Solution for teacher in organising learning case associated with practical situations in high school

JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1075.2015-0290 Educational Sci., 2015, Vol. 60, No. 8A, pp. 236-242 This paper is available online at SOLUTION FOR TEACHER IN ORGANISING LEARNING CASE ASSOCIATED WITH PRACTICAL SITUATIONS IN HIGH SCHOOL Chu Cam Tho Faculty of Mathematics and Informatics, Hanoi National University of Education Abstract.Vietnamese mathematics teachers continue to waste time to equip students which specified in the textbook and give them the process. Students are not encouraged to discover the challenging exercises that require practicable problem solving ability and complicated thinking formulas, so they are not interested in Math. The problem is that: - Why is it so difficult to teach Mathematics using practical situations? - Can Vietnamese teachers teach Mathematics using practical situations? - How can high school math teachers learn to teach Mathematics using practical situations? To answer three above questions and figure out solutions for teacher to organize teaching case associated with practical situations, this article shows several researches and recommendations. Keyword: Mathematics teaching method, practical situations, high school, teaching case, learning case. 1. Introduction In the real life, mathematics knowledge is frequently used. Having solid mathematics background helps people calculate or estimate rapidly and have logical thinking to solve well not only academic problems but also daily ones. In high school, besides being useful in learning Maths, Physics, Biology, Chemistry, mathematics knowledge also provides students many chances in forming and developing key competencies, namely calculating, logical thinking, problem solving, self-study, communication, cooperating, self-control and technology applying skill (Tran Kieu and co-authors, International senimar of capacity orientation training’s report, Ministry of Education and Training, 2012) Recently, in teaching method innovation wave helps people realize the goal of teaching which aims to bring theory into practice. However, in mathematics teaching, the results of that wave did not meet the requirement. Teachers still did not aware the role of Maths and the influence of teaching methods in student’s learning way. Teachers still waste time to repeat students which specified in the textbook and give them the processed exercises (Nghi Bui Van, 2013). Students have no chance in discovering the challenging exercises that require practicable problem solving ability and complicated thinking formulars, so they are not interested in Maths lessons (Tran Vui, 2010a, 2010b) Received: 15/7/2015. Accepted: 01/9/2015 Contact: Chu Cam Tho, e-mail: camtho@hnue.edu.vn 236 Solution for teacher in organising learning case associated with practical situation in high school The problem is that : - What are the difficulties that impact on Mathematics teaching method that associated with practical situations? - Are teachers able to organise Mathematics teaching cases that associated with practical situations? - How to help Maths teachers in organising Mathematics teaching cases that associated with practical situations in highschool? To answer three above questions and figure out solutions for teacher to organize teaching case associated with practical situations, this article shows several researches and recommendations. 2. Researching result 2.1. Rationale of Mathematics teaching associated with practice requirements UNESCOCultural and Educational program of The United Nations has set the 21st century goal of education is learning to know, learning to do, learning to live together, and learning to be. Therefore, high school education has to create learning activities that be applicable in real life, put learning from practice as main content and teaching method. Recently, educational policy makers all over the world start reforming Mathematics education by reforming content, program and student’s learning method (Garet and co-authors, 2001). These reforming efforts focus on developing problem solving capacity (PSC), Mathematics reflecting and communicating skill in order to help students achieve their both deep and wide Mathematics academic knowledge and gain more career and learning opportunities in the future (National Council of Teachers of Mathematics (NCTM), 2000). Figure 1. Model of Mathematics problem solving capacity (Wu, 2003) According to the above analysis, the capacities that Mathematics education programs care about more or less relate to Mathematics applying in practice, such as problem posing and solving 237 Chu Cam Tho capacity (Figure 1) and modeling capacity. On another hand, Mathematics history demonstrated