![• A variety of strategies for solving problems empowers children to explore
alternatives and develops confidence, reasoning, and mathematical creativity.
Ps help gauge an individual’s critical thinking skills.
3. PROBLEM POSING
Problem Posing is another way to help students with problem solving is to encourage them to write, share,
and solve their own problems. Through problem –posing experiences, students become better aware of the
structure of problems, develop critical thinking and reasoning abilities, and learn to express their ideas clearly.
I is often helpful to begin problem posing by having students modify familiar problems.
Four principles of problem posing:
The 4 principles foe helping students as they learn to pose problems are:
1. Focus students’ attention on the various kinds of information in problems: the kinds of information a
problem may give us [the known], the kind of information we are supposed to find [the unknown], and
the kinds of restrictions that are placed on the answer. Encourage students to ask “what if’ questions. For
example, what if we switch what is known in the problem and what is unknown? What if we change the
restrivtions?
2. Begin with mathematical topics or concepts that are familiar.
3. Encourage students to use ambiguity [what they are not sure abou or what they want to know] as they
work toward composing new questions and problems.
4. Teach students about the idea of domain [the numbers we are allowed to use in a particular
problem].Extending or restricting the domain of a problem is an interestin way to change it.](https://image.slidesharecdn.com/mathematicalprocess-220121104410/85/Mathematicalprocess-9-320.jpg)
Mathematicalprocess
- 1. Process of mathematics Reasoning, logical thinking, problem solving and connection.
- 2. Process of mathematics: Definition: mathematical process means thinking and reasoning, calculation and salvation by mathematical methods.
- 3. Continued…… • They include 1. Reasoning 2. Logical thinking 3. Problem solving and 4. Connecting etc….
- 4. Reasoning: • Mathematical reasoning happens through conjectures, investigating and representing findings and explaining and justifying conclusion. • “Reasoning can be thought of as the process of drawing conclusions on the basis of stated assumption and sense making can be defined as developing an understanding of a situation, context, or concept by connecting it with existing knowledge.”
- 5. 9. Sequence of comparison Many coders their entire careers without ever having to implement an algorithm that uses dynamic programming. However, dynamic programming pops uo in a number of important algorithms. One algorithm that most programmers have probably used, even though they may not have known it, finds differences between two sequences. More specifically, it calculates the minimum number of insertions, deletions, and edits required to transform sequence A into sequence B. For example, lets consider two sequences of letters, ”AABAA” and “AAAB”. To transform the first sequence into the second, the simplest thing to do is delete the B in the middle, and change the final A into a B. This algorithm has many applications, including some DNA problems and plagiarism detection. However, the form in which many programmers use it is when comparing two versions of the same source code file. if the elements of the sequence are lines in the file, then this algorithm can tell a programmer which lines of code were removed, which ones were inserted, and which ones were modified to get from one version to the next.
- 6. 2.3. MATHEMATICAL PROCESS Definiton:- Mathematical process means thinking and reasoning and reasoning, calculation and salvation by mathematical methods. They include reasoning, problem posing, argumentation, justification, abstraction, generalization, etc 1)REASONING Mathematical reasoning happens through making conjectures, investing and representing findings and explaining and justifyingconclusions. 70 UNDERSTANDING DISCIPLINE AND MATHEMATICSH “Reasoning can be thought of as the process of drawing conclusions on the basis of evidence or stated assumption and sense making can be defined as developing an understanding of a situation, context, or concept by connecting it with existing knowledge.” Reasoning and sense making are intertwined. Consider how a student solved this question: EX 18+27=?+29 ”Twenty-nine is two more than 27so the number in the box has to be two less then 18 to make the two sides equal so it’s 16,”(2). Instead of calculating one side of the expression as 45 and then figuring out the number to add to 29 to get to 45, she has simplified the calculation by comparing the numbers and has realized 29 is two more than 27 so the number added had to be two less than 18. This is a great example of reasoning and sense making! EX 252-152 here the child apply a2-b2= (a+b )(a-b) Two types of reasoning 1) Inductive reasoning : Ochildren explore and record results, analyze observations, make generalizations from patterns, and test these generalizations. 2) Deductive reasoning : Occurs when children reach new conclusions based upon what is already known or assumed to be true.
- 7. Advantages of Mathematical reasoning: • Helps children think logically and make sense of mathematics. • Develops confidence in their abilities to reason and explain their mathematical thinking • High-order inquiry challenges children to think and develop a sense of wonder about mathematics. • Mathematical experiences in and out of the classroom should provide opportunities for children to engage in inductive and deductive reasoning.
- 8. 2. PROBLEM SOLVING Mathematical problem solving- is a problem that is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. The process of working through details of a problem to reach a solution is called problem solving. Problem solving may include mathematical or systematic operations and can be a gauge of an individual’s critical thinking skills. Problem-solving situations call upon children to retrieve previously learned information and apply it in new or varying situations .Knowing the basic arithematic skills, knowing when to incorporate them into new contexts ,and then being able to do so are three distinct skills. “Students need to explore mathematics through solving problems. Learning through problem solving should be the focus of mathematics at all grade levels. When children encounter new situations and respond to questions of the type, “How would you……?”, “can you……?, or “What if……?”, In order for an activity to be problem – solving based, if must ask children to determine a way to get from what is known to what is sought. If children have already been given ways to solve the problem, it is not problem solving but practice. Advantages of problem solving • The problem- solving approach is being modelled. • Children develop their own problem- solving strategies by being open to listening, discussing, and trying different strategies. • A true problem requires children to use prior learning in new ways and contexts. • Problem solving develops and builds depth of conceptual understanding and student engagement. • Problem solving is a powerful teaching tool that fosters multiple and creative solutions . Creating P S environment make children actively look for, and engage in finding solutions.
- 9. • A variety of strategies for solving problems empowers children to explore alternatives and develops confidence, reasoning, and mathematical creativity. Ps help gauge an individual’s critical thinking skills. 3. PROBLEM POSING Problem Posing is another way to help students with problem solving is to encourage them to write, share, and solve their own problems. Through problem –posing experiences, students become better aware of the structure of problems, develop critical thinking and reasoning abilities, and learn to express their ideas clearly. I is often helpful to begin problem posing by having students modify familiar problems. Four principles of problem posing: The 4 principles foe helping students as they learn to pose problems are: 1. Focus students’ attention on the various kinds of information in problems: the kinds of information a problem may give us [the known], the kind of information we are supposed to find [the unknown], and the kinds of restrictions that are placed on the answer. Encourage students to ask “what if’ questions. For example, what if we switch what is known in the problem and what is unknown? What if we change the restrivtions? 2. Begin with mathematical topics or concepts that are familiar. 3. Encourage students to use ambiguity [what they are not sure abou or what they want to know] as they work toward composing new questions and problems. 4. Teach students about the idea of domain [the numbers we are allowed to use in a particular problem].Extending or restricting the domain of a problem is an interestin way to change it.