Designing interdisplinary projects – A suitable way in mathematics integrated teaching

14 HNUE JOURNAL OF SCIENCE DOI: 10.18173/2354-1075.2018-0164 Educational Sciences, 2018, Volume 63, Issue 9, pp. 14-23 This paper is available online at DESIGNING INTERDISPLINARY PROJECTS – A SUITABLE WAY IN MATHEMATICS INTEGRATED TEACHING Nguyen Phuong Chi Faculty of Mathematics and Informatics, Hanoi National University of Education Abstract. Integrated teaching requires teachers to organize and guide students to synthesize knowledge of mathematics and other curriculum subjects to solve problems. Integrated teaching is important because it helps to motivate students, give them opportunities to engage in authentic activities, develop their integrated skills and especially develop their problem solving competence. As an instructional strategy, project-based learning engages students in authentic learning through project work. This approach is appropriate in integerated teaching because it emphasizes learning activities that are long-term, interdisciplinary and student- centred. This paper is aimed to make clear the concepts of integerated curriculum, integrated teaching, project- based learning and interdisciplinary project. In addition, the author proposes the process to design interdisciplinary project work for mathematics classroom and show an illustrate example of this kind of project. Keywords: Integrated curriculum, integrated teaching, project – based learning, interdisciplinary project, mathematics integrated teaching. 1. Introduction Nowadays, mathematics education in Vietnam is changing from content–oriented to competence–oriented. The 29/NQ-TW resolution of fundamental and comprehensive innovation for the Vietnamese education emphasized that the goal of education is to develop for students the practical competence and the competence of applying learned knowledge to the reality. For this reason, the integrated subjects will be constructed to establish the combination among the subjects. The career orientation, practical activities, experimental activities and out of school activities will be more considered ([2]). Integrated teaching or integrated curriculum is currently a trend in the world. This kind of teaching requires teachers to organize and guide students to synthesize knowledge of mathematics and other curriculum subjects to solve problems. Integrated teaching is important because it helps to motivate students, give them opportunities to engage in authentic activities, develop their integrated skills and especially develop their problem solving competence ([11],[16]). Received May 7, 2018. Revised July 25, 2018. Accepted September 1, 2018. Contact Nguyen Phuong Chi, e-mail address: chinp@hnue.edu.vn Designing interdisplinary projects – a suitable way in mathematics integrated teaching 15 One suitable way to teach mathematics in the integrated orientation is applying project-based learning. As an instructional strategy, project-based learning engages students in authentic learning through project work. This approach varies markedly from the traditional teacher-centred classroom and provides students with an “interdisciplinary, student centred” activity that is “integrated with real world issues and practices” ([17]). If teachers can construct interdisplinary projects in the orientation of integrated teaching, students can realize the application of mathematics in others subjects or areas and develop their integrated skills to adapt the continuous changes in everyday lives. This paper aims to answer the following questions: - What is integrated teaching? - What is project – based learning? Why is this approach suitable with integrated teaching approach? - How to design interdisplinary projects in the orientation of integrated teaching for the mathematics classroom? 2. Content 2.1. Integration, Integrated curriculum and Integrated teaching The idea of combining two or more disciplines, pedagogical approaches, groups of people, or skills was first appeared in curricular contexts in the 1920s under the title 'core,' interdisciplinary and integrated curriculum have been widely associated with the progressive education movement ([9],[12],[15]). The main purpose of an integrated curriculum is to develop problem solving competence for students and prepare them for lifelong learning. Researchers may use different words such as “integrated teaching”, “integrated curriculum”, “integration”, “ integrated course”, “cross-curricular teaching” or integrated study” but we should not give definitions for all of this. In this paper, I would like to use the concepts of integration and integrated curiculum from Jacob ([7]) as follow: - “Integration” is "a knowledge view and curricular approach that consciously applies methodology and language from more than one discipline to examine a central theme, issue, problem, topic, or experience.”. - An “interdisciplinary curriculum” is "a knowledge view and curriculum approach that consciously applies methodology and language from more than one discipline to examine a central theme, issue, problem, topic, or experience". The above definition implies that an integrated curriculum applies skills and vocabulary from more than one subject area to examine a central topic ([13]). The Association for Supervision and Curriculum Development (ASCD) maintains that integrated curriculum encompasses different approaches but remains “a way of teaching and learning that does not depend on division of knowledge into separate subjects. Topics are studied because they are interesting and valued by teachers and students concerned, not because they appear in a required course of study ([1]). Another concept that I would like to mention to is “integrated teaching” or “integrative approach”. According to Hartzler ([6]), the “integrated curriculum provides Nguyen Phuong Chi 16 the context for learning, however, instructional practices must make these connections explicit.” The instructional practices can be made explicit in “integrated teaching”. Thus, the concept of “integrated teaching” can be understood as follow: - “Integrated teaching” or “integrated approach” is what teachers apply the “intergrated curriculum” in the teaching process. Yager et al (1981) emphasized that in integrated approaches, the pedagogy is issues oriented and the teacher is someone who is aware "of the needs, problems, and interests of the community and the society where he or she lives and teaches" ([18]). 