使用樂高機器人研究數學分數教學之成效分析

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(1)國立屏東教育大學資訊科學系碩士論文使用樂高機器人研究數學分數教學之成效分析. The Research of Using LEGO Mindstorms to Teaching Fraction Number. 研究生：辛. 宜. 指導教授：施弼耀. 中華民國. 一O二. 博士. 年七月.

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(3) 中文摘要本研究目的是應用 LEGO Mindstorms 這套教具，創造出一個真實的學習環境來讓學生認識數學單元裡的分數。目的在於項讓學生了解並認知了解到在現實生活中學習分數的意義與目的。因此打破以往的傳統教學模式，以往的學習方法，來增進並刺激學生們學習。本研究利用 Schon（1987）指出，提出了「在行動中求知」（knowing in action）及「在行動中反省」（reflection in action）的學習概念。前面這兩個概念，即是情境學習理論的重要理論之一，也是本研究提高學生的學習成效，並推動良好的學習策略的關鍵要素。. 關鍵字：數學分數、LEGO Mindstorms、在行動中求知、在行動中反省、情境學習理論。. I.

(4) Abstract The purpose of this research is to apply LEGO Mindstorms to develop an authentic learning environment for teaching fraction. Students are wondering about the purpose of learning mathematics in real life. Therefore, bridge the knowledge and experience will motivate their learning. Schon situated learning (1987) proposed a "knowledge in action" and "reflection in action," to show that environment is important for learning. Meanwhile, context learning theory is one of the important content and to improve the effectiveness of learning, because good learning strategy is the key to effectiveness.. Keyword: Fraction , Knowledge in action , Reflection in action , LEGO Mindstorms ,. Situated learning. II.

(5) Acknowledgements 本研究論文可以順利的完成，首先要誠摯的感謝. 施主任弼耀，這兩年來用. 心指導並且適時地提供協助與關心，敦敦教導，並且總是不厭其詳地給予指導與鼓勵。讓我在這兩年裡獲得許許多多寶貴的經驗與知識，才能順利完成這篇碩士論文。在寫撰寫論文的期間，要感謝我的同學、朋友這兩年來的幫助，讓我的研究生涯過得多采多姿，也留下許多美好難以忘懷的回憶；另外要特別感謝一直陪伴在身旁的家人，總是無條件地幫助我及支持我，做我強大的後盾，讓我能順利的渡過這段求學生涯。許許多多的感謝內心的感謝無法用言語表達，如今所得的成果絕不是一人所及，而是有各位親朋好友的幫忙與協助才能在此與各位分享我的喜悅，謝謝各位協助與支持。. 辛. 宜. 謹誌. 一ｏ一年七月. III.

(6) CONTENTS 中文摘要..................................................................................................... I Abstract ..................................................................................................... II Acknowledgements .................................................................................III CONTENTS............................................................................................ IV Contents of Figures ................................................................................ VI Contents of Tables ................................................................................. VII Chapter 1 Introduction.............................................................................1 Chapter 2 Literature Review ...................................................................2 2.1 Fraction ..............................................................................................2 2.1.1 Concept of fractions ....................................................................2 2.1.2 Aliquots concept ..........................................................................3 2.1.3 The concept of a whole................................................................3 2.1.4 Concept of equivalent fractions ...................................................4 2.2 Robot-Related Applications in Educational Field .............................4 2.3 Instruction and learning perspectives ................................................6 2.4 Situated Learning in Education .........................................................7 Chapter 3 Methodology ............................................................................8 3.1 Research Design ................................................................................8 3.2 Research sample ..............................................................................10 3.3 Research instruments .......................................................................11 3.3.1 Design of teaching activities .....................................................11. IV.

(7) 3.3.2 Teaching tool .............................................................................12 Chapter 4 Results ....................................................................................13 4.1 Object of study.................................................................................13 4.2 Data collection .................................................................................14 Chapter 5 Conclusion .............................................................................18 References ................................................................................................19. V.

(8) Contents of Figures Figure 1 Ignore given in units of volume Q1................................4 Figure2 Ignore given in units of volume Q2…………………....4 Figure 3 Controlled by the molecule Q1 ......................................4 Figure 4 Controlled by the denominator Q1 .................................4 Figure 5 Controlled by the denominator Q2………..……….….4 Figure 6 Design of curriculum and teaching theory .....................9. VI.

