Constructivism: A Paradigm Towards Improved Teaching
By: Lerry Tan Cabalinan
Preliminary: A Retrospect of My Teaching Career
I was employed at Southern Christian College, located at the southern part of the Philippines in June 2001 as Executive Secretary to our Human Resource Development Officer. My functions were mostly administrative. It was in the second semester of that year that the school needed a part time mathematics teacher to teach basic mathematics subjects in the tertiary level. Our Human Resource Development Officer (HRDO) approached me to ask if I could teach those subjects knowing that I am a Bachelor of Science in Applied Mathematics graduate. I was hesitant to accept it because I did not have any background in the teaching profession. However, he insisted that I have to accept the teaching job because it would not only increase my salary but also it would help me grow personally. The second reason struck me most. Therefore, I accepted the teaching job.
Since then, I have been teaching basic mathematics subjects. As the days passed by, I found out that I have a passion for teaching and everyday it is growing. Every time I am in my class, I teach them the best I can embracing appropriate teaching strategies and methods for the optimization of the learning process. Such approaches were acquired in the seminarworkshops organized by our school and outside organizations such as the Australian funded programthe Basic Education Assistance for Mindanao (BEAM). In my classrooms, I engaged my students in socalled “technical interest”, as described by Habermas (Grundy, 1987). It is one of the fundamental human interests which influence how knowledge is constructed. My students were directed and lectured in a teachinglearning process that involves motivation, presentation of the subject matter, utilising quizzes and examinations as ways to evaluate their progress.
Despite my half a decade of teaching experience, it seemed that something was still lacking. I felt that I needed to do and explore more on teaching aspects especially related to student learning. From the start of my teaching career I already knew that teaching mathematics is a tough job. It is a challenge for a teacher to let students feel and like mathematics and make it as interesting as their other subjects. Students label mathematics as a dreaded disease. They feel that they have no freedom to express their own ideas or opinion in a mathematics classroom. Those are alternative conceptions that affect students’ learning. Another aspect that affects students’ learning is the language and culture (Tytler, 2002). In our country, even though English is our second language and our medium of instruction, still, students find it difficult to deal with the subject matter in a classroom and sometimes I ended up lecturing in our first language that is, Pilipino or Tagalog.
Reflecting on all those fundamental aspects that affect students’ learning, I realized that I don’t only need to explore teaching aspects and effective students’ learning but also for me to reform and change my practices and views from being a traditionalist teacher to a postmodern one. It is hard to accept but it is the reality, I viewed mathematics as a memorization of formulas and science as accumulation of facts (Treagust et al, 1996). We are not yet half way with our SMEC 611Learning in Science and Mathematics unit endeavours at SMEC but my learning started to unfold “my being a teacher”. My horizon and views on students’ effective learning and mathematics and science subjects are beginning to broaden. The desire and eagerness to learn more about student learning, understanding, prior knowledge, and conceptions especially about science and mathematics, constructivist perspective on learning, probing understanding, and teaching approaches are growing significantly. I want to share everything I gained here at SMEC with my colleagues, especially in the Teacher Education Department.
Introduction
Education is very important to one’s life. It is an essential tool for everyone to be prepared for the future. It is about lifelong learning. Education exists to prepare children for their broader adult roles in the society and it provides knowledge, awareness, training, and skills needed by people in adult life. It is the teacher that helps learners in such preparations. As nurturers we need to change our views and improve our teaching practices for the better that is, embracing new and improved approaches so that our students will be equip with necessary learning and understanding to face the world. Whatever will be the future of our students reflects not only what the school is but the teachers and administrators also. We should bear in mind that the essence of successful instruction and good schools comes from the thoughts and actions of the teachers and school leaders (Glickman, Gordon, & RossGordon, 1998).
I am writing this paper as a “wake up call” not only for myself but also for my colleagues at Southern Christian College especially in the Teacher Education Department who are reluctant for change. I know to change is difficult and some people often resist it; however, as teachers at Southern Christian College we are committed to take initiatives to improve student learning and teacher performance. As teachers, we are expected to take on the role of being a lifelong learner to keep abreast of our field and maintain and further develop our expertise.
This paper is my means to encourage my colleagues that one way to change is to embrace a constructivist epistemology of teaching and learning, a view that acts as a powerful theoretical referent “to build a classroom that maximizes student learning” (Tobin & Tippins, 1993, p. 7 as cited in Treagust et al., 1996). Also, this paper provides my colleagues an understanding and knowledge why it is important to know what students know prior to commencing a new topic in science and mathematics and some ways in organising the teaching and learning process for improved learning.
Students’ Prior Knowledge: Teachers Should Know