2.2. Integrated models In attemps to help teachers understand curriculum integration, various authors have presented their models of integrated curriculum ([4],[5],[7],[8],[14]). There are similarities and differencies between authors’ models and approaches of integration but in general, all of them try to describe different methods and degrees of integration as guidelines for educators and teachers to implement in the curriculum and apply in the teaching process. In this paper, I try to apply multidisplinary integration from Drake & Burns (2004) and shared or webbed models for integration from Robin Fogarty (1991). These approaches and models are presented specificcally as follow: - Multidisplinary integration of Drake & Burns ([4]): - Shared model of Robin Fogarty ([5]): Two disciplines focus on shared concepts and skills. Knowledge of the two disciplines are connected through a common topic. -Webbed model from Robin Fogarty ([5]): Multidisciplinary approaches focus primarily on the disciplines. Teachers who use this approach organize standards from the disciplines around a theme ([4], p.8). The disciplines are taught separately but they are connected through a common theme. In this approach, teachers do not need to change the content of the disciplines too much. The squared is a broad theme based on knowledge of many disciplines. The disciplines are taught separately but lean to the common theme. Designing interdisplinary projects – a suitable way in mathematics integrated teaching 17 The above mentioned models have the same property that they try to connect disciplines through a common topic. To apply these models, I will construct interdisciplinary projects which satisfy the following conditions: - The topic of the project is the approach of two or more subjects, one of them is mathematics. - The topic origins from real life situation or situations form other school subjects. - To perform the project, students have to integrate knowledge and skills of mathematics and other school subjects. 2.3 Project – based learning According to Nguyen Van Cuong & Bernd Meier ([10]), project-based learning is an approach in which learners perform a complex task integrated with real world issues and practices. This task is performed actively by learners, from identifying goals, making plan to performing, assessing and creating suitable products. Following is some features of project-based learning ([10]): - Topic relates to situation: The topic of the project origins from situations of the society, profession and real life. The task of the project should contain problems which are suitable with capacities of learners. - Meaningful to the society: Project-based learning can help to connect learning in school to the reality. In ideal cases, project-based learning can bring positive effects to the society. - Student initiated and student interests inquiry: Students can participate in choosing topics and content which are suitable with their capacities and interests. - Integrated content: Learners have to integrate knowledge of various areas or subjects in order to solve a complex task. - Practice skills and reality experience: During performing the project, learners have to combine theory with real world issues and practice. Because of this, they can consolidate and extend learned theory, develop their practice skills and their reality experience. - High independent learners: In project-based learning, learners have to participate actively in the teaching and learning process. This requires and encourage their responsibilities and their creation. Teacher mainly only advise and guide students. However, the level of independence should base on students’ capacities and experience. - Colaborative learning: Projects are often performed by groups. There are collaborations among groups and divisions of works among members in each group. - Create products: During performing the project, products are created. These products are not limited in only theory, they also can be material products-results of practice activities. These products can be used, published or introduced. The above features indicate that project-based learning emphasises learning activities that are long-term, interdisciplinary and student-centred. More specifically, project-based learning is valuable in that they enable pupils to: ([3]) - integrate skills (in applying knowledge; speculative thinking; communication skills; ability to manipulate ideas and materials; etc.) and knowledge from a variety of sources in the process of developing useful outcomes. Nguyen Phuong Chi 18 - become more autonomous – i.e., able to plan, investigate and research aspects of their own learning through taking increasing responsibility for the direction of their own work. The aims of encouraging students to integrate skills and to become autonomous are also parts of the rationale for integrated teaching. Besides, both integrated teaching and project-based learning support problems which origin from real life or other disciplines. Therefore, project-based learning is suitable with the integrative orientation in the teaching process. The problem now is how to construct interdisciplinary projects for the mathematics classrooms. This will be presented in the next part. 2.4. The process of designing interdisciplinary projects for mathematics classroom Interdisciplinary projects are projects which require knowledge and skills of two or more school subjects in the solving process. Here we need to design interdisciplinary projects for mathematics teaching, then these projects must require knowledge of mathematics and other school subjects. Based on the project-based learning process mentioned in Nguyen Van Cuong & Bernd Meier ([10]), I propose the process to design an interdisciplinary project as follow: Step 1: Choose a project topic: To define a topic for the project, teachers need to have a look at the curriculum of mathematics and other subjects, identify knowledge standards and skill standards to find the integrated teaching content. Then they should try to connect the teaching content to the problems of real life. Teacher should raise questions such as: - Which content can be integrated? Why? - Does the topic include a complex task? - Does the topic involve a genuine transfer and integration of knowledge, skills and understanding of mathematics and other