(9) Contents of Tables Table 1. Group Sex Statistics ......................................................10 Table 2. Test_avg Group Statistics ..............................................14 Table 3. Independent-Samples t Test ..........................................14 Table 4. Post-Test Answer Rate Statistics ...................................15 Table 5. Prost-Test Group Statistics ............................................16 Table 6. Post-Test the Independent- Samples t Test ...................17 Table 7. 95% Confidence Interval of the Difference ..................17. VII.

(10) Chapter 1 Introduction In traditional classroom, teachers always use an oversimplified way to provide students with knowledge or information in learning fraction number. Although fraction number plays an important role in our daily life, many students are not familiar with it. Graphs are mainly used in teaching fraction number in traditional learning and it results in a memorized knowledge without understanding. Meanwhile, the theories are not well understood and it is difficult for students to apply in different fields. Eventually, students’ motivation is reduced. The purpose of this research is to apply LEGO Mindstorms to develop an authentic learning environment for teaching fraction number. An authentic shopping mall environment is designed to combine with LEGO NXT Robotics for teaching fraction number where the situation is connected with students’ real life. Students are wondering about the purpose of learning mathematics in real life. Learning activities with LEGO Mindstorms robotics have become very popular in different education environments. Many researchers have discussed their effects relating to student performance; LEGO Mindstorms is widely believed that they can be used to motivate learning environment. According to Model of School learning theory (Carroll, 1963), two factors affect students are where to learn and time to learn. Meanwhile, time to learn contains students’learnig speed, quality of teaching, and students' understanding. Therefore, how to develop an authentic learning environment will benefit motivation and performance.Use LEGO Mindstorms to develop an authentic learning environment for teaching fraction number. To show that environment is important for learning. Meanwhile, context learning theory is one of the important content and to improve the effectiveness of learning, because good learning strategy is the key to effectiveness. 1.

(11) Chapter 2 Literature Review 2.1 Fraction The fraction is come from Latin, the mean is broken. The concept originated fraction measurement geometry, the number and nature of the arithmetic operation. In the Columba(1989) and Hunting(1983) are studies indicate it is difficult for children to learn fraction. Focus on equal portions, simple fractions, unit volume and conceptually equivalent fractions. The fraction in mathematics includes many concepts. A fraction simply may be as. , A. necessarily an integer, for example,. . Where A, B is not is the score. The. research fraction to four projects to discuss and analyze and research: 2.1.1 Concept of fractions Piaget, Inhelder , and Szeminska (1960/1970) that students understand the relationship between fractions, you must go through several stages of learning, Piaget called these stages as anticipatory scheme.For example: learning is gradual, students first learn two equal portions, followed by quartering. Piaget et al. Found that students in the treatment length and area fraction related problems, will first handle 1/2, then 1/4, 1/3, 1/5, 1/6. 2.

(12) 2.1.2 Aliquots concept The aliquots refers to a continuous quantity or discrete subdivide into several parts, and each part should be as large (or as much). Bergeron and Herscovics (1987) study shows children aliquots concept is not complete, for example, the majority of third-grade students in dealing with the issue of fraction plates. Only noticed fraction board split into several pieces. Each part of division did not notice whether want to wait. 2.1.3 The concept of a whole The concept of a whole also call unit-whole. That is Fraction Concepts under the sub-concepts (Behr, Wschsmuth & Post ,1988). Figueras, Filloy, and Voldemoros (1987) and Figueras (1989) the children identified unit amount of difficulty into the following three types (Yuh-Chyn Leu, 1991): 1. Ignore given in units of volume Q1: How many of orange in the circle (Figure 1). Q2:. of the bricks coloration (Figure 2).. 2. Controlled by the molecule Q1: How many grapes have colored (Figure 3). 3. Controlled by the denominator Q1: Circle the Q2:. (Figure 4).. balloons. Please filled balloons (Figure 5). 3.

(13) Figure 1. Figure 2. How many grapes have colored Figure 3. Figure 4. Figure 5. 2.1.4 Concept of equivalent fractions Equivalent fractions concept refers to schoolchildren solution "as a fraction symbol or several in several languages to render, and a unit fraction or the contents of more than one substance" concept of required questions (Yuh-Chyn Leu and Jheng-Syong Yu, 2002).. 2.2 Robot-Related Applications in Educational Field The rapid development of new technologies of modern information technology, education researchers can now apply to the actual program to enhance the learning experience and 4.

