Problem solving is central to computing and engineering education, but it is not clear what is the best way to engage students with developing problem-solving skills. Are there better ways in other disciplines?
Article Is it Visual? The importance of a Problem Solving Module wit...
Hello all,
I think you have put your finger on a fundamental in problem/project based learning (PBL). As an art and English teacher in an engineering university in France, letting go of one's fear of being wrong, therefore judged by one's peers, inhibits creativity. The teacher's role in setting a comfortable zone for errors is vital . for all disciplines.This phemenon is also true within a tight academic hierarchy, when in a meeting people are scared of participating for fear of verbal bullying.
Within the classroom, the dynamic teacher/student is different and in my opinion more conducive to developing self-confidence and innovation.
Best.
Catherine
I think the best way is to eliminate the options. In the beginning as start to the problem-solving session, list all the possible hypothesis and then start investigating and eliminating the options till you reach the solution.
Now in order to teach the students we need to tell them to list down what ever they think can be a solution and what factors influence each, then go to theory and investigate each option. Count the positive and negative points for each option. Option with maximum positives will fall out as best possible solution....
I totally agree :-) First, the students should be given small real-world problems that they can solve at home in a manageable amount of time. Then in the classroom there should be a vivid discussion among them whereas the teacher should moderate and guide the discussion. This process what Abid has already mentioned is also practiced in the industry. So, for students it is good when they already get used to this kind of thinking.
I entirely agree with what has been said but perhaps we need to go with some students a level before this though and address some fears around risk taking and mistakes. All of us when we learnt to be engineers and computer scientist, will have got 'something wrong' or 'learnt from our mistakes' and I believe we need to teach them initially that this is ok and then we can move it to more formalised approaches. It is interesting when you give problems to primary school children (5-10 year olds) they seem less fearful of making mistakes and in will with guidance usually come up with something surprisingly good solutions. Anecdotally, give the same task to some (not all) 14 year olds or even some young undergraduates and they spend a lot longer to get there and again anecdotally come up with less creative solutions even with the same guidance available. Have they learnt to be more fearful of getting it wrong from school?
Hello all,
I think you have put your finger on a fundamental in problem/project based learning (PBL). As an art and English teacher in an engineering university in France, letting go of one's fear of being wrong, therefore judged by one's peers, inhibits creativity. The teacher's role in setting a comfortable zone for errors is vital . for all disciplines.This phemenon is also true within a tight academic hierarchy, when in a meeting people are scared of participating for fear of verbal bullying.
Within the classroom, the dynamic teacher/student is different and in my opinion more conducive to developing self-confidence and innovation.
Best.
Catherine
Hi All ,
I am also in to complete agreement with the discussion. But inaddition to that is been proposed , I strongly feel that the problem statement should be made to understand clearly. A completely understood problem is HALF solved. So inorder to make them understand the problem statement , they should have the fundamental knowledge of the basics in the topic. Once the problem is understood Isolate it . meaning what are the factors for the root cause of it. Isolating will make the solution 90% clear. Then apply the relative theorem or formulae and arrive at the result.
This develops the Confidence in the students.
-Ravi.
Dear all,
Here is a video about an experiment led by Coventry university in the Department of Computing and the Digital Environment using an interesting problem/project based learning methodology over 6 weeks. I find it really inspiring and would like to share it with you. Please share your comments.
http://www.coventry.ac.uk/ec/~pevery/cc/
Best.
Catherine
This project is really challenging! But what after the six weeks? Normal teaching will disappoint a lot! OK, make longer projects. But at the end: how do you provide credits? From where do you know the abilities of the individuals? Exams could provide insight. But then you must ensure by which way ever that they learned at least the basics you wanted to teach them.
I like that idea but have not enough imagination how to set up a three years project (several sub-projects, i.e. two projects a semester) that can ensure the whole education. With that scheme our problem changes from knowledge provision (teaching) to knowledge testing and certificating.
