59中英文雙語數(shù)學(xué)教育專業(yè)外文文獻(xiàn)翻譯成品中學(xué)數(shù)學(xué)教學(xué)中的向量計(jì)算以及立體幾何

1、<p>　　外文標(biāo)題：VECTOR CALCULUS AND SOLID GEOMETRYAT TEACHING OF MATHEMATICS AT SECONDARY SCHOOL</p><p>　　外文作者：LUCIA RUMANOVÁ </p><p>　　文獻(xiàn)出處: Acta Didactica Universitatis Comen

2、ianae Mathematics,Issue6,2006 </p><p>　　英文2389單詞， 12963字符，中文3702漢字。</p><p>　　此文檔是外文翻譯成品，無需調(diào)整復(fù)雜的格式哦！下載之后直接可用，方便快捷！只需二十多元。</p><p>　　VECTOR CALCULUS AND SOLID GEOMETRYAT T

3、EACHING OF MATHEMATICS AT SECONDARY SCHOOL</p><p>　　LUCIA RUMANOVÁ</p><p><b>　　Abstract</b></p><p>　　Paper is presentation analysis of problem in the theory of dida

4、ctic situation and the evaluation of experiment with using statistical program CHIC. Problem analysis is task of stereometry for students from secondary schools. Aim of experiment was mention on problems with application

5、 of knowledge of different part of mathematics at solution of stereometry problem.</p><p>　　Key words: theory of didactic situations, analysis a priori, analysis a posteriori, statistical program C.H.I.C., s

6、olid geometry, synthetic geometry, vector calculus, analytic geometry</p><p>　　INTRODUCTION</p><p>　　One of the long – lasting problems in teaching mathematics at secondary school is the problem

7、 of relations among subjects, respectively the continuity of mathematics content and the content of other subjects. However, a specific prob- lem is the continuity or the co-ordination of individual parts of mathematics

8、in the process of education. In this work I want to pay attention to this part of teach- ing mathematics, specifically geometry ? focus on the relation between solid geometry from the vec</p><p>　　We know th

9、at the pupils are taught the basics of vector algebra and analytic geometry already in the 8th or 9th grade at the primary school. Later on they get other information with the notion of vector and its operations (sum, od

10、ds...) in the first grade at secondary school, and this part is mostly used as a tool for knowledge analytic geometry, for example equations of the straight lines, planes, ... and later, for the analytic geometry of coni

11、cs, balls, and so on.</p><p>　　Another problem is little attention paid to application of the vector calculus to solve the tasks of solid geometry. These tasks are taught in other parts only by the synthetic

12、 geometry, as well as little time spent for application tasks in other subjects (physics, geology, geography, etc.). Students usually don’t find relative with other subjects at solution of solid problems whereupon their

13、know- ledge they don’t know or don’t tried to apply.</p><p>　　AIMS OF RESEARCH</p><p>　　The goal of research is therefore emphasize problems of students at secondary school with solving solid pr

14、oblems, with application their knowledge (from differ- ent part of mathematic) in solid geometry, as well as mention problems of students to find connection between parts of mathematics and other learning subjects.</p

15、><p>　　Then the aim of research is also experimental verify validity of the hypothe-</p><p>　　ses H1–H4 and eventually suggest solutions of effectiveness education of analytical (vector) geometry w

16、ith relating parts of mathematic and thereafter enhancement education between learning subjects at secondary school.</p><p>　　Abovementioned problems we summarized to following hypotheses:</p><p&g

17、t;　　H1 The solid geometry is taught at secondary school separately, i. e. students are separately taught axiomatic, separately deal with synthetic geometry, separately analytic geometry, and so the sequence of various ap

18、proaches is minimal or any.</p><p>　　H2 In mathematics textbook there aren’t examples with unification character, which would promote elimination limitations (to fault) listed in H1.</p><p>　　H3

19、 Students of secondary school with the established educational schedule ha- ven’t enough ability to apply their knowledge of the vector calculus in other areas of mathematics, apart from analytic geometry, and that in th

