Knowledge Representation...(IJMECS-V9-N6-2)

Knowledge Representation...(IJMECS-V9-N6-2)
Knowledge Representation...(IJMECS-V9-N6-2)

I.J. Modern Education and Computer Science, 2017, 6, 9-16

Published Online June 2017 in MECS (https://www.360docs.net/doc/766536780.html,/)

DOI: 10.5815/ijmecs.2017.06.02

Knowledge Representation by Analogy for the Design of Learning and Assessment Strategies

Walid Mestadi

Ibn Tofail University, Faculty of Science, Kenitra, Morocco

Email: mestadi.walid@https://www.360docs.net/doc/766536780.html,

Khalid Nafil

Software Project Management Research Team, University Mohammed V, ENSIAS, Rabat, Morocco

Email: k.nafil@https://www.360docs.net/doc/766536780.html,.ma

Raja Touahni

Ibn Tofail University, Faculty of Science, Kenitra, Morocco

Email: rtouahni@https://www.360docs.net/doc/766536780.html,

Rochdi Messoussi

Ibn Tofail University, Faculty of Science, Kenitra, Morocco

Email: messoussi@https://www.360docs.net/doc/766536780.html,

Abstract—The difficulty of learning a novel knowledge may not be the same for each learner. Often instructors try to find the easiest way to make a new knowledge understandable by most learners, but few of them give importance to the use of analogies which is the common practice in real life situations. This paper attempts to highlight that learning by analogy allows making the understanding of a novel and complicated knowledge easier. We first propose a model that represents the desired knowledge in an abstract way which allows us to find analogies in different domains. Based on these analogies, learning and assessment strategies can be derived in order to improve the learning outcome. Secondly, the design of a computer system that integrates the analogies, learning and assessment strategies into a digital learning environment is proposed.

Index Terms—Learning by Analogy, Analogy Model Design, Learning and Assessment Strategies, Knowledge Structuring, Digital Learning Systems.

I.I NTRODUCTION

Due to the progress of information and communication technologies (ICT), access to information has become easy and fast. Nowadays, we are witnessing an exponential sharing of knowledge in all fields through digital resources (website, files, tutorial, courses and videos). Education takes advantage of the availability of these resources to improve the learning outcome. However, the variety and the amount of these resources are not sufficient to improve learning. A meaningful learning occurs when learners are able to transfer the acquired knowledge into novel situations [15, 10, 14].

The desired knowledge contained in these digital resources should be modeled in order to make them memorable and understandable. Authors of these resources such as instructors and experts in the educational field try to represent complex (abstract or novel) knowledge either by a simple (concrete) representations [14, 12] and/or by using analog representations [16, 18]. An example of this latter could be a human heart which can be represented as a pump or an electronics capacitor, an eye by a camera, a brain by a computer [6]. Also, a network routing can be represented as a road network.

Learning through analogies is a powerful mechanism [3, 1], specific to the human reasoning [5, 17] and promotes the learning outcome and the knowledge transfer from a familiar situation to a novel one [13, 2, 8, 7, 6].

The analogy is often used in problem-solving, explanation, argumentation, inference [17], transfer of expertise (software engineering) and discovery [8]. It involves several fields of research, such as psychology, artificial intelligence, philosophy [5], medicine, economics, and law [17].

However, the use of analogies in the learning process is not obvious [9, 3] and can lead to misinterpretations (if it is not used carefully), especially when learners are unable to separate the acquired knowledge from the analogies [8, 13, 3]. Therefore among the issues that can be faced, we have:

?The difficulty of finding analogies that represent the desired knowledge.

?The need for a standard that describes how to integrate analogies into the learning process.

?The assurance that learners can separate the knowledge to understand from the analogy.

?The assurance that learners can use the acquired knowledge in a novel situation.

This paper is inspired by the work of [11] which proposes a knowledge structuring for learning by levels. This paper attempts to address the issues listed above, and its main contributions can be summarized as follows: ?We propose a model and a process to support the instructor in designing analogies.

?Based on the analogies we develop learning strategies to improve learning outcome and

assessment strategies to check if the learners can

transfer the acquired knowledge.

?We propose a design of a computer system that aims to integrate analogies, learning and

assessment strategies into a digital learning

environment.

The rest of the paper is organized as follows: the next section, examines some related works, section III describes the proposed model of analogy design, section IV provides a case study illustrating the different aspects of the proposed model, section V describes the computer system design and finally section VI concludes the paper.

II.S TATE OF THE A RT

Several research works attempt to normalize the use of analogies in the learning process. In the design of analogies, two domains A and B are called analogs, if there is a structural matching between elements of the domain A called source and those of the domain B called target, which implies that the conclusions made in one of the domains are also true for the other [17, 4, 1].