The following books are excellent:
1- K.A.Stroud - Engineering Mathematics 5e.djvu
2- Stroud K.A., Booth D.J. Advanced engineering mathematics (4ed., Palgrave-Macmillan, 2003)(ISBN 12.djv
They are very easy to use and self-teaching. it use programming method of teaching and learning.
In first year at university (Applied Physics at University of Strathclyde) there was a first term topic 'Scientific Method in Practice'. No exam in it, just an instructor led exploration of finding the answer to some simple questions like 'In a painting in a particular chapel, why does Jesus have a golden halo, but the apostles have black halos?", "Why is the sky blue?" or "Why is the sea blue?".
The clever addition was to encourage us to question the question, so instead of "Why is the sky blue?" it became "Is the sky blue?". That encouraged us to look deeper into the question. That kind of picks up on an earlier point about fully understanding the problem.
It has to be said that a good teacher / instructor helps massively too. They need to allow the students to explore the possibilities but keep them on track to the 'answer'.
Give problems that require creative thinking. Since no one is used to them, work through the thought process on a few of them in class. Rinse and repeat.
I feel the best way to teach Problem solving is:
give interesting problem solving that they should be able to correlate to the real word situation.
More than getting the solution to the problem, the main focus should be on the process of solving it. like the approach, type data structures used, design etc.
Among the variables that influence to get students to learn to solve problems identifies variables that refer to both the dimension of learning as a dimension of education. The former include the four following: a) the importance of declarative knowledge about the specific content of the problem, b) the repertoire of general and specific strategies that can start the subject to solve the specific problem, c) role of metacognitive strategies, and d) the influence of the individual components and mood of the person who solves the problem.
Some items that can be considered in teaching problem solving are:
1.Analysis. The student divides the problem into more basic components, examines and seeks relationships between different elements. The student performs actions such as reading, rereading, select data, record title data, represent data from the statement.
2. Planning. The student organizes the process of solving the problem. Actions are performed as selecting the overall strategy for solving the problem; probe or explore possible actions to resolve the problem, explain a set of orderly procedures to execute; organize data or perform actions to solve the problem.
3. Execution. The student performs a set of actions and mathematical procedures to solve the problem. The student performs actions such as executing a mathematical procedure (right or wrong), perform calculations, enter or copy data.
4. Review. The student takes action to control, check the validity of the resolution process or the results that you obtain and possible errors. The student performs actions such as verbal questioning the validity of some outcome or resolution procedure; find errors piecemeal; review systematically the input data, solving procedures used and made mathematical calculations.
Some considerations suggested by Pozo et al. (1994) to be considered by teachers when framing, solve and evaluate the solution of a problem are:
In the statement of the problem
1. Ask open-ended tasks, which support several possible ways of solution and even several possible solutions, avoiding closed tasks.
2. Modify the format or defining problems, avoiding the student to identify a form of presentation with a type of problem.
3. Diversify the contexts in which there is the application of the same strategy, making the student works the same types of problems at different times of the curriculum and at different conceptual contents.
4. Tasks pose a format not only academics but also in everyday settings and meaningful to the student, the student seeking to establish connections between the two types of situations.
5. Adapting the definition of the problem, the questions and the information provided to the objectives of the task, using, at various times, more or less open formats, according to these same goals.
6. Use problems for various purposes during development or teaching of a subject sequence, preventing practical tasks appear as illustration, demonstration or modeling of some contents previously submitted to the student.
During the solution of the problem
7. Accustom students to make their own decisions about the settlement process and to reflect on the process, granting increased autonomy in the decision making process.
8. Promote cooperation between students in performing tasks, but also encourage discussion and different viewpoints, that oblige explore the problem space to confront the solutions or alternative solution paths.
9. To provide students with the information they need during the solution process, performing support work, directed more to ask questions or encourage in students
habit of asking you to answer the students' questions.
In assessing the problem
10. Evaluate more resolution processes followed by the student that the final correction of the response.
11. Rate particularly the extent to which this process involves pre-planning solution, a reflection during task performance and self-assessment by the student of the proceedings.
