Training and developing algorithmic thinking for students in technical universities though the course of descriptive geometry

MINISTRY OF EDUCATION AND TRAINING HANOI NATIONAL UNIVERSITY OF EDUCATION HOANG VAN TAI TRAINING AND DEVELOPING ALGORITHMIC THINKING FOR STUDENTS IN TECHNICAL UNIVERSITIES THROUGH THE COURSE OF DESCRIPTIVE GEOMETRY Major: THEORY & METHODOLOGY OF MATHEMATIC EDUCATION Code: 62 14 01 11 THE SUMMARY OF DOCTORAL DISSERTATION IN SCIENCE EDUCATION HA NOI – 2016 The work was completed at: Department of Mathematics - Hanoi National University of Education Scientific supervior: Prof Bui Van Nghi PhD Reviewer 1: Assoc Prof Trinh Thanh Hai PhD Thai Nguyen University of Sciences Reviewer 2: Assoc Prof Nguyen Xuan Thao PhD Hanoi University of Science and Technology Reviewer 3: Assoc Prof Nguyen Anh Tuan PhD Hanoi National University of Education The dissertation will be defended before the Council of dissertation assessment or at: Hanoi National University of Education At: on ……/……/ 2016 The dissertation can be further referred at: - National Library of Vietnam - Library of Hanoi National University of Education PREAMBLE Reason of study + Improvement of learner’s capability: Conference of UNESCO in 2003 presented a report which analyzed clearly significant changes on the need and demand of knowledge society for students, especially capability of problem solution and innovation of thought + Role of Descriptive geometry in Technical universities: Helping learners to present and read drawings, and build up the cooperation and creativity in career + Practical teaching of descriptive geometry shows that: Although this course is very essential for the profession, its results of teaching and studying are not high One of the reasons is the method of teaching and studying, of which students not grasp the algorithm in each solution If an appropriate method is applied, this weakness will be improved to foster the effectiveness of teaching and studying + Development of thinking for students: To understand and solve problems on descriptive geometry, students are not only good at spatial imagination but also be able to solve problems in a logical and accurate manner and well apply procedures, basic mathematical problems and other rules of basic procedures and problems In addition, students are encougared to propose the alternative ways to solve mathematical problems by different procedures All those things create a type of thought, called Algorithmic Thinking It is not only necessary for the course of descriptive geometry but also for the life + Regarding to the relevant researches: There are several researches on the development of innovative thinking, logical thinking, algorithmic thinking for students, but they not mention about training and developing algorithmic thinking for students of technical universities For the above mentioned reasons, the chosen subject is “Training and developing algorithmic thinking for students of technical universities though the course of descriptive geometry” Scientific theory According to the theoretical and practical base on development of algorithmic thinking for learners, if during the course of descriptive geometry, trainers equip students the basic algorithm and create opportunities for them to propose algorithm as well as improve gradually the level of algorithmic application, students shall have better learning outcomes and develop their algorithmic thinking Goal and mission of study + Goal: Proposing methods of training and developing algorithmic thinking for students of technical universities through the course of descriptive geometry,in order to help students with better learning results and development of algorithmic thinking + Mission of study: To gain the above goals, the missions include: (1) Brief introduction on thinking; algorithmic thinking and its role, through published scientific documents (2) Practical investigation on the studying of descriptive geometry and development of algorithmic thinking for students of technical universities (3) Proposing methods of training and developing algorithmic thinking for students of technical universities through the course of descriptive geometry,in order to help students with better learning results and development of algorithmic thinking (4) Implementation of pedagogical experiment to evaluate the posibility and effectiveness of the study Research method Main methods applied in this thesis are: + Theoretical studies (performing tasks (1), (3)); + Survey and Observation (performing tasks (2), (4)); + Pedagogical experiment (performing tasks (4); Objects and scope of study - Object of study is a process of teaching descriptive geometry, training and developing algorithmic thinking for students of technical