20、is case only formally.</p><p>　　H4 Students of secondary school are not able in ample measure to be aware of the continuity of synthetic and analytic geometry (vector calculus) in solution of particular prob

21、lem situations. Similar situation applies to University students who will be teachers of mathematics.</p><p>　　PREPARATION OF THE EXPERIMENT</p><p>　　In accordance with the tenets theory of dida

22、ctic situations frame: within the frame of the didactic situation S3 (noosferic didactic situation) we made an analy- sis of math textbooks for secondary schools, an analysis of various mathematical materials, where the

23、goal was to choose a useful problem for students and which would help us to find out reply to already formulated hypothesis H1, H2, H3 and H4 in the introduction. Our goal was to seek such a problem, which the students w

24、ere not able to </p><p>　　The task for the students in this experiment was to try giving an example from the solid geometry with exploitation knowledge out of analytic geometry and vector calculus. (What we

25、awaited results). Results of experiment have mention problems with solving solid problems, with application their knowledge (from different part of mathematic) in solid geometry, as well as mention problems of students t

26、o fin connection between parts of mathematics and other learning subjects. Results of this experime</p><p>　　The task was:</p><p>　　Given is a cube ABCDEFGH and K-point, L-point, M-point, N-poin

27、t, so that K-point is centre of upper surface EFGH, L-point is centre of the AB, M- point belong to AE, where,and N-point belong to BG.Are the points K, L, M, and N coplanary?</p><p>　　Based on the above-me

28、ntioned criteria the final sentence of the given task can be interpreted in several different ways, their experimental attesting will be the part of our following research of this field.</p><p>　　Q1: Vector

29、calculus ? exploitation collinearity of vectors or coplanarity</p><p>　　of vectors</p><p>　　Q2: Analytic solution ? writing general equation of plane assigned three</p><p>　　from fo

30、ur given points and then we prove incidence of fourth point into plane</p><p>　　Q2´: Analytic solution ? writing parametric equation of plane assigned</p><p>　　three from four given points

31、and then we prove incidence of fourth point into plane</p><p>　　Q2´´: Analytic solution ? writing parametric equations of two lines from</p><p>　　given fourth points and then we fount

32、out their relative position (if they construct of plane)</p><p>　　Q3: Synthetic approach ? construction section of plane of cube and then we</p><p>　　prove incidence fourth point into plane</

33、p><p>　　Q4: Vector calculus ? exploitation attributes of “barycentre</p><p>　　POSSIBLE STRATEGIES OF STUDENTS SOLUTION – ANALYSE A PRIORI OF PROBLEM DESIGNATION TO EXPERIMENT</p><p>　　

34、we construct the section plane LMN of cube ABCDEFGH and than</p><p>　　we attest: ? K ∈LMN ? (That they are single calculations – for examples: solution with exploitation follows Figure 2 or exploitation rese

35、mblance be- tween triangle)</p><p>　　And then the question is:</p><p>　　We solve the system of equations:</p><p>　　For parameters t ?????and s ???2 , the equations have a solution,

36、there out resulting</p><p>　　The problem is: Are the vectors LS and LK collinear? (point S is a centre</p><p>　　of line segment MN ). If the vectors are collinear, so the K-point, L-point, M-<

37、;/p><p>　　point, N-point are coplanar.</p><p>　　For the vector LS resulting these terms:</p><p>　　By means of substitution relations and simple reforms resulting term:</p><p

38、>　　K-point is a barycentre of E(1), G(1), L-point is a barycentre of A(2), B(2), M-point is a barycentre of A(2), E(1) and N-point is a barycentre of B(2), G(1).</p><p>　　And then, the question is: What i

39、s barycentre G of this points set {A(2),</p><p>　　B(2), G(1), E(1)} ?</p><p>　　From the facilities of barycentre ? G is barycentre of {M(3), N(3)} and{K(2), L(4)}</p><p>　　Analysis

40、a-priori problem had been formulated and teacher’s activity in a-didactic situation</p><p>　　The base of didactic research is the test students´ reactions in the given di- dactic situation. So as we cou