12. Rate the reflection and depth of solutions achieved by students rather than the speed with which they are obtained.
Problem solving is not a lesson to be taught, it is an approach to be developed among the student / participant. In professional education I believe that there are four steps through which individual are expected to be acquainted viz. knowledge, skill, understanding and knowhow. Knowledge can be taught, skill can be developed though experimentation and understanding comes with application of knowledge and skill orientation. This is possible, when he / she is assigned open end problems, wherein they can follow the unknown path for arriving at particular solution by application of subject knowledge and skill acquired. Here individual will develop an approach for out of box thinking. This will result in developing creativity among individual for diagnosing the problem and finding viable solution useful for developing problem solving approach.
My students are very interesting in the course of problem solving. I divide the course in two parts. The first one is composed by lectures with the fundamentals of the techniques and modelling . The subject are combinatorial optimization, constraint satisfaction problems, and techniques to solve CSP (arc-consistency, forward checking) and finally local search and metaheuristics.
In the second part of the course, each student develops a project, beginning with the state-of-the-art in a particular application problem, he must use a technique to solve it. For a same problem I give a different technique to be applied to at least two students. Each of one makes a report including how he used the technique, the design decisions taken, results, graphs, and gives comparison
between their algorithms and those existing in the state of the art with conclusions about the work. A final presentation is required.
A very good book to use is "How to solve it", in this book many puzzles are proposed to motivate students.
Some very good thoughts expressed here. In science and engineering this problem has a very quick answer, though:
- study history: how problems, real and specific problems, first came about, then were solved
- give students real and specific design challenges, that require a completed "thing" to be built
Look at the old problems, force them to find a new answer. Force discussion and trouble shooting; make them fail and over come; force them to discuss errors and roadblocks. Grade down only for giving up, pass those how meet the requirements of a solution, patent and publish the great and unique.
I found the following book in a colleagues office, and I liked it so much I bought my own copy -- "Puzzle Based Learning: An introduction to critical thinking, mathematics, and problem solving" by Zbigniew Michalewicz and Matthew Michalewicz.
http://www.puzzlebasedlearning.edu.au/
It proposes a lot of ideas on how to frame a problem so that solution techniques can then be applied.
I also liked the "Puzzle Based Learning" book another I like is "How to think like a Programmer" by Paul Vickers. Especially for problem solving the first few chapters (though the rest of book is good for the programming skills development aspects).
http://www.howtothinklikeaprogrammer.com/forum/index.php
I think the problem with the puzzle and proof approach to teaching problem solving is that it misses the point that real problem solving isn't generally one brilliant insight then walking in glory; problem solving is a thousand minor insights and a lot of work.
It makes the class harder to teach, but it also makes it clear that great achievements are not just an exercise for an Einstein who can vividly visualize the universe, but also is in the reach of those of us who can only clearly see one small obstacle at a time.
Without reading most of the answers preceding my own because of a shortage of time, I will just add that probably the most productive method is to use essay questions where one has to formulate and structure a reply, as opposed to multiple-choice questionnaires or examinations which have essentially dumbed-down the human animal over the course of the last 40 years. Essay answers require the formulation of thought, usually in a constructive algorithmic fashion (for lack of a better momentary description). You have to put it together so that it makes sense to the receiver. You are not simply practicing memorization and associative replies as you would do with a multiple-choice selection process. I remember being in transition to high school from junior high when they made that change for me, and it was devastating - suddenly we, as students, were to be rewarded for simple memorization and regurgitation techniques. It changed the whole gameplan of how and what we were expected to learn and get measured for that learning. We could no longer use examinations (and this may be a key point) as I still like to do, as a further learning tool. It becomes a feedback and clarification of what you did and did not comprehend. And as with any realm of thought, it is about the ability to practice learning.