Duit in [1] proposes a formal definition of analogy relations; R1 and R2 are analogous, if they have partially or totally identical characteristics in their structures (see Fig. 1). However, the analogy relation between R1 and R2 represents an analogy of first level (Fig. 1 label (A)). The identical characteristics are represented by the model R m. This latter one can be analog with another model R x. However, the analogy relation between R m and Rx represents an analogy in a more abstract level than that between R1 and R2.

Fig.1. Comparisons of structures between two domains (extracted from

[1]).

Winston in [17], proposes an object-oriented descriptive representation for the design of analogies. He focuses on the identification of the similarities between parts (desired knowledge). He combines the instances of the elements that constitute an act, such as objects, object attributes, relations, agents and additional information. Gentner in [4], proposes a structure mapping theory. It considers the field of study as a system of objects composed of a set of attributes and linked by relations. The matching is done through four types of similarities literal, relations, object attributes and simple. These types make it possible to structure several situations when designing analogies [1].

Williams in [16], propose a design of a virtual learning game that uses analogies, in which the learner/player is asked to complete a task such as comparing between real cases and analogies cases presented side-by-side in a game world.

Mestadi in [11] propose three levels for structuring knowledge. These levels result from the observations on the use of examples for explanation. They highlighted that while switching between examples some elements may or may not change their nature. Nature here means that an element can be a physical or a logical object, an action or an agent.

A. Synthesis

The elements used in the design of analogies, namely: objects, object attributes, and object relationships, are almost similar to elements used in the object-oriented programming (OOP) paradigm. These elements are used to design the static and the dynamic aspects of information systems (IS).

The static aspect is used to design a conceptual model using instances of the elements of the OOP, for example, objects (car and person) may be linked with the relation (drive or repair). To design a robust model, it is necessary to use instances of objects in a higher level of abstraction, for example instead of using a "car" we could use a "vehicle".

The dynamic aspect is used to design conceptual model that show the transition of state and the evolution of objects in time. For example, the object instance "car" may be in one of the states: off, on, broken down or out of service and the object instance "water" may be in the liquid, solid or vapor state.

The works of [17, 4, 1] give less importance to the dynamic aspect of the design of analogies and use elements instances in a low-level abstraction, while [16] represent the desired knowledge and the analogies only by the static aspect.

III.T HE P ROPOSED M ODEL

In this section, the mechanisms behind the transition from a standard representation of knowledge into one or more analogies representations are described.

In a learning session, often, the instructor gives analogies between elements that may not have the same structure and nature. Generally, the element in one field does not have the same nature as those in another one, for instance, "human brain" could be compared to a

"Computer Microprocessor", this similarity could be represented in a static and/or in a dynamic aspect.

The abstract representation of elements of a field of study is important in finding analog examples. The abstraction could be defined as the isolation of the elements from their context (avoiding the specific characteristics of the field), and their projection in elements of another field that may have or not the same nature [11]. Therefore, the nature of the elements of a field of study can be:

? A physical agent (i.e. a living being)

? A logical agent (i.e. artificial intelligence)

? A physical object (i.e. a machine, table)

? A logical object (i.e. a computer program)

? A physical action (i.e. controlling, hitting, producing, consuming)

? A logical action (i.e. thinking, talking)

Table 1 illustrates an example of the representation of the elements with and without respecting their nature. Table 1. Two examples of elements representation with and without

respecting their nature.

Representing an element with another having the same nature imposes a strong constraint when searching of analogies. If an element’s nature is "physical or logical object", the correspondent element must have the same nature, on the other hand representing an element without taking into consideration its nature does not make a constraint for the correspondent element, since it

is represented as "object".

The proposed process of the design of the analogies is shown in Fig. 2.

The process consists of the following steps:

?Static aspect representation: in which the main elements of the field are identified. Also, the

functions of each one and the relations between

them at a higher abstraction level are identified.

?Dynamic aspect representation: in which the interactions of theses elements with or without

respecting their nature are defined.

?Analogies: in which we search instances that respect the interactions of the elements with or

without respecting the nature.

Fig.2. The proposed process for the design of the analogies

The design of the dynamic aspect allows designing the behavior of elements in response to actions made by other elements.

IV.C ASE S TUDY

In this section, we present our case study that shows the use of the proposed model to elaborate analogies which allow us to design learning and assessment strategies that could be integrated into the learning process.

Let’s assume that the desired knowledge is from the field of medicine, specifically the Blood Circulation also called Circulatory System (CS). Intuitively, an analogy can be identified, such as the Wastewater treatment (WT). The elements that make up a WT have several characteristics in common with those of the CS, are the pumping, the canalization, the treatment, etc. The study of the WT can be a good learning ground to understand the concept of the CS.

A. Static aspect representation

To represent the static aspect, we first identify the elements, their functions and the relations between them (Table 2). Therefore, the main elements

involved in the CS are: “heart”, “Lungs”, “Organs” and “Blood”.