(14) learning, such as multimedia, interactive whiteboard, smart phones, and robots performing a variety of information and communication technology tools. According to educational researchers that the robot as an instructional assistant or a learning companion can enhance learners’ learning motivation and learning performance (Barker & Ansorge, 2007; Chen, Hung, Lee, & Wei, 2010; Chung,et al., 2010; Fasola & Mataric, 2010; Johnson, 2003; Klassner & Anderson, 2003; Mitnik, Recabarren,Nussbaum, & Soto, 2009; Ruiz-del-Solar & Aviles, 2004). Furthermore, using robot as an instructional assistant or a learning companion, can also enable instructors to provide learning content which facilitating learners to interact with real objects through navigating digital learning content (Jermann, Soller, & Mühlenbrock, 2001).For example, while learners are learning physics, the robot can utilize its capabilities, including rotation, mobility, and acceleration, to explain the Newton’s laws of motion (Mitnik, Nussbaum, & Soto, 2008). In the near future, school-age children are predicted to have educational robots accompanying them in the learning process and assisting them in comprehending the learning materials (Jones, Jo, & Han, 2006). Before discussing robot applications in educational field, it would be important to analyze the types of robots in general.The purpose of this research is to apply LEGO Mindstorms to develop an authentic learning environment for teaching fraction number. 5.

(15) 2.3 Instruction and learning perspectives The two main perspectives, namely learning and instruction, are included in this research. From the learning perspective, learners’ problem solving abilities are very important and could be cultivated through adopting appropriate pedagogies in learning processes. How to cultivate problem solving ability is very critical during childhood while a learner is beginning to learn and receive instruction. Therefore, from the learning perspective while designing the SORC.Using the LEGO Mindstorms NXT to teaching goal is to train and cultivate learners’ problem solving abilities From the instruction perspective, if instructors simply use oral lectures to explain learning materials, sometime learners are not able to comprehend the meaning. In such a situation, instructors can use physical objects or tangible tools for providing learning help. For example, instructors could utilize physical learning materials to enhance learners’ realization about learning contents. However, the problem is that how could an instructor acquire the real-time progress status of each individual learner so as to provide instant help. Traditional learning is no any information and communication technology support. The ICT advancements have made technology enhanced learning (Chen, Lin, & Kinshuk, 2008;Schiaffino, Garcia, & Amandi, 2008) .. 6.

(16) 2.4 Situated Learning in Education "Situated learning" the emergence of the term attention, by the Brown, Collins, & Dugid (1988) and other people. Prior to this, Schon (1987), specialized industry certified professionals learning model of study, Suchman (1987) observation of human-computer interaction phenomena of the people operating the copier, and lave (1984,1987) ethnographic study pairs the popular name of the traditional craft apprenticeship learning process, contains a situated of learning concept (the Zhongbang You, 1994). Knowledge is like language that about situational learning. Many different areas like physical concepts. The learning ( Aufshnaiter, & Welzel, 1997; Limei Yu, 1993), mathematical problem-solving capacity of training Yang (Schoenfeld, 1985; Lampert, 1986; Zhongbang You, 1994), and map cognitive abilities training (Griffin, 1995) empirical results are consistent: the meaning of knowledge must be through use the context of heritage. Learning should be enculturation complete process. In the real-life situation use to expertise opportunity. students understands cultural needs.. 7. Order to meet the.

(17) Chapter 3 Methodology The purpose of this research is to apply LEGO Mindstorms to develop an authentic learning environment for teaching fraction. This study selected the four third grade class of students to investigate object. Have two groups is the experimental group (EG) and the control group (CG).. 3.1 Research Design In. traditional. classroom,. teachers. always. use. an. oversimplified way to provide students with knowledge or information in learning fraction number. Although fraction number plays an important role in our daily life, many students are not familiar with it. Graphs are mainly used in teaching fraction number in traditional learning and it results in a memorized knowledge without understanding. Meanwhile, the theories are not well understood and it is difficult for students to apply in different fields. Eventually, students’ motivation is reduced. In this research use to situated learning and cognitive learning theory are architecture (Figure 6).. 8.

(18) Subject Matter. Students. Logical reasoning. Teaching Objectives Design of curriculum Material. Planning. Designing. Worksheet. Situated Learning. Learning Environment Feedback. Cognitive Learning Theory. Stimulus. Teaching theory Organism Response Consequencece. Evaluation Result Satisfied-goal. Unsatisfied-goal. Advanced learning. Remedial teaching. teaching. Figure 6 Design of curriculum and teaching theory. 9.