school subjects? - Is it suitable with learners’interests? - Does it have reality meaning? - Does it result in an enhanced experience for the learner? Step 2: Identify the project goals To indentify the aims of the interdisplinary project, teachers need to: - Check which knowledge needs to be achieve, which skills need to be trained in each subject. - Identify which competencies can be developed through the topic, especially interdisciplinary competencies. Step 3: Prepare questions, tasks and solutions In this step, teachers need to do the following: - Identify oriented questions to help students in investigating problems and necessary interdisciplinary knowledge. - Identify tasks that students need to do during performing the project. Designing interdisplinary projects – a suitable way in mathematics integrated teaching 19 - Prepare advice and material source for students to construct a proposal and make a plan to answer the questions or do the tasks (Students can divide in groups and make the plan themselve, or they can do it under teachers’ guides) Step 4: Define assessment tools In this step, the following should be notified: - Teacher should design assessment tools for each task so that teacher can adjust the result of the task. - Teacher should encourage students to participate in the assessment and self- assessment process. Some assessment tools can be: - Individual assessment sheets: given to students at the beginning of the project, collected at the end of the project. These sheets help students to assess their competencies themselves and know their changes before and after the project. - Cooperative assessment sheet: given to all students in a group. Each student uses this sheet to assess the cooperative ability of other members in the group. - Project book: given to students at the beginning of the project. This book help teacher to assess the performing process of students. Project book includes initial ideas, performing plan, works division sheets, information, pictures, group discussion sheets, assessment tables. 2.5. Illustrated example Following is an example of an interdisciplinary project which integrates the two subjects Mathematics and Biology through the four –step process. This project can be used in teaching mathematics at grade 11 in upper-secondary schools. PROJECT TITLE: MITOSIS – FUNDAMENTAL BASE FOR REPRODUCTION Step 1: Choose a topic Look at the mathematics and biology curricula at upper-secondary level, we can find that: - In Mathematics, “geometric progression” is an important topic in the upper- secondary level because it has many application in real life and in other disciplines. - In Biology, “geometric progression” can be applied to find how fast a cell reproduce. - Thus, we can choose a Mathematics – Biology interdisciplinary project named “Mitosis – fundamental base for reproduction” Step 2: Identify the project goals - The knowledge needs to be consolidated: In Biology: Mitosis (Grade 10). In Mathematics: Geometric progression and its properties (Grade 11). - The interdisciplinary skill needs to be achieved: Students know how to apply the general term formula of a geometric progression to find the number of cells reproduced in mitosis processes. Step 3: Prepare questions, tasks and solutions Nguyen Phuong Chi 20 Introduce the topic: E. coli is a type of bacteria that normally live in the intestines of people and animals. E.coli can also appear in food products and water resource. The appearance of E.coli in water resource is also a criteria to measure how clean the water source is. Most varieties of E. coli are harmless or cause relatively brief diarrhea. But a few particularly nasty strains can cause severe abdominal cramps, bloody diarrhea and vomiting. Can you imagine how fast E.coli reproduce? What people should do to avoid diseases caused by E.coli? This is a problem in Biology which can be explained by using knowledge in Biology and Mathematics. To help students investigate problems and interdisciplinary knowledge, teachers can give them the following oriented questions: Question 1: The reproduction of E.coli is called “mitosis”. Thus, what is mitosis? Question 2: Can you search information of the time that an E.coli cell needs for one time of mitosis? Question 3: To know how fast E.coli reproduction, please investigate that after one day, how many E.coli cells have been reproduced from one E.coli cell? Find out which mathematics knowledge should be used to answer this question? Question 4: What people should do to avoid diseases caused by E.coli? Based on the above oriented questions, teachers can plan to divide students in 3 groups and give each group the following tasks: Task 1 (for Group 1): Read again the Biology textbook at grade 10 to review the concept of “Mitosis”. Task 2 (for Group 2): Search information of the time that an E.coli cell needs for one time of mitosis. Task 3 (for Group 3): Read again the Algebra and Analysis Textbook at grade 11 to review the concept of a “geometric progression” and its properties. Task 4 ( for Group1,2,3): Answer the question 4. Task 5: (for Group 1,2,3): Discuss about how to avoid diseases caused by E.coli. Teachers should prepare the solutions for the oriented questions and the tasks as follow: Task 1:What is mitosis? Mitosis is the usual method of cell division, characterized typically by the resolving of the chromatin of the nucleus into a threadlike form, which condenses into chromosomes, each of which separates longitudinally into two parts, one part of each chromosome being retained in each of two new cells resulting from the original cell. Task 2: What is the time that an E.coli cell needs for one time of mitosis? If E.coli is apropriately grown, after each 20 minutes, one E.coli cell can be divided into two new E.coli cells. Task 3: The concept of geometric progression and its properties A geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. Designing interdisplinary projects – a suitable way in mathematics integrated teaching 21 - The n-term an of a geometric progression can be found by the formula: an = a1. qn-1, where a1 is the first term of the geometric progression and q is its common ratio. Task 4: Answer for the question 3 From the result of task 2, we know that: After 20 minutes, the number of E.coli cells is 2. After the next 20 minutes, the number of E.coli cells is 2.2 = 22 = 4. After the next 20 minutes, the number of E.