This course I’d like to introduce PBL in my courses of Maths, in the second year of Secondary School (12-13-year-old students). I'm planning and open problem that they have to solve using their knowledge on proportions and percentages. 

Level: 2nd grade of Secondary Education (12-13-year-old students)

Topic: volumes, areas, proportions, percentages, properties of materials, 2D computer design, 3D computer design… 

With this question I’d like to drive the students to the study of geometry and proportions via a problem that, even is not going to be applied (at least for the moment), is a realistic one and whose solutions could be put into practice. 

The question is, for sure, open-ended and, probably, engaging to them (in this point I’m not completely convinced) as they are going to work in a problem that concerns their daily life. 

With respect to the learning goals, I guess the problem will lead the students to learn about surfaces and volumes, as they would have to model the garden and playground space via a scale-model using real figures or computer 3D design (may be both techniques) and thus, many teams will end making a physical scale-model they will have to use also proportions, and also construct regular solid models to simplify the real objects (trees, walls, changing rooms buildings, etc.). 

Of course, this project would also involve another content apart from mathematical aspects (ITC skills, properties of materials, local varieties of trees and bushes…) and if I’m able to design it properly, skills such as leadership, self-confidence, cooperation, etc. 

In my courses it depends on the subject. I’ve got my students working in groups in all the subjects most of the time, but it doesn´t mean that they have interdependent tasks, share responsibilities or depend on each other to arrive to the goal. 

In ITC subjects (Informatics and Technology) I think that I have manage to organize the development of the courses to promote effective collaboration and students really work in that way, though sometimes it’s hard to make them accept that they can only succeed if they work together and cooperate in taking decisions and assuming team’s responsibilities. 

For me it’s more difficult to achieve this goal in Maths. Except for some sessions (usually 1 or 2 per unit) in which I prepare specific cooperative activities, my students are in groups and though they use to interact and help each other, their collaboration is not effective in the sense that their work doesn´t fit the conditions previously mentioned. That’s why I’m planning to design my PBL in the subject of Maths. 

The external collaboration will help the students to connect with real world and that what they are doing has a meaning and could be used in real life. On the other hand, a person who is working continuously in a topic and knows the actual problems that could appear in the process of developing a project will be able to make the students go deeper in the knowledge of this topic. 

I think that it is possible to find collaboration inside and outside the school. Could it be partners experts in one topic (app development for ITC, competition organization for Physical Education, economics in general for a project administration, etc.). From outside the school it would be nice to count with help of some parents that are working in a field related with the topic of one project (business people, restaurant owners, lawyers, architects, (graphic) designers, pharmaceuticals, nutritionists, etc.). I’m quite sure that there are a lot of them with a lot of to explain in our classes and willing to do it. We can also think about collaboration from people from the business around the school (besides, most of them bring their children here) or from some colleagues from other schools that have experience with a determinate kind of project or field of work. It would be a good idea, as well, to find researchers in the topic related with our project, but I find it more difficult. 

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