让数学思想方法在学生脑海里扎根

从目前的情形看来,广大教师对于在教学中渗透数学思想方法都有了一个初步的认识,但是纵观整个课堂教学,却存在不少问题。那么,我们一线教师面临的教学现状如何?在教学过程中渗透数学思想方法遇到哪些典型问题?学生掌握数学思想方法的程度到底如何?针对教学中遇到的问题与困惑有什么对策?本期专题,我们邀请名师以及知名教研员与您一起探讨。

七年级下学期期中复习点拨

学习完了一元一次方程、二元一次方程组、一元一次不等式(组)等知识,需要对涉及的重点知识作一总结和归纳,以便灵活运用知识解决问题.

Icon memory research under different time pressures and icon quantities based on event-related potential

In order to obtain related brain electrical components and neural bases of physiology assessment of icon elements in a digital human-computer interface the modified sample-delay matching task experimental paradigm is used under different time pressures 4 000 and 2 000 ms and different icon quantities three five and ten icons on icon memory based on event-related potential ERP technology.Experimental results demonstrate that P300 has significant volatility changes and the maximum amplitude around the middle line of the parietal area PZ and P200 has obvious volatility changes around the middle line of the frontal and central area FCZ during icon cognition.P300 and P200 amplitudes increase as tasks become more difficult.Thus P300 latency is positively correlated with task difficulty. ERP research on the characteristics of icon memory will be an important reference standard in guiding user neurocognitive behavior and physiology assessment on interface usability.

一道课本习题的开放探究性设计

科学的本质是探索未知,科学的发现来自于探究过程.普通高中数学课程标准提出:"教材的呈现应为引导学生自主探索留有比较充分的空间,有利于学生经历观察、实验、猜测、推理、交流、反思等过程.在进行教学设计时,可以通过设置具有启发性、挑战性的问题,激发学生进行思考,鼓励学生自主探索,并在独立思考的基础上进行合作交流,在思考、探索和交流的过程中获得较为全面的体验和理解."数学教学作为科学发现在教学上的一种特殊形式正越来越多地被提倡运用探究性教学.

“数”中思“形”,“形”中觅“数”——例谈初中数学数形结合的解题技巧

数与形是数学中的两个最古老,也是最基本的研究对象,两者相互联系,称这为"数形结合"或"形数结合".就初中数学而言,数形结合就是在形象与抽象思维的交叉运用中,以数助形,以形助数,互相促进,协调发展.因此,数形结合思想是学生解决问题中的一种很重要的方法,是把许多知识转化为能力的"桥".

FTIR Spectroscopic Study of Broad Bean Diseased Leaves

[Objective] The aim was to indentify diseased leaves of broad bean by vibra- tional spectroscopy. [Method] In this paper, broad bean rust, fusarium rhizome rot, broad bean zonate spot, yellow leaf curl virus and normal leaves were studied using Fourier transform infrared spectroscopy combined with chemometrics. [Result] The spectra of the samples were similar, only with minor differences in absorption inten- sity of several peaks. Second derivative analyses show that the significant difference of all samples was in the range of 1 200-700 cm2. The data in the range of 1 200- 700 cm＇ were selected to evaluate correlation coefficients, hierarchical cluster analy- sis （HCA） and principal component analysis （PCA）. Results showed that the correla- tion coefficients are larger than 0.928 not only between the healthy leaves, but also between the same diseased leaves. The values between healthy and diseased leaves, and among diseased leaves, are all declined. HCA and PCA yielded about 73.3% and 82.2% accuracy, respectively. [Conclusion] This study demonstrated that FTIR techniques might be used to detect crop diseases.

数学思想方法在有理数运算中的应用

数学习题浩瀚无边,问题又可变式发散,这样习题就林林总总,题量就千千万万,但是蕴涵在问题中的数学思想方法总是永恒不变的。

数形结合教学思想之我见

我国著名数学家华罗庚教授指出:"数形结合百般好,隔裂分家万事非."这句话说明了"数"和"形"是紧密联系的,事实上"数"往往借助于"形","形"往往又离不开"数".经常运用数形结合的方法,能帮助学生类比、发掘,解剖其所具有的几何模型,有利于帮助学生深化思维,扩展知识,提高能力.如何让学生在解决数学问题中熟练运用数形结合的方法解决问题呢?我觉得应从以下几方面入手:

如何在教学中找回失落的“数学应用意识”

近年来受应试教育的影响,致使师生的"数学应用意识"失落,随着数学的应用越来越广泛,数学课程中强化数学的应用意识已成为发达国家的共识,《数学课程新标准》明确规定:"要使学生受到把实际问题抽象成数学问题的训练,形成应用数学的意识."重视数学应用,将标志着我们的数学教育进一步走向未来、走向世界.

