## Theory

This section offers various support materials on bringing more thinking in your classroom.

The purpose of any algorithm is to help one reach the mastery level when it is no longer necessary. This is when we can speak about competence being developed and the initial problem gone (resolved). The learner has acquired what has been learned and is ready for a new competence cycle with new problems. This brings us to the two important outcomes of this stage: the need for the algorithm gone and a new problem recognised.

By the end of Stage 4, the learner is able to do the following:

• make a choice in any problematic situation that falls under the definition of the problem s/he has been working upon
• compare own algorithm for dealing with the problem with those developed by peers and optimise the algorithm if necessary
• collect the data when the algorithm does not seem to work and define a possible new problem

Learning to test one's hypothesis and being able to find its flaws is a central idea behind Stage 3.  Specific learning outcomes will depend on the approach to (dis)proving the hypotheses in a given discipline. In case of the empirical approach to testing, the learner develops an algorithm for dealing with the chosen problem.

By the end of Stage 3, the learner is able to do the following:

• Show the data collected as a result of following the hypothesis
• Select the data where the hypothesis “failed” and choose those examples that will help to further improve the hypothesis
• Demonstrate how the proposed algorithm helps to resolve the problem with previously selected data

It is important to add that the learner should be disposed to treat own hypotheses as models that have drawbacks and applicability limits.

In order to specify the problem chosen at Stage 0, it is necessary to be clear about the elements we are dealing with. This question may appear trivial, however it is the one learners often fail to answer, especially if one asks for more than a mere repetition of the title of a textbook topic. It often takes a very long time to understand the meaning behind such "obvious" things as a sentence in the language classroom or a triangle in a maths lesson. The idea of Stage 1 is to give the learner a chance to "play" with whatever s/he is dealing with in order to reveal those properties that may not be on the surface.

As a result of this “game”, the learner is able to build the “passport” of the elements involved in his/her problem or describe them via parameters and values. This is the main outcome of this stage.

By the end of working at Stage 1, the learner is able to do the following:

• find and recognise the elements s/he is dealing with
• describe elements via parameters and their values
• distinguish between the elements or their forms
• do all of the above in the context of his/her objectives on resolving the chosen problem

The situation of choice is one of the most difficult moments to the learner. Should I put a comma here? Is it a good idea to give as many examples as I can? Which of the formulae is the most suitable one? Instead of a mere guess, the learner masters the skills of developing a hypothesis. The hypothesis on resolving the chosen problem is the main outcome of Stage 2.

By the end of working with Stage 2, the learner is able to do the following:

• define the essential parameters in the context of the chosen problem
• establish a connection between various values of the defined parameters in the "passport"
• formulate a hypothesis on resolving the initial problem based on the established connection

In the language of a teacher, Stage 0 is about diagnostics. The idea is very simple: test what you are going to teach.

Starting with a series of diagnostic tasks helps one understand the need for further learning. In other words, the learner must face a problem. Definition and acceptance of the problem is the main outcome of this stage.

By the end of working at Stage 0, the learner is able to do the following:

• formulate what (s)he would like to achieve (desired result)
• give examples of own mistakes (obstacles)
• explain how the mistakes prevent from achieving the result
• define learning objectives for further work

### Subcategories

This category includes articles that can help you understand the Stages of Competence Development better.

This category includes articles that can help you understand the Thinking Task Framework better. Please note that Thinking Task Framework is a fairly simple model that is useful as an introduction into teaching thinking. For deeper understanding, please refer to the model of Stages of Competence Development.

This category contains structured reflections of teachers who have been trying to implement the TA in their work and would like to share some lessons learned.

This category contains materials that can help you in the process of sharing your experiences on this site. Please note that the site is changing all the time, so some posts need updates. If you notice such a post, feel free to update it and make the life of your colleagues easier.

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