universities - Scope of study: Content, teaching program of the descriptive geometry course in the technical universities New contribution of the study + For theoretical Perspectives - Generalize the domestic and abroad researches and systematize theoretical perspectives on algorithm, algorithmic thinking and development of algorithmic thinking in teaching mathematics - Actual situations on training and developing algorithmic thinking for students in teaching and learning the course of descriptive geometry in technical universities - Propose possible and effective solutions for training and developing algorithmic thinking for students in teaching and learning the course of descriptive geometry in technical universities + For pracical perspectives - Study results contribute to the innovation and improvement of teaching and learning quality of descriptive geometry in technical universities - It is a useful reference document for colleagues and students in technical universities Defended issues (1) There are domestic and aboard researches on algorithm, algorithmic thinking and development of algorithmic thinking in teaching Mathematics, Informatics, Computer Science, however the issues of training and developing algorithmic thinking for students in technical universities during the course of descriptive geometry has not been studied yet (2) There are some shortcomings on teaching and learning descriptive geometry in technical universities that affect the teaching effectiveness and quality of this course (3) Mesures to train and develop the algorithmic thinking for students in technical universities during the course of descriptive geometry proposed in this research are possible and effective Study structure Besides preamble and conculsion, this thesis consits of 03 chapters Chapter 1: Theoretical and practical base Chapter 2: Measures to train and develop algorithmic thinking for students in teaching Descriptive geometry Chapter 3: Pedagogical experiment Chapter THEORETICAL AND PRACTICAL BASE 1.1 Brief of study 1.1.1 Abroad researches on algorithm and algorithmic thinking 1.1.1.1 For algorithm and teaching algorithm * Research on the appearance of “algorithm”, Morten Misfeldt (2015) indicated that: The appearance of the algorithm is associated with the birth of Mathematics Evgeniy Semakin Khenner and Igor (2014) stated: The algorithm describes the sequence of actions (plan), which are performed strictly according to the instructions to solve the problems in a finite number of steps According to Robert J Sternberg (2000), in daily life, we have learned some algorithms and ocassionally created it to guide others to something * Research on teaching algorithm, Evgeniy Semakin Khenner and Igor (2014) stated: The algorithmic teaching has also appeared very early, in the form of puzzle or fun maths The book of Levitin Anany (2008) presented many algorithms and exercises with programming puzzles and algorithms The book of Thomas H Cormen (2009) introduced the algorithm 3E, which is used at many universities worldwide Marasaeli, Jacob perrenet, Wim M.G zwaneveld jochems and Bert (2011) has proposed four abstract levels in the algorithmic thinking of students corresponding to those of algorithm as follows: (1) Implementation level; (2) Program level; (3) Object level; and (4) Problem level 1.1.1.2 For algorithmic thinking Studies of algorithmic thinking in a foreign country are consistent with the concept of algorithm in Informatics According COMAP (Consortium for Mathematics and Its Applications) (1997): "Algorithmic thinking" is one kind of a mathematical thinking The expression of algorithmic thinking is: Application of algorithm; Development of algorithm; Analysis of algorithm; Noting the problem without algorithmic solution According to Gerald and Julia Moschitz Futschek (2011), algorithmic thinking is an important capability in Informatics that can be separated with the learning of computer programming 1.1.2 Domestic researches 1.1.2.1 For algorithm and teaching algorithm In essence, each calculation, rules for calculation and solving the equations are algorithm In Geometry, there are some algorithms such as: drawing with a ruler and compass At university, algorithms are also found, for example: calculating the definite, higer equatations, matrix inversion and determinant… Nguyen Ba Kim and Vu Duong Thuy (1992) defined the algorithm as followings: “The algorithm is considered as a descriptive rule of the clearly accurate instructions helps people (or machines) to perform a series of actions with the aim of achieving its propsed goals or solving a certain problem It is not an exact definition but merely a statement which helps us to imagine the concept of algorithm intuitively” Bùi Văn Nghị (1996) used