Math 2270: Designing Principles

Math 2270: Designing Principles

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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 potentially be able to engage their mathematical exploration using appropriate tools .a good designing principle should encompass creation of cognitive conflict, making connection among representation keeping the exposition shorter by not involving so many steps and is simply straight forward and provide informal analysis before formal analysis. However, with increased technology, more simplified ways has been invented to teach mathematics. These simplified technologies have been used same work to be completed by hand, more efficiently and accurately is referred as amplifier. Reorganizer on the other hand is used to change the way of thinking in math, the task, at most cases would have been difficult to accomplish without engaging technology.

Analysis

From our case, Task A has been categorized as  an amplifier. However, this does not meet  the design principle  since the  parameter  provided  to be used technologically does not support  the users experience  in supporting  his or her thinking  since it does not provide very meaningful  observation  looking on relationship that exists between the parameters. Literally, provided parameters to be used for intersecting cords in GeoGebra are definitely contradicting, which requires critical thinking to understand the concept explained. For instance, checking on provided segment and line, a student may find it hard to clear distinguish their differences, since both cases looks similar. Connection between presentation cannot be easily establish , 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 simple. The design  has also failed in providing informal analysis before the formal one, an aspect that tend to make the process to difficult to understand ,since even establishing the  accuracy of the segment  and arcs  is typically hard.

However task B is categorized as reorganizer and has met the design requirements. This is because; task has tried to simplify the intensity of the problem, by supporting the thinking of the learner on concepts of polygon. The learner can typically have a correct and meaningful observation on the relationship of what he or she understands. The process has also encouraged the use of relevant mathematical tool that goes hand in hand with the real representation of a polygon. The task be has also  simplified  the steps to be  followed in regards to construction  of a polygon, where  informal analysis  has been prioritized , followed by formal where learners are required to take various measurement 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 process that are stipulated in examining special 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 task can both be handled on hand or using technology. To suit the design principle, formulas used should satisfy the learners thinking. Formulas used in solving cubic polynomial in the article fully support learners thinking on 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   connection that arise from presentation provided  at the end of solving the problem. The entire process should also be made short easy and comprehensible, not necessarily following more steps, that may sound hard for students to easily absorb all concepts. For instance, the task can be made as a 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 slider on the graph you can insert minimum gradient and the graph together with gradient will be plotted successfully.

This 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 it can be successfully and accurately   computed