Hello everybody,
Thank you for sharing your thought on PBL which are all pertinent. Here is what the Aalborg UNESCO chair in PBL considers to be the 9 fundamentals in PBL, and the 16 fundamentals for the MIT. The question of the question is of course of vital importance in project based learning. Being able to identify a question set in real life and being able to generate an analysis and a synthesis offering new solutions as a team is the ultimate target. Prior to it, it is necessary to organise many activities in which problems can be experimented in the classroom to allow the required skills to become in-built. But beyond these skills, the ability to know which knowledge is needed to solve the problem is also vital.
sorry it seems that I could only attach a document at the time, here is the AAlborg one.
Best,
Catherine
I think that you can't teach problem solving. You can only show different approaches to problem solving or give students problems which require nonstandard approach. The problem solving is something one needs to learn on their own solving different problems, the more different the better. Good skills are developed during the whole life starting from childhood based on any kind of problem solving like crosswords and similar activities.
I agree the development of problem solving skills need to started ideally as early as possible. Also people problem solve all the time; as an adult if you can't you couldn't function. But I still believe we/I need to look at how we help students to enhance their problem solving skills or even to not hinder them enhancing their skills in this area. As an example confidence to learn from mistake and not being too risk adverse. University should be, to a certain extent, a 'safe' place for students to make some mistakes that learn from with the guidance of tutors.
To solve a problem is important to consider some additional tools that can contribute to the analysis and construction of answers to the classic questions of what? how? and for what?:
• Brainstorming. This technique is used to encourage participation from each member of the team. Brainstorming helps to break people out of the typical mode of approaching things to produce new and creative ideas. It creates a climate of freedom and openness, which encourages an increased quantity of ideas.
• Root Cause Analysis. The objective of Root Cause Analysis is to find the fundamental cause for a problem. One way is to ask "Why?" five times or more to really get at the root of the problem.
• Cause and Effect Diagrams. This diagram is drawn to represent the relationship between an effect (the problem) and its potential causes. The diagram helps to sort-out and relate the interactions among the factors affecting a process.
• Pareto Charts. A Pareto Chart shows a frequency distribution where each bar on the chart show the relative contribution of contributing problems to the larger problem. It help to identify where to focus energy to obtain the most positive impact.
• Flowcharting. A Flowchart is a map that shows all the steps in a process. It helps in understanding the process and making sure all steps in the process are addressed.
• Decision Matrix. A Decision Matrix is useful when faced with making a difficult decision. The options or alternatives are listed in the left-hand column and the selection criteria is listed across the top row. Each of the options are rated against the selection criteria to arrive at the best logical decision.
Just to establish the obvious point - if you can study "it" in a book, express it as a multiple choice test or a five paragraph essay, or capture it in an algorithm or a MBA's business chart, "it" is probably not creativity, at least not in the science and engineering sense.
If you give me a hammer, and I can swing it, did I build something?
Hey problem solving can be demonstrated by solving a problem Just solve a problem with students where both teacher ans students take part. Highlight the important steps. The method so that the students get the method and students can do the rest themselves.
Problem solving is not the same as creativity. Creativity starts when you recognize that the approach documented in your textbook *doesn't* provide an answer that meets the requirements you've been given for the solution of your problem. The parts that can be studied are methodical approaches to defining both requirements and testing that identify the need for creative solutions.
The issue aggravated by the academic/business approaches suggested here is that the traditional approach is to redefine the problem to make the method at hand serve. That is: remove the need for constructive creativity.
I am Agree with Gonzalo Galileo Rivas Platero · 13.37 · 13.84 · Tropical Agricultural Research and Higher Education Center
To solve a problem is important to develop an structured system to solve problems 1rst You have to identify well the problem.
2nd You have to teorize and analyze the causes. In order to find the solutions
3th You have to theorize and study differentes alternatives to solve problem
4th You have to evaluate alternatives and select the optimal
In tha way you need some tools as have been explained by Gonzalo Galileo Rivas that can contribute to the analysis and construction of answers to the classic questions of what? how? and for what?:
• Brainstorming. This technique is used to encourage participation from each member of the team. Brainstorming helps to break people out of the typical mode of approaching things to produce new and creative ideas. It creates a climate of freedom and openness, which encourages an increased quantity of ideas.