41、ld make the test to realize at the first we had to do the full analysis of didactic situation itself.</p><p>　　Part of the experiment is the integration individual phases of the problem</p><p>　

42、　solution to system of levels in the analyse didactic situation.</p><p>　　This is the tablet composition of milieu and with it associated types of didac- tic situations (Margolinas 1994).</p><p>

43、;　　ANALYSE OF TEACHER’S WORK (DESCENDING ANALYSIS)</p><p>　　S3 – noosferic situation – on this stage we analysis the math textbook for sec- ondary school (2nd or 3rd class), analysis various mathematical mat

44、erials (educa- tional schedule…), specifically study of solid geometry, vector algebra and ana-</p><p>　　lytic geometry. We want to choose problem, which the students were not able to</p><p>　　s

45、olve with the learnt simple algorithms and students can use knowledge from different parts of mathematics and other learning subjects. Finish of noosferic situation will be the milieu for the next situation.</p>&

46、lt;p>　　S2 – constructional situation – teacher will try to find examples, that were defined in noosferic situation S3 and on the other side in situation S1, in which they will be able to realize. Goal was to choose a

47、useful problem for students which would help him to find reply to already formulate hypothesis H1, H2, H3 and H4. They are examples which students can abet in examples solution Q1, Q2, Q2´, Q2´´, Q3 a Q4.&

48、lt;/p><p>　　S1 – project situation – in situation S1, teacher writes a text of the example</p><p>　　and he “projects” his solution. Student is one on teacher’s consciousness. This is a situation, w

49、hich involves student’s activity, too. The student can solve prob- lem in a way that he constructs the section plane of cube, and then he finds out if other point is point of plane; or the student solves a problem that h

50、e writes parametric equation of plain and he finds out if the fourth point is the point of the plane; or he applies exploitation collinearity of vectors or coplanarity or exploita- ti</p><p>　　S0 – didactic

51、situation – in this situation we analysis and do institutionalisa- tion of the new knowledge and we formulate the problem. Teacher takes care of</p><p>　　designed goals and he follows student’s solution, too

52、. It is a situation where the</p><p>　　analysis of teacher’s work and analysis of student’s work meet, and the didactic situation will be the result of the teaching process</p><p>　　CONCLUSION&l

53、t;/p><p>　　Problem at teaching solid geometry is sequence single parts of mathematics within solid geometry. With this problem relate too solutions of solid geometry problems. Concrete, students have problem so

54、lve problem, students could solve problem in different theoretical frame with reference to their level of knowledge and sciential level at secondary school, but which the students were not able to solve problem only with

55、 the learnt simple algorithms.</p><p>　　The goal of research is mention problems with application students´ knowledge at solving problem from different part of mathematic in solid geometry and also expe

56、rimental verify validity or invalidity of the hypotheses with using peda- gogical experiment.</p><p>　　Experiment was realized also in university (future teachers of mathematics) and confirmed us that there

57、is similar problem with application students´ knowl- edge from different parts of mathematics in solid geometry and also from other subjects. Whereupon, teacher prefer concrete parts in teaching (in lessons of mathe

58、matics) and so teacher often disuse examples with unification character.</p><p>　　Conclusion of the work includes collections of the tasks and we want (of course) expand any interesting application problems

59、(tasks) from solid geome- try, which we can improve on lessons of mathematics. Consequently, correction of collections of these tasks for practical use as part of texts in books of mathe- matics for secondary schools. In

60、 continues of experiment we want to try making educational texts some parts of solid geometry. Educational texts will be especially orientated to coordinat</p><p>　　REFERENCES</p><p>　　Balacheff

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80、中的向量計(jì)算以及立體幾何</p><p>　　LUCIA RUMANOVÁ</p><p><b>　　摘要</b></p><p>　　在本文中，呈現(xiàn)了對(duì)教學(xué)情境理論中的問題和對(duì)CHIC使用統(tǒng)計(jì)程序的實(shí)驗(yàn)評(píng)估的分析。 分析的問題是有關(guān)于中學(xué)立體幾何。 實(shí)驗(yàn)的目的是在數(shù)學(xué)不同部分知識(shí)中去解決立體幾何的應(yīng)用問題。</p>