Table 2. Functions performed by each element using infinitive verbs and their synonyms in a high level of abstraction

The verbs and their synonyms are used to identify other elements who share the same functions, such as, the function pumping of the element ?heart? which could be founded in a capacitor, a water pump…etc.

The definition of relations between the elements such as sending and receiving the blood between the heart, the lungs and the organs, allows us to refine the search of correspondent elements. The static aspect alone does not allow the identification of concepts hardly perceptible such as the cycle concept which is fundamental in the CS. Therefore the dynamic representation is important.

B. Dynamic aspect representation

The dynamic aspect consists of the representation of flow interaction between elements of study's field, then an abstract representation of those elements while respecting their nature and finally, an abstract representation without respecting the nature of those elements. The table 3 below gives an example of these three representations. The representation of the interaction flow by a descriptive form may cause a difficulty in the interpretation (Table 3). Thus, we propose the use of a visual tool such as flow chart.

Table 3. Representation of the interaction flow between elements

(a)

(b)

(c)

Fig.3. (a) Representation of the CS, (b) representation of CS respecting the nature of the elements, (c) representation of CS without respecting

the nature of the elements.

Fig. 3 (a), represents the interaction flow of the CS. Fig.

3 (b) shows the interaction flow of elements respecting the nature of the elements of the CS, while Fig. 3 (c) shows the interaction flow without respecting their nature.

C. Search of analogies for CS

The representation of the interactions flows in Fig. 3 (b) and Fig. 3 (c) will be used in the search of analog examples. Fig. 4 shows a representation of WT that is analogous to the CS Fig. 2 (a).

From this perspective, the representation in Fig. 4 is an instance of the representation in Fig. 3 (c) and not of the one in Fig. 3 (b), since the elem ent “Humans”is of a different nature than the eleme nt “Organs”. Therefore, the example in Fig. 3 (a) (source) and Fig. 4 (target) are analogs compared to the representation in Fig.

3 (c).

Fig.4. Analogue representation of the Wastewater treatment The elements that constitute the WT are similar in nature to the CS elements, except for the element "humans" which is a "physical agent". This element can be replaced by another element that respects the nature of the source element which is a "physical object" such as a "House" or a "Nuclear Plant". This latter also involves replacing the "filter" element by a "cooler", the "clean water" by "cold water" and "waste water" by "hot water". When the analog example does not contain all the elements of the field of study, the combination of several analogies from different fields becomes necessary. For example, the elements that make up a Power Plant and its relation with the consumers are similar to the Circulatory System, with the exception of the "cycle" concept, which can be represented by the "hydrological cycle".

D. Learning and Assessment Strategies Respectively, the elements of the field of study, the analogs that do and do not respect the nature of the elements are organized in three levels called 3KL, which are: Domain Knowledge (DKL), Nature Domain Knowledge (NDKL) and Concept Domain Knowledge (CDKL).

The transition's order between the 3KL levels allows proposing learning and assessment strategies: Learning with analogies from the two levels NDKL and CDKL which uses simple representations either from other fields or real life, may help learners to better understand the field of study. Evaluating learners in the NDKL and CDKL levels helps to determine whether they are able to identify the elements of the field of study.

V.T HE S YSTEM D ESIGN

This section presents a system design that aims to integrate of analogies in the learning process. This system offers to the instructor the possibility to structure the desired knowledge and its analogies as activities. It also allows the definition of the progression, to test and get the feedback of several learning and assessment strategies. The system is expected to be integrated into existing Digital Learning Environment as a “plug-and-play” or as an independent learning support tool.

An overview of the system is shown in Fig. 5. It consists of the following blocks: in the Structured Knowledge block, the instructor defines the elements of the field of study and their analogies in the learning and the assessment stages respectively in the DKL, NDKL and CDKL levels.

The Strategy Block contains the strategies (defined by the instructor) to be tested during the learning process. The Activity Block contains the sequence of generated activities based on the Structured Knowledge and Strategy Blocks. The Result Interaction Block contains the results of the learner's interactions with the activities.

Fig.5. An overview of the proposed system.

During the learning process, the learner can be in a "learning" or "assessment" state. The integration of learning and assessment analogies allows us to introduce other states in addition to the states of the learning process. As presented in the previous section, the elements in the field of study and their analogies are organized in the 3KL levels.

Therefore, the learner may be in one of the following states: learning or assessment state in the DKL, in the NDKL or in the CDKL. The combination of these states in a specific order allows the development of several strategies.

In order to facilitate the encoding of these strategies by the core system, the use of a finite state automaton (Fig. 6) is adequate. It allows us to represent a given strategy by a sequence of numbers and characters, respecting the alphabet of the automaton. For example, the strategies '01ae2ae3ae45' and '01a2e45' designate respectively the activities in the following order:

?

Learn (DKL), Assess (DKL), Learn (NDKL), Assess (NDKL), Learn (CDKL), and Assess (CDKL).

