Teaching Students Resourcefulness Skills

November 6, 2012

Being resourceful means being able to get the information and results you need.  It takes practice, but is a skill that is of benefit in many areas of life.

Problem Solving Success results from a combination of:

  • Necessity  (This problem has to be solved.)
  • Knowledge (Underlying Principles have to be understood.)
  • Resourcefulness/Creativity  (Open-mindedness and confidence when a solution is not obvious.)
  • Persistence (Relentless effort)

Steps to be  Resourceful:

  • Evaluate a proposal.
  • Realize that mistakes and choosing wrong directions are inherent in the process.
  • Take action.
  • After each attempt, use the experience to pick up a clue from the result, make a change and try again.  Working Questions may help change the perspective and pick up a new lead.  A new lead is crucial; a common frustrating mistake is to just keep trying the same thing again.
  • Repeat.

Working Questions–Put aside the current approach and consider these questions:

  • What requirements are not met by the current proposal?
  • What is your goal?
  • Where is the effort most needed.  Is that where it is being put?
  • What are other perspectives on the problem?
  • What are other ways of thinking about resources?

Forward: What resources are  required and not currently available?

Backward: What can be done differently with the resources available?

  • Who has information to contribute a different skill or perspective?
  • What is one more idea to try?
  • Has a similar problem been solved by someone else or in a different context?
  • How can search engines be used effectively?

The first choice of search terms is often not the most effective.

Use the results of the initial effort to identify more appropriate key words)

Consider searching “images” .  This can be an efficient way to scan information.

Learn and apply advanced search techniques to focus search results.


Effective Quantitative Problem Solving Methods

January 5, 2010

Solving applied quantitative problems is both an art and a skill. People often give up early even though they have the ability to solve them. Often, it is because they do not have a clear idea of a few key points of the problem solving method. The three topics below can help you to become more effective with solving these problems.

1. Understand the Problem Solving Process

Expect to be confused and frustrated “I have no idea what to do.”

Confusion and frustration are part of the process of learning. The important point is not to be defeated by them. Everyone in a college course has the ability to do the assigned problems. No exceptions, you have gotten into the college program. The problems may be difficult and require significant effort, but you should be confident that you can do them.

After you work through confusion a few times, confidence (and persistence) will begin to grow.

Experiencing confusion and frustration is similar to weathering a summer storm. The storm often comes on suddenly and strongly, but then it passes and the sunshine returns.

Watching is not doing

Problem solving is a participatory sport, not a spectator sport. Hearing an explanation, or seeing a worked out problem is different from being able to do it. Make the effort to do the problems, not just follow the explanations.

The explanation is the first step, but you must go beyond it. For exams, you will be asked to solve problems yourself and demonstrate that you can do that. You will not be asked if you can understand the explanation given in class.

2. Effective Thinking

Identify a Known Starting Point–The First Step to Ending Frustration

Suppose that you fall down a steep hill. First you grab on something to stop the    fall. Then, you pull yourself back up a step at a time using rocks, trees or whatever is within reach to grab on and use. Getting started on a problem is like that.

Read the problem with the intent to understand the words and content, not to solve it. If you are not clear how to begin, take a step back and find a fact that you do know. The important point is to find a foothold to begin.

Example Starting Points:

A worked out example.

A definition of a key word that is in the problem.

A diagram.

A short conversation with a classmate or a teacher.

It is important that you look and find a starting point to progress, rather than allowing time to go by.

Understand by DOING the worked out examples.

If you have worked examples available, COVER the solution and work it out yourself. If the examples are not understood, it is usually a waste of time to spend much effort on the new problem before understanding this. Go back to the earlier step and find a new starting point.

After doing the example yourself, read the new problem slowly, understand what it is stating and what it is asking. See how the information in the new problem relates to the earlier examples. The examples will show you which formulas or equations are needed. Formulas are the key that turns the words of a problem into symbols. It may help to draw a diagram.

3. Doing the Math

Stay organized so that it is easy to retrace your logic when you make a mistake.

Write slowly and neatly. Sloppy writing leads to errors. Leave plenty of blank space to make it easier to follow. There is the temptation to just write things down and hope for the best. This approach takes more time in the long run. Errors are part of the process and it is much faster to find them when the work can be easily traced back.

Make the units work for you.

Know the units of the final answer to the problem. Keep these in mind so that your solution is consistent.

Every time you write a number or symbol down, include the unit right after it in clear writing. Keep track of the units throughout. Inconsistent units can alert you to logical errors.

When a spicy meal is prepared, the spices are added during the cooking process. They are part of the food. If spices are added when the meal is served, the taste is not nearly as good. Units are like that. Make them an integral part of cooking the problem.

Do the calculations last–after the set up is right.

Get the logic right before you do the math. Then, substitute the numbers for the symbols of the equation. Set up all of the numbers and units before you do the calculation.