the definition on algorithm of the two above authors and added the concept “algorithmic procedure” Vương Dương Minh (1996) studied “Development of algorithmic thinking for students while teaching numeration system in high schools" The author has given a definition of algorithm as follows: "Algorithm is an accurate and simple rule of limited numbers of primary actions following a definite order specified on the object so that we will obtain desired results after perporming that procedure” Some authors also identified the two concepts, "algorithm" and "algorithm" such as works of Chu Cẩm Thơ (2015), Nguyễn Chí Trung (2015) 1.1.2.2 For algorithmic thinking and development of algorithmic thinking There are domestic researches on development of algorithmic thinking for students For instance, a research of Vũ Quốc Chung (1995) on fostering capacities of thinking for students in the final grade of primary school; a work of Nguyễn Thái Hòe (1997) on training the thinking for students via mathematic exercises; works of Nguyễn Đình Hùng (1996), Nguyễn Văn Thuận (2004) on developing logical thinking for students; awork of Tôn Thân (1995), Trần Luận (1996) on fostering creative thinking for students Among the domestic researches on algorithm and algorithmic thinking, it can be counted for Trần Thúc Trình (1975), Nguyễn Bá Kim (1992, 2011, 2015), Vương Dương Minh (1996) Bùi Văn Nghị (1996) Nguyen Ba Kim (2011) suggested that algorithmic thinking is shown in the following activities: (i) Implementing the activities following the certain order in accordance with a provided algorithm; (ii) Anlalyzing an activity based on performance of its components in a certain order; (iii) Describing exactly the process of conducting an activity; (iv) Generalizing an activity on a group of objects from an activity; (v) Comparing different methods to perform the same work in order to find the optimal solution Based on the research results on algorithm and algorithmic thinking, the conclusion is summarized as follows: - The domestic and abroad authors agree with the concept of algorithm in Computer Science and Informatics However, the researchers in mathematics education in domestic schools only concern about the concept of algorithm in intuitive manner Meanwhile, researchers in Computer Science and Informatics can not stop at this limit, especially when they need to prove the non-existence of an algorithm to solve a problem; an algorithm based on the Turing machine or recursive function are required - It is nesscessary to distinguish algorithm in science from algorithm in daily life If a solution process does not consit of specific and clear actions to gain a good result, it only is considered an algorithmic-like process - Many abroad authors assumed “algorithmic thinking” in the meaning of strict in Computer Science and Informatics; some domestic authors considered algorithmic thinking as an algorithmic-like process 1.2 Concepts on algorithm and algorithmic thinking in this thesis 1.2.1 Algorithmic concepts In this thesis, we assume: The algorithm is considered as a descriptive rule of the clearly accurate instructions helps people (or machines) to perform a series of actions with the aim of achieving its propsed goals or solving a certain problem 1.2.2 Algorithmic thinking concepts We assume that: Thinking is a cogitative way to perceive things, phenomena, and the natural and social relationships and human that is expressed through notion, judgments, and inference These concepts not concentrate on the psychological nature of the cognitive process, but appearance (more intuitive) on the thinking Algorithmic thinking is applied to solve problems through not only algorithm but also “algorithmic process" or “algorithmic-like process" 1.3 Descriptive geometry course in technical universities 1.3.1 Brief history of descriptive geometry Descriptive geometry was introduced by Gaspard Monge (1746-1818) and used in French education system since Century XVIII In Vietnam, since the year 60s of the previous century, when the first universities was established, descriptive geometry was taught officially in Univerity of Technology and Science 1.3.2 Brief introduction of descriptive geometry Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures This course equips the leaners knowledge and skills to understand and draw the technical drawings Knowledge of descriptive geometry is basic, compulsory and minimum for a student in technical universities In descriptive geometry, each point A in the space is represented by only a pair of projection (A1, A2) on two planes of perpendicular projection And vice versa, each pair of projection (A1, A2) on two planes of perpendicular projetions identifies point A in space Thus the representation of