Peer Review

The material is based on quadratic optimization without letting the technicality to get in the way. The concepts are valid, and the content is complete and appropriate. The approach is appropriate under human supervision. This material is good to let students get to understand the issue at stake, freely explore, elaborate conjectures and come up with answers in a non-threatening environment (no equations apart from one of the parabolas).

Questions that have been asked are rhetorical and there is no attempt to enter or validate the answers that users may come up with. There is no final answer. So, one might leave the simulation without having understood what it was about. Therefore, without human guidance or incentive, it might be difficult for a student to complete this material.

The learning goal of optimization is clear, and it can be used for that purpose. However, there is more since we are interested in the parameters for which the situation is such and such... This is much more demanding than simply understanding an optimum, but the flexibility of the material is not so great that it could be used in a variety of different ways. In this simulation, student has to fiddle with the parameters in order to achieve some particular states, such as the maximum perimeter for x=1, which is a=1, and where the maximum is reached for both the perimeter and the area (ba=3 and the rectangle is a square). But the answers to these questions, or the algebraic tools to tackle them, are not given. A parabola in the form of y=-ax^2+b is shown, driven by the parameters a and b, together with an inscribed rectangle between the x-axis and the parabola. The side of the rectangle is draggable. The associated perimeter and area  can be drawn. The issue is to understand how these two (quadratic) functions behave and where they reach their maxima, and how this maximum depends on the parameters. The final answer (1/a for the perimeter and √(b/3a) for the area) is not given and not so easy to get so this material is surely intended as an introductory material, or else the prerequisite knowledge is much higher: basic algebra and parabola summit computation.

The flexibility of the material is not great. It can be used for 2 purposes: understanding the notion of maximum (of the perimeter or of the area depending on fixed parameters a,b), and the much more demanding task of understanding how this maximum behaves relatively to the parameters: a and b. There is no algebraic or numerical development afterwards.

The parameters are set to an interesting choice so the user is invited to drag what can be dragged (the side of the rectangle), then they are invited to check the boxes that can be checked by making the graphs of the area and perimeter appear and disappear. 

There are questions but nowhere to enter an answer in the new feature of Geogebra classroom which would be ideal in this setup: questions can be asked, answers can be given and checked, students’ results can be gathered and discussed.