Algorithms
Algorithms are step-by-step procedures or formulas for solving problems or performing tasks. In mathematics, algorithms are used to solve equations, find patterns, and analyze data. They are essential tools for computer science, cryptography, and various fields of mathematics, providing systematic approaches to problem-solving and decision-making.
4 Key excerpts on "Algorithms"
eBook - ePubTeaching Mathematics in Grades 6 - 12
Developing Research-Based Instructional Practices
- Randall E. Groth(Author)
- 2012(Publication Date)
- SAGE Publications, Inc(Publisher)
...In their numerical work, mathematicians also engage in activities such as looking for patterns, making and testing conjectures, and visualizing quantities (Cuoco, Goldenberg, & Mark, 1996). To help students develop numerical habits of mind similar to those of mathematicians, it is imperative for the curriculum to include much more than just numerical computation. Additional aspects of numerical thinking to be explored in this chapter include number sense and estimation, proportional reasoning, understanding generalizations of arithmetic, working with number systems and number theory, understanding vectors and matrices, and combinatorial thinking. Algorithmic Thinking Advantages of Algorithms Usiskin (1998) defined an algorithm as a “finite, step-by-step procedure for accomplishing a task that we wish to complete” (p. 7). Students encounter many Algorithms as they progress through school. Those for long division, multidigit multiplication, and solving linear equations are among the most common. School curricula have favored teaching Algorithms largely because they are powerful, reliable, accurate, and fast (Usiskin, 1998). Once an algorithm for performing a mathematical task is known, it can be performed with minimum effort. Algorithms form an important part of the infrastructure of mathematics because they provide tools that are essential for handling tasks that would otherwise be more difficult and time-consuming (Wu, 1999a). Pedagogical Difficulties with Algorithms Despite the power and advantages of Algorithms, it is necessary to proceed with caution when teaching them. Usiskin (1998) warned that students sometimes blindly accept the results of Algorithms or apply them overzealously. Blind acceptance of results is detrimental when students think they have performed all the steps in the algorithm correctly, but have actually taken a misstep to produce an unreasonable answer...
eBook - ePub- James Bird, Helen Caldwell, Peter Mayne, James Bird, Helen Caldwell, Peter Mayne(Authors)
- 2017(Publication Date)
- Learning Matters(Publisher)
...This can be achieved without the need for ‘expert’ knowledge and even in many cases without the need to use a computer! The New Collins Concise English Dictionary (2011) defines Algorithms as any method or procedure of computation, usually a series of steps. Computational thinking should be seen as a problem-solving process, which incorporates the use of Algorithms by analysing and logically organising data. Lesson idea: introducing Algorithms This lesson focus is on Algorithms being a sequence of precise instructions and related to the need for digital devices also to have precise instructions, in order to follow a preset program with a predetermined outcome. Before you start Be clear in your own mind what an algorithm is and how the concept can be embedded in a cross-curricular way. Pupils need to be grouped according to ability. Things you need • Toaster, bread, knife and margarine for the teacher demonstration. • Laminated cards – on each card should be one of the steps for cleaning teeth (the sequence has been decomposed into smaller steps), Blu-tack, mini-whiteboards. Context After an initial teacher demonstration, this particular lesson plan focuses on creating an algorithm for cleaning teeth, which would link well to personal, social, health and economic education, and with a topic on ‘All About Me’. The principle of this lesson could also be used in many different contexts, for example, crossing a road, making a sandwich, getting dressed. Learning objectives • To understand the term ‘algorithm’. • To understand the precise nature of Algorithms. • To understand that Algorithms provide the precise instructions for common digital devices. Lesson outline In order for pupils to understand the term ‘algorithm’, they need to create some of their own and try them out in the physical sense...
eBook - ePubRules
A Short History of What We Live By
- Lorraine Daston(Author)
- 2022(Publication Date)
- Princeton University Press(Publisher)
...1195–c. 1256) Algorismus vulgaris, were used as standard university texts and helped to naturalize the Arabic loan-word as a synonym for the four basic operations of addition, subtraction, multiplication, and division. 7 Current dictionary definitions vary according to area of application (mathematics, medicine, informatics), but in contrast to the original narrow associations of the word with reckoning by Indian numerals, most modern definitions broaden its meanings to include any step-by-step procedure used in calculation or problem-solving. A standard reference work on computer programming captures both the colloquial and the technical senses of the word in its definition of the word algorithm : “The modern meaning of algorithm is quite similar to that of recipe, process, technique, procedure, routine, rigmarole, except that the word ‘algorithm’ connotes something just a little different. Besides merely being a finite set of rules which gives a sequence of operations for solving a specific type of problem, an algorithm has five important features [finiteness, definiteness, input, output, effectiveness].” 8 The formal specification of each of those five desiderata has generated a large technical literature in logic, mathematics, and informatics, and the approaches of these fields are not always convergent: for example, a sequential procedure that terminates in n steps, where n is a very large number but less than infinity, may satisfy the mathematician’s criterion for finiteness but leave a computer programmer who must take into account computation time dissatisfied. However, from a historical perspective, such technical debates played a minor role before the twentieth century. For preceding centuries, the core meaning of the word algorithm was the solution of specific problems by step-by-step procedures of calculation. But long before the word there was the thing...
- Linda Daniela, Linda Daniela(Authors)
- 2020(Publication Date)
- Routledge(Publisher)
...299). As stressed by Hromkovič and Lacher (2017, p. 4) already Euclid formulated Algorithms in his ‘Elements’, among them being the famous Euclid’s algorithm. The term ‘algorithm’ is due back to al-Khwarizmi, who wrote a book about Indian digits around the year 825. Humankind tried to develop Algorithms as long as anyone can remember. People generated knowledge in order to understand the world around them and specially to apply this knowledge to develop ‘procedures’ to reach their goals Fellows et al. (2005 in Tekerek & Altan, 2014, p. 133) described algorithm as “a set of instructions that are required to follow for completing a task”. Furthermore, Grover and Pea (2018) argued that Algorithms and AT, together with patterns and pattern recognition, abstraction and generalization, evaluation, and automation, are the key components of CT, whereas Hromkovič et al. (2017) claimed that even though AT and CT were introduced in different eras and consider these two concepts to be equivalent and interchangeable, at times, they can be expressed as the same concept. For Futschek (2006), AT is an ability that is necessary at any stage of the problem-solving process. In the Czech Republic, educational blocks-based programming environment Scratch and educational robotics (e.g., LEGOMindstorms, ozobots) are being introduced into schools to develop pupils’ computational thinking following the idea that pupils would “become not merely passive consumers of computer technology but rather active designers of computer programs and applications” (Dewey, 2017). The aim of this case study is to identify changes in Czech elementary school pupils’ (grade 5 and 6) AT through programming in Scratch 2.0. Literature review Some computer scientists are not convinced that CT enhances general cognitive skills (e.g. problem-solving skills). Denning (2017, p. 37) declares that, “many education researchers have searched for supporting evidence about it but have not found any”...