spatial projection on two planes of perpendicular projections shall totally define the size and shape of geometrical figures All problems of descriptive geometry are problems of the formatting image; every problem has only one answer Hence, application of algorithm to solve the problems of descriptive geometry can be considered 1.3.3 The expression , the level of algorithmic thinking of students and the opportunity to develop algorithmic thinking in teaching descriptive geometry at the Technical University of block 1.3.3.1 The expression, the level of algorithmic thinking of students expressed through descriptive geometry module Thinking algorithm University students Technical block manifested in descriptive geometry module through the ascending levels of the following: i) To comply with the basic algorithm known in the course of payment; ii) Imagine , performing the entire process of solving the problem, solve the problem according to the block diagram, process simulation or language, or algorithms written into the program; iii) Know how to apply these algorithms known during problem solving; iv) May participate in the proposal, design algorithms in the process of accounting; 2.2 Basic definitions and knowledge in descriptive geometry 2.3 Methods to train and develop algorithmic thinking for students in teaching descriptive geometry 2.3.1 Method 1: select some basic algorithmics and train stydents to well apply them into basic maths in Descriptive geometry 2.3.1.1 Method base: base on the learners; base on the difficulty of descriptive geometry course; base on the content of descriptive geometry 2.3.1.2 Method implementation approach First and foremost, we need to select some basic algorithmics.Those are procedures that problems in Descriptive Geometry will be inferred to If students are trained to be skillfull in those basic Algorithmics, there are more chances for them to solve simple descriptive geometry problems We selected the following basic algorithmics: - Determine a point on a line; - Determine the intersection point of a common line and the projected planes (trace of line); - Determine the vertical projected plane (projected by) (P) contains a given line a (a1, a2); - Determine the true magnitude of a line segment; - Define a line perpendicular to the plane Specifically, Basic algorithmics 1: Determine a point on a line In descriptive geometry, there are some common problems as follows: determine the intersection point of two intersected lines, determine a point of a given triangle or a given tetrahedron, and identify a point in a generatrix of a cylindrical or conical surface These problems are all defined as determining a point on a line Hence, we decided that the algorithmics to determine a point of a straight line is a basic algorithmics Situation 1: line d is a normal line (not perpendicular to the axis x, algorithmics to identify A in d as follows: Step 1: Identify A1  d1 Step 2: Identify A2  d2 so that A1A2  x Situation 2: line d is a special line (which is perpendicular to axis x, also called an edge line) – determined by two points B (B1, B2) and C (C1, C2), algorithmics identifies point A on line d as follows Step 1: determine A1  B1C1 Step 2: determine A2  B1C2 so that A1A2  x, single ratio of a three-point set B1,C1,A1 equals to , single ratio of a three-point set B2,C2,A2: (B1C1, A1) = (B2C2,A2) Therein (BC,A) = AB is a single ratio of a three-point set B, C, A on a AC straight line From this basic algorithmics, we can infer the following algorithmics to solve basic problems: Problem 1.1 Determine a point on plane (ABC): given point M on plane (ABC) = (A1B1C1, A2B2C2) Determine the projection by M2 when vertical projection M1 is known (Figure 1) Algorithms for solving the problem as follows: Step 1: Determine I1 = B1C1 ∩ A1M1; Step 2: Apply basic algorithm to identify I2; Step 3: Apply basic algorithm to identify M2; (If B1C1//A1M1, we identify I1 = B1C1 ∩ A1M1 and follow the same procedure) Figure Problem 1.2 Determine a point on a plane of tetrahedron ABCD Problem 1.3 Given a quadrilateral ABCD  (P) = (V1P, V2P), known vertical projection A1B1C1D1, determine projection by A2B2C2D2 Projection 1.4 Given a plane (ABC), make line b of the plane with given height x Problem 1.5 Determine a point on a cone of revolution Algorithmics 2: determine intersection point of a line and projected planes Given line a (a1, a2), determine intersection point M of a and (P1) and intersection point N of a and (P2) Algorithmic steps to solve the problem as follows: If a straight line is not parallel to the plane of projection, the procedure for determining trace a following Step 1: Determine M2 = a2 ∩ x; Figure Step 2: Apply basic algorithm to identify M1; Step 3: Determine N1 = a1 ∩ x; Step 