? Learn (DKL) and Assess (NDKL).

The number in the start and in the end of the strategy are specific to the proposed system '0********* 45'.

Fig.6. Design of the system core as by an automaton.

Fig. 7 represents the entities of the proposed system represented by a class diagram. The Hierarchy entity represents the structure of the desired knowledge, such as a summary and the self-relation represent the depth.

Fig.7. An entities class diagram of the proposed system

The Activity entity represents learning or an assessment activity specified by the attribute "type", the attributes "level" refers to the membership of the activity to one of the proposed 3KL levels. The Strategy entity represents strategies to be tested by the instructor. The Progression entity represents learner's progressions, strategies, and scores. The Profile entity contains learner's information.

Fig. 8 represents the interaction of a learner with the proposed system by a sequence diagram. After the authentication of the learner, the Presentation and Logic loads the current progression and the strategy to apply. This latter is then interpreted by the Core which returns a sequence of activities to the Presentation and Logic block which is responsible for the Human Machine Interface interaction (HMI) and the storage and retrieval of

information and activities.

Fig.8. The design of interaction between the learner and the proposed

system by a sequence diagram

VI. C ONCLUSION

This paper deals with the use of analogies in the learning process and its advantages. We have proposed a model and a process that support the design of analogies from static and dynamic aspects. To illustrate this, a case study is provided in which the different phases of the process are explained. These analogies are organized in what we called 3KL levels which allow the elaboration of several learning and assessment strategies. We have also proposed a design of the computer system that integrates the analogies in the learning process. This proposed system can be a “plug -and-play” or an independent learning support tool.

It’s a given that the use of analogies in the learning process adds diversified activities that allow breaking the monotony of learning in a field of study. In addition, each learner has a different way of learning. Thus if we manage to find the adequate strategy for a given learner, he or she may have a better chance in learning and understanding any field of study.

The issue with the proposed model is its dependence on the skills of the instructors for structuring knowledge in the 3KL levels. Also, it still requires the definition of an abstract and limited vocabulary to describe the functions and the relations of any elements, allowing us to represent any field of study at a higher abstraction level with a unified language.

R EFERENCES

[1]Duit, R. (1991). On the role of analogies and metaphors in

learning science. Science education, 75(6), 649-672. [2]Zhang, F. (2014). L'application de l'analogie dans

l'enseignement du fran?ais en Chine (Doctoral dissertation, Dijon).

[3]Gentner, D., Levine, S. C., Ping, R., Isaia, A., Dhillon, S.,

Bradley, C., & Honke, G. (2016). Rapid learning in a children's museum via analogical comparison. Cognitive science, 40(1), 224-240.

[4]Gentner, D. (1983). Structure mapping: A theoretical

framework for analogy. Cognitive science, 7(2), 155-170.

[5]Gregan-Paxton, J., & John, D. R. (1997). Consumer

learning by analogy: A model of internal knowledge transfer. Journal of Consumer Research, 24(3), 266-284.

[6]Gunning, T. G. (1996). Creating reading instruction for all

children. Allyn and Bacon, Order Processing, PO Box 11071, Des Moines, IA 50336-1071.

[7]Harrison, A. G., & Treagust, D. F. (1993). Teaching with

analogies: A case study in grade 10 optics. Journal of Research in Science Teaching, 30(10), 1291-1307.

[8]Harrison, A. G., & Treagust, D. F. (2006). Teaching and

learning with analogies. In Metaphor and analogy in science education (pp. 11-24). Springer Netherlands. [9]Holyoak, K. J., & Thagard, P. (1989). Analogical

mapping by constraint satisfaction. Cognitive science,

13(3), 295-355.

[10]Mayer, R. E. (2002). Rote versus meaningful learning.

Theory into practice, 41(4), 226-232.

[11]Mestadi, W., Nafil, K., & Touahni, R. (2015, October).

Knowledge structuring for learning by level. In Intelligent Systems: Theories and Applications (SITA), 2015 10th International Conference on (pp. 1-6). IEEE.

[12]Moreno, R., Ozogul, G., & Reisslein, M. (2011). Teaching

with concrete and abstract visual representations: Effects on students' problem solving, problem representations, and learning perceptions. Journal of Educational Psychology, 103(1), 32.

[13]Sander, E. (2002). L'Analogie, fondement de nos

apprentissages. La Recherche, (353), 40-43.

[14]Sloutsky, V. M., Kaminski, J. A., & Heckler, A. F. (2005).

The advantage of simple symbols for learning and transfer.

Psychonomic bulletin & review, 12(3), 508-513.

[15]Tardif, J., & Meirieu, P. (1996). Stratégie pour favoriser le

transfert des connaissances. Vie pédagogique, 98(7), 4-7.

