Types of Problems

(Overall View) | (Example Oriented Approach) | (Theoretical Approach) | (Types of Problems) | (Collection of Problems)

 

Intitial State Transformation Goal / End State Type of Problem
x x x completely solved problem
x x - basic problem / basic definition problem

(i.e. mental arithmetic, constructing a triangle, learning vocabulary, ...)
- - x inversion of a basic problem

(i.e. number puzzle: with an imaginary number certrain given operations are calculated and the sum given. The imagined number is to defined.)
x - - problematic basic definition problem

(i.e. paint a layout of your room)
- x x inversion of a basic definition problem with a known way of calculation

(i.e. a new type of tent is to be developed, fitting three people with a peripheric plenum of 1 m³ per person, and a lying surface of 0,8m x 1,8m per person.)
x - x rational problem or: the finding of a strategy

(i.e., Frank always wins the game: "Take" How does he do it? Rules; 20 sticks are in the table, one after the other teammates take 1,2 oder 3 sticks. Whoever takes the last sticks is the winner.)
- x - invitation to generate tasks

(i.e. Develop exemplified tasks for the three basic problems of percentage calculation!)
- - - open problems / problems with a given state

(i.e. Find the mathematic optimum for packaging, or how long will it take, to have complete exchange of water in a pool?)

 

With these eight types of problems we can achieve something important in educational psychology: the advantage of a change of perspective and the use of networking within a topic.

Examples for Problem Typification

Identify teh type of goal for the following problems. Describe briefly what you need to know to successfully complete those problems! Hints for a goal1: of the problem belows. What type of problem is missing? Give an example for it!

 

  1. Construct a triangle ABC with the following given details: length c, height on c and b.
  2. 45 kg of copper are melted together with zinc and 80 kg of brass. Give the percentage of zinc!
  3. Note if the following statements are true or false:
    i. Every square is a rectangle.
    ii. Evere rectangle is a square.
    iii. Every rectangle is a trapezoid.
    iv. Every square is a kite square.
    v. Every kite is a rhombus.
    vi. Every rhombus is a kite square.
    vii. Every parallelogram is a trapezium.
    viii.� Every trapezium is a rhombus.
    ix.� Every trapezium is a parallelogram.
  4. Show, that in all triangles the sum of the angles on the inside is 180°.
  5. Why does the p-q-formula apply to all quadratic equations?
  6. Give possible measurements for 2 differently shaped prism-like figures with a volume of 1 dm³.
  7. How many scoops of ice cream doeas a vender have to sell to be abgle to live of it all throughout the winter?
  8. Draw two parallels with a distance of 4 and a third straight line that cuts both. Construct all points that have the same distance to all the three lines.
  9. Is there a precept for the formation of the following numbers: 18 15 22 and 29 36 43?�
  10. How can you calculate the approximate height of a tower without climbing it and with only little means?

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