4: Apply basic algorithm to identify N2 If a is frontal (a2 // x), the intersection N of a and (P2) is identified by B1 and B2 above; If a is surface (a1 // x), the intersection M of a and (P1) is identified by B3 and B4 above Use the basic algorithmics 2, we can solve the basic problems on finding traces of a plain Problem 1.6 Given (P) determined by intersected lines a (a1,a2), b (b1,b2), a and b not parellel to axis x Find traces of plane (P) Problem 1.7 Determine the intersection of the vertical projection plane (P)= (V1P,V2P) with plane (Q) = (a//b) Problem 1.8 Determine the intersection of the vertical projection plane (P)= (V1P,V2P) with plane (Q) = (V1Q,V2Q) Basic algorithmics 3: Determine the vertical projection plane (projection by) containing a given line Basic algorithmics 4: indentify the real magnitude of a segment Basic algorithmics 5: identify a line perpendicular to a plane Problem 1.9 Identify distance from point A (A1, A2) to plane (P) in following cases: (P) = (V1P, V2P);b) (P) = (a x b) Problem 1.10 Identify distance from A to line d 2.3.2 Method 2: Train the students to use some mehods to demonstrate algorithmics in teaching descriptive geometry 2.3.2.1 Method base: base on the significance of the block diagram; base on teaching method of algorithmics 2.3.2.2 How to implement the method + When teaching Descriptive Geometry, teachers need to combine analysis to solve problems with algorithmic demonstration This combination will clarify the analysis and the students also can learn about algorithmic demonstration Lecturers can select some cases and activities for modeling, and then ask students to practice some similar cases Example 2.3.1: when teaching about second basic algorithmics, besides this oral description, we can demonstrate algorithmics by simulation language as follows: Beginning: If a1 // x Then a a ∩ P2 = ϕ, a ∩ P1 = M, with M2 = x ∩ a2, M1M2 x; And if a1 x Then consider a2 If a2//x then a ∩ P1 = ϕ, a ∩ P2 = N so N1 = x ∩ a1, N1N2 x if a2 x then a ∩ P1 = M so M2 = x ∩ a2, N1= a1 x, M1M2 x, N1N2 x ending Schematic illustration (Figure 3): Figure + Instruct students to practice some similar examples Example 2.3.2 Demonstrate algorithmics by block diagram to identify the line perpendicular to plane Schematic illustraction: (Figure 4) (a) (b) (c) Figure 2.3.3 Method 3: create opportunites for students to joind hands in building and propose some algorithmics in solving some problems in descriptive geometry 2.3.3.1 Method bases: Base on process of training and develop algorithmic thinking mentioned in orientation in chapter 2; base on plate-tectonic theory and operational perspective; base on the needs of developing capacity of leaners; base on memory effectiveness; base on course contents; 2.3.3.2 How to implement the method (1) Select the problems demonstrates many cases and give chance for leaners to cooperate, discuss, propose algorithmic solution for each case Example 3: Relative position of two distinguished lines, situations: Situation 1: two normal lines; Situation 2: one normal line and one special line Situation 3: two special lines: with two normal lines, possibilities for two projections of the same name: intersected by two, parallel by two, an intersected pair and a parallel pair When two projection pairs of the same name intersect by two: whether two intersection points lie on the same alignment line The same possibility happens for the rest of situations Hence, a discussion among students can be organized: what is the relative position of each following schemetic? (Figure 5) Figure 2.3.4 Method 4: Apply different algorithmics in descriptive geometry and practical application 2.3.4.1 Method base + Base on objectives of the descriptive geometry course of technical universities; + Base on the orientation of developing capacity for learners; 2.3.4.2 How to implement the method First approach: train the students to identify the intersection of two surfaces in line with level of increasing difficulty: interface of 02 polyhedrons; interface of 01 polyhedron and 01 curved surface; interface of 02 curved surfaces; intersection of 03 surfaces We need to combine several times of following algorithmics: - Algorithmics to identify intersection of two planes; - Algorithmics to identify the intersection point of line and plane; Moreover, we need to use auxiliary planes and identify intersection points of both planes on each auxiliary plane The problem now is to identify the intersection of lines on the auxiliary plane For example: find the intersection of of two cylindrical surfaces: let (R) parallel to generatrix of two cylinders; find intersection of two conical surfaces: let (R) go through conical peak and parallel to the generatrix of the cylindrical surface; find