[16]Williams, D., Ma, Y., Feist, S., Richard, C. E., & Prejean,

L. (2007). The design of an analogical encoding tool for game‐based virtual learning environments. British Journal of Educational Technology, 38(3), 429-437.

[17]Winston, P. H. (1980). Learning and reasoning by analogy.

Communications of the ACM, 23(12), 689-703.

[18]Qin, G., Sun, S., Ye, H., & Lu, D. (2011). Strategies on

Teaching Reformation for Mechanical Manufacturing Technology. International Journal of Education and Management Engineering (IJEME), 1(6), 70. Authors’ Profiles

Mestadi Walid received his M.S. degree

in software quality in 2012 from Ibn

Tofail University, Faculty of science,

Kenitra- Morocco. Currently he is

preparing a PhD at the same faculty. His

research interests include learning, serious

games, software architecture and artificial

intelligence.

Khalid Nafil is currently professor of

Software Engineering at University

Mohammed V in Rabat - ENSIAS. He

received his PhD in Computer Science

from the University Mohammed V in

Rabat, Morocco since 1997. His main

research interests are Cost Estimation,

Software Testing, Serious Games, Software Process Improvement, Software Engineering Education.

Touahni Raja is currently professor at

Ibn Tofail University, Faculty of science,

Kenitra- Morocco. She received his PhD

in Microelectronics from the University

Paul Sabatier, Toulouse, France, in

September 1986. In 2001, she received the

Ph.D degree in the field of Data Analysis

at the same faculty. His main research interests are Image Processing, Data Analysis, Artificial Intelligence, Cognitive Science and Artificial Thinking, Computer Vision.

Messoussi Rochdi is currently professor

at Ibn Tofail University, Faculty of

science, Kenitra- Morocco. He received

his PhD degree in solid state physics from

the University of Nantes, France, in 1990.

In 2001 he received the master degree in

the use of IT for learning from the

University of Strasbourg, France. For the last 15 years, he has been carrying out research, about Human Computer Interaction to promote learning and education. His main research interests are Artificial Intelligence, Computing in Social science, Arts and Humanities.

How to cite this paper: Walid Mestadi, Khalid Nafil, Raja Touahni, Rochdi Messoussi,"Knowledge Representation by Analogy for the Design of Learning and Assessment Strategies", International Journal of Modern Education and Computer Science(IJMECS), Vol.9, No.6, pp.9-16, 2017.DOI: 10.5815/ijmecs.2017.06.02

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的度数;

三角形强化训练和深化 ? 1、如图a 是长方形纸带,∠DEF=25°,将纸带沿EF 折叠成图b ,再沿BF 折叠成图c ,则图c 中的∠CFE 的度数是_________°. 解析: 由题意可知折叠前,由BC//AD 得: ∠BFE=∠DEF=25°将纸带沿EF 折叠成图b 后, ∠GEF=∠DEF=25° 所以图b 中,∠DGF=∠GEF+∠BFE=25°+25°=50° 又在四边形CDGF 中,∠C=∠D=90° 则由:∠DGF+∠GFC=180° 所以:∠GFC=180°-50°=130° 将纸带再沿BF 第二次折叠成图C 后 ∠GFC 角度值保持不变 且此时:∠GFC =∠EFG+∠CFE 所以:∠CFE=∠GFC-∠EFG=130°-25°=105 2、在Rt △ABC 中,∠A =90°,CE 是角平分线,和高AD 相交于F ,作FG ∥BC 交AB 于G ,求证:AE =BG . 解法1: 【解析】证明:∵∠BAC=900 AD ⊥BC ∴∠1= ∠B ∵CE 是角平分线 ∴∠2=∠3 ∵∠5=∠1+∠2 ∠4=∠3+∠B ∴∠4=∠5 ∴AE =AF

过F作FM⊥AC并延长MF交BC于N ∴MN//AB ∵FG//BD ∴四边形GBDF为平行四边形 ∴GB=FN ∵AD⊥BC,CE为角平分线 ∴FD=FM 在Rt△AMF和RtNDF中 ∴△AMF≌△NDF ∴AF=FN ∴AE=BG 解法2: 解:作EH⊥BC于H,如图, ∵E是角平分线上的点,EH⊥BC,EA⊥CA, ∴EA=EH, ∵AD为△ABC的高,EC平分∠ACD, ∴∠ADC=90°,∠ACE=∠ECB, ∴∠B=∠DAC, ∵∠AEC=∠B+∠ECB, ∴∠AEC=∠DAC+∠ECA=∠AFE, ∴AE=AF, ∴EG=AF, ∵FG∥BC, ∴∠AGF=∠B, ∵在△AFG和△EHB中, ∠GAF=∠BEH ∠AGF=∠B AF=EH ,∴△AFG≌△EHB(AAS) ∴AG=EB, 即AE+EG=BG+GE, ∴AE=BG. 3、如图,等腰直角三角形ABC中,∠ACB=90°,AD为腰CB上的中线,CE⊥AD交AB 于E.求证∠CDA=∠EDB.