• Root Cause Analysis. The objective of Root Cause Analysis is to find the fundamental cause for a problem. One way is to ask "Why?" five times or more to really get at the root of the problem.
• Cause and Effect Diagrams. This diagram is drawn to represent the relationship between an effect (the problem) and its potential causes. The diagram helps to sort-out and relate the interactions among the factors affecting a process.
• Pareto Charts. A Pareto Chart shows a frequency distribution where each bar on the chart show the relative contribution of contributing problems to the larger problem. It help to identify where to focus energy to obtain the most positive impact.
• Flowcharting. A Flowchart is a map that shows all the steps in a process. It helps in understanding the process and making sure all steps in the process are addressed.
• Decision Matrix. A Decision Matrix is useful when faced with making a difficult decision. The options or alternatives are listed in the left-hand column and the selection criteria is listed across the top row. Each of the options are rated against the selection criteria to arrive at the best logical decision.
Hello,
For problem solving is important to build an open relation with your students.
Lab/seminaries attendance is "required" but a cooperation is more useful.
Then, as already stated here - is important to avoid "comfortable" problems or to redefine them for an easy answer. That is not the case in real world (except you are able to negociate with your client). Thus I try to avoid round numbers like 1Kohm , 1khz...50KHz ... or already known situations/ examples
Then is important to encourage every point of view - regardless if does not lead to the desired solution. It is important to learn that there are wrong paths, but some deserves more or less to be analyzed. A wrong path approach should be explained without to accuse the solver. All must learn from this like a real team.
Funny stories / jokes related to technical topics might help to connect minds to the problem or to fix what was discovered.
Reveal examples from your own experience.
I am agree with Velentin, and you can use study cases which put them in a similar as real situation, put a film and reflect together and analize the different aspects to find differents aspects of the problem causes a alternative solutions.
I have an excersice form the professor Dr. Joaquín Tena of EADA in Spain which help me to do this with my students... I will share with you... But, please cite the source
1. Make students interested in problems first.
2. If they know the problems well, they will take interests in problem-solving too.
3. For that one has to be a good influencer in effective communicating.
@Samit Gupta absolutely true. The biggest advantage that teachers have is that when excited, when interested, people are problem solvers by nature.
The downside is that, to me, you are really saying that to teach problem solving one must have great teachers; a great teacher is one who can stimulate an interest in the subject.
1st is the 1st!!!!!!! I am agree with Taylor and Gupta, but you need to use some strategies in a way that all you enjoy solving the problems together...... You can be fun... cool studying, and you need some aids to provoke the stimulation ... The video discussion is an strategy the roleplay game is an other and study cases.... All are very effetive is you try to motivate and to make an enjoyable class for problem solving!!!!!
Chalk and talk is the best way to teach students to understand the concepts clearly and for practical and effective teaching, teaching with models and videos will be successful.
And in teaching, the satisfaction comes, only if u teach using chalk and talk approach.
1 more suggestion, The teacher need to communicates well and speak louder, even the student in the last should hear. So, that, the students will surely listen and put interest in the subject..
I agree that students need to be interested in the problems first, I also think though there is an element of 'ownership'. After, some initial skills development, to get the students engagement there needs to be be a change in ownership of the problem, from the tutor to the student.
An example of what I mean is the student's language should change from "What do you want me/we to do next?" to "This is what I/we thinks should come next".
Again, I find the contrarian part of me coming to the front - There is a basic danger in looking to focus on teaching problem solving: losing the idea of teaching a domain. Engineers need to be taught physics and mathematics, for instance, as well as problem solving. American secondary schools are now infamous for teaching problem solving, empathy, and self esteem, but failing to provide reading, math and science understanding.
I would suggest that the critical leap is to teach problem solving as well as the core disciplines in the given area of study. The only solution I know, in science and engineering: build something.
James Taylor touched a Point regarding my teaching experience for a Group of American engineering students. His comment regarding "American secondary schools ... failing to provide reading, math and science understanding" seem to reflect the Problems of the students in my mechanical Engineering class. While the shortcomings in physics and mathematics reduces their ability or success in correct Engineering Problem solving. This Problem is more severe with the male than with the female students by the way (just personal Observation).