the intersection of two conical surfaces: let (R) contain line connecting two peaks of both cones… Example 4: Identify the intersection between an oblique prism with base ∆DEF and a cone S.ABC in the schematic in Figure 6a a b Figure Possible steps to identify the intersection of these two faces: - Identify the auxiliary cross section of vertical projection , δ,… to find the intersection of sides d, e, f of the prism and the cone, we have peaks 1, 2, 3, - Identify the auxiliary cross section of vertical projection by ,… to find the intersection of sides of cone with prism, we have peaks 5, The result is the schematic as in figure 6b * For the intersection of two curved surfaces: we can devide students into groups for researching of each following pairs: (1) Identify intersection of conical faces which share the same base; (2) Identify intersection of a conical face with peak S and a cylindrical face which share the same base; (3) Identify intersection of two conical faces which not share the same base;; (4) Identify the intersection of two cylindrical faces share the same base; (5) Identify the intersection of a conical face and a spherical face; (6) Identify intersection of a cylindrical face and a spherical face Second approach: Combination between Descriptive Geometry and Technical drawing Technical Drawing Module is considered a direct application of the knowledge of Descriptive Geometry In Technical Drawing, students must reach the following requirements: from a drawing, students have to imagazine and present the objects on the axonometric view Descriptive geometry will help us overcome the difficulties in visualizing the object and know the intersection of the two surfaces in the space from given drawings Therefore, during Descriptive geometry, teachers need to train students to be familiar with the drawings and understand the design idea of the drawing Example Given 03 objects as Figure Identify the intersection of surfaces? Present those intersections on multiview drawing Figure Third approach: Assign each group of students to perform the assignments: Researching an architectal work or creating an architectual form based on the intersection of 02 surfaces Example Design "pluripotent" bottle cap which can cover three types of bottles as follows: A round cap with diameter of a; A square cap with a side of a; A isosceles triangle cap with the bottom side of a and its height of a (Figure 9) Figure The needed cap should be the common part of three circular cylinders with vertical sections respectively in shape of the three above mentioned bottles The problem will be determined to identify the intersection of three cylinder surfaces (three surfaces of these three cylinders) 2.4 Conclusion of Chapter Our solution is to focus on training algorithms in soving the problems of descriptive geomestry for students This solution has helped students to learn this course more efficiently and develop their algorithmic thinking We asume that the initial actions should be noted to form, train amd develop gradually algorithmic thinking for students Firstly, students need to become familiar with the basic algorithm (foundation, core) and practice to master that through basic problems (Method 1); training them some forms of algorithmic represetation (Method 2); Then they can propose their own algorithims in a simple way (Method 3) Finally, the measure to help them to combine and apply many algorithms effectively (Method 4) Chapter PEDAGOGICAL EXPERIMENT 3.1 Pedagogical experiment purposes, methods and organization 3.1.1 Purposes of pedagogical experiment Pedagogical experiment aims at assessing the feasibility and effectiveness of measures in training and developing algorithmic thinking for technology students through the module of Descriptive Geometry proposed in the thesis 3.1.2 Pedagogical experiment methods and organization Pedagogical experiment is conducted in two phases, with units per phase: Phase 1: Unit to be taught from September to 14, 2013, Unit from September 23 to 28, 2013, at the Hanoi campus of University of Mining and Geology The class chosen for pedagogical experiment was K58 Oil Refinery (with 60 students), taught by Lecturer Hoang Van Tai, in curriculums presented in Section 3.2 of the thesis; whilst the control class was K58 Engineering Geology (with 60 students) taught by Lecturer Le Thi Thanh Hang, in self-written curriculum Unit –“Determining traces of a plane" practice (tasks on position estimates, including periods); Unit - "Distance" practice (tasks on trigonometry including periods) Phase 2: Unit to be taught from September to 13, 2013, Unit from September 22 to 27, 2013, at the Vung Tau campus of University of Mining and Geology The class chosen for pedagogical experiment was