Identify Instructional Design That in Line with Teacher’s Philosophy

Mathematics instructional design is a practice of creating students’ mathematical experiences which make the acquisition of knowledge and skill more efficient, effective, and appealing.

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.

Good instructional design takes into account the role the on-screen presentation plays and the role the instructor plays in the experience for the learner. Good instructional design will help to avoid what our math student is experiencing as she tries to grapple with solving linear equations. Good instructional design therefore has to provide accessible skill attainment. (1)

I think the instructional design that appropriate with students is design that developed by Vygotsky, that is social development theory. I choose this theorem because I think that vygotsky theorem development is very close to students, so if we use it on teaching learning process, it will be success.  Vygotsky theory can be explained bellow:

Vygotsky's theory of social cognitive development is complementary to Bandura's social learning theory. Its major thematic thrust is that "social interaction plays a fundamental role in the development of cognition" (Kearsley 1994e). Most of the original work of this theory was done in the context of language learning in children.

An important concept in Vygotsky's theory is that "the potential for cognitive development is limited to a certain time span which he calls the 'zone of proximal development' (Kearsley 1994e). He defines the 'zone of proximal development' as having four learning stages. These stages "range between the lower limit of what the student knows and the upper limits of what the student has the potential of accomplishing"  (Gillani and Relan 1997, 231). The stages can be further broken down as follows (Tharp & Gallimore 1988, 35):

Stage 1 - assistance provided by more capable others (coaches, experts, teachers);

Stage 2 - assistance by self;

Stage 3 - internalization automatization (fossilization); and

Stage 4 - de-automatization: recursiveness through prior stages.

The four stages can be expressed in following diagram:

Another notable aspect of Vygotsky's theory is that it claims "that instruction is most efficient when students engage in activities within a supportive learning environment and when they receive appropriate guidance that is mediated by tools" (Vygotsky 1978, as cited in Gillani & Relan 1997, 231). These instructional tools can be defined as "cognitive strategies, a mentor, peers, computers, printed materials, or any instrument that organizes and provides information for the learner." Their role is "to organize dynamic support to help [learners] complete a task near the upper end of their zone of proximal development [ZPD] and then to systematically withdraw this support as the [learner] move to higher levels of confidence."  ⁽²⁾

This theorem means that teacher can’t teach high topics to students so they can’t understand the topics. But teacher also can’t teach low topics so students very easy to understand the topics and they don’t care to the topics.

The advantages of using this theorem are:

1. By using Vygotsky theorem, students’ psychology is very well, so it can develop their social interaction.
2. Cognitive development is limited to a certain range at any given age.