81、<p>　　關(guān)鍵詞：理論情境、實(shí)驗(yàn)前分析、試驗(yàn)后后分析、統(tǒng)計(jì)程序C.H.I.C、立體幾何、綜合幾何、向量計(jì)算、解析幾何</p><p><b>　　引言</b></p><p>　　在中學(xué)數(shù)學(xué)教學(xué)中，長(zhǎng)期存在的問題之一是學(xué)科間的關(guān)系問題，分別是數(shù)學(xué)內(nèi)容的連續(xù)性和其他學(xué)科內(nèi)容的問題。 然而，一個(gè)具體的問題是數(shù)學(xué)的各個(gè)部分在教學(xué)過程中的連續(xù)性或協(xié)調(diào)性。 在這項(xiàng)工

82、作中，我想關(guān)注數(shù)學(xué)教學(xué)的這一部分，特別是幾何學(xué)，重點(diǎn)關(guān)注向量計(jì)算、立體幾何與立體幾何教學(xué)方法之間的關(guān)系。</p><p>　　眾所周知，小學(xué)生在八年級(jí)或九年級(jí)已經(jīng)被教授過向量代數(shù)和解析幾何的基礎(chǔ)知識(shí)。 后來，他們?cè)谥袑W(xué)一年級(jí)學(xué)習(xí)向量及其運(yùn)算的概念，并且這部分主要用作解析幾何知識(shí)學(xué)習(xí)的工具，例如直線方程線條，平面計(jì)算......以及后來的錐形、球形等解析幾何。</p><p>　　另一個(gè)很少

83、關(guān)注的問題是向量計(jì)算的應(yīng)用以及在立體幾何問題解決的應(yīng)用。 這些任務(wù)只在其他部分以綜合幾何學(xué)的方式教授，而其他科目（物理學(xué)，地質(zhì)學(xué)，地理學(xué)等）對(duì)該方面的應(yīng)用很少提及。 學(xué)生通常沒有找到該學(xué)科與其他學(xué)科的關(guān)系，發(fā)現(xiàn)這些關(guān)系有利于解決他們不知道或不會(huì)的立體幾何問題。</p><p><b>　　研究目標(biāo)</b></p><p>　　因此，此次研究的目標(biāo)是強(qiáng)調(diào)中學(xué)生解決立體幾

84、何的問題，并將他們的知識(shí)（來自數(shù)學(xué)的不同部分）應(yīng)用于立體幾何中，本次研究還會(huì)提及學(xué)生發(fā)現(xiàn)數(shù)學(xué)部分與其他學(xué)習(xí)科目之間的聯(lián)系。 之后的研究先假設(shè)H1-H4的有效性并進(jìn)行實(shí)驗(yàn)驗(yàn)證假設(shè)，最終提出向量幾何以及與數(shù)學(xué)相關(guān)部分在教育解決方案上的有效性，以提升中學(xué)的學(xué)習(xí)科目之間的聯(lián)系。</p><p>　　根據(jù)上述問題我們總結(jié)為以下假設(shè)：</p><p>　　H1 立體幾何學(xué)是分別都是在中學(xué)教授的，即 學(xué)

85、生被分開去教授公理化，分別去處理綜合幾何、單獨(dú)分析幾何，所以各種方法的序列最小或者以任何其他方式排列。</p><p>　　H2在數(shù)學(xué)教科書中沒有具有統(tǒng)一性的例子，這將有利于H1中列出的問題的解決。</p><p>　　H3在學(xué)校按照作息時(shí)間上學(xué)的中學(xué)學(xué)生除了解析幾何外，還沒有足夠的能力將其在數(shù)學(xué)的其他領(lǐng)域的應(yīng)用知識(shí)應(yīng)用于向量計(jì)算，這種情況只會(huì)發(fā)生在學(xué)校。</p><p

