Problem-based learning (PBL) is a student-centered instructional strategy in which students collaboratively solve problems and reflect on their experiences. It was pioneered and used extensively at McMaster University, Hamilton, Ontario, Canada. Characteristics of PBL are:

• Learning is driven by challenging, open-ended problems.
• Students work in small collaborative groups.
• Teachers take on the role as "facilitators" of learning.

Accordingly, students are encouraged to take responsibility for their group and organize and direct the learning process with support from a tutor or instructor. Advocates of PBL claim it can be used to enhance content knowledge and foster the development of communication, problem-solving, and self-directed learning skill.

(From Wikipedia)

PROBLEM-BASED LEARNING (PBL)

PBL is a learner-centered educational method.

In PBL learners are progressively given more and more responsibility for their own education and become increasingly independent of the teacher for their education. PBL produces independent learners who can continue to learn on their own in life and in their chosen careers. The responsibility of the teacher in PBL is to provide the educational materials and guidance that facilitate learning.

PBL is based on real world problems

In PBL learning is based on the messy, complex problems encountered in the real world as a stimulus for learning and for integrating and organizing learned information in ways that will ensure its recall and application to future problems. The problems in PBL are also designed to challenge learners to develop effective problem-solving and critical thinking skills.

(from http://www.pbli.org/pbl/pbl.htm)

Journal Matematik

Orientations of School Mathematics In Malaysia - Parmjit Singh

Kertas ini membincangkan tentang perkembangan mata pelajaran matematik di sekolah dari segi pembelajaran, pengajaran adan kurikulumnya yang merupakan komponen-komponen utama dalam pendidikan matematik. Ketiga-ketiga ciri ini dibincangkan berasaskan objektif-objektif matematik seperti yang terkandung dalam huraian sukatan mata pelajaran sekolah menengah di Malaysia. Kurikulum matematik sekolah selama ini yang menekankan penghimpunan fakta dna pengetahuan tidak mampu untuk merangsang pemikiran pelajar. Ini adalah kerana sistem pendidikan kita terlalu berorientasikan peperiksaan, akibatnya para guru serta pelajar "mengajar, belajar" untuk peperiksaan dan ini tidak memadai untuk merangsang pemikiran pelajar. Adakah pelajar-pelajar sekolah yang mendapat "A" dalam matematik di peperiksaan kebangsaan merupakan pelajar-pelajar yang berkemampuan berfikir serta menyelesaikan masalah-masalah 'non-routine' dalam matematik? Satu lagi persoalan yang dibincangkan dalam kertas ini adalah mengenai istilah konsep pemahaman (understanding) pelajar-pelajar dalam matematik yang kerap digunakan dalam kalangan para pendidik. Isu yang dibincangkan adalah mengenai jenis pemahamam yang dipraktikkan atau dititiberatkan di alam persekolahan matematik masa kini iaitu "instrumental understanding" dan "relational understanding". Kertas ini tidak menawarkan sesuatu yang baru ataupun suatu formula yang ajaib untuk mengatasi masalah-masalah yang dibentangkan di atas tetapi hanya sebagai suatu pentas untuk 'perturb' pemikiran para pendidik mengenai sistem pendidikan matematik di sekolah-sekolah di Malaysia.

Algebra.....

1. A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.
2. A set together with a pair of binary operations defined on the set. Usually, the set and the operations include an identity element, and the operations are commutative or associative.

(answer.com)