Write a summary of the article in not more than 500 words;
This article was written by Ian Sheppard, an Australian teacher who has taught mathematics for 30 years. In 2004, he started working in a new school where he focused on the Year 12 (age 16-17) mathematics courses. He used constructivist and inquiry based approaches to handle his class. Sheppard worked at Australian Science and Mathematics School (ASMS), with support and encouragement from the mathematics staff. ASMS caters final 3 years of schooling before entry into higher education, designed for highly collaborative, interactive and student-directed teaching and learning. Majority of students comes from local area with wide variety of abilities and aspirations. The school provides strong emphasis on the disciplines of science and mathematics, lifelong learning, relevance of science and mathematics to the world’s future, interconnectedness of knowledge and importance of human communication in all its forms.
Sheppard’s student majority were from MAT (Mathematics and Abstract Thinking) course, had learnt mathematics using constructivist and inquiry-based approach in their Year 10 and 11. Though Year 12 mathematics course is exam-based, Sheppard decide to let the students continue learning under the same approach. The learner is responsible for their own learning. He desire to teach for understanding, rather than for algorithmic proficiency. He rejected to teach using textbook approach. Sheppard want more students to enjoy what they were doing, not just gain a sense of achievement in being able to do mathematics.
The course was centered on core investigations. The worksheets presented problems embedded in conversation or story line. They covered key ideas outlined in the curriculum statement, extensions for further investigations was provided for interested students or who aspiring to an ‘A’. The materials were written in such a way that students can work by themselves, anytime and anywhere. In scheduled class, students usually worked in groups with teacher support.
After complete the core investigation, students make an entry in their notebook, creating their own text book which was permitted in all tests.
Communication of mathematics is promoted by presentation and sharing of findings, through Unseen Orals and Public Presentation Pieces (PPP). The audience consisted of teacher and other groups who had concentrated on different problems. Students demonstrated high level of engagement. A quiz will be conducted each week to allow students to check their understanding and ability to apply the concepts.
During the course, teacher acts more as a facilitator rather than a broadcaster of knowledge. Teacher spends very little time talking to whole group, but to individual or small group, responding to the students’ concern. Most of the students were able to learn well. Some were largely independent, using peer support to clarify and develop understanding while others relied more extensively in staff for directional and support. The classroom atmosphere was collaborative and informal.
Through this course, students increasingly learn independently. Learning occurs as part of a process of constructing knowledge; learners communicate their questions, intuitions, conjectures, reasons, explanation and ideas. Moreover, learning involves developing knowledge, skills and dispositions to think and act in ways which determined by individual effort, the setting of personal goals and self awareness.
Discuss, in not more than 500 words,
(i) how the learning theory shapes your understanding of how students learn mathematics;
(ii) if there are, in your understanding, learning theories that are especially relevant to the teaching and learning of math?
Though many teachers doubt constructivist approach is efficient enough in covering a set syllabus, but with much effort, we will manage to do it.
It is important that students enjoy learning mathematic and make it their responsibility. This will encourage the development of lifelong learners. Teacher should allow space for individual approaches to learning, as different students learn at different ways and rates. Teacher should be flexible to develop a cooperative classroom culture.
In a conducive and encouraging environment, most students are able to learn effectively, though some might relied on facilitator for direction and support. Many students may not fully understand at first time, as it takes time for them to modify existing schema. Hence they should be allowed time to use multiple approaches for understanding. Drill and practice is rather meaningless if students cannot understand what there was doing.
Students construct their own understanding; teacher cannot feed them with information. It is essential for students to understand key ideas; the rest will follows much more easily.
Students can learn mathematics as part of a process of constructing knowledge. By solving problem where the mathematics is presented implicitly, students develop their understanding of the mathematics. By solving problem students reflect upon what they had learned. Also, students will be able to direct their learning according to their interest, capability, goals and current workload.
Teacher understands students more than the curriculum or textbook do. So, curriculum documents and textbook just provide the guidance for designing materials and learning opportunities. Teacher should arrange curriculum according to the development of students.
Creating note book help students to reflect on mathematics and focus on the underlying principles.
Students should learn in group, as it can contribute to the collaborative climate of the classes. The collaborative climate can be further enhanced by the team teaching approach. The extensive use of group work encourages collaboration and the communication of questions, intuitions, conjectures, reasons, explanations and ideas. The learning is refined as students freely discuss their ideas and argue a case until they come to a shared understanding.
Students enjoy working with teacher rather than working for the teaching. In the shared classroom, teacher should act as a facilitator instead of a transmitter of understanding. Before students able to work independently, teacher should stay beside them to model their learning.
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