86、>　　H4中學(xué)的學(xué)生無法充分地了解綜合和分析幾何（向量運(yùn)算）的連續(xù)性</p><p>　　特定問題的情況。 類似的情況也適用于將來會(huì)成為數(shù)學(xué)老師的大學(xué)學(xué)生。</p><p><b>　　實(shí)驗(yàn)的準(zhǔn)備工作</b></p><p>　　根據(jù)教學(xué)理論的教學(xué)情境框架：在教學(xué)情境S3（新教學(xué)情境）的框架內(nèi)，我們對(duì)中學(xué)的數(shù)學(xué)教科書進(jìn)行了分析，分析了各種

87、數(shù)學(xué)材料，其目標(biāo)是對(duì)學(xué)生來說選擇一個(gè)有用的問題，并且可以幫助我們找到對(duì)引言中已經(jīng)提出的假設(shè)H1，H2，H3和H4的回應(yīng)。 我們的目標(biāo)是尋找這樣一個(gè)問題，學(xué)生們無法用簡(jiǎn)單的算法解決問題，在數(shù)學(xué)教科書中通常不存在這些類型的問題。</p><p>　　在這個(gè)實(shí)驗(yàn)中，學(xué)生的任務(wù)是嘗試從已經(jīng)學(xué)習(xí)的立體幾何知識(shí)學(xué)中解析出幾何和向量演算。 （這正是我們期待的結(jié)果）。 實(shí)驗(yàn)結(jié)果提出了解決立體幾何問題的方法，并將他們的知識(shí)（來自數(shù)

88、學(xué)的不同部分）應(yīng)用于立體幾何中，并提出學(xué)生將數(shù)學(xué)部分與其他學(xué)習(xí)科目聯(lián)系起來的問題。 這個(gè)實(shí)驗(yàn)的結(jié)果必須說明學(xué)生如何使用這些計(jì)算單位中獲得滿足感。</p><p><b>　　任務(wù)是:</b></p><p>　　已知立方體ABCDEFGH 和點(diǎn)K, 點(diǎn)L,點(diǎn) M,點(diǎn) N, 點(diǎn)K在立體圖形上面EFGH的中心位置, L點(diǎn)上線段AB的中點(diǎn), 點(diǎn)M AE上, ,點(diǎn) N 在線段

89、BG上，.那點(diǎn) K, L, M, 和點(diǎn) N 共面嗎?</p><p>　　根據(jù)上述標(biāo)準(zhǔn)，已知任務(wù)的最后一個(gè)要解答的問題可以用幾種不同的方式來解釋，他們的實(shí)驗(yàn)證明將成為我們對(duì)這一領(lǐng)域后續(xù)研究的一部分。</p><p>　　問題1：向量計(jì)算--向量的共線性或向量的共面性知識(shí)的提煉</p><p>　　問題2：解析解 - 寫出從四個(gè)已知點(diǎn)分配三個(gè)平面的一般平面方程，然后證

90、明第四個(gè)點(diǎn)進(jìn)入平面的入射角。</p><p>　　（1）問題2：解析解 - 寫出從四個(gè)已知點(diǎn)分配三個(gè)平面的平面參數(shù)方程，然后證明第四個(gè)點(diǎn)進(jìn)入平面的入射角。</p><p>　?。?）問題2：解析解- 從已知的第四點(diǎn)寫出兩線段的參數(shù)方程，然后我們找出它們的相對(duì)位置（如果它們是平面的構(gòu)造）</p><p>　　問題3：綜合方法 - 立方體平面截面，然后證明第四點(diǎn)的入射角

91、。</p><p>　　問題4：向量計(jì)算---“重心屬性”的提煉</p><p>　　4學(xué)生解決問題可能出現(xiàn)的策略 - 實(shí)驗(yàn)中分析指定問題的先決個(gè)前提</p><p>　　我們構(gòu)造ABCDEFGH立方體的剖面LMN</p><p>　　b）我們證明：？K∈LMN？ （它們是單一計(jì)算 - 例如：利用圖2的解決方案或三角形之間的相似性）。<

