable and more acceptable. So the introduction of this method provides an effective approach to improving the quality, efficiency, automatic and smart level of high-rise structures form selection design.

Enterprise modeling method of calculation-independent model level

Aimed at deficiencies in the development and implementation of Enterprise Service Architecture （ESA） software, an ESA software developing mode based on Model Driven Architecture （MDA） is put forward. This mode includes a calculation-independent model （ CIM ）, a platform-independent model （ PIM ）, a platform-specific model （PSM） and a code level. Based on this mode, the modeling architecture of CIM level is presented. CIM here includes a global model, a process model, an information model and an organization model. The modeling elements of global model, process recta-model, information recta-model and organization meta-model are defined in detail and the relationship between them is described. The reflecting relationship between these models is established as well.