课堂提问应从何入手

"学贵有疑。"提问能吸引学生的注意,启发学生的思维。为此,在数学教学中,教师应精心设计问题,引导学生带着问题去思考、去领悟。这样,才能开拓学生的思路,使学生产生积极探求解决问题的强烈愿望,准确地掌握学习目标。那么,数学教学中提问应从哪些方面入手呢?1.问在重点处每节课都有它的重点,只有把重点逐一攻克,这节课的教学任务才算基本完成。因此,我们要在教材的重点处设计有坡度。

Quantitative Relationship Between Multi-Angle Polarized Reflectance and BRDF of Rock

The traditional remote sensing mainly detects the ground vertically to obtain the 2D information but it is hard to get adequate parameters for the quantitative remote sensing to invert land features. The multi-angle observation can get more detailed and reliable 3D structural parameters of targets, so it makes the quantitative remote sensing applicable. During the process of reflecting, scattering and transmitting the electromagnetic wave, minerals and rocks could reveal the polarized features related to the nature of themselves. Therefore, it has become a new approach of quantitative remote sensing to detect multi-angle polarized information of minerals and rocks. In respect that the polarized reflectance always goes with the bidirectional one, we can obtain the 3D spatial distribution of targets by a polarized means together with detecting its bi-directional reflectance. From the perspective of multi-angle polarized remote sensing mechanism, the quantitative relationship between multi-angle polarized reflectance and the BRDF is studied in this paper. And it is testified that the bi-directional reflectance, polarized reflectance of 45° and the mean value of polarized reflectance are equal to that of the corresponding azimuth angle, zenith angle, detection angle and detection channels in 27t space by experiment.

Quantitative determination of PFC3D microscopic parameters

It is important to calibrate micro-parameters for applying partied flow code(PFC)to study mechanical characteristics and failure mechanism of rock materials.Uniform design method is firstly adopted to determine the microscopic parameters of parallel-bonded particle model for three-dimensional discrete element particle flow code(PFC3D).Variation ranges of microscopic of the microscopic parameters are created by analyzing the effects of microscopic parameters on macroscopic parameters(elastic modulus E,Poisson ratio v,uniaxial compressive strengthσc,and ratio of crack initial stress to uniaxial compressive strengthσci/σc)in order to obtain the actual uniform design talbe.The calculation equations of the microscopic and macroscopic parameters of rock materials can be established by the actual uniform design table and the regression analysis and thus the PFC3D microscopic parameters can be quantitatively determined.The PFC3D simulated results of the intact and pre-cracked rock specimens under uniaxial and triaxial compressions(including the macroscopic mechanical parameters,stress−strain curves and failure process)are in good agreement with experimental results,which can prove the validity of the calculation equations of microscopic and macroscopic parameters.

Quantum Secure Direct Intercommunication with Superdense Coding and Entanglement Swapping

A quantum secure direct intercommunication scheme is proposed to exchange directly the communicators＇ secret messages by making ase of swapping entanglement of Bell states. It has great capacity to distribute the secret messages since these messages have been imposed on high-dimensional Bell states via the local unitary operations with superdense coding. The security is ensured by the secure transmission of the travel sequences and the application of entanglement swapping.

Volatility-volume relationship of Chinese copper and aluminum futures market

Following Bessembinder and Seguins,trading volume is separated into expected and unexpected components.Meanwhile,realized volatility is divided into continuous and discontinuous jump components.We make the empirical research to investigate the relationship between trading volume components and various realized volatility using1min high frequency data of Shanghai copper and aluminum futures.Moreover,the asymmetry of volatility-volume relationship is investigated.The results show that there is strong positive correlation between volatility and trading volume when realized volatility and its continuous component are considered.The relationship between trading volume and discontinuous jump component is ambiguous.The expected and unexpected trading volumes have positive influence on volatility.Furthermore,the unexpected trading volume,which is caused by arrival of new information,has a larger influence on price volatility.The findings also show that an asymmetric volatility-volume relationship indeed exists,which can be interpreted by the fact that trading volume has more explanatory power in positive realized semi-variance than negative realized semi-variance.The influence of positive trading volume shock on volatility is larger than that of negative trading volume shock,which reflects strong arbitrage in Chinese copper and aluminum futures markets.