92、/p><p><b>　　問題是：</b></p><p><b>　　列出方程式就是:</b></p><p>　　參數(shù)中 t=3/2 ?， s ?=??2 , 方程有解，結(jié)果是</p><p>　　問題是：向量LS和LK是否共線？ （點(diǎn)S是線段MN的中心）。 如果向量是共線的，那么K點(diǎn)，L點(diǎn)，M點(diǎn)，

93、N點(diǎn)是共面的。</p><p>　　向量LS會(huì)帶來下面的關(guān)系：</p><p>　　通過替代關(guān)系和簡(jiǎn)單的替換得到下面的關(guān)系式：</p><p>　　K點(diǎn)是E（1），G（1）的重心，L點(diǎn)是A（2），B（2）的重心，M點(diǎn)是A（2）的重心，E（1） N點(diǎn)是B（2），G（1）的重心。</p><p>　　然后，問題是：這個(gè)點(diǎn)集的重心是什么？是{A（2

94、），B（2），G（1），E（1）}？</p><p>　　重心的前提條件?G是{M（3），N（3）}和{K（2），L（4）}的重心</p><p>　　實(shí)驗(yàn)之前的問題已經(jīng)得到表述以及教師在教學(xué)情境中的教學(xué)活動(dòng)</p><p>　　教學(xué)研究的基礎(chǔ)是測(cè)試學(xué)生在已知情景中的反應(yīng)。 因此，我們可以在第一時(shí)間進(jìn)行測(cè)試，我們必須對(duì)教學(xué)情況本身進(jìn)行全面分析。</p>

95、<p>　　部分實(shí)驗(yàn)是在分析教學(xué)情境中，將問題解決方案的各個(gè)階段整合到各層次系統(tǒng)中去。</p><p>　　這是平面構(gòu)成和與其相關(guān)的情況說明類型（Margolinas 1994）。</p><p>　　教師工作分析（減少分析的部分）</p><p>　　S3 - 創(chuàng)新情境- 在這個(gè)階段我們分析數(shù)學(xué)教科書（二年級(jí)或三年級(jí)），分析各種數(shù)學(xué)材料（教育計(jì)劃...

96、），具體研究立體幾何、向量代數(shù)和解析幾何。我們想要選擇問題，學(xué)生不能用學(xué)習(xí)過的簡(jiǎn)單算法解決問題，學(xué)生可以使用數(shù)學(xué)和其他學(xué)習(xí)科目的不同部分的知識(shí)。創(chuàng)新情境的完成將為下一情境做好鋪墊。</p><p>　　S2 - 構(gòu)造情境 - 教師將嘗試尋找例子，這些例子在S3的創(chuàng)新情境中有定義，另一方面也在情境S1中去定義，他們將能夠認(rèn)識(shí)到這些例子。目標(biāo)是為學(xué)生選擇一個(gè)有用的問題，幫助他找到已經(jīng)提出假設(shè)的H1，H2，H3和H4四

97、個(gè)問題的答案。他們是學(xué)生們可以利用的例子，即Q1，Q2，Q2'，Q2“，Q3和Q4解決問題的例子。</p><p>　　S1 - 計(jì)劃情況 - 在情況S1中，教師寫下一個(gè)例子的文本，然后“投射”到他的解決方案中。學(xué)生會(huì)受教師意識(shí)的影響。這也是一種涉及學(xué)生活動(dòng)的情況。學(xué)生可以通過構(gòu)建立方體截面的方式解決問題，然后發(fā)現(xiàn)其他點(diǎn)是否為平面點(diǎn);或者學(xué)生解決他編寫平面的參數(shù)方程的問題，并且發(fā)現(xiàn)第四點(diǎn)是否是該平面的點(diǎn);

