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 studentcentred. 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.
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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.