(19) 3.2 Research sample In this research sample is the third grade students. They are never use the LEGO NXT. We use the LEGO NXT to teaching fractions. The study subjects select the third grade students. Use situated learning theory to teaching fractions. In this research have two groups. First group is a experimental group (EG). The research students total of 128 people. There are 64 people in this group. This group has 33 boys and 31 girls. Second group is control groups (CG). This group has 32 boys and 32 girls in this group have 64 people (Table 1. Group Sex Statistics). Have two groups: one group use LEGO NXT teaching while the other group is use to traditional teaching. Using LEGO NXT teaching in the research project called the experimental group (EG). Be traditional teaching of this group is called control group (CG). So the experimental group is using the LEGO NXT to teaching student. Control group is using the traditional teaching student in this research.. Groups. All Persons Boy. Girl. 31. 33. 64. 32. 32. 64. 63. 65. 128. Experimental (LEGO NXT Teaching) Control (Traditional Teaching) Total. Table 1. Group Sex Statistics. 10.

(20) 3.3 Research instruments 3.3.1 Design of teaching activities This research tool designed teaching activities according to the literature, textbooks, expert opinions, researchers in the field of practical teaching experience to study.Study was divided into the EG and CG. The CG to textbook-based teaching objectives are divided into(Mathematics textbooks in): 1. The simple fractions. 2. Concept of fractions. 3. Aliquots concept. 4. The concept of a whole. 5. Concept of equivalent fractions. The EG to use the LEGO NXT to teaching objectives are divided into: 1. That student to know what is fractions. 2. Can use LEGO interpretation of scores (proper fraction, improper fractions, mixed numbers). 3. Fraction computing use of Lego. 4. Using LEGO concept of to understand equivalent fractions. 5. Design the one mark to teaching students how to apply fraction.. 11.

(21) 3.3.2 Teaching tool Use the LEGO NXT to teaching student. That student can know the fractions. Design the mark to that student can use LEGO NXT to know apply the fractions. The research this equipment cause by LEGO NXT student motivation to learn. And using LEGO NXT students from the traditional teaching through practical teaching and writing. on. the. blackboard. teaching. plane. into. three-dimensional. There are conventional 2D into 3D.With LEGO teaching model to enhance students' learning effectiveness. Literature cited in the post-test mode. Post-test questions are divided into five major projects, namely concept of fraction, concept of fractions, aliquots concept, the concept of a whole, concept of equivalent fractions.. 12.

(22) Chapter 4 Results 4.1 Object of study Object of Study in the third grade students of regular class, a total of 128. In order to study explanation diagnosed results can be effectively teaching. We chose a semester school third grade the mathematical test scores are compared. Choose the most difference in average scores for the study in four classes. In this research two groups person number is 64 people. EG and CG were divided into two groups, their mathematical average of the pre-test were 75.6667 and 75.6458 (Table 2. Test_avg Group Statistics). Using the Independent-Samples t Test to Validation that four classes quite mathematical ability. We propose the following hypotheses: : : If the F-test of significance> 0.05, should receive two equal the population variance of the null hypothesis should therefore be read [equal variances assumed] out T-test test results. F-test of significance was 0.205> 0.05, should receive two equal population variance null hypothesis. It should read. 「equal. variances assumed」 out of the T-test results. When t = 0.024、 df = 126 、『 sigificance （ 2-taile ）』 0.981 > 0.05(Table 3. Independent-Samples t Test). By Independent-Samples t Test found that these four classes of students math degree and no significant differences.. 13.

(23) Groups. N. Mean. Std. Deviation. Std. Error Mean. EG. 64. 75.6667. 5.36301. .67038. CG. 64. 75.6458. 4.63324. .57916. Test_avg. Table 2. Test_avg Group Statistics. Levene's Test for. t-test for Equality of Means Equality of Variances. F Equal variances. Test_avg. Sig.. 1.622. assumed. t. .205. Equal variances not assumed. Sig.. Mean. Std. Error. (2-tailed). Difference. Difference. df. 0.24. 126. .981. .02083. .88590. 0.24. 123.397. .981. .02083. .88590. Table 3. Independent-Samples t Test. 4.2 Data collection A total of 128 students engaged in the research to learn fractions. Not only in the third grade students also have the professional training students. In this research average is 9-year-old. 64 students are taught in traditional environment and other 64 students are taught with authentic LEGO Mindstorms with a pre-test and post-test. The result of the research reveals that the performance and motivation of students engaged in the authentic Lego Mindstorms environment are better than that of traditional education. In. traditional. classroom,. teachers. always. use. an. oversimplified way to provide students with knowledge or. 14.