My answer is actually a question: Is there a repository of interesting problems to learn and try solving? I always think of high-school physics (Newtonian) as an excellent field to learn that art. It seems to be (to me) less boring than mathematical challenges which are (by nature) too abstract. There is a fundamental problem solving art even before going into the different disciplines specializations.
I remember a study of progress in writing skills. The teacher had the students copy (write or type) one or more paragraphs from various works of literature and measured an improvement in the students' writing. I think a "walk-through" clever solutions is a great teaching aid.
One of the greatest experiences I had in my biomedical engineering classes was a series of journal club seminars, often taught by a long-time researcher in the field. Over the course of a year and a half the class traced the critical papers in the area of defibrillation, from the turn of the last century to the present. I have never been instructed by someone with such a grasp of the history of the field, who could express the understanding at that point in history then explain the insight that made the paper or experiment under consideration crucial.
A grasp of the development history is huge - not just repeating the experiments, which can be important, but understanding the order of it, the motivation of it and the limits which prevented faster development, or made clever solutions necessary.
One interesting consequence is that this becomes a great repository of teaching problems. Updating experimental methods, extending analysis of the data, based on current understanding, or often simply re-examining and re-displaying the data in that original work is often an insight building exercise.
@Joseph Mcelroy It seems to me that you describe the classic approach to teaching in the arts, that is, copy a master work, employing the same technique that the original artist, the painter or sculptor, used. I think there is something to be said for separation - a clear understanding of the tools, their competent journeyman use, and the domain in which those tools are applied, where creative application of the tools is expected.
I think
1) Give them many questions about the subjects or problem (motivation )
2) Give them the information(diferents forms)
3) Make differents groups
4) Give them a prudential time for study, discuss , make a sumarize and conclusions.
5) They should be explain about it and discuss with their classmate
6) Finally the teacher ask them many questions and rerinforce the conclusions and put real cases and his experience.(Put grades, motivation)
7) Aplications, excercise
8) The next class make some questions about it. (put grades)
Thats all
Thanks
I think
1) Give them many questions about the subjects or problem (motivation )
2) Give them the information(diferents forms)
3) Make differents groups
4) Give them a prudential time for study, discuss , make a sumarize and conclusions.
5) They should be explain about it and discuss with their classmate
6) Finally the teacher ask them many questions and rerinforce the conclusions and put real cases and his experience.(Put grades, motivation)
7) Aplications, excercise
8) The next class make some questions about it. (put grades)
Thats all
Thanks
In the everyday world, the first step and sometimes the hardest before solving a problem is recognizing that the problem exists
This implies that students not only need help to solve problems but also to recognize them. Because sometimes, problems? Invent?? so that train students to solve problems that were previously designed for them, not prepared, in effect to make a choice for themselves of the important problems. In conclusion, students should be taught not only how to solve problems but the ability to be able to recognize the problems worth solving.
The ability to think is a complex skill or, rather, a set of skills developed along different lines. Furthermore, the knowledge does not match. Business thinking is the ability to apply knowledge effectively. The more knowledge you have the more likely that the thought is richer and more effective intellectual running. People with a lot of knowledge can differ greatly in their ability to think, to apply what they know.
Learning to think helps improve intellectual performance in abstract matters and better school performance and competence in social situations.
Through the knowledge taught in the curriculum areas, teachers can and should emphasize the importance of participation, exploration and discovery as strategies of knowledge by students.
In general objectives at this stage areas, specifically include different aspects of teaching thinking. Although the use of thinking strategies seems more related to the scientific content of some subjects, in all areas of cognitive control required to plan, manage and implement these strategies to other learning situations.
To motivate positive thinking is needed:
1 - Present the students moderately difficult tasks, adequate, or too easy, or too difficult for their realization is an occasion to perceive or experience who are proficient. Messages should be avoided involving excessive criticism and give importance on the contrary, job well done to all.
