For my last project in this master program, I would like to design a learning activity about addition of positive and negative integers. I concern on this problem because based on several interviews that I have done right exactly before leaving Indonesia, some teachers stated that their students faced serious problem with it. Why does it happen? and how will my design would be? Well, this post will be my first series of development that would be happen during the study for my thesis. Check this out.
This is one of assignments given when I was in Realistic Mathematics Education course. We have to describe what steps that the articles show.
The Hypothetical Learning Trajectory (HLT)
By : Dwi Afrini Risma (F112661)
Simon used a brilliant metaphor to describe how a teacher needs to make planning before teaching, i.e. journey metaphor. Based on this metaphor, in order to reach the learning goal, teacher has to make a learning trajectory in which give a guideline for every learning step made. This trajectory is not only describes how the learning process started but also how to shift students progress in thinking from model of to model for. An actual teaching experience in the classroom perhaps will differ from the design because of the students’ thinking and big idea. When teacher experience this situation, they have to revise the design and may implant the new design. This cyclic process is introduced by Simon (1995) with the term hypothetical learning trajectory (HLT).
In Koeno Gravemeijer article, Measurement and Flexible Arithmetic can be begun by situating the classroom teaching experiment on measurement and arithmetic in context of the research that proceeded. In this learning, the goal is to helps students develop a framework of number relations, which would enable them to construe flexible computation strategies for addition and subtraction up to 100. In the design, we use ruler as a model of iterating some measurement unit and the empty number line as a model for of mathematical reasoning. The trajectory of this activity can be seen in the following scheme. Baca lebih lanjut