Correlation of the quantifiable parameters of blood flow pattern derived with dynamic CT in solitary bronchogenic adenocarcinoma

Objective:To evaluate the correlation of the quantifiable parameters of blood flow pattern derived with dynamic CT in solitary bronchogenic adenocarcinoma(SBA).Methods:46 patients with solitary bronchogenic adenocarcinomas (SBA)(diameter≤4 cm)underwent multi-location dynamic contrast material-enhanced(nonionic contrast material was administrated via the antecubital vein at a rate of 4 mL/s by using an autoinjector 90 mL,4×5 mm or 4×2.5 mm scanning mode with stable table were performed)serial CT.Precontrast and postcontrast attenuation on every scan was recorded.Perfusion (PBA),peak height(PHBA),ratio of peak height of the SPN to that of the aorta(BA-to-A ratio)and mean transit time(MTT)were calculated.The correlation between peak height of the aorta(PHA)and parameters of the SBA(PHBA,BA-to-A ratio,PBA,and MTT)and those among parameters of the SBA were assessed by means of linear regression analysis.Regression equation among parameters of the SBA were obtain by means of stepwise regression.Results:The correlation between the SBA peak height(PHBA,36.78 HU±12.02)and the aortic peak height(PHA)was significant(r=0.506,P<0.0001).No significant cor- relation was found between the BA-to-Apeak height ratio(15.33%±4.55)and the aortic peak height(r=0.130,P=0.388> 0.05)as it was between the SBA perfusion(PBA,31.86 mL/min/100 g±9.74)and the aortic peak height(r=0.049,P=0.749 >0.05).The SBA perfusion correlated with the PHBA and the BA-to-A peak height ratio(r=0.394,P=0.007<0.05;r=0.407, P=0.005<0.05).The PHBA correlated positively with the BA-to-A peak height ratio(r=0.781,P<0.0001).Mean transit time was 14.84 s±5.52.PBA=18.500+0.872×BA-to-A ratio.BA-to-A ratio=4.467+0.295×PHBA.Conclusion:The linear correlation between the SBA perfusion and BA-to-Aratio and that between BA-to-Aratio and PHBA can be expressed by equation. It is possible to design a simpler scanning procedure of investigation of bronchogenic adenocarcinoma angiogenesis.

QUASI-SYNCHRONOUS MULTICARRIER DS-CDMA USING Z-COMPLEMENTARY SEQUENCES

In this paper, a multicarrier DS-CDMA system which employs Z-Complementary Se- quences (ZCS) as spreading code is investigated. The new system can not only eliminate multipath interference and Multiple Access Interference (MAI), but also support flexible number of users com- pared with system using Orthogonal Complementary (OC) codes. Multicarrier DS-CDMA using OC codes can be regarded as a special case of our proposed system. Zero Correlation Zone (ZCZ) of ZCS can be flexibly adjusted to meet the requirements on the user number and maximum multipath and in- ter-user delay, in this way, more users can be supported without losing interference-free property. The effectiveness of the proposed system is validated through theoretical analysis and simulation results.

New autocorrelation topological indexes and their application in QSAR study

Considering the problems of classical structure parameters that existed in the study of quantitative structure activity relationship (QSAR). Two new groups of autocorrelation topological indexes V(t), E(t), (P(t)) and A(t), B(t), C(t), D(t) were developed on the basis of molecular topology and autocorrelation function in mathematics. The first group were obtained from Van der Waals volume, electronegativity and topological vertex degree;and the second group were obtained from the different combination of topological vertex degree.Corresponding softwares of ATIJP and ATITP have been developed for calculating these two new groups of indexes. Better results have been obtained from the application of these indexes in QSAR study.

Study of the relationship between acupuncture dose and effect

Acupuncture dose-effect relationship is the essential feature of acupuncture and the key factor of acupuncture’s therapeutic effect.It is a comprehensive category,including needle direction,needle strength,needle depth,selection of specific techniques,length of time between acupuncture treatment sessions,length of needle retention time,and frequency of treatment,all of which play a decisive role in the curative effect and prognosis of diseases[1].

A Quantitative Structure Property Relationship for Prediction of Flash Point of Alkanes Using Molecular Connectivity Indices

Many structure-property/activity studies use graph theoretical indices, which are based on the topological properties of a molecule viewed as a graph. Since topological indices can be derived directly from the molecular structure without any experimental effort, they provide a simple and straightforward method for property prediction. In this work the flash point of alkanes was modeled by a set of molecular connectivity indices （Х）, modified molecular connectivity indices （ ^mХ^v ） and valance molecular connectivity indices （ ^mХ^v ）, with ^mХ^v calculated using the hydrogen perturbation. A stepwise Multiple Linear Regression （MLR） method was used to select the best indices. The predicted flash points are in good agreement with the experimental data, with the average absolute deviation 4.3 K.

Airborne Pollen Grains Of Afyon, Turkey

The airborne pollen grains of Afyon have been studied for a two_year period (1999-2000) with a Durham sampler. A total of 14 367 pollen grains belonging to 40 taxa have been identified and recorded with some unidentified ones. Of them, 6 732 were identified in 1999 and 7 635 in 2000. Of the total pollen grains, 69.67% were arboreal, 26.64% non_arboreal and 3.68 % unidentified. The majority of the investigated pollen grains were from Pinus, Gramineae, Cupressaceae, Platanus , Chenopodiaceae/Amaranthaceae, Quercus, Ailanthus, Moraceae, Juglans , Salix, Cedrus and Rosaceae. The highest level of pollen grains was in May.