All students need to be informed of the arbitrary by someone else.
As this excerpt states, that which is arbitrary needs to be informed to the students. This includes the names of things (ex. a four sided shape is called a square), the symbols we use (which have previously been agreed upon), and the conventions we follow (such as why the SI units have the values they have). Students must memorize the association between word and thing it represents. The arbitrary lies in the realm of memory.
Some students can become aware of what is necessary without being informed of it by someone else.
As this excerpt suggests, that which is necessary does not need to be informed. It just is. So it goes. These things can be worked out based on properties and relationships. Relating to previous readings in this course, we require some of those from the arbitrary to explain the necessary. The necessary lies realm of awareness.
In teaching lessons and units, the arbitrary and necessary are interleaved and ubiquitous throughout our teaching. We know how to draw that line, but our students are new to the content, and learning may be improved with greater intentionality on how we introduce different things to our students. For instance, we may follow inquiry-based activities for students to discover arbitrary things using their own vocabulary before we tell them what the word society has agreed upon is. As the last excerpt suggest, the arbitrary is unavoidable. However, I would like to place emphasis on the necessary in terms of assessing how my students are learning. This may include not penalizing arbitrary-related mistakes or by including more visuals so students know the square is the square and not another polygon. As the reading suggests, we can divide curriculum into that which cannot be worked out (might be so), the arbitrary, and can be worked out (must be so), the necessary – it is important for students to also understand which is which.
There is usually a historical context to where the arbitrary things come from. One way to combat the cognitive overload students may experience from dealing with the arbitrary is to include those historical contexts. There is no reason why 360 degrees makes a full circle, but if we teach that the Babylonions used a system based on 60, this may help.
The arbitrary has to be memorized, but what is necessary is about educating their awareness.
No comments:
Post a Comment