Write-Up #2

Question

For demonstration, is it better to graph 5 graphs at once or produce them in sequence adding one at a time? What are the pedogogical implications of this observation?

From my experiences in a classroom, I have found that the smaller the "bites" of information that you feed to your students, the more they understand and retain. Usually if the students see one step at a time, they keep an open mind and try to comprehend the new information they have received. On the other hand, if a teacher bombards a student with information that they have never seen and expect them to keep trying to get it, in most cases the students will become unmotivated to grasp the new material before they fully comprehend it.

Let's look at a quadratic equation, specifically a parabola. If I show the following graph to a group of students who have never seen the graphs of parabolas before, the students will panic.

Students have so much mathematics anxiety, there is no need to perpetuate their anxiety. If the goal is for the students to see that a graph corresponds to an equation, this is definately not the approach to take. It would be much better to show them the following graphs:

The graph below is of the equation

However, if the goal is to show the students that these are some of the many possibilities of quadratic equations, then showing the 5 graphs at once is okay.

In the end, the most important things to consider is the objective that the educator has for the students and the students' prior knowledge of the subject. So use common sense when giving the students new material. Try not to bombard them with all of the details at once.

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