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【免费下载】中学教材全解 七年级数学上北师大版期末检测题含答案

图2图图 期末检测题 【本检测题满分:120分,时间:120分钟】 一、选择题(每小题3分,共30分) 1.(2013?湖南张家界中考)-2 013的绝对值是( ) A.-2 013 B.2 013 C. D.12013 12013 -2.已知两数在数轴上的位置如图所示,则化简代数式,a b 的结果是( ) 12a b a b +--++A.1 B. C. D.-1 23b +23a -3.某商店把一件商品按标价的九折出售(即优惠10%),仍可获利20%,若该商品的标价为每件28元,则该商品的进价为( ) A.21元 B.19.8元 C.22.4元 D.25.2元 4.(2013?湖南株洲中考)一元一次方程的解是( ) 24x =A. B. C. D.1x =2x =3x =4 x =5.如图,,则与之比为( )11,,34 AC AB BD AB AE CD ===CE AB A.1∶6 B.1:8 C.1:12 D.1:16 6.如果∠1与∠2互补,∠2与∠3互余,则∠1与∠3的关系是( ) A.∠1=∠3 B.∠1=180°-∠3 C.∠1=90°+∠3 D.以上都不对 7.如图是某班学生参加课外兴趣小组的人数占总人数比 例的统计图,则参加人数最多的课外兴趣小组是( ) A.棋类组 B.演唱组 C.书法组 D.美术组 8.某中学开展“阳光体育活动”,九年级一班全体同学分别参加了巴 山舞、乒乓球、篮球三个项目的活动,陈老师统计了该班参加这三项活动的人数,并绘制了如图所示的条形统计图和扇形统计图.根据这两个统计图,可以知道该班参加乒乓A B C D E 第5题图 习题到位。在管设备进行调整使度内来确保机组

新人教版七年级下册数学知识点整理

最新版人教版七年级数学下册知识点 第五章相交线与平行线 一、知识网络结构 相交线 相交线垂线 同位角、内错角、同旁内角 平行线:在同一平面内,不相交的两条直线叫平行线 定义 : __________ __________ ________ 平行线及其判定判定 1:同位角相等,两直线平行 判定 2 平行线的判定:内错角相等,两直线平行 相交线与平行线判定 3:同旁内角互补,两直线平行 判定 4:平行于同一条直线的两直线平行 平行线的性质性质 1:两直线平行,同位角 性质 2:两直线平行,内错角 性质 3:两直线平行,同旁内 性质 4:平行于同一条直线 相等 相等 角互补 的两直线平行命题、定理 平移 二、知识要点 1、在同一平面内,两条直线的位置关系有两种:相交和平行,垂直是相交的一种特殊情况。 2、在同一平面内,不相交的两条直线叫平行线。如果两条直线只有一个公共点,称这两条直线相交;如果两条直线没有公共点,称这两条直线平行。 3、两条直线相交所构成的四个角中,有公共顶点且有一条公共边的两个角是邻补角。邻补角的性质:邻补角互补。如图 1 所示,与互为邻补角,与互为邻补角。+=180°;+ =180° ; + =180°;+ =180°。321 4 4、两条直线相交所构成的四个角中,一个角的两边分别是另一个角的两边的图 1反 向延长线,这样的两个角互为对顶角。对顶角的性质:对顶角相等。如图1

所示,与互为对顶角。=; =。 5、两条直线相交所成的角中,如果有一个是直角或90° 时,称这两条直线互相垂直, 其中一条叫做另一条的垂线。如图 2 所示,当= 90°时,⊥b。 a 垂线的性质:2 1 3 4 性质 1:过一点有且只有一条直线与已知直线垂直。 图 2 性质 2:连接直线外一点与直线上各点的所有线段中,垂线段最短。 性质 3:如图 2 所示,当 a⊥ b 时,==== 90°。点到直线的距离:直线外一点到这条直线的垂线段的长度叫点到直线的c距离。 6、同位角、内错角、同旁内角基本特征:21 3 46 a 75 8 ①在两条直线 ( 被截线 ) 的同一方,都在第三条直线 ( 截线 ) 的同一侧,这样 b 同位角。图 3 中,共有图 3 的两个角叫对同位角:与是同位角; 与是同位角;与是同位角;与是同位角。 ②在两条直线 ( 被截线 )之间,并且在第三条直线 ( 截线 ) 的两侧,这样的两个角叫内错角。图 3中,共有对内错角:与是内错角;与是内错角。 ③在两条直线 ( 被截线 ) 的之间,都在第三条直线 ( 截线 ) 的同一旁,这样的两个角叫同旁内角。图 3中,共有对同旁内角:与是同旁内角;与是同旁内角。 7、平行公理:经过直线外一点有且只有一条直线与已知直线平行。 平行公理的推论:如果两条直线都与第三条直线平行,那么这两条直线也互相 平行。c 2 3 1 4 6 5 平行线的性质:a78性质 1:两直线平行,同位角相等。如图 4 所示,如果 a∥ b,图4 b 则 =; =; =; =。

