Making research about open questions

blog, en, mtbos, mtbos-week2, work, open questions, research

[This post is part of MTBoS mentoring program [2]. This is post number #2 and is related to “My favorite” topic [3].]

I work in an adults school. My official curriculum [1] stablishes that my students of the last course, ESPA 4th1, have to make an scholar’s work about anything which “involves mathematical ideas and procedures” and they have to deliver a memorandum of the following process and their main conclusions. The teacher has to guide them through the process. This is my favorite.

When I change from teenagers education to adults school, this was my main challenge. I had not done this before. After two years in the adults school, I can defend myself against this. My main constraint is the time: the time for doing the work is very limited. My course is just 4-month course and I have to teach 3 lessons. So a month per lesson. And we have one month for the work. And they have to redact in a scientific style the work and they usually do not have any idea of how to do it. So, how do I do?

  • I have 4 classes per week. In the first month, I spend one class per week to make a mock work2. We try to answer to the question: “Which is the most non-contaminant can in the market?” It serves to us to see the 5 phases in a scientific work:
  • After this mock work, I push them out for thinking their question of the work. In my opinion “Without question there is no answer to give” and so there is no possible work. After a month, if someone does not have any question, I give them a list of possible questions or topics.
  • After that, I continue normal classes and I assign them a big homework: start the research and feedback with me any progress, difficulty or decission they’ve made. In this moment I use the theorical authonomy of 18+ years persons3. I encorage to share and ask me anything in any moment, in any class, via email or in the flesh. I remember their duty to deliver the memorandum, I ask them how is their progress once a week and how close is the deadline.
  • In the final two weeks of the course, they write the memorandum. This is the most difficult thing for them. Telling things in assay mode, reasoning each step, giving reasons of each assertion and being impartial are very difficult things for them because they usually do the contrary. I have to teach them “Linguistics” instead of Mathematics.

At the end, it is worthy: each student ends with an answer to a question. The answer could be less or more “developed” (with more or less confidence in its argument) but each of them achieve to solve the question scientificly4. The following are the titles of some works (translated from catalan, their original language)5:

  • Comparison between the gregorial calendar and arabian calendar (Comparació entre el calendari gregorià i el calendari musulmà)
  • Study about the increase of the muscular brute force and muscular resistance in a period of two months (Estudi de l’increment de la força bruta muscular i de la resistència muscular en un temps de dos mesos)
  • Explanation and description of the numerical systems (Explicació i descripció dels sistemes de numeració)
  • Working of existing calendars until the present and explanation of leap-years (Funcionament dels calendaris existents fins a l’actualitat i explicació del funcionament dels anys de traspàs)
  • How much does an epidemic take to kill the population of Mallorca (Quan de temps estaria una epidèmia a acabar amb la població de Mallorca?)
  • Gambling games: from which I could get more? (Jocs d’atzar: amb quin guanyaria més?)
  • \(\pi\), division between the perimeter and diameter of a cicle (\(\pi\), divisió entre el perímetre i diàmetre d’un cercle)
  • Study about crimes in Balearic Islands (Estudi dels delictes a les Illes Balears)
  • How many handicapped people will be in 2020? (Quantes persones amb discapacitat hi haurà l’any 2020?)
  • Types, calculate and elaborations of present bar codes (Tipus, càlcul i elaboració dels codis de barres actuals)
  • Methods for calculating the Consumer Price Index and elaboration of a personal CPI (Métodos para calcular el IPC y elaboración de un IPC personal)
  • Practical testing of the \(\pi\) number and determination of committed error (Comprovació pràctica del valor del nombre \(\pi\) i determinació de l’error comès)
  • Study about Basa metabolic rate and types of diets (Estudi del metabolisme basal i tipus de dietes)
  • How they calculate the unemployment rate (Com es mesura la taxa d’atur?)
  • Study about how the protection affects the endangered animals (Estudi sobre com afecta la protecció als animals en perill d’extinsió)
  • Aplications from Mathematics to diets and sport (Aplicacions de les matemàtiques en el tema de les dietes i l’esport)
  • How did the countries of the world face the economical crisis? (Com varen afrontar la crisi econòmica els països del món?)
  • Analysis of linear, exponential and logistic model in the growth of population (Anàlisi dels models lineal, exponencial i logístic del creixement de la població mundial)
  • Study about the \(CO_2\) emissions of modern vehicles (Estudi sobre les emissions de \(CO_2\) dels vehicles moderns)
  • In the EU, the widest country is the more dense? (Dins la UE el país més extens és alhora el més dens?)
  • What would be the most cheap way to travel to Amsterdam? (Quina seria la trajectòria a seguir per arribar a Amsterdam de ma manera més econòmica possible?)
  • Study about the fuel station in Campos (Estudi de quina benzinera és més econòmica a Campos)
  • The number \(\pi\): history and study of several methods of approximation (El nombre \(\pi\): la història i l’estudi dels diferents mètodes d’aproximació)
  • Relation between the growth of vegetables and the Fibonacci succession (Projecte d’investigació de la relació entre el creixement de vegetals i la successió de Fibonacci)


[1] Cultura de les Illes Balears, C. d’Educació i. Ordre de la consellera d’Educació i cultura de 22 de juliol de 2009, per la qual s’estableix el currículum de l’educació secundària per a persones adultes que condueix a l’obtenció del títol de graduat en educació secundària obligatòria a les illes balears. 2009.

[2] Explore the MTBoS. A new exploration! 2015.

[3] Explore the MTBoS. Week 2 of the 2016 blogging initiative! 2016.

[4] Wikipedia. Education in the united states. educational stages. 2016.

  1. which I think it is formally equivalent to 10th grade of USA [4]

  2. My students have not written a scientific work. If I want they to write it, they need at least one chance to learn.

  3. I suppose that we have to guide the teenagers…

  4. Obviosly there are students who don’t pass the work, but normally it’s due to their absence of work not due to the lack of reasoning in their argument.

  5. Any mistake with the translation is mine