that firstly, mathematics knowledge came from practice researching and even when it is abstract, it still come for serving reality. If students cannot realize connection of Maths and reality, high school education will lose its role; this was generalized in mathematics characteristics analysis (Kim Nguyen Ba, Mathematics teaching method, 2006) One of recent researches in teaching method associated with practice is Mathematics teaching through survey. This is a teaching approach formed and popular in Education researchers and Maths teachers Association in the UK from 1960s; and was recognized as an effective one since it allows students have an exciting and highly interactive learning environment (Bailey, 2007; Jaworski, 1994; Orton and Frobisher, 1996; Ponte, 2007; Vui Tran, 2010; Duyen Nguyen Thi, 2013) Nowadays, International student assessment programs highly appreciate Mathematics knowledge practice applicable capacity (PISA, IB, so on). It is a challenge for Vietnamese Education on the integration way to ensure training objectives and meet social requirements. 2.2. Difficulties in teaching aims to apply Mathematics in practical in high school In 2012, we conducted a survey of 216 secondary school teachers in Hanoi and Quang Ninh about Mathematics teaching activities. The result is that, in 216 respondents, there are 100% asked people said that almost all (80 – 85%) teaching hours spent on calculating activities, included exercise checking and assigning; 197 respondents (91.2%) said they usually skip exercises, practical model exercises, because they themselves lack of documents, experiences and they don’t think it’s useful for students examinations. Some others think that their students don’t like to do practice related exercises and do not recognize the applicable role of Mathematics into real life. On another hand, while studying some documents of Mathematics teachers and lesson assessment guiding of Hanoi Education and Training Department and Quang Ninh’s one, we found that the criteria “experience innovation” and “practical related teaching” were still not be cared. Compared with some others, namely having excellent students, having fulfillment profiles and recorded documents, “innovative content and teaching methods” is hard to achieve by teacher. While taking part in assessing teachers experience innovation, we recognized that they still choose the “traditional” problems to write like: practicing Mathematics task solving skill, focusing on one type of exercise. Even if some contest was held in order to improve applying background knowledge on practice capacity that authors joined namely The Creative Teacher by teacher National Office and Microsoft; multi – subjects knowledge application and integrating teaching by Secondary Education Department – Ministry of Education and Training; or Science for students, there are rarely qualified Mathematics entries appeared. Vietnam has joined the PISA, but the impact of these contests on Mathematics teaching and learning is not high. However, no denial that open – Mathematics task style and practice – related one are advantages. These styles and contents usually create excitement and help students be more active in learning. 2.3. Measure that help teachers design practice related teaching situation In this article, the measurements was drawn while helping 4 teachers, namely: Tam Dang Thi Minh – teacher of Hanoi Alpha School, Hai Nguyen Huu – postgraduate student, 22th course 238 Solution for teacher in organising learning case associated with practical situation in high school of Hanoi National University of Education (HNUE), Dung Nguyen Thuy – teacher of Trung Vuong Secondary School, Tham Tran Thi – class 10, Uong Bi Education College, part-time course student, design their practice related teaching situation. We take some measures with purposes: - Helping teachers recognise the role of Maths and applying Mathematics knowledge in practice. - Analysing suitable lesson aim for students. - Researching and thinking about practice related knowledge and situation when teaching Maths regularly. - Design and organise practice related teaching situation well. The first: Media helps teachers recognize the role of Maths and applying Mathematics knowledge in practice Through direct discussion with the teachers above, we found that, teachers often lack of motivation and confidence in the properly implement teaching aim and method. Therefore, firstly, we want to help teachers rebuild teaching motivation by supplying scientific information and practical limitation due to the deviation from target teaching. The result is that teachers, who took part in our plan, were impressed and they found another practical reality beside what they usually do (said, Tham Tran Thi