(完整版)七年级下册数学知识结构图

第五章知识结构如下图所示: 第六章知识结构 第七章知识结构框图如下:

(二)开展好课题学习 可以如下展开课题学习: (1)背景了解多边形覆盖平面问题来自实际. (2)实验发现有些多边形能覆盖平面,有些则不能. (3)分析讨论多边形能覆盖平面的基本条件,发现问题与多边形的内角大小有密切关系,运用多边形内角和公式对实验结果进行分析. (4)运用进行简单的镶嵌设计. 首先引入用地砖铺地,用瓷砖贴墙等问题情境,并把这些实际问题转化为数学问题:用一些不重叠摆放的多边形把平面的一部分完全覆盖.然后让学生通过实验探究一些多边形能否镶嵌成平面图案,并记下实验结果:

(1)用正三角形、正方形或正六边形可以镶嵌成一个平面图案(图1).用正五边形不能镶嵌成一个平面图案. (2)用正三角形与正方形可以镶嵌成一个平面图案.用正三角形与正六边形也可以镶嵌成一个平面图案. (3)用任意三角形可以镶嵌成一个平面图案, 用任意四边形可以镶嵌成一个平面图案(图2).

观察上述实验结果,得出多边形能镶嵌成一个平面图案需要满足的两个条件: (1)拼接在同一个点(例如图2中的点O)的各个角的和恰好等于360°(周角); (2)相邻的多边形有公共边(例如图2中的OA两侧的多边形有公共边OA). 运用上述结论解释实验结果,例如,三角形的内角和等于180°,在图2中,∠1+∠2+∠3=180°.因此,把6个全等的三角形适当地拼接在同一个点(如图2), 一定能使以这点为顶点的6个角的和恰好等于360°,并且使边长相等的两条边贴在一起.于是, 用三角形能镶嵌成一个平面图案.又如,由多边形内角和公式,可以得到五边形的内角和等于 (5-2)×180°=540°. 因此,正五边形的每个内角等于 540°÷5=108°, 360°不是108°的整数倍,也就是说用一些108°的角拼不成360°的角.因此,用正五边形不能镶嵌成一个平面图案. 最后,让学生进行简单的镶嵌设计,使所学内容得到巩固与运用.1.利用二(三)元一次方程组解决问题的基本过程 2.本章知识安排的前后顺序

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Web of Knowledge平台服务功能使用简介 ISI Web of Knowledge为读者提供了个性化服务和定题服务功能。个性化定制指用户可以在Web of Konwledge主页上注册并设置自己密码,然后每次登录后即可浏览自己订制主页,包括:保存检索策略、建立并编辑自己经常阅读期刊列表;浏览保存检索策略、及时了解一个定题服务是否有效及过期时间。 电子邮件定题服务可让用户方便地跟踪最新研究信息。新定题服务功能允许用户通过web of science中任一种检索途径(普通检索、引文检索、化学结构检索)创建定题服务服务策略,将检索策略保存并转化为用电子邮件通知定题服务。 如图,在Web of Knowledge主页右侧提供了个性化定制服务和定题服务管理功能,下面就这几项功能一一说明如下: 图一:web of knowledge主页 一、注册 点击“Register”超链接,进入注册页面。如图二:分别按要求填入您电子邮件地址,您选择密码以及您姓名。您可以选择自动登录或者普通方式进入您个性化服务管理功能。自动登录可以免除您每次登录Web of Knowledge平台时输入电子邮件地址和密码。该功能使用是cookie技术。如果使用公共计算机,最好选择普通登录方式。 在完成以上操作之后,点击“Submit Registration”完成整个注册过程。

图二:用户注册页面 二、登录 作为注册用户,您可以实现以下功能: ?自动登录到Web of Knowledge平台。 ?选择一个自己常用开始页面,每次登录后则自动进入该页面。 ?将检索策略保存到ISI Web of Knowledge服务器。 ?创建用户关注期刊列表以及期刊目次定题服务。 登录时,在web of knowledge主页右侧输入您电子邮件地址和密码,点击“Sign in”则可进入您个人定制信息服务管理页面。 三、个人信息管理和选择开始页面 点击“My Preferences”超链接,可以编辑个人信息和选择开始页面。 编辑个人信息: 点击“Edit my Information”超链接可以更新您联系信息,如电子邮件地址、密码及姓名。如图三。

