Defining computational thinking for Mathematics and Science
That is the title of an article by Weintrop et al (2016) in which they provide a platform for integrating computational thinking (CT) in mathematics and science education. An interesting article because it gives an idea of how to focus on CT outside the field of computer science. The design they choose to integrate CT is a taxonomy of goals focused on mathematics and science. Based on their own research, they eventually reach 4 categories: data practices, modeling and simulation practices, computational problem solving practices and system thinking practices. The main reason for the authors to integrate CT into mathematics and science is that these subjects better match the reality of science today. In addition, the authors indicate, the use of computational tools and skills can increase understanding of math and science.
In the article, they continue to CT itself, CT in K12 education, the ever-increasing role of computation in mathematics and science and the method they used to reach their taxonomy. Regarding the increasing role of computational methods, they argue that increasing computational power can solve ever more complex problems, thereby changing science and preparing students to do so.
The taxonomy
Taxonomy consists of four categories. Each category is again divided into a number of practices. I do not know how to translate the best practices as the authors themselves make a separate point of it. At first they talk about skills (skills) but...
Concerns were raised, for example, a request that we move from the conditions necessary to make it more widespread and more demanding to reinforce what it means to use these concepts, as well as reflect major changes in mathematics and science standard landscape.
Perhaps that method, practice or competencies could be a translation for this. For now, just let me know about practices.
In the article they explain each practice and then every practice every part. I will give it a brief summary.
1. Data-practice
Data, as the authors indicate, is the core of scientific and mathematical activities. The way data is collected, created, analyzed, manipulated and visualized changes quickly. Students should learn that data is not organized in structures, but that you have to apply it yourself.
1a. Collecting Data
By observing and measuring data can be collected. Computational tools can be used to collect data. At the end of the article, the authors call an example of such a computational tool: The Tracker Video:
1b. Creating Data
Using computer simulations, scientists can create data. For example, to investigate the evolution of a galaxy. This data is otherwise unavailable because, for example, these types of processes would take too long without simulations.
1c. Manipulating Data Data manipulation
is meant to be able to merge data, filter, clean, normalize and data sets. Hereby I have to think of being able to work with excel for example. The authors elsewhere in the article still have tools like Tinkerplot, Fathom and SimCalc.
1d. Analyzing Data Analyzing Data
When analyzing data, you are looking for patterns, deviations, defining rules to categorize data, determine trends, and make relationships. Now that so much data is available (big data) it is important that you can use computational tools to analyze the data.
1st. Visualizing data (data visualization)
Computational tools can help visualize data so you can talk to others. Think of charts and graphs. But also dynamic, interactive visualizations.
2. Modeling and simulation practices (models and simulations)
In science, making, refining and using models about phenomena is an important starting point. You can think of flowcharts, diagrams, equations, chemical formulas, computer simulations and physical models. Models can be used to predict what a reality will be. The authors do not specifically mention static representations of phenomena that can be simulated by the computer. Models make it possible to investigate questions and test hypotheses that may be too expensive, too dangerous, too difficult or impossible to perform.
2a. Using Computational Models to Understand a Concept
A computational tool can be a good learning tool to understand a concept such as ecosystem dependencies and how objects in a driftless environment behave. Looking for examples I found Wikipedia on this comprehensive list of computational models, but I also had to think of the GoLabs such as Ton de Jong , and the studies of simulations by Wouter van Joolingen with, for example, SimSketch.
2b. Using computational models to find and test solutions Testing
various hypotheses without spending too much time and money.
2c. Assessing computational models
How does the phenomenon affect reality? What abstraction are built into the model? And what are the abstractions on the reliability of the model?
2d. Designing computational models
Technological, methodological and conceptual decisions should be taken. This is a design process still on paper.
2nd. Constructing computational models
This is really about building computational models. This requires programming knowledge.
3. Computational problem solving practice (computational problem solving ability)
It concerns the applied computer science that helps to further the science. As students program, develop algorithms and make computational abstractions, this can have a positive effect on studying mathematical and scientific phenomena.
3a. Preparing problems for computational solutions
Problems are not always automatically solved by a computer program. The art is to formulate the problem so that it is appropriate to get started with a computational tool.
3b. Computer programming
This involves understanding computer programs of others and writing programs themselves. Programming concepts that are important here are conditional logic, iterative logic, repetition, abstractions (including subroutines and data structures). Not everyone needs to be a programmer, give the authors, but basic knowledge is important.
3c. Choosing effective computational tools
This is the question which program best suits your problem. What are the possibilities and what are the limitations?
3d. Assessing different approaches / solutions to a problem
If there are more ways to do something then it is important that you make the right choice. You can think of costs, time, durability, reusability and flexibility.
3rd. Developing modular computational solutions (Modular computational solutions)
It is a matter of clipping a process into steps or pieces. Such that they can easily be reused, can be used for other purposes and easier to detect errors.
3f. Creating computational abstractions (capable of making abstractions)
Determining what the main lines are and what the details. This helps in writing a computer program, generalizing, visualizing data and determining the scope or scale of a problem.
3g. Troubleshooting (troubleshooting and debugging)
Troubleshooting issues, systematic testing of the system to isolate the problem, and reproducing the problem to test possible solutions.
4. System thinking practices
There are problems that can only be solved if you look at the system as a whole and not to the individual components. System thinking is therefore an important skill. Examples of systems that you should study as a whole are natural selection and population changes in nature, the human respiratory system and the general gas laws. They also terminate the term cross-cutting concepts that once again encountered the theory of science and technology. Computational means can be a powerful means of understanding systems.
4a. Investigating a complex system as a whole (
Sometimes studying a system) Sometimes it is more effective to study a system as a whole instead of the individual components. That means you should be able to omit some details. Computational means such as models and simulations are handy for use.
4b. Understanding the relationships within a system
Although it is useful to study systems as a whole, it is also useful to know how separate components interact.
4c. Thinking in levels
It is a question of distinguishing between different levels in a system and by doing research.
4d. Communicating information about a system
If you are examining a system, it is the art of communicating about the results. Visualizations and infographics can help. Importantly, the question is what you and not present.
4th. Defining systems and managing complexity
What are the limits of the system you want to investigate? A system must be so defined that it is useful and productive.
The authors have made a beautiful design in which they look at how CT in mathematics and science can play a role. My idea is that science (research learning) in particular has led to this. At least I have the idea that the structure as a whole lends itself mainly to research learning. The individual parts could, in my opinion, be well embedded within mathematics. Accounting mathematics is especially an application and not so much the purpose.
Thanks for reading.
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