and Hai Nguyen Huu). We set up a closed group on social network and a website ( to share teaching ideas, documents and experience. For 2 years, our members have shared on there and they no longer feel alone or differential. At the same time, these experiences helps them overcome difficulties. The result is: Tham Tran Thi selected her graduation thesis and experience innovation related the content: “designing PISA exercises for secondary school students”. Dung Le Thuy took part in the Creative teacher, and was in the final round. She also be an impressive teacher when taking a sample lesson in front of whole school and applying reforms on Maths, Physics and advisor’s work what she has never done before. Hai Nguyen Huu chose the graduation thesis content about “designing practice related teaching situation and training modeling capacity for students”. Tam Dang Thi Minh has applied knowledge of learning project organizing for 6, 7 grade students in Alpha school since early teaching period. The second: Applying Lesson study model and creative Science and Technology technique in order to help teachers design an effective lesson. According to Jica organization’s researches (Saito co-authors, 2007; Lewis, 2009), before building professional activity model, teachers would be helped to have good study lesson, it is the sufficient condition to not only be confident but also like and be convinced of the researching problem’s benefits. We also refer to the study of serveral concerned contents include open problem and mathematics survey. Thanks to the research of Vui Tran (2010), Duyen Nguyen Thi (2012), Handbook PISA (Ministry of Education and Training) we gathered into a material to help teachers with more resources and scientific basis knowledge. In order to help teachers design an effective lesson, we suggest that teachers answer questionnaires: - Who will learn this lesson? - What do students learn this lesson for? 239 Chu Cam Tho - Currently, how do teachers teach this lesson? - Are we able to improve the way of teaching this lesson in order to accord with learner? - What does practical situation related to this lesson? Besides, we used brainstorming and the technique of focal objects (Dung Phan, 2007; Tho Chu Cam, 2010) in order to help teachers more creatively. It is worth sharing that brainstorming being conducted via Groups on social network not only help teachers solve the difficulties of time and space (groups of teachers in many different schools) but the advantages are that all feedback is true. Focal objects paid attention were contents related to the last question "What does practical situation relate to this lesson?" Using these technique, teachers were more confident, opener in thinking and were able to suggest more practical situations. For example, firstly, Hai had never suggested any practical situation related to integral for two days. But after focusing in images associated with "the tip" in solid revolution, Hai spent time observing and he recognized hills in Nghia Do Park or reservoir of hydroelectric may be a good suggestion for his lesson. Then, Hai discussed with other teachers in order to improve his lesson. When Dung had difficulty in finding application of the highest common factor (HCF) and lowest common multiple (LCM) in practice, teachers in Groups took ideas grouping, planting vegetables in plot, organizing party table (Tham), (Tam), ... Figure 2. The adjusting mechanism of the modeling process (Nam Nguyen Danh, Trung Tran, Cuong Dang Xuan, Hong Nguyen Van, 2011) Here is a model that describes the adjusting mechanism to simplify the modeling practical situations into learning situations (Figure 2). Another task is designing learning activities, however this is difficult for teacher. We suggested teachers should use the technique “think about students” in three steps as follows: 240 Solution for teacher in organising learning case associated with practical situation in high school (1) Choose three students from different groups of level and character, then design learning activities for each of them. (2) Put the remaining students into three groups. At this stage, teachers need to predict the difficulties which students can encounter. (3) Design activities for students to overcome the difficulties. We encourage teachers to use that technique combines with two suitable techniques for practical situation teaching, namely four corners and learning in station. The creation of the corners and the station will ensure the aims: divided level, self - control learner and create excitement for students. After completing design lessons, teachers in Group on social network comment on it. Teachers edit lesson plans before teaching experiment. We record teaching experiment videos and upload them to social networks to share them with other teachers. 