98、或者他將向量的共線性或共面性應(yīng)用于“重心”問題的解決（但這種解決方案沒有任何假設(shè)）。</p><p>　　S0 - 教學(xué)情境 - 在這種情況下，我們分析并對(duì)新知識(shí)進(jìn)行總結(jié)并給出結(jié)論以及制定問題。老師考慮到教學(xué)的目標(biāo)，并對(duì)學(xué)生的解決方案進(jìn)行評(píng)價(jià)。這是一種分析教師工作和分析學(xué)生工作的情境，而教學(xué)情境將是教學(xué)過程的結(jié)果。</p><p><b>　　結(jié)論</b></

99、p><p>　　在教授立體幾何時(shí)出現(xiàn)的問題是數(shù)學(xué)立體幾何問題的某一部分。有了這個(gè)問題，也就解決了立體幾何問題。具體來說，學(xué)生有問題解決問題，學(xué)生可以參照他們?cè)谥袑W(xué)的知識(shí)水平和學(xué)習(xí)水平在不同的理論框架下解決問題，但學(xué)生只有用學(xué)習(xí)過的簡(jiǎn)單算法才能解決問題。</p><p>　　研究的目標(biāo)是提出學(xué)生知識(shí)應(yīng)用在解決立體幾何中不同部分?jǐn)?shù)學(xué)問題的知識(shí)方面存在的問題，并通過教學(xué)實(shí)驗(yàn)驗(yàn)證假設(shè)來驗(yàn)證其有效性或無

100、效性。</p><p>　　實(shí)驗(yàn)也在大學(xué)（大學(xué)生是未來的數(shù)學(xué)教師）中進(jìn)行，并證實(shí)我們?cè)趹?yīng)用學(xué)生的知識(shí)中存在類似的問題，這些問題來自立體幾何學(xué)中不同部分的數(shù)學(xué)以及其他學(xué)科知識(shí)。因此，教師更喜歡教學(xué)中的具體部分（在數(shù)學(xué)課上），所以老師經(jīng)常摒棄具有統(tǒng)一性的例子。</p><p>　　這項(xiàng)工作的結(jié)論包括各個(gè)任務(wù)的集合，我們（當(dāng)然）希望從立體幾何中擴(kuò)展任何有趣的應(yīng)用程序問題（任務(wù)），這可以提高數(shù)學(xué)課

101、程的質(zhì)量。 因此，作為中學(xué)數(shù)學(xué)書籍文本的一部分，對(duì)這些任務(wù)的收集并進(jìn)行修正以供實(shí)際使用。 在接下來的實(shí)驗(yàn)中，我們希望嘗試寫出教育性論文來解決立體幾何體的某些部分問題。 課本教材將特別針對(duì)立體幾何中各個(gè)部分知識(shí)之間的協(xié)調(diào)性，從而更多提及科目之間的關(guān)系，即提到應(yīng)用其他學(xué)科（尤其是物理學(xué)）的知識(shí)應(yīng)用于立體幾何教學(xué)和解決立體幾何問題的可能性。</p><p><b>　　參考文獻(xiàn)</b></p

102、><p>　　Balacheff N.: Une étude des processus de preures en mathématiques chez des éléves de college, Gre-</p><p>　　noble, 1998</p><p>　　Berthelot R.: The role of sp

103、atial knowings in the elementary teaching of geometry, Zborník brati-</p><p>　　slavského seminára z teórie vyu?ovania matematiky, 2001</p><p>　　Bereková H., Földesi

104、ová L., Hríbiková I., Regecová M., Tren?anský I.: Slovník teórie didak- tických situácií, 1. ?as?, Zborník 4 príspevkov na seminári z teórie vyu?ovani

105、a matematiky,</p><p>　　Univerzita Komenského, Bratislava, 2001</p><p>　　Bereková H., Földesiová L., Regecová M., Krem?árová L., Slávi?ková M., Tren?a

106、nský I., Vankú? P., Zámo?íková Z.: Slovník teórie didaktických situácií, 2. ?as?, Zborník 5 príspevkov na</p><p>　　seminári z teórie vyu?

107、ovania matematiky, Univerzita Komenského, Bratislava, 2003</p><p>　　Brousseau G.: Fondaments et méthods de la didactique des mathématiques, Recherches en Didac-</p><p>　　tique des