七年级数学下册全部知识点归纳

第一章:整式的运算 单项式 式 多项式 同底数幂的乘法 幂的乘方 积的乘方 同底数幂的除法 零指数幂 负指数幂 整式的加减 单项式与单项式相乘 单项式与多项式相乘 整式的乘法 多项式与多项式相乘 整式运算 平方差公式 完全平方公式 单项式除以单项式 整式的除法 多项式除以单项式 一、单项式 1、都是数字与字母的乘积的代数式叫做单项式。 2、单项式的数字因数叫做单项式的系数。 3、单项式中所有字母的指数和叫做单项式的次数。 4、单独一个数或一个字母也是单项式。 5、只含有字母因式的单项式的系数是1或―1。 6、单独的一个数字是单项式,它的系数是它本身。 7、单独的一个非零常数的次数是0。 8、单项式中只能含有乘法或乘方运算,而不能含有加、减等其他运算。 9、单项式的系数包括它前面的符号。 10、单项式的系数是带分数时,应化成假分数。 11、单项式的系数是1或―1时,通常省略数字“1”。 12、单项式的次数仅与字母有关,与单项式的系数无关。 二、多项式 1、几个单项式的和叫做多项式。 2、多项式中的每一个单项式叫做多项式的项。 3、多项式中不含字母的项叫做常数项。 4、一个多项式有几项,就叫做几项式。 5、多项式的每一项都包括项前面的符号。 6、多项式没有系数的概念,但有次数的概念。 7、多项式中次数最高的项的次数,叫做这个多项式的次数。 三、整式 1、单项式和多项式统称为整式。 2、单项式或多项式都是整式。 3、整式不一定是单项式。 4、整式不一定是多项式。

5、分母中含有字母的代数式不是整式;而是今后将要学习的分式。 四、整式的加减 1、整式加减的理论根据是:去括号法则,合并同类项法则,以及乘法分配率。 2、几个整式相加减,关键是正确地运用去括号法则,然后准确合并同类项。 3、几个整式相加减的一般步骤: (1)列出代数式:用括号把每个整式括起来,再用加减号连接。 (2)按去括号法则去括号。 (3)合并同类项。 4、代数式求值的一般步骤: (1)代数式化简。 (2)代入计算 (3)对于某些特殊的代数式,可采用“整体代入”进行计算。 五、同底数幂的乘法 1、n个相同因式(或因数)a相乘,记作a n,读作a的n次方(幂),其中a为底数,n为指数,a n的结果叫做幂。 2、底数相同的幂叫做同底数幂。 3、同底数幂乘法的运算法则:同底数幂相乘,底数不变,指数相加。即:a m﹒a n=a m+n。 4、此法则也可以逆用,即:a m+n = a m﹒a n。 5、开始底数不相同的幂的乘法,如果可以化成底数相同的幂的乘法,先化成同底数幂再运用法则。 六、幂的乘方 1、幂的乘方是指几个相同的幂相乘。(a m)n表示n个a m相乘。 2、幂的乘方运算法则:幂的乘方,底数不变,指数相乘。(a m)n =a mn。 3、此法则也可以逆用,即:a mn =(a m)n=(a n)m。 七、积的乘方 1、积的乘方是指底数是乘积形式的乘方。 2、积的乘方运算法则:积的乘方,等于把积中的每个因式分别乘方,然后把所得的幂相乘。即(ab)n=a n b n。 3、此法则也可以逆用,即:a n b n =(ab)n。 八、三种“幂的运算法则”异同点 1、共同点: (1)法则中的底数不变,只对指数做运算。 (2)法则中的底数(不为零)和指数具有普遍性,即可以是数,也可以是式(单项式或多项式)。 (3)对于含有3个或3个以上的运算,法则仍然成立。 2、不同点: (1)同底数幂相乘是指数相加。 (2)幂的乘方是指数相乘。 (3)积的乘方是每个因式分别乘方,再将结果相乘。 九、同底数幂的除法

(完整word版)北师大版七年级数学下册三角形难题全解

来源:2011-2012学年广东省汕头市潮南区中考模拟考试数学卷(解析版) 考点:三角形 如图,已知,等腰Rt△OAB中,∠AOB=90o,等腰Rt△EOF中,∠EOF=90o,连结AE、BF. 求证:(1)AE=BF;(2)AE⊥BF. 【答案】 见解析 【解析】解:(1)证明:在△AEO与△BFO中, ∵Rt△OAB与Rt△EOF等腰直角三角形, ∴AO=OB,OE=OF,∠AOE=90o-∠BOE=∠BOF, ∴△AEO≌△BFO, ∴AE=BF; ( 2)延长AE交BF于D,交OB于C,则∠BCD=∠ACO, 由(1)知:∠OAC=∠OBF, ∴∠BDA=∠AOB=90o, ∴AE⊥BF. (1)可以把要证明相等的线段AE,CF放到△AEO,△BFO中考虑全等的条件,由两个等腰直角三角形得AO=BO,OE=OF,再找夹角相等,这两个夹角都是直角

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