How to Develop Mathematical Design

Instructional mathematical design is a practice of creating students’ mathematical experiences which make the acquisition of knowledge and skill more efficient, effective, and appealing. The purpose of a learning design is to achieve the best solution in solving the problem by utilizing a number of information available. Thus, a design emerged as the human need to solve a problem faced. There are four basic components in the planning of instructional design. The fourth term represents the following questions:

1.         Characteristics of students or teaching participants

2.         Destination

3.         Learning strategies

4.         Evaluation procedures

An instructional design consists of instructional design in general and design of teaching learning mathematics. The elements of instructional design in general are various or type; background or the philosophy; and also the example. The elements of design of teaching learning mathematics are various or type; background; example; comparison or reach marking; and appropriate design.

Before a teacher starts to teach in a class, first he must determine the philosophy, nature; method; and ethic or esthetics, and also the psychology of mathematics. After that he can teach the students that can be in innovative learning or traditional learning. During teaching learning processes there are many aspects that influence it. They are class management, theory or paradigm, context or culture, assessment, learning resources (textbook), philosophy; pedagogy; psychology, media or teaching aid, students worksheet, curriculum or syllabi (lesson plan), method or approach, and also class management. Teacher also must be pay attention on the references and implementation of the learning process. The references consist of formal object and mathematics object. For example to reach an international level, there are some process start from publishing, objective mathematics, reflecting, subjective mathematics, criticizing, and back to publishing.

Here, I will explain about the learning resources, media or teaching aid and students’ worksheet. Learning resources are all good sources of data, people, and the particular form that can be used by learners in learning, either separately or be combined to facilitate learners in achieving learning goals or achieve a certain competence.

There are two types of learning resources:

-    Learning resources are designed (learning resources, by design), the learning resources that are specifically designed or developed as a component of an instructional system to provide facilities directed learning and formal.

-    Learning resources are used (learning resources, by utilization), the learning resources that are not designed specifically for the purpose of learning and its existence can be found, implemented and utilized for the purposes of learning. This learning resources may take from:

a.  Message: information, teaching materials, etc

b. People: teachers, students, etc

c.  Materials: books, pictures, etc

d. Tools or equipment : computer, white board, etc

e.  Approaches, methods, techniques of solving problems

f.  Environment: class, library

Thus, we can conclude that learning resources can be come from many ways, not only based on books and teacher’s note like traditional methods.

Teaching aids is a tool used by teachers, facilitator, or tutors to help learners improve reading and other skills, illustrate or reinforce a skill, fact, or idea and relieve anxiety, fears, or boredom, since many teaching aids are like games.

The aim of teaching aid is to motivate the students to apply his full attention to materials. There are many kinds of teaching aids; they are mathematics card, interactive presentation, worksheet, etc.

One of the characteristics of innovative learning is developing student’s worksheet. It caused the paradigm of learning is learning mathematics is doing some exercises. So we need teaching aids, and on of teaching aids is student’s worksheet.  Student’s worksheet or LKS is a worksheet that contains the information and command/instruction from teachers to students to do a learning activity in the form of work, practice, or in form of the application of learning outcomes to achieve a goal.

A good student’s worksheet must complete the characteristics of worksheet, which is student’s worksheet can promote students to construct their own knowledge of mathematics. On developing student’s worksheet, teacher can use discovery methods, they are structure guide discovery and unstructured guide discovery. So, a student’s worksheet is not only collection of many exercises.

Then, there are four steps in developing good student’s worksheet:

a.     Determining the instructional aims by analyzing the students by identify who are our students and knowing the character of our students

b.     Collects the materials that we need based on instructional aims

c.     Arranging the students worksheet, at least there are materials, tasks, and exercises

d.    Checking the student’s worksheet is it consistent with the instructional aim or not.