K59 Drilling and Production (with 53 students), taught by Lecturer Hoang Van Tai, in curriculums presented in Section 3.2 of the thesis; whilst the control class was K59 Mining Geodesy (with 51 students) taught by Lecturer Vu Huu Tuyen, in self-written curriculum The units were identical as in Phase The lecturers of pedagogical experiment classes and control classes teach the same subject, of approximately the same age, seniority and pedagogic capacity (as identified by the Department) 3.1.3 Pedagogical experiment preparation Step 1: Preparing lesson plans and questionnaire for observers and students on experimental lessons Step 2: Department discussion, aiming to an agreement on experiemental teaching purpose, organization, content, method and result assessment, and on the test (questions, pedagogical goals, scale and answer key); Step 3: Conducting experimental lessons, collecting comments of observers and students through the questionnaire Step 4: 45-minute test after each lesson for the experimental class and control class occured at the same time, with the same questions and answer keys Step 5: Pedagogical experiment results processing 3.1.4 Pedagogical experiment hypothesis Students would have a better understanding of the topics, distributing to the development of their algorithmic thinking if taught to the curriculum based on training methods for algorithmic thinking development as proprosed in Chapter II of the thesis 3.2 Pedagogical experiment content (Experimental lesson plans attached in the thesis) 3.3 Pedagogical experiment result assessment + Qualitative Assessment: by questionnaires done by 226 students participating in the lessons and 20 observers + Quantitative Assessment: by two tests after each experimental lesson: classifying, creating table charts, bar charts and statistical hypothesis testing For instance, the comparation of post-experimental result of the 1st test of the 1st phase between the experimental class and the control class is demonstrated in the chart below: Chart Comparation of the 1st test result 3.4 Summary of Chapter III Pedagogical experiment was conducted in two phases, each one of them took place at the campus of University of Mining and Geology (in Hanoi and Vung Tau), with two classes taught by pedagogical experiment and two control classes Pedagogical experiment results are assessed by tests with participation of 240 students (both times) and 20 observers Despite the fact that the pedagogical experiment was conducted in a small scale, the results have shown that: - The feasibility and effectiveness of pedagogical experiment plans were reassured; - Dual goals obtained in experimental lessons: The students having a better understanding of lesson contents and contributing to the development of their algorithmic thinking CONCLUSIONS AND RECOMMENDATIONS CONCLUSION The thesis has the following results: (1) Briefly introduce domestic and abroad research results on teaching algorithm and development of algorithmic thinking for learners; (2) Present the sientific base of development of algorithmic thinking for students in technical universities through teaching the descriptive geometry: Conception of algorithm, algorithmic thinking, demand and means for development of algorithmic thinking for learners (3) Propose 04 methods to train and develop the algorithmic thinking based on required procedures and goals of the descriptive geometry course for students in technical universities (4) Carry out the pedagogical experiment at two educational facilities of University of Mining and Geology (Hanoi and Vung Tau) REQUEST Oriented curriculum development , capacity -oriented learners, so it takes time for students to apply what they have learned into practice career , solve problems arising from the practice Thus the increase in the length module , increasing the time and enhance the practice of occupational activity is an important issue and needed Opinion, should have at least credits of this module can be reduced by difficulties in teaching and learning modules for both teachers and students PUBLISHED WORKS OF THE AUTHOR RELATING TO THE THESIS Hoang Van Tai – Vu Huu Tuyen (2012), Designing situations of teaching the procedure defined the poit projection via “Trigonometry problem” in Desriptive Geometry, Journal of Education Science, ISN 0868 – 3662, No 84, page 28 – 30 Hoang Van Tai (2014), Development of algorithmic thinking for students through teaching Descriptive Geometry, Journal of Science, ISN 0868 – 3719, Volume 59, page 121 – 128 Hoang Van Tai – Nguyen Thi Huong Lan (2015), Algorithmic thinking in problems defined the trace of plane (Descriptive Geometry), Journal of Science, ISN 2354 – 0753, Special edition in 10/2015, page 123 – 125 Hoang Van Tai – Nguyen Thi Huong Lan (2015), Cooperative teaching “Defining the intersection line of 02 quadric planes” in Descriptive Geometry at University of Mining and Geology, Journal of Education, ISN 2354 – 0753, Special edition in 10/2015, page 126 – 128 Hoang Van Tai (2016), Algorithm development thinking for students of technical universities through block modules descriptive geometry, Journal of Education Science, ISN 0868 – 3662, Special edition in 01/2016, page 45 – 47 Hoang Van Tai (2016), Algorithm development thinking and problemsolving capacity for students in teaching descriptive geometry, Journal of Science, ISN 2354 – 0753, No 377, page 47 – 49 [...]