MathMagic: Computational and Mathematical Thinking

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Presentation transcript:

MathMagic: Computational and Mathematical Thinking Pedro Lealdino Filho Dr. Christian Mercat pedro.lealdino@etu.univ-lyon1.fr christian.mercat@math.univ-lyon.fr

Computational and Mathematical Thinking? A problem solving processes that includes a number of characteristics and dispositions. They are essential to the development of computer applications, mathematical products, also supporting problem solving across all disciplines.

Computational Thinking Decomposition: Breaking down data, processes, or problems into smaller, manageable parts. Pattern Recognition: Observing patterns, trends, and regularities in data. Abstraction: Identifying the general principles that generate these patterns Algorithm Design: Developing the step by step instructions for solving this and similar problems. Computational Thinking

Weintrop, D. , Beheshti, E. , Horn, M. et al Weintrop, D., Beheshti, E., Horn, M. et al. J Sci Educ Technol (2016) 25: 127. Defining Computational Thinking for Mathematics and Science Classrooms

Mathematical Thinking Specialising: Trying special cases, looking at examples. Generalising: Looking for patterns and relationships - Abstraction. Conjecturing: Predicting relationships and results. Convincing: Finding and communicating reasons why something is true. Mathematical Thinking

How to develop an algorithm which performs the Mathematical Trick? I can guess the birthday of a person using five cards. How to develop an algorithm which performs the Mathematical Trick?

Solving Problem How to Solve It (Polya, 1945) Understand the problem Devise a Plan Carrying out the Plan Look Back Solving Problem How to Solve It (Polya, 1945)

Solving the problem: Let’s use some tools to help us to create the algorithm.

Breaking the Problem - Example: Let’s say we are using Scratch to develop our first prototype of the Magical Trick. All of sudden you realize that you probably have to use the concept of power. What’s the new problem? Is there only one solution?

Content Mathematics: Number - Exploring numbers in other bases. Representing numbers in base two. Mathematics: Algebra - Continue a sequential pattern, and describe a rule for this pattern. Patterns and relationships in powers of two. Computer Science: Arrays - Storing numbers into an array. Computer Science: Conditional - Taking decisions based in logical expressions. Computer Science: Binary numbers.