Doing the calculations at the end makes it easier to distinguish between errors in the logic applied to the problem and math errors.

Check for reasonableness and unit consistency.

Remember that all of these problems relate to the physical world. In some cases, you may have an idea or estimate of the range that the numerical answer should be. If it is far off, then, you can begin to check.

Keep these points in mind, when you find yourself “losing it” working on a problem. You can surprise yourself by the difference they can make.

Strategies for Difficult Exams may be useful when it comes time for the test.


Working Smart—Strategies for Difficult Exams

January 17, 2008

Most students give away a half a letter grade by not showing all that they know on tests, particularly those requiring problem solving skills.  It’s worth a few minutes to improve the strategy to do well.  Here are some suggestions.

Just pick one or two that is appropriate for you to keep in mind.

Take a deep breath before beginning in order to calm your mind. Racing forward in the first few minutes can lead to careless errors that are difficult to identify and correct.

Preview the test before you answer anything. This gets you thinking about the material. Make sure to note the point value of each question. Quickly estimate how much time you should allow for each section according to the point value. This preview should only take a minute or two.

Read the directions Never assume that you know what the directions say.

Underline with a pencil what you are asked to do. This will force you to focus on the answer.

Keep track of the time and progress during the test.

Answer the easy questions first. This will give you the confidence and momentum to get through the rest of the test. You are sure these answers are correct.

Go back to the difficult questions. While looking over the test and doing the easy questions, your subconscious mind will have been working on the answers to the harder ones. For problems with multiple parts (i.e. a, b,c,d), and use the earlier sections for hints to solve the later parts.

Answer all questions.  

Avoid careless errorsThink before you start writing.  When the writing starts on the wrong track, it is very difficult and time consuming to rethink the problem and start over.

Review the test carefully, especially the easy questions.

Use all of the time allotted for the test.

Show all your work (especially when partial credit is awarded) and write as legibly as possible.

Strategies for working on quantitative problems are outlined in Effective Quantitative Problem Solving Methods


Teaching Problem Solving to Students—Using Tools and Resources

November 9, 2006


If the problem at hand is to drive a nail into a board, you need a hammer. The right tool and it’s a simple matter. Without it, you can’t get the job done. Worse, if you don’t know that you need a hammer, there is just a nail, a board, and increasing frustration.

 

Problem solving also requires the use of the appropriate tools to make progress. For straightforward problems, the use of tools is often not noticed. It’s when students begin to tackle more complex problems, that it is necessary to explicitly use tools and resources. For some students, it’s a habit that has to be learned.

Tools are personal skills that can be applied to the problem at hand. Examples are mathematics, the scientific method, previous experience, and analytical insight.

Resources are people, materials, and information that can be found and made available for use. Resources often take the form of expertise that can be sought out for a specific need.

The difficult teaching part is to help the students recognize that specific skills or information are needed in order to resolve more complex problems. There is an irresistible temptation to plunge right into the problem or project. It is like trying to drive the nail without a hammer. The students quickly get mired and never really get back to putting full effort into it. The problem solving approach is replaced by a hope that the problem will solve itself.

This is the time for the teacher to take a step back with the student and identify what tool or resource must be applied to the problem. A valuable exploratory question:

“What else do I need to solve this problem?”

This question interrupts the drive to jump into the trying to work out a solution. It introduces the idea that something essential may not be available at the beginning of the problem.

“What else?” is an exploration that ultimately makes the solving the problem possible. However, there is a tendency to provide a general answer to this type of question. The student should be encouraged to get the detail needed so that an action can actually be taken.

Referring to the initial example with the board and nail: An answer of “something to hit the nail with” is moving in the right direction to work on the problem, but it is not quite enough. “Hammer” increases the detail to a level in which the task can get done.

The question also reinforces the idea that additional tools may be required for complex problems and that it is part of the job to identify and use it. Then, appropriately equipped, the student can go back to the problem as it was stated.

Finally, reinforce the use of tools/resources and emphasize that is the general method to keep in mind for future problems.

 A related article is Teaching Problem Solving to Students–The Cycle of Confusion/Resourcefulness/Confidence.


Teaching Students Problem Solving— Goal and Strategy

October 24, 2006

At some time, often as early as middle school, the complexity of school activities ratchets up a notch. Simple reading assignments are replaced by projects requiring multiple steps such as a paper requiring research. Clubs begin taking on more involved projects. There is a transition here and just a little guidance about problem statements and strategy can go a long way toward making it successfully. A problem statement, strategy plan, and a method to stay on track can help students to manage larger problems and projects.

State the Problem/Goal

Often, the goal is clear to everyone and stating it seems to be unnecessary. Sometimes though, there is a misunderstanding about the problem or goal. Any confusion on this point can lead to wasted time and work leading to an unsuccessful project. A key question to answer:

“What does a successful project look like?”

As simple as it sounds, take the time to answer this question and state the desired result clearly. The student should be able to visualize the finished product. The goal must be a quantifiable, physical fact.