... base of development of algorithmic thinking for students in technical universities through teaching the descriptive geometry: Conception of algorithm, algorithmic thinking, demand and means for development of algorithmic thinking for learners (3) Propose 04 methods to train and develop the algorithmic thinking based on required procedures and goals of the descriptive geometry course for students in technical. .. basic knowledge to understand and draw technical drawings, also contributes to develop spatial imagination, algorithmic thinking, creative thinking for students, engineers, architects, industrial art painter during their work Therefore, teaching the course of descriptive geometry in the direction of training and development of algorthmic thinking for students of technical universities are justified... Descriptive Geometry In Technical Drawing, students must reach the following requirements: from a drawing, students have to imagazine and present the objects on the axonometric view Descriptive geometry will help us overcome the difficulties in visualizing the object and know the intersection of the two surfaces in the space from given drawings Therefore, during Descriptive geometry, teachers need to train students. .. goals obtained in experimental lessons: The students having a better understanding of lesson contents and contributing to the development of their algorithmic thinking CONCLUSIONS AND RECOMMENDATIONS CONCLUSION The thesis has the following results: (1) Briefly introduce domestic and abroad research results on teaching algorithm and development of algorithmic thinking for learners; (2) Present the sientific... of teaching discriptive geometry 2.2 Basic definitions and knowledge in descriptive geometry 2.3 Methods to train and develop algorithmic thinking for students in teaching descriptive geometry 2.3.1 Method 1: select some basic algorithmics and train stydents to well apply them into basic maths in Descriptive geometry 2.3.1.1 Method base: base on the learners; base on the difficulty of descriptive geometry. .. geometry, the learners are required to have spatial imagination and logically reasoning ability 1.4.2 Investigating practical situation of teaching and learning descriptive geometry in technical universities We have designed and used Questionnaire on teaching and learning the descriptive geometry for 250 2nd year students - term 57 and 58 at two educational institutions of the University of Mining and Geology... surfaces of these three cylinders) 2.4 Conclusion of Chapter 2 Our solution is to focus on training algorithms in soving the problems of descriptive geomestry for students This solution has helped students to learn this course more efficiently and develop their algorithmic thinking We asume that the initial actions should be noted to form, train amd develop gradually algorithmic thinking for students. .. following basic algorithmics: - Determine a point on a line; - Determine the intersection point of a common line and the projected planes (trace of line); - Determine the vertical projected plane (projected by) (P) contains a given line a (a1, a2); - Determine the true magnitude of a line segment; - Define a line perpendicular to the plane Specifically, Basic algorithmics 1: Determine a point on a line In. .. descriptive geometry course of technical universities; + Base on the orientation of developing capacity for learners; 2.3.4.2 How to implement the method First approach: train the students to identify the intersection of two surfaces in line with 3 level of increasing difficulty: interface of 02 polyhedrons; interface of 01 polyhedron and 01 curved surface; interface of 02 curved surfaces; intersection of 03... TRAIN AND DEVELOP ALGORITHMIC THINKING FOR STUDENTS IN TEACHING DISCRIPTIVE GEOMETRY 2.1 Measures building orientation (1) Orders of measures should be suitable to procedures of forming and developing algorithmic thinking for students (2) Measures proposed should be suitable to students and perception process of leaners (3) Measures should be feasible and effective (4) Measures aim to innovate the