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‘Mathland’ as a cultural setting in which ideas of mathematics become
natural, personalized, and humanized
The idea of “talking mathematics” to a computer can be generalized to a view of
learning mathematics in “Mathland”; that is to say, in a context which is to learning
mathematics what living in France is to learning French. [Mindstorms, p. 6]](https://image.slidesharecdn.com/algorithmicthinkinganddigitalfabrication12-131123025757-phpapp02/85/Algorithmic-thinking-and-digital-fabrication-1-2-12-320.jpg)
Uploaded byPrabhat Kumar
Algorithmic thinking and digital fabrication (1) (2)
This document discusses developing a new programming platform to teach algorithmic thinking and spatial reasoning through digital fabrication. It aims to make programming accessible to those with minimal computer knowledge by removing misconceptions and making it as simple as manipulating blocks. The methodology involves studying existing platforms like Logo and Scratch, conducting user studies, and conceptualizing a new platform that allows users to see program state, follow program flow, and create programs by reacting and abstracting. It will utilize constructionism and allow users to iteratively design, test and improve their creations. The document outlines initial prototype development and areas for future work such as interface design and testing.
Algorithmic thinking and digital fabrication (1) (2)
- 1. ALGORITHMIC THINKING AND DIGITALFABRICATION Guide: Prof. Pradeep G. Yammiyavar Prabhat Kumar Rishika Jain Harshit Agrawal
- 2. Aim To make iteasy for people to understand spatial reasoning and simultaneously enhance algorithmic thinking through an easy to use programing platform.
- 3. Objective Remove misconceptions thatpeople have related to programing. Make learning programing and understanding of algorithmic thinking as simple as manipulating blocks on screen Motivate algorithmic thinking by relating code to a visual output on the screen and to a tangible output of personal creation Platform that helps teaching programing in a way that is accessible to people with minimal computer knowledge
- 4. Objective Remove misconceptions thatpeople have related to programing. Make learning programing and understanding of algorithmic thinking as simple as manipulating blocks on screen Motivate algorithmic thinking by relating code to a visual output on the screen and to a tangible output of personal creation Platform that helps teaching programing in a way that is accessible to people with minimal computer knowledge
- 5. Objective Remove misconceptions thatpeople have related to programing. Make learning programing and understanding of algorithmic thinking as simple as manipulating blocks on screen Motivate algorithmic thinking by relating code to a visual output on the screen and to a tangible output of personal creation Platform that helps teaching programing in a way that is accessible to people with minimal computer knowledge
- 6. Objective Remove misconceptions thatpeople have related to programing. Make learning programing and understanding of algorithmic thinking as simple as manipulating blocks on screen Motivate algorithmic thinking by relating code to a visual output on the screen and to a tangible output of personal creation Platform that helps teaching programing in a way that is accessible to people with minimal computer knowledge
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- 9. Logo Mathetic (knowledge aboutlearning) aspects of Turtle Geometry Turtle geometry is an aid to learning other things because it encourages the conscious, deliberate use of problem-solving and mathematic strategies (in order to learn something, first make sense of it) Play Turtle. Do it yourself. Turtle circle is an incident of syntonic learning
- 10. Logo Transitional Object :bridge between concrete and formal reasoning Logo turtle - a ‟mathematical creature‟ that can move forwards or backwards and turn right or left in response to programmed commands. Kids can identify with the turtle The link to formal reasoning through the turtle is effected in large part by a procedural language(Logo) (hence, logo+turtle - real screen-based transitional object) Might be experienced by children as simultaneously cognitive and emotional artifacts. Is entirely screen-based and affects different kids to different extents There is a need to rethink design of effective transitional objects objects and in the light of new material technologies.
- 11. Logo Microworld of TurtleGeometry Microworlds serve as incubators of powerful ideas, productively constrained, selfcontained cognitive worlds Again completely screen based in LOGO Computationally enhanced construction kits can serve as micro worlds (Eisenberg, 2003) We aim to empower kids to build their own construction kits, a microworld that is partially computational and partially tangible
- 12. Logo ‘Mathland’ as acultural setting in which ideas of mathematics become natural, personalized, and humanized The idea of “talking mathematics” to a computer can be generalized to a view of learning mathematics in “Mathland”; that is to say, in a context which is to learning mathematics what living in France is to learning French. [Mindstorms, p. 6]
- 13. Logo Decomposition Papert refers toit as breaking down a program into "mind-size bites”. Logo uses the metaphor of "teaching the turtle a new word”. The need for subprocedures is discovered and they are taught to the turtle.