2 - Provide the student experiences of autonomy that generate self-satisfaction, which gives them perform interest simply because of them.
3 - Teaching students to plan time to work and know what are the minimum conditions of the learning environment (light, location, temperature ...).
4 - It is important to involve the family to work with schedules and control the physical conditions favoring the study.
5 - The activities to implement technical programs of study should be undertaken outside of the teaching process. On the contrary, they have to respond to a fully incorporated into development planning of curriculum subjects.
I am agree with Gonzalo...... But at the practices (my thought)..... I have developed some steps:
1st step is that they understand what and why .... What is the problem and which are the causes of the problem.....
2nd step is to achieve they agree with the argumentation with all group or in a small teams...... you can use to make easy with different approaches the subject they are looking for..... Using different tools to organize they ideas... Pareto, Ishikawa, multicriterial matrix, correlation diagram..... Explaining some methods to solve problems, that are used commonly
3rd step is to demonstrate the applicability of the tools you are trying to introduce with a real problem they can introduce
4th step is to deconstruct the problem, and to correlate causes and efects using the tools explained before..
5th step is to leave them in small groups to argument the problem and causes, and choicing the best tool to solve problem..... And demontrating by using them......
In the process of teaching problem solving, we must consider first the question Why teach thinking? "Which has many answers. How reasonable is one one of them in particular is likely to depend, on how one conceptualizes the thought or what aspect (s) of thought like
emphasize one. Increase people skills to solve well can increase their income. Getting people to be more observant, can aesthetically enrich your life. Should not be surprised if the acquisition of better listening skills, increase social interaction. Learning to observe controversial events from the point of view of others, would similar beneficial effect. Learn to analyze and evaluate arguments critically, should make one less susceptible to manipulation and washing brain, as well as a knowledge of several approaches may be illogical used to influence the behavior and beliefs shape.
Becoming more critically reflective, one can probably challenge established ideas, institutions and ways of doing things. But this can be unfortunate seen only by those who believe that the old ideas, the institutions and ways are impossible to improve. And if such a belief is true we are in serious trouble.
While sharing much with the rest of the animal kingdom, we are unique in the degree to which our behavior is controlled cognitively, in instinctive opposition. We have options and the ability to choose. We have the ability to foresee the consequences of our choices and to evaluate our options before choosing between them. Not only can we see the past, but imagine a range of possible futures. We are not limited to view things only from our own peculiar views, but we are able to treat, at least, to see them from the specific viewpoints
other people.
We are capable of such things, but these skills need to be cultivated because we are also able to blindly follow authority, act without thinking the consequences of our actions, our opinions have shaped and our behavior and illogical arguments composed by an amazing
variety of persuasions illogical, believe that the future will be what will and will not take
steps to do what it could be and failing to make any effort to see the things from the point of view of others.
If we are serious about learning to think, we must learn ourselves become better thinkers. We must be prepared to have our own beliefs and opinions competitive in the marketplace of ideas. Our conception of a thinking person must acknowledge that not all thinking people, think equal. Not all reach the same conclusions given certain events. Certainly not have the same insights, or be creative or inventive in the same way. Maybe all we can hope for is to share a love for the truth and a promise of rationality, but this is already much, really. We try to teach thinking in the broadest sense. The risks of not doing so, are unacceptable. And our hope should be that studentslearn more than we yet know how to teach.
There are many different ways to teach problem solving, especially in a scientific and engineering context, but there are a number of common steps/elements that should be used to introduce the problem and ultimately solve the problem.
0. Problem Introduction: problem solving objective(s) provided here (teacher)
1. Problem Context: clarify problem; determine subproblem(s) to solve (student)
2. Problem Hypothesis: determine information/tools for solution (student/teacher)
3. Problem Solution (Approach): determine process(es) to solve problem (student)
4. Record/Document: try approach(es); document results; problem solved! (student)
5. Implement Solution(s): demonstrate solution; describe solution to others (student)
Obviously, the teacher will be involved in each step to provide insight and guidance, but the bulk of the work is done by the student. The teacher can really help by providing information in Step 2 to help the students increase their subject matter knowledge which will help them solve the problem. Students in this model learn (on their own) the importance of subject matter expertise (domain knowledge) in solving problems. They learn that different areas of expertise, knowledge and skill are required to solve problems. Teachers should provide their expertise in Step 1 as well, but only after the students have exhausted their knowledge in their initial attempts.