3. Conclusion For more than a year of implementation, the team has achieved significant results. We have built the teaching and learning situations such as teaching projects: "Bridge" theme associated with three straight points – Mathematics 6, “Business” associated with the topic Statistics - Algebra 7, Project "Occupational Choice" - Algebra 10, "Graphs of quadratic functions" - Algebra 10, HCF – LCM - Mathematics 6, "Explorers of the Human Body" - joint project Biology - Mathematics 6, "Applications of integrals - Analysis 12,"Should we play lots? "- Probability, Algebra and Calculus 11. Although the Ministry of Education and Training require teachers to pay attention and perform design learning activities associated with practical situation. However, from the above studies, we found that the design of situations associated with the practice is not an easy task for teachers. This is not new in the history of education in Vietnam, but for teachers, the teaching routine and pressure from the examinations has created certain obstacles. The results from case studies of four teachers showed that, if teachers have positive and frequent helped hand, they can improve their teaching in order to create the circumstances associated with the practice, in accordance with local conditions and their own ability. REFERENCES [1] Dung Phan, 2010. Creative Methodology. Young Publiser. [2] Ba Kim Nguyen, 2006.Maths teaching method.Hanoi National Education University Publiser. [3] Van Nghi Bui, 2009. Applying Mathematics theories in practice in High schools. Hanoi National Education University Publiser. [4] Van Nghi Bui, 2011. Serial teacher training program (Bacholor degree and Teacher certificate). National Proceeding of Mathematics Education in High schools, Vietnam National Education Publisher. [5] Van Nghi Bui, 2013. Training Mathematics culture to students. Science Magazine, National Education University, No.58 [6] Tho Chu Cam, 2010. Student thinking stimulation messure application in High school Mathermatics teaching. Educational PhD thesis, Hanoi National Education University. [7] Vui Tran, 2007. Using lesson researching to well Mathematics knowledge practicing. Science and Education Magazine, Hue Education University, ISSN 1859 – 1612, No.1(1)(2007). 241 Chu Cam Tho English reference: [8] Anthony, G. Walshaw, M., 2009. Characteristics of Effective Teaching of Mathematics: A View from the West. Journal of Mathematics Education, Vol. 2, No. 2, pp.147-164. [9] Ayres, P. & Sweller, J., 2000. Why Investigations Should Not Be Compulsory in the Years 9–10 Mathematics Courses. Literature Review: Report on Investigational Tasks in Mathematics in Years 9–10 for Advanced and Intermediate Students. New South Wales: University of New South Wales. [10] Bailey, J., 2007.Mathematical investigations: A primary teacher educators narrative journey of professional awareness. In J. Watson & K. Beswick (Eds.) Mathematics: Essential Research, Essential Practice. Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia: MERGA (Vol 1, pp 103-112). [11] Garet and co-authors, 2001. Peer Coaching: Changing classroom practive and Enhancing Student Achivement. www.life-slc.org/learningprinciples/Peer_Coaching.pdf [1] Lewis, C., Perry, R. & Hurd, J., 2009. Improving mathematics instruction through lesson study: A theoretical model and North American case. Journal of Mathematics Teacher Education, 12(4), 285-304. [12] Morgan, C., 1998. Writing Mathematically: The Discourse of Investigation. London: Routledge/Falmer. [13] Nguyễn T Duyến, 2013. Exploring lesson study as a medium to develop mathematics content knowledge for teacher through practice, Proceedings of the 6th International Conference on Education Refrom (ICER 2013): ASEAN Education in the 21st Century, pp 151-159. [14] Ponte, J. P., 2007. Investigations and explorations in the mathematics classroom. ZDM, 39(5-6), 419-430. [15] Saito, E., Harun, I., Kuboki, I., & Sumar, H., 2007. A study on the partnership between school and university to improve mathematics and science education in Indonesia. International Journal of Educational Development, 27(2), 194–204. [16] Tran Vui, 2010a. A combined abduction-induction stratery in teaching mathemtics to gifted students with computer through dynamic representations. Proceeding of Apec Conference on Replicating Exemplary Practices in Mathematics Education. Samui, Thailand. [17] Tran Vui, 2010b. Using open ended task with visual presentations in connecting lesson study with formative assessement. Proceedings of Apec – Chiang Mai International Conference IV: Innovation of Mathematics Teaching and Learning through Lesson Study- Connection between Assessement and Subject Matter. Chiang Mai, Thailand. 242