Understanding by Design : Mathematics


The Context

As a matter of practice, the curriculum in the Philippines is revised every ten years, but the rapid rate of change in education and the fast obsolescence of knowledge necessitate a continual revisiting and updating of the curriculum to make it responsive to emerging changes in the needs of the learner and the society. Thus, the refinement of the curriculum remains to be a work in progress.

Aside from the issue of relevance, the refinement of the secondary education curriculum was guided by the need, as articulated in the Education for All Plan 2015, to streamline its content in order to improve student mastery and contribute to the attainment of functional literacy. This became a primary consideration in the design of the curriculum and the formulation of standards and the essential understandings from which the content of the curriculum was derived.

The results of national and international assessments were reviewed and analyzed for their implications for teaching and learning. The findings were used to further tighten the standards and improve the delivery of the curriculum and the teaching-learning process. The results of the evaluation of the implementation of the 2002 Basic Education Curriculum were likewise considered in the review of the curriculum. The findings and recommendations (see Annex A) guided the training of teachers and the capacity-building of school heads in managing the pilot test of the curriculum in 23 secondary schools nationwide.

The Process

The refinement of the curriculum followed the Understanding by Design (UbD) model developed by Jay McTighe and Grant Wiggins.

The curriculum design has the following elements:

Stage 1

A. Results/Desired Outcomes, which define what students should be able to know and do at the end of the program, course, or unit of study; generally expressed in terms of overall goals, and specifically defined in terms of content and performance standards

A.1. Content standards, which specify the essential knowledge (includes the most important and enduring ideas, issues, principles and concepts from the disciplines), skills and habits of mind that should be taught and learned. They answer the question, “What should students know and be able to do?”

A.2. Performance standards, which express the degree or quality of proficiency that students are expected to demonstrate in relation to the content standards. They answer the question, “How well must students do their work?” or “At what level of performance would the student be appropriately qualified or certified?”

B. Essential Understandings, which are the big and enduring ideas at the heart of the discipline and which we want the children to remember even long after they leave school

C. Essential Questions, which are open-ended, provocative questions that spark thinking and further inquiry into the essential meanings and understandings

D. Curriculum Objectives, which are expressed in terms of knowledge and skills that teachers can use as guide in formulating their own classroom objectives

Stage 2

A. Assessment, which defines acceptable evidence of student’s attainment of desired results; determines authentic performance tasks that the student is expected to do to demonstrate the desired understandings; and defines the criteria against which the student’s performances or products shall be judged.

B. Products and Performances, which are the evidence of students’ learning and a demonstration of their conceptual understanding, and content and skill acquisition

Stage 3

A. Learning Plan, which details the instructional activities that students will go through to attain the standards

A.1. Instructional Activities, which are aligned with the standards and are designed to promote attainment of desired results. Questions to guide the review of Stages 1 to 3 are provided in Annex B.

A series of consultations with critical stakeholders: students, teachers, school heads, parents, supervisors, industry, local government officials, the religious, and experts from the academe, among others, were made to validate and further refine the formulation of standards, the essential understandings, the essential questions, and the assessment criteria and the tools to measure students’ products and performances. Workshops were conducted to draft the curriculum documents, write the instructional plan and develop lesson exemplars.

Teachers were trained and school heads from the 23 identified pilot schools underwent capacity-building to prepare them for the management of the try-out of the curriculum. The schools were identified based on their location (i.e., Luzon, Visayas, Mindanao) and the type of program (i.e., regular high school, specialist high school) they offer.

Meetings with school heads and classroom visits were made on a quarterly basis to monitor the try-out of the curriculum. Teachers’ feedback on the lesson guides became the basis for further refinement of the standards and the other elements of the curriculum.

Education supervisors were later trained on providing instructional support to teachers. A follow-through training was subsequently conducted to further equip them with the tools of supervision given the requirements of the program.


Initial feedback from the teachers has been useful in further improving the design of the curriculum. What has evolved from the try-out is a core curriculum that builds on and retains the principles of the 2002 BEC (i.e., constructivism, integrative teaching) and integrates the richness of the special curricular programs (Arts, Sports, Engineering and Science Education Program, Journalism, Technical-Vocational Program, and Foreign Language). The latter shall be offered in schools as special interest areas which children can pursue among many other career options in livelihood education. The curriculum has the following features:

What is being envisaged is that the core curriculum shall be implemented with special curricular programs: special program in the arts (SPA), special program in sports (SPS), special program in journalism (SPJ), special program in foreign language, special science/math (S&T), technical-vocational program (tech-voc) being offered on the side, to develop the students’ multiple intelligences.

Mathematics Curriculum Framework

The goal of basic education is functional literacy for all. In line with this goal, the learner in Mathematics should demonstrate the following core competencies: problem solving, communicating mathematically, reasoning mathematically and making connections and representations.

The macro skills critical to these four competencies are computational skills and comprehension, application to real life, creative and critical thinking and visual imagery.

These competencies and skills are expected to be developed using approaches such as practical work/outdoor activities, mathematical investigations/games and puzzles, and the use of ICT and integration with other disciplines. The theories underpinning these approaches are Experiential Learning of David Kolb, Constructivism and Cooperative Learning.

Values inherent in Mathematics such as accuracy, patience, honesty, objectivity, creativity and hard work are developed integratively in the teaching-learning process.


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