Please try mind mapping. It will make many ideas to the stundets. Then you introduce case one by one. It works as I already used..
I ran across this related article, http://tinyurl.com/kzetdcm. To the extent that Google hires "problem solvers", there is this interesting comment: "when I was in college and grad school is that you knew the professor was looking for a specific answer. You could figure that out, but it’s much more interesting to solve problems where there isn’t an obvious answer. You want people who like figuring out stuff where there is no obvious answer."
There is more discussion there worth bringing into this, but the problem with trying to teach problem solving is that two untested problems challenge, that the student's bias and usual focus is satisfying the professor, not tackling an unsolved problem, and that the professor may not know how to solve a problem.
I have been teaching Engineering classes for a total of 4 years. The best way to teach problem-solving is from day one present tasks to the students for them to propose a solution. And very importantly, when that task is accomplished, remind them how much engineers can do. A gradual degree of complexity has to be added to future tasks. I also found important to point out to students which of the basic sciences they had to use to solve a given problem. I believe that helps students to build an organized way of thinking.
Some guiding questions that can help solve a problem:
What do I want?
What do I have?
What prevents you from having what you want?
How does the problem persists?
What am I doing to keep the problem?
What results I've had so far?
What I learned from them?
The answers can be ordered brainstorm and then place them on a map of concept for analyzing possible solutions. It is important to consider a view from the perspective of systems thinking, which is based on the perception of the real world in terms of wholes for analysis, understanding and action, unlike the approach of the scientific method, which can see only parts of it and disjointed way.
Would recommend the teachings on Creative Problem Solving by Prof Min Basadur
https://www.researchgate.net/publication/262068858_Creative_Problem-Solving_Process_Styles_Cognitive_Work_Demands_and_Organizational_Adaptability
Article Creative Problem-Solving Process Styles, Cognitive Work Dema...
Dear Colleagues,
Good Day,
The formulation of the problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.
---- Albert Einstein
"Tips and Techniques
Communicate
Have students identify specific problems, difficulties, or confusions. Don’t waste time working through problems that students already understand.
If students are unable to articulate their concerns, determine where they are having trouble by asking them to identify the specific concepts or principles associated with the problem.
Make students articulate their problem solving process.In a one-on-one tutoring session, ask the student to work his/her problem out loud. This slows down the thinking process, making it more accurate and allowing you to access understanding.
When working with larger groups you can ask students to provide a written“two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems.
Two-Column Solution (Math)
Two-Column Solution (Physics)
Encourage Independence
Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
Have students work through problems on their own. Ask directing questions or give helpful suggestions, but provide only minimal assistance and only when needed to overcome obstacles.
Don’t fear group work! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others
Be sensitive
Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing positive reinforcement to let students know when they have mastered a new concept or skill.
Encourage Thoroughness and Patience
Try to communicate that the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.
Expert vs. Novice Problem Solvers
Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills, a teacher should be aware of principles and strategies of good problem solving in his or her discipline.
The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book How to Solve It: A New Aspect of Mathematical Method(Princeton University Press, 1957). The book includes a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.
“The teacher should put himself in the student’s place, he should see the student’s case, he should try to understand what is going on in the student’s mind, and ask a question or indicate a step that could have occurred to the student himself.” — George Polya, How to Solve It
Novices in a particular field typically have not yet developed effective problem solving principles and strategies. Helping students identify their own problem solving errors is part of helping them develop effective problem solving skills."
Dear Colleagues,
Good Day,
Please, see the attached link which is related to the thread, it has the title "Tips To Teach Kids Math Problem Solving Skills", .....
http://tutoringmaths.blogspot.com/2014/08/tips-to-teach-kids-math-problem-solving.html
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