How do you look violent while modeling

Ideas to prepare
and implementation of the modeling phase


In the following text it is assumed that all pupils in the class only deal with the real problem "Species Extinction in Our Time - Crises of Evolution" will deal with. This selection was made by the teacher alone or after a discussion with the young people in the class.

Overview of all pages prepared for the real problem
 In the sitemap to "extinction of species today: depleted nature? - crises of evolution" an overview is given of (a) all prepared aids for mathematical modeling, (b) the use of new tools and (c) the self-organization of learning.
Teachers should consult this sitemap when preparing their lessons. Because in this way they also recognize what they can point out in the classroom as a moderator.
The additional information on the issue (including facts and data sets) is deliberately not always formulated in the language of the "pupils". The everyday life of television and the press as well as science is reflected here.    
Addressee groups,
that are addressed with this real problem

With the real problem "Species extinction in our time - crises of evolution", pupils in grades 8 to 11 can be addressed in mathematics as well as in politics and / or economics. However, it is realistically assumed that the project will be carried out in math.

Relation to society and opportunities for cooperation
with other subjects

With "Some glimpses of the extinction of species today and the crises of biological evolution"Teachers - and also young people - can see the social significance of species conservation for future generations and how quickly developments are happening today and possibly irreversible.
Cooperation with the subject teachers for politics and / or economics may therefore be not necessary, but helpful. Perhaps there is also a mother or father among the parents in the small group who is competent in the relevant issues. These parents and also the mentioned subject teachers can be called in as advisors for the small group and invited to the school if the small group deals with detailed questions on the matter, among other things.

And what does all of this have to do with math?

If this problem is dealt with in mathematics lessons, the focus is on mathematical modeling. Depending on the selected sub-problem, the following math can occur:
from grade 8 or 9
Perceive and / or collect data on the facts and present them in value tables and graphs;
Compare and interpret line or bar charts or histograms; if necessary read off doubling times;
Use the created graphs to formulate extrapolations or forecasts or trends. Specify the uncertainty of a forecast.
Planning a survey, designing questionnaires, carrying out a survey, evaluating the survey using the means of descriptive statistics and interpreting the evaluation;
Calculate extrapolations, formulate and interpret forecasts; Growth function;
Model and simulate internal and external system dynamics.
from grade 10 as before and:
Function concept, function term determine on the basis of points; "Speed" of growth; Derivative function; Minimi and maxima;

Small group work based on division of labor on different questions about the problem

The youngsters can use a Possible image discussions and a message about the "death by the wayside" get into the topic.
After a short discussion in the whole class, the possible questions lead to "Are species extinct today? Decline in biodiversity? How steadily, how hard? Crises in Biological Evolution? "Invites students to choose, based on their interests, to work on one of the following areas:

This decision for one question area already leads to the formation of small groups. Further decisions about which analysis or construction or questioning requirements should be carried out then lead to a final, work-sharing, small group work in the class.
Remarks:The previously specified pages can be printed out and distributed to the small groups like worksheets. They only need the computer when the young people want to do research on the Internet or want to get mathematical aids or want to present or discuss something on the forum.


Description and presentation of general and content-related skills

All colleagues who want to help with the preparation of solution ideas are cordially invited.
Contact partner see information


Competencies that students can acquire in class:

  • in the analysis of effective factors of species extinction and decline in biodiversity
  • in analyzes of the "severity" of species extinction and the decline in biodiversity
  • in further analyzes to accelerate the shrinkage of the rainforest
  • with further analyzes to accelerate the decline of the species
  • in the construction and simulation of internal and external system dynamics for the shrinking of species and of the rainforest
  • in the construction and simulation of a "vicious circle" between weapons production and wars
  • in the design, evaluation and interpretation of a survey on the reasons for the extinction of species and the values ​​of biodiversity

If the analyzes, simulations and surveys are carried out, the written results can be used to diagnose which competencies were acquired and to what degree.

Mathematics as a means of knowledge
 In answering the sub-questions of this real problem, mathematics is a means of deepening knowledge of developments and relationships.    
The role of
Math teacher
 During the preparation and also in the modeling phase, the math teacher usually takes on the role of one competent laypersons.    

Research on the Internet should not be completely prevented. But it can be restricted. There are commented links on the Internet.
When working on the real problem, it is primarily about mathematics and not about the media-pedagogical goal of learning to research on the Internet. This goal can be addressed, but is not central.

Formulation of the results
and presentation of the results
 There is a real problem on the entry page Notes for school pupils.
It can be helpful for teachers to take note of this when preparing the lesson. Because the texts can be printed out and distributed to the young people as a working aid.
The presentations of the pupils have two functions: First, the young people can experience that all presentations together solve the problem more comprehensively. So teamwork made sense.     

Secondly, the presentations form the introduction to the systematisation (following the modeling phase) of "invented" or used math.
As a rule, the "mathematical aids" help with systematisation.
It always joins in, whereas international communication can mean another opportunity in the fall of each year.

International communication and cooperation on the topic is another option
 The real problem is prepared in such a way that it can be solved more comprehensively through the division of labor.
The learning and working environment also provides a forum and a gallery for this purpose, which can also be used for collaborative work.
An international understanding makes sense from the point of view of the matter and is not artificial. See also the Notes for school pupils.
It can be helpful for teachers to take note of this when preparing the lesson. Because these texts can also be printed out and, if necessary, hung up.   

Side effects:
New goals with new media


Comments on "New goals with new media" can be found in the Learning and working environments "designing schools" and "learning with new media" to find.

 The Godparents In this working environment, all colleagues ask for additions or test reports.
In addition to a "paper form", the open forum "Cooperation between teachers" or the closed forum "Didactic questions about math lessons" in this working environment can also be used for feedback.