- 14. Logo Interface Turtle indicates thestate Anthropomorphic metaphor in language
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- 16. Bloom‟s taxonomy sorts learning objectivesby cognitive complexity Knowledge: the student can recall specific facts or methods. This level is characterized by verbs such as enumerate, name, and define. Comprehension: the student understands the meaning of facts or concepts. This level is characterized by verbs such as explain, discuss, and paraphrase. Application: the student can solve problems by applying knowledge to new concrete situations. This level is characterized by verbs such as produce, implement, and solve. Analysis: the student can break down information into its parts to determine motives or causes, or to make inferences. This level is characterized by verbs such as analyze, discriminate, and infer. Synthesis: the student can combine elements in new ways to produce novel wholes. This level is characterized by verbs such as create, compose, and invent. Evaluation: the student can make judgments about material in light of selected criteria. This level is characterized by verbs such as appraise, critique, and compare.
- 17. The SOLO taxonomy sortslearning outcomes by structural complexity PreStructural: a response at this level misses the point or consists of empty phrases, which may be elaborate but show little evidence of actual learning; Unistructural: this kind of response meets only a single part of a given task or answers only one aspect of question. It misses other important attributes entirely; Multistructural: the response is „a bunch of facts‟. It expresses knowledge of various important aspects, but does not connect them except possibly on a surface level. The learner sees „the trees‟ but not „the forest‟; Relational: the response relates and integrates facts into a larger whole that has a meaning of its own. It is no longer a list of details; rather, facts are used by the learner to make a point; Extended abstract: a response at this level goes beyond what is given and applies it to a broader domain.
- 18. Introductory Programming Coursesare demanding in today‟s era. In comparison to its esteemed status in other subfields of education, these taxonomy have received relatively little attention in programming education until recent years.
- 19. Introductory Programming Coursesare demanding in today‟s era. In comparison to its esteemed status in other subfields of education, these taxonomy have received relatively little attention in programming education until recent years.
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- 21. User Type 1:People venturing into the world of programing
- 22. Programing Misconceptions Program execution Theprogram flow Parameter passing Trace Unnecessarily strict rules Viability
- 23. Users Type 2:Spatial Thinking Skills
- 24. Problems Identified Measuring oflength and area. Iteration of standard units Need to apply multiplicative reasoning to the measurement of area. Learning how to represent angle mathematically. Children are more aware of angle in the context of movement (turns). An important aspect of learning about geometry is to recognise the relation between transformed shapes (rotation, reflection, enlargement). This is also difficult, since children‟s pre-school experiences lead them to recognise the same shapes as equivalent across such transformations, rather than to be aware of the nature of the transformation.
- 25. Observations Young school childrenhave difficulty with the idea of decomposing shapes into parts Difficulty with the inverse process of composing new shapes by combining two or more shapes to make a different shape exists. The barrier: these are unusual tasks for children who might learn how to carry them out easily given the right experience.
- 26. How to teachSpatial Thinking space representation reasoning
- 27. Conceptualizing a newenvironment
- 28. The programing environmentshould allow the learner to Read the vocabulary: what do these words mean? Follow the flow: what happens when? See the state: what is the computer thinking? Create by reacting: start somewhere, then sculpt Create by abstracting: start concrete, then generalize
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- 34. Any programming systemmust have Individual things Groups of things Commands that operate on things Ways to repeat commands Ways to make choices Ways to create chunks Ways to combine those chunks Motivation
- 35. How fab canhelp experiential education constructionism critical pedagogy The motivation of being able to create and put together a concept, in the form of a personal structure makes the activity compelling, as it results in the forming of an intellectual attachment to, or engagement with the software part of the process. Students can investigate an object from all angles helping in developing spatial reasoning.
- 36. Why Fab: Iterativecycle of creative learning think creatively communicate clearly plan systematically learn continuously analyze critically work collaboratively design iteratively
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- 38. Revolve - Solve- Evolve - Resolve 4 different ways of thinking of 3D models that combine spatial reasoning skills with algorithmic thinking Method A : Spin around an axis Method B : Move the Turtle - Body Syntonic (Spatial Thinking) Method C: Construction Kits Method D: Deconstruction
- 39. But essential priorlearning Training to understand 3-Dimension world inside computer screen (Space, Representation and Reasoning)
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- 43. Method A: SpinAround the axis
- 44. Method B :Move the Turtle
- 45. Method C: ConstructionKits Source: http://www.thingiverse.com/thing:15754
- 46. Method D: Deconstruction Source:http://blog.ponoko.com/2012/03/19/a-sophisticated-program-to-create-laser-cuttable-3d-forms/
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- 50. Future Work User interfacedesign Development Testing
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