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How to Foster Critical Thinking - Problem Solving Skills

How to Foster Critical Thinking & Problem Solving Skills

The ability to think critically and solve problems is useful in many areas of work and study. These skills can be taught and learned separately, although critical thinking is often useful in problem solving. Thinking critically means considering things objectively, including the pros and cons or problems and benefits of a topic or situation. Thinking critically enables you to take a balanced look at a topic which is useful for essays but also for making decisions in real life. Problem solving skills are useful in many situations such as, working out math equations, working out the best route to get somewhere or deciding how many people you need to hire to finish a project.

Critical Thinking

Determine the facts. To think critically, you must be objective and that means differentiating between what you assume, or what you think you know, and what is factual. You may need to perform some research to ascertain more detail. This could involve spending time at the library, searching online or talking to colleagues or people from other organizations. Gathering data and establishing the facts is key to being able to critically think about something and solve related problems.

Assess your data. Think of resources you can use to determine more facts and consider the value of those resources. Are they biased? Are they based on someone's interpretation of the facts? Are they only relevant to one country or culture? Are they historical? Interrogating your data sources will help you interpret that data effectively and critically.

Balance your perspective. If time allows, using a wide variety of data sources will help you balance your perspective and help you to think about a topic openly and without prejudice. If you are on a tight deadline and you think your research may not give a full picture of the topic, bear this in mind when you assess the data you have.

Practice your critical thinking. You don't have to wait for an essay to be assigned to you at college, you can employ critical thinking in all kinds of situations. If you've just watched a movie that made you laugh, think about why it made you laugh. If you believe in God, think about the reasons why you believe in God and consider what other perspectives there may be and why they came about. You don't always have to do lots of research, unless you really are studying for a college assignment or work. Thinking critically can become a habit you use everyday in all kinds of situations. Once you have mastered thinking critically it will help you solve problems.

Problem Solving

Think logically. Logic is often the key to problem solving. For example, if a company employs five people but they have too much work, then the logical solution is to hire more staff. Working out how many people to employ and how many people the company can afford to employ are further, related problems that will also have one or more logical solutions. Thinking critically can help you to work out logical solutions and solve problems.

Research your problem. Make sure you know exactly what needs to be achieved and if there are any timescales, budgets or other similar issues involved. Then you'll be able to logically think through possible solutions until you've solved your problem.

Make it a habit. Completing sudoku games, crosswords and jigsaw puzzles are more than just ways to pass the time. They are all exercises in problem solving that you can use every day to make problem solving a habit. Puzzles like these are easy to solve because you understand the rules. If you're presented with a puzzle or problem you don't understand then it's time to use critical thinking.

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Critical thinking and problem solving Essay by

critical thinking and problem solving

Critical Thinking and Problem solving

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Numerous decisions are taken every day. People choose when to get up on a certain morning. what clothing to wear. and whether to read a particular book. Most of the decisions made throughout the day are relatively trivial or inconsequential. It probably does not matter too much if it is decided to sleep an extra 15 minutes on a certain morning or if a blue shirt is

selected rather than a green one. However. some of the decisions can carry substantial consequences. Choosing to get an undergraduate or graduate degree. deciding on a new job or career. or selecting one vendor out of many candidates to be the long-term supplier of a company of a necessary resource are important decisions that are likely to have a significant and meaningful impact. Learning understanding. and applying critical thinking and problem-solving skills can improve the quality of the decisions that mean the most to us. The research also explores some fields where critical thinking proves a pathfinder in finding the correct solution to a problem

Critical Thinking and Problem Solving

Critical thinking and problem solving have been identified as essential skills for college students. Problem solving is defined as a step-by step process of defining the problem. searching for information. The goal of problem solving is to find and implement a solution. usually to a well defined and well- structured problem. Critical thinking is a broader term describing reasoning in an open-ended manner. with an unlimited number of solutions. The critical thinking process involves constructing the situation and supporting the reasoning behind a solution. Traditionally. critical thinking and problem solving have been associated with different fields. critical thinking is rooted in the behavioral science. whereas problem solving is associated with the math and science disciplines. Although a distinction is made between the two concepts. in real life situations the terms critical thinking and problem solving are often used interchangeably. In addition. assessment tests frequently overlap or measure both skills. Problem solving is defined as understanding the problem. being able to obtain background knowledge. generating possible solutions. identifying and evaluating the process. and exhibiting problem-solving dispositions

It is easy to fall into routine ways of thinking instead of being creative. The accompanying display lists some common barriers to creative thinking

A major block to creativity is groupthink (going along with the majority opinion while personally having another viewpoint. Nurses or the employees of the company. who engage in groupthink generally. wish to avoid interpersonal conflict. It takes intellectual courage to think something new and different from one 's peers. and then act on those thoughts. Independent thinking is a hallmark of persons who think critically and creatively

Critical Thinking and Problem Solving

Critical thinking includes problem solving and decision making processes. People use problem solving in their daily lives. With the problem-solving method. problems are identified. information is gathered. a specific.