The expected date of completion should also be included. If it is a group project, write it down so that everyone can agree.

Make a Strategy Plan

For a project with multiple steps, a plan that the student has made himself can help to keep the work on track. The strategy plan outlines a roadmap for the project or problem solving activity. The strategy is written down before the actual work begins. Once the plan is made, there must be an intention to follow it.

 

Two questions that can guide making the plan are:

“What are the steps required to complete the project?”

“Why is this action being done?”

The plan essentially allows a big project to be reduced to a sequence of smaller tasks, each of which can be done by the student. The progress of the work can also be checked against the plan.

For example, if the assignment is to write a paper about the pyramids. The goal statement may be the subject of the paper, the length, the number of references required, the format, and the due date. A strategy plan could include the sources for the research, the completion date for the research, analysis of the research, and submission of the first draft.

Expect Changes—Stay on Track

Not even the simplest project follows the plan. Changes are not a big deal if they changes get things moving back in the direction of the stated goal.

The original plan provides a basis for making these changes. The overall question is the similar:

“Why is this change needed?”

“How is it related to reaching the goal?”

One risk with changes is the student can lose sight of the goal and drift off in some other direction. These questions can help to focus the child on the reason for doing the work in the first place. A reality check keeps the work on track.

 

With a little experience, this framework of a problem statement, a strategy plan, and method to stay on track can be used intuitively on other projects.

related articles are: Teaching Problem Solving to Children-The Cycle of Confusion/Resourcefulness/Confidence and Teaching Problem Solving to Students–Tools and Resources 

 


Teaching Students Problem Solving—The Cycle of Confusion/ Resourcefulness/Confidence

October 21, 2006

“I am completely lost and do not understand this at all!”

Who among us has not let out this wail when wrestling with computers? We have all been confronted with a seemingly insoluble problem in the operation of a computer. These problems appear unpredictably in different areas—software bugs, network connections, hardware failures, and viruses to name a few. The initial situation appears dire, but over time, individuals find ways to resolve the issues and get back into operation. These methods may include trial and error, consulting friends and vendors, or even looking at the instructions. Confusion, resourcefulness, and confidence all come into play.

Resourcefulness and confidence are important traits that can be learned to develop more proficient problem solving skills. However, since the immediate focus is usually on the content of the problem (Get that computer working!) many people, especially children, are unaware of this cycle role in the problem solving process. These traits can best be discussed when there is no immediate crisis.

Confusion
Problems, by their very nature, often present ambiguous, frustrating situations. Confusion is a normal reaction and often arises early in the problem solving process. If confusion is unexpected and disorienting, the ability to work on effectively solve the problem diminishes. When people are not comfortable with confusion, emotional flashpoints often erupt.

One way to recognize the negative effects of confusion is by a lack of specificity in the complaint. (“I am completely lost. or “I don’t know anything about this.”)

In teaching problem solving, emphasize that confusion is a natural part of the problem solving process. Plan for it. The first step develop an awareness that being confused is expected and not a big deal. Then, the direction is to accept and become comfortable with the ambiguity of the situation so that the focus can be on working on problem itself. Teach students to recognize the emotional component of confusion, and to take the time to let the emotions settle so that they are able to work at their best ability.

Resourcefulness
Resourcefulness is the capacity to find new approaches when earlier paths are blocked. The direction is to show the child a way to allow the energy of confusion to be used in an effectively. An excellent first step is to interrupt the reinforcing action of the confusion. The most common method is to take the time to propose alternative ideas.

Typical questions that can help redirect the energy to new options:

“Can the problem be restated in a different way?”

“What do I know about this subject?”

“Who may know more about this than me?”

The questions may only take a few minutes to consider. However, it is also an important step to begin to identify other paths and different ways of seeing the problem. New possibilities for thinking about the problem can open up. The confusion doesn’t necessarily end, but the hold on the mental functions is weakened.

Building Confidence

Use personal examples from their own experience of confusing problems that they resolved. Talk through the steps in detail. Highlight the ways that the options were expanded. Although this approach may appear obvious, children do not always recognize their own process of learning.

Returning to the example with computers: Young people especially have confidence in their computing ability. Often, they have developed more proficiency in computers than their parents. Take a specific example of a problem they have resolved. Explore with them how they felt when the problem surfaced, how their understanding grew, what operating problems they faced, how they overcame them and their increased skill by confronting and solving the problem. This exercise introduces the ideas of confusion, resourcefulness and confidence in a way that they have experienced. They can see this for themselves. As confidence grows, so do the problem solving skills.

Finally, emphasize that the skills are theirs and can be applied to other subjects—like math!

Related articles are: Teaching Problem Solving toStudents–Goals and Strategy
and Teaching Problem Solving to Students–Tools and Resources

Detailed methods are outline in Strategies for Difficult Exams

and  Effective Quantitative Problem Solving Methods