(24) information in learning fraction number. This research use LEGO Mindstorms to develop an authentic learning environment for teaching fraction number. To show that environment is important for learning. There are 10 post-test quiz questions. Is divided into five major projects, namely: namely concept of fraction, concept of fractions, aliquots concept, the concept of a whole, concept of equivalent fractions. Each project has four problems.. 4.3 Data Analysis Object of Study in the third grade students of regular class, a total of 128. The post-test have five points. Observe these five characteristics of the students can understand what part is relatively weak. By these five points can come to understand that these two teaching methods, what kind of teaching methods, students answer a higher rate (Table 4 Post-Test Answer Rate Statistics). In answer rate may be found, EG answer rate in the CG. Affect student achievement is that there are significant differences in Q5. EG=71.87% > 56.64%=CG in the Q5. . Q1(n=4). Q2(n=4). Q3(n=4). Q4(n=4). Q5(n=4). EG. 90.23%. 85.15%. 79.29%. 73.82%. 71.87%. CG. 80.85%. 75.78%. 65.62%. 68.75%. 56.64%. Table 4. Post-Test Answer Rate Statistics. 15.

(25) n: A project of four questions. Q1: Namely concept of fraction. Q2: Concept of fractions. Q3: Aliquots concept. Q4: The concept of a whole. Q5: Concept of equivalent fractions.. EG and CG were divided into two groups, their mathematical average of the post-test were 80.39 and 69.53(Table 5. Prost-Test Group Statistics).. Groups. N. Mean. Std. Deviation. Std. Error Mean. EG. 64. 80.39. 4.823. .603. CG. 64. 69.53. 5.096. .637. Post-Test. Table 5. Prost-Test Group Statistics. Use the Independent-Samples t Test. EG and CG which a teaching mode to learn better. We propose the following hypotheses: : F-test of significance was 0.604> 0.05, should receive two equal population variance null hypothesis. It should read 「equal variances assumed」 out of the T-test results. Sigificance（2-taile） 0.000 > 0.05 (Table6. Post-Test the Independent- Samples t Test). Do not accept the null hypothesis. EG and CG can be considered teaching methods will affect the student's learning.. 16.

(26) Levene's Test for. t-test for Equality of Means Equality of Variances. Sig. F. Sig.. t. Mean. (2-tailed) Difference Equal variances assumed. .270. .604. Std. Error. df. 12.382. 126. Difference. .000. 10.859. .877. .000. 10.859. .877. Post-Test 12.382 125.619. Equal variances not assumed. Table 6. Post-Test the Independent- Samples t Test. In the case have significant difference. EG and CG must further explore which one was better. In the 95% Confidence Interval of the Difference can be found. EG value minus the value of CG between ranged from 9.124 to 12.595 (Table7 95% Confidence Interval of the Difference). Visible upper and lower bounds are considered the normal range. EG represents the value of minus 95% of the value of CG is positive. Can be inferred: EG better learning results than CG.. t-test for Equality of Means 95% Confidence Interval of the Difference. PostTest Equal variances assumed Equal variances not assumed Table 7.. Lower. Upper. 9.124. 12.595. 9.124. 12.595. 95% Confidence Interval of the Difference. 17.

(27) Chapter 5 Conclusion In traditional classroom, teachers always use an oversimplified way to provide students with knowledge or information in learning fraction number. Although fraction number plays an important role in our daily life, many students are not familiar with it. Graphs are mainly used in teaching fraction number in traditional learning and it results in a memorized knowledge without understanding. Meanwhile, the theories are not well understood and it is difficult for students to apply in different fields. Eventually, students’ motivation is reduced. Object of Study in the third grade students of regular class. In order to study explanation diagnosed results can be effectively teaching. We chose a semester school third grade the mathematical test scores are compared. Choose the most difference in average scores for the study in four classes. In this research two groups person number is 64 people. By Independent-Samples t Test found that these four classes of students math degree and no significant differences. A total of 128 students engaged in the research to learn fractions. Not only in the third grade students also have the professional training students. In this research average is 9-year-old. 64 students are taught in traditional environment and other 64 students are taught with authentic LEGO Mindstorms with a pre-test and post-test. Schon situated learning (1987) proposed a "knowledge in action" and "reflection in action," to show that environment is important for learning. The purpose of this research is to apply LEGO Mindstorms to develop an authentic learning environment for teaching fraction. Students are wondering about the purpose of learning mathematics in real life. Therefore, bridge the knowledge and experience will motivate their learning. 18.

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