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Promoting Critical Thinking And Problem Solving Essay

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Promoting critical thinking and problem solving in mathematics education is crucial in the development of successful students. Critical thinking and problem solving go hand in hand. In order for students to learn mathematics through problem solving, they must also learn how to think critically. Critical thinking has not been at the forefront of teaching strategies in schools. Teachers need to see the importance and the need to begin promoting these key strategies. Critical thinking is such an important aspect for

Becoming a critical Thinker
The process of critical thinking possess many definitions although may be self explained as a highly.

children to learn in school. Many adults today have no idea on how to think critically. This is very sad because thinking critically can broaden your mind and give you such a feeling of intelligence and self-confidence. It used to be that teachers just taught material and gave the answers without any explanation of how the answer can to be. The reason they never gave an explanation was because they were never taught to think critically or even if they

Our Tax System Needs Changing
Our current tax system is complex, costly, and unfair. Surely, America can do better for our children than redistribution and regulation. Our nation is over four trillion dollars in debt.

were, teaching critical thinking is a lot harder than just giving students the answer. We, as future teachers, need to take our job seriously and not always try to find the easy way out when it comes to teaching material. We need to realize the importance of critical thinking and not put it on the back burner. Another reason that many adults today do not think critically is that many educators have believed that only certain students are capable of

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thinking critically. Critical thinking strategies are usually only taught to the “advanced” ;students or the college prep students. Those students with lower grades and in vocational programs are not expected to use these strategies and therefore they are not introduced to them. This is very upsetting because everyone needs to learn these strategies. Critical thinking strategies are not only for the intelligent in an academic setting. These strategies can be used in everyday life. They can be used for finances,

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relationships, and even in life choices. People lacking these critical thinking strategies can be very impulsive and make a lot of choices that end up hurting them in many ways. I read an article by Thomas Sowell called Justice and Injustice. I really enjoyed this article because he emphasized how children on welfare have only about half as many words directed at them as children of working-class families and less than one-third as many words as children whose parents are

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professionals. He also noted how painful this is because scientists have found that the physical development of the brain is affected by how much interaction young children receive. This then links critical thinking with social and economic status. If educators continue to show higher expectations for more “well-off” ;students and lower expectations for others than we will never be able to help a child off welfare or give every child the chance and ability to succeed. Another article I read

Career
The decision to choose a new career was extremely important to me. The function of a career is not just to provide a means to.

was entitled Intolerance is a

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Skills Needed for Mathematical Problem Solving (5)

Skills Needed for Mathematical Problem Solving (5)

3.2 Skills in Problem Solving

Basic mathematical skills such as solving equations and inequalities are necessary for mathematical problem solving. Formulating a problem can be very demanding but simplifying and solving the equation obtained, for example, is necessary to answer the question in the problem. Students who cannot manipulate algebraic expressions will definitely have difficulties in problem solving.

Our students, at UGRU, have difficulties in reading with understanding and extracting the information from the text of the problem. This skill has to be taught explicitly to our students. It is the first step in problem solving and students cannot make any progress if the problem is not understood.

3.3 Thinking and Reasoning in Problem Solving

Critical thinking is needed in all steps of problem solving. Students do not look back critically at the solution of a problem once it is solved. They tend to accept whatever answer they have obtained. Critical thinking is needed when extracting information from the text of the problem, formulating and solving the problem and analyzing the solution obtained. I now give an example of a problem that may be used to give opportunities to students to think critically.

Problem 6: Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Is it possible to find the width of the river using the given information?

Students are guided to make a diagram and write the equations to formulate the problem.(see solution in appendix A)

Let t = 0 be the time when the two boats start moving. Let S1 and S2 be the constant speeds of the two boats and t1 the time when they first pass each other and t2 the time when they pass each other for the second time. Let X the width of the river.

Fig. 4: Diagram including unknowns in problem 6.

Because there are five unknowns and only four equations in the above system of equations. students are tempted to say that it is not possible to find the width X of the river. This particular problem can be used to generate activities where students will have to think in order to come up with a correct answer to the question in the problem. Enough time should be given to students to discuss such a challenging problem. They should be allowed to work in groups and if students cannot finish the work in class, they should be allowed to continue solving the problem as a homework assignment. Students will not benefit if the solution is given to them without giving them enough time to investigate this type of problems. Learning will take place through the time and efforts spent on finding a solution even if they have difficulties finding one. These types of problems involve a lot of thinking both to understand the problem and to come up with a solution and they are necessary if we want our students to develop their thinking skills to the highest level possible and become genuine problem solvers.

It is not difficult to design problems that can activate students thinking. One has to avoid problems with one obvious solution. Note that the question in problem 6 does not say �find the width of the river" but �is it possible to find the width of the river using the given information?". A question of the type �find the width of the river" already assumes that it is possible to find the width X. However questions of the second type are more demanding and therefore suitable to develop thinking skills.

Open ended problems, usually with many valid answers, can also be used as tools to generate activities where students have to think in order to come with answers. Useful discussions can be generated in order to compare all valid answers generated by students. I now give an example of an open ended problem.

Problem 