There are a lot of challenges in teaching mathematics. One challenge is to know what the prior knowledge is of our students and how they acquire it before we commence a new topic. Our students bring with them an array of prior knowledge and conceptions of the world in coming in to our classes (Tytler, 2002), “they are not empty vessel”(p. 15). Gunstone (1995) emphasized that, “the ideas and beliefs which students holds about learning/teaching/appropriate roles are themselves personal constructions derived from previous experience”(p. 9). It is essential for teachers to be aware of and utilise the prior knowledge of students and have some insights into students’ understandings. Such understanding can be categorised as rote, observational, insightful, and formal (Buxton, 1978). Or it can be relational understandingknowing what to do and why or instrumental understanding–rules without reasons (Skemp, 1976). But whatever kind or level of understanding our students’ have, it is still essential to establish clearly what the students’ think and should attend carefully to their responses. In this sense, teachers can use the information of students’ prior knowledge to create instruction which can avoid the misunderstanding of concept.
Looking for patterns of students’ prior knowledge and understanding is a constructivist approach to teaching. Teachers should be aware of thinking patterns that students typically use for them to anticipate and appreciate their students’ understanding (Dominick & Clark, 1996 as cited in Killen, 2003). Teachers should teach students appropriate thinking skills for them to think constructively rather analytically (De Bono, 1996 as cited in Killen, 2003) since constructive thinking focuses on depth of perception, organization of thinking, creativity, information, emotion, action, and interaction. This notion supports what Bodner (1986) said about constructivist model of knowledge that is “knowledge is constructed in the mind of the learner” (p. 873). Points of constructivism had been mentioning above, so, we need to go further in this aspect for have a deeper understanding.
Aspects of Constructivism
Constructivism is a powerful contemporary paradigm of making sense of how students’ learn and based on the works of psychologists Jean Piaget and Lev Vygotsky. It is a theory of about knowledge and learning which well developed in the recent years. Bryman (2001) asserts that in constructivism social phenomena and their meanings are not only produced through social interaction but are in a constant state of change or revision. In this perspective, learning constructs new presentations and models of reality as human meaningmaking endeavours.
Constructivism is a poststructuralist psychological theory (Doll, 1993) that interprets learning as a recursive, interpretive and building process interrelating with the social and physical world. It also depicts how structures and deeper understanding emerges from a learner as she/he struggles to create meaning. The central organizing principle can be generalized across experiences.
Clements and Battista (1990) emphasized that constructivism is different from traditional instruction and a curricula view of teaching and learning that is based on the students submissively “absorbing” the content or subject matter introduced by others; e.g. authoritative adults, and that teaching is just a transmission of a set of established skills, ideas and concepts.
Furthermore, tenets of constructivism are introduced to further understand students’ learning and their understanding especially with relation to their previous knowledge before a new topic will be introduced. These tenets are also embraced by some proponents:
· Children create or invent knowledge (Clements & Battista 1990).
· Learning should not be regarded as an implanting process (Tytler, 2002).
· Children create new knowledge by reflecting on their mental and physical actions (Clements & Battista 1990).
· Learning is a construction of personal meaning (Tytler, 2002).
· No one true reality exists, only individual interpretations of the world (Clements & Battista 1990).
· Learning is a social process in which children grow into the intellectual life of those who surround them (Bruner, 1986 as cited in Clements & Battista, 1990).
· Learners have the final responsibility for their own learning (Tytler, 2002).
Since knowing what students’ prior knowledge is very much essential to constructive teaching – learning process, we also need to know and understand different constructivist views on learning for us to have a bigger picture of our students’ thinking and understanding in our classroom.
Constructivist Perspectives on Learning
Tytler (2002) introduced three perspectives. He named the first as the personal constructivist perspective. In this view, learning outcomes depend not only on the learners’ learning environment set but also on their knowledge as well. It involves construction of meanings. Learners construct meaning starting from the day they are born and through out their lives, since it is a continuous process.
The second view that Tytler (2002) discussed in his paper is the radical constructivist perspective. In this perspective, knowledge is actively constructed by the learner, and whatever knowledge we build up should be regarded of as having an adaptive function to help us face the world rather than as the discovery of underlying reality (Von Glaserfield, 1993, 1996 as cited in Tytler, 2002). It denies the possibilities that knowledge is directly transmitted between teacher and learner.
The third perspective is the social constructivism. Tytler (2002) stressed that “a social constructivist position focuses our attention on the social processes operating in the classroom by which a teacher promotes a discourse community. This discourse community occurs when students and the teacher ‘coconstruct’ knowledge” (p. 19). Teachers need to function in a classroom as much the same way as the learners do.
Constructivist Approaches for Teaching: Way for Improved Learning

Embracing constructivist approaches to organise teaching of one specific topic in mathematics is one way to improve students’ learning. Tytler (2002) referred these approaches as Constructivist/Conceptual Change (C/CC). In all the learning cycles and models Tytler mentioned, the more profound and interactive cycle introduced by Glasson (1993, as cited by Tytler, 2002) is what I considered more applicable in teaching mathematics. The emphasis of this cycle (Figure 1) is more on social constructivist views into the vitality of language in building conceptions, and the ensuing requirement for clarification and negotiation.



Figure 1. The Glasson’s Learning Cycle
In these cycle, students’ prior knowledge of the subject matter or content are challenged by the teachers by intentionally urging them to explore an event on which their predictions are based, even if such events are possibly not correct. After the exploration, a discussion follows for the students to reevaluate their prior knowledge. In this process for improved learning, students can incorporate exact copies of teacher’s understanding. For the part of the teacher, it explores his/her role in as to how his/her knowledge, understanding, experiences, and philosophy of mathematics support students’ improved learning.
Sample Lesson Plan in Mathematics Using Glasson’s Learning Cycle
Year Level : First Year Secondary Students Section : Heterogeneous Class No. of Students : 40 Prior knowledge required : Fundamental operation of numbers, Fractions, Decimals 
Lesson 1: Topic Title: Percent
§ Teaching Strategy Applied: Glasson’s Learning Cycle To teach this lesson using Glasson’s Learning cycle: exploration, clarification and elaboration.

§ Exploration The teacher begins exploring students’ view about percent by engaging the students in the following activity: – Students will be divided into heterogeneous and cooperative learning groups of 5. – Each group will be given words such as fraction, decimal, and percent. – Students are required to define each word based on their prior knowledge. – After 10 minutes, one representative from each group will present to the class about their output.

§ Clarification After the presentation, the teacher will establish the concept about the topic. Then he/she will provide motivating experiences related to the topic. After which a discussion will follow for the students to reevaluate their ideas. Then the teacher will interpret and clarifies students’ views. 
§ Elaboration
To elaborate further students’ understanding of the topic, students are again divided into groups (same group in the first activity). They will imagine a restaurant as their setting. Each group will be given a set of menufor their imaginative meal and paper bills (play money)as their budget. Each member of the group will have an opportunity to order whatever they desire from the menu. Have the students calculate the bill for his or her imaginative meal: – find the cost of the meal, – the amount of a tip, (They can argue among themselves whether to give or not to give a tip and how much is considered a reasonable tip) – sales tax, and the – total cost.
Another discussion will follow by: – Asking the students how they used and linked their previous knowledge with the new concept to answer the questions in the activity given.
– Discussing with the students on the data and results. Let the class assign to each member of their group the task to share the result. Each member can choose what problem they would like to discuss and share results.
– Asking the students how they interpreted the problem. Let them say step by step the procedures they use in finding the answer. Explanations should include the proper use of terms on the concepts of percent.
– Asking the students to discuss the relationship between fractions and percents.
– Asking the students what they learn today and how does it relate to their lives right now.

Conclusion
I had been teaching in traditional methods for years and I believe that applying in my classroom the learning cycle introduced by Glasson, it is one way to step forward to postmodern approach of teaching and learning. Even criticism to these approaches is noted, that it is better for the students not to challenge their prior knowledge but rather let science or mathematics ideas grow alongside such knowledge until their greater usefulness is evident, I am still affirmative that this cycle is much more applicable for improved learning.
As to aspect of improved teaching, I believe that I presented in this paper the fundamental aspects and theories of constructivism that my colleagues need to know, for them to acquire some insight into improving teaching. With the approaches discussed, one thing that my colleagues should consider is the prior knowledge or concepts our students have, because these are critical elements and should be taken as a starting point (Tylter, 2002).
I further believe that if the teachers’ knowledge and skills improve, the students will also improve. The college will be transformed into a learning community where it creatively adapts to the neverending changes in education and society (Hardy, 2004). Successfully addressing teachers’ needs for new and improved teaching approaches can effect significant and longterm school change. As Wooden (1997: 143, as cited in Hiebert, Gallimore & Stigler, 2002) stressed:
“When you improve a little each day, eventually big things occur….Not tomorrow, not the next day, but eventually a big gain is made. Don’t look for the big, quick improvement. Seek the small improvement one day at a time. That’s the only way it happens – and when it happens, it lasts.”
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