Reflection of the First Meeting at Mathematics Instructional Design

Mathematics instructional design was born from the general instructional design. Generally, the important things in the instructional design are various, background and the example. However, mathematics needs more specific things to make it mathematics. Aspects on mathematics will be added reach marking aspects and appropriate aspects. When we have already known about those aspects, then the problem will be going as how to develop the mathematics instructional design. To develop it, we first should be known any aspects influence teaching learning process. So many aspects influence teaching learning process: class management, paradigm/theory teacher use, context/culture, assessment, learning resources, philosophy of teaching, teaching aides, worksheet or activity sheet, syllabi or lesson plan, also method and approach.

(scheme of teaching learning process and its factors)(1)

 

We start from the paradigm, we are going to go to the new paradigm of teaching that students as the main actor in the teaching learning process, students centre. Leaving the old paradigm that teacher as the main actor in education, Indonesia has so many new paradigm of teaching and many methods known by teachers. Both method and approach are students centre and give many chance to students to do competition. Realistic Mathematics, Problem Solving, Constructivism, and others today be the popular approach. I personally like problem solving and problem solving to construct student’s mind.

Lesson plan is teacher’s detailed description of the course of instruction. A daily lesson plan is developed by a teacher to guide class instruction. When a teacher develops any lesson plan, he must remark some important things of arranging lesson plan. They are taking into account the individual difference of learner, encourage active participation of learners, developing culture of reading and writing, provide feedback and follow up, linkage and integration, applying information and communication technology. There are so many ways to teach –we will discuss it at point various method of teaching, so there is also many strategy and creativity creating lesson plan.

Student’s work sheet is one of instrument teacher can use to construct knowledge of his student. Base on problem base learning, students’ work sheets is the soul of this method. Student is given chance to make any relation between one material to another material, make representation, and also do problem solving. By this method, not only constructing the knowledge but also constructs the spirit and soul to create a good personal. There are two types students’ worksheet based on explanation of Marsigit:

Unstructured Student’s Worksheet

Unstructured student worksheet is the sheet that contains the means for the subject matter, as a tool for learner activities that used to deliver lesson. Here, student worksheet is teaching tools that can be used to accelerate learning, encouraging learning among individuals, contain few instructions, written or oral to direct work on learners.

Structured Student Worksheet

This student worksheet contains structured information, examples and tasks. It is designed to guide learners in a work program or subject, with little or no help coaches to achieve learning objectives. It is prepared on the instructions and guidance, so it cannot replace the role of teachers in the classroom.

This reflection is not complete without the cognitive scheme because the important is how to construct the knowledge. Cognitive scheme is not far from schemata. There are some choice of method to educate make the education world be shiny. The new paradigm, students construct their knowledge. Also, we can’t transfer of knowledge to the students. The new paradigm also said that teacher is just as facilitator, not dominate his students, and then teacher must make curriculum that satisfy their students ability. That is some application of scaffolding in learning mathematics. Scaffolding itself is to be defined as interaction among the older to the younger that make the younger can do things beyond his ability(2). Based on mean of scaffolding, this is near to the Zone Proximal Developing (ZPD) of Vygotsky. In ZPD, a student will be developing their ability –in this case, student get problem beyond his  ability- when he gets tutorial from the expert people, teacher or friends that have been expert. Before ZPD, a student has factual and actual area. Both factual and actual areas are the ability of the student to learn by himself or by media but without any people help him. Schemata, based on Piaget on forumpenelitian.blogspot.com(3),, are a human thinking that structured. Schemata have other name cognitive structures. This schema can change and develop to be new schema by assimilation and accommodation processes. Assimilation is cognitive processes that allow student to integrate the new information or experience into student’s old schemata to the new schemata. Accommodation is restructuring the old schemata to new schemata because of experience or information, but can’t be integrated easily like assimilation. A schema is quite important in contextual learning. From the real problem, schema is to be the way also bridge connect real problem to the abstract things in mathematics. Marsigit (2010) show us the iceberg concept by the picture above. From the real problem, start to construct schema continue by constructing knowledge by doing assimilation and accommodation, student construct new scheme to the abstract mathematics(4).

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(1) This scheme captured from Fauzia Rahmawati’s book depend on Marsigit explanation on February 21^st, 2012.

(2) Martini. 2010. Model Pembelajaran Scaffolding. http://martinis1960.wordpress.com/2010/07/29/model-pembelajaran-sc

Accessed at 20:27 September 19, 2011

(3) Forumpenelitian.blogspot.com. Problem Based Learning terhadap Hasil Belajar Matematika. http://www.slideshare.net/guestf6b63af/problem-based-learning-terhadap-hasil-belajar-matematika/download

Accessed at 04:25 September 20, 2011

(4) Marsigit. 2010. Pendekatan Matematika Realistik pada Pembelajaran Pecahan di SMP.  http://staff.uny.ac.id/sites/default/files/penelitian/Marsigit,%20Dr.,%20M.A./Pendekatan%20Matematika%20Realistik%20pada%20Pembelajaran%20Pecahan%20di%20SMP_Penataran%20PMRI%20SMP%20BILANBGAN%20PECAHAN%20MARSIGIT.pdf

Accessed at 05:04 September 20, 2011