Designing Principles

Designing Principles

Introduction 

Designing activities for student learning mathematics needs a lot of accessible and relevant methods in performing and understanding different concepts. In this case, before designing its essential to consider the user experience in terms of how they may view the mathematical invariant relationship, supporting their thinking, make and test mathematical conjunctures that potentially modify the learners thinking and fostering their curiosity. The learner should possibly be able to engage their mathematical exploration using appropriate tools .a ethical designing principle should encompass the creation of cognitive conflict, making connection among representation keeping the exposition shorter by not involving so many steps and is straight forward and provide informal analysis before formal analysis. However, with increased technology, more simplified ways have been invented to teach mathematics. These simplified technologies have used the same work to completed by hand, more efficiently and accurately is referred to as amplifiers. Reorganizer, on the other hand, is used to change the way of thinking in math; the task, in most cases, would have been challenging to accomplish without engaging technology.

Analysis

From our case, Task A is categorized as an amplifier. However, this does not meet the design principle since the  parameter provided used technologically does not support the users’ experience in helping his or her thinking since it does not give significant observation looking at the relationship that exists between the parameters. Provided parameters to be used for intersecting cords in GeoGebra are contradicting, which requires critical thinking to understand the concept explained. For instance, checking on the produced segment and line, a student may find it hard to distinguish their differences since both cases look similar clearly. The connection between presentation cannot be quickly established, an aspect that makes the process too involving and length as opposed to the requirement of designing principle where it should always be direct and straightforward. The design has also failed in providing informal analysis before the formal one, an aspect that tends to make the process difficult to understand since even establishing the accuracy of the segment and arcs is typically hard.

However, task B is categorized as a reorganizer and has met the design requirements. They meet the design requirements is because; the task has tried to simplify the intensity of the problem by supporting the thinking of the learner on concepts of the polygon. The learner can typically have a correct and meaningful observation of the relationship of what he or she understands. The process has also encouraged the use of a relevant mathematical tool that goes hand in hand with the real representation of a polygon. The task has simplified the steps to follow regarding  the construction of a polygon, where informal analysis is prioritized, followed by formal where learners are required to take various measures to reduce cognitive conflict and supporting their curiosities in knowing more detailed information about the polygon.

Therefore, reorganizer and amplifier are essential tools used to teach mathematics technologically. This can only be achieved if correct design principles are applied. For example, from the article investigating zeros of Cubic’s with GeoGebra,” the steps and processes that are stipulated in examining unique properties of polynomials should be modified. The process is categorized as both amplifier and reorganizer. This is because some tasks can only be best be handles by only engaging technology while other simple tasks can both be handled on hand or using technology. To suit the design principle, formulas used should satisfy the learner’s thinking. Methods used in solving cubic polynomial in the article fully support learners thinking about what he or she understands. This is supported by the fact that where mathematical observation is made meaningful relationship is easily formed in learner’s mind, which fosters curiosity.

However, despite the article being meaningful to learners, it also needs some modification, especially on the process of its simplicity and easiness for student understanding. Instead, the task has to consider asking informal analysis before formal analysis, which will gauge what the students understand about the topic hence helping the student to figure and finding out the connection that arises from the presentation provided at the end of solving the problem. The entire process should also be made short manageable and comprehensible, not necessarily following more steps, that may sound hard for students to absorb all concepts easily. For instance, the task is    reorganizer in the following way:

Task

1. What is the general property of cubic polynomial?
2. Familiar with Geogebra insert the formulae

• To construct a tangent line to , the slider button will be used and parameterize tangent with its slope at any give n point, e.g. (0, 4).

1. Using the slider on the graph, you can insert the minimum gradient, and the chart together with an angle plotted successfully.

The procedure is a reorganized technological means which complies to all processes that best satisfies the design principle. To perform this task manually may be impossible, but by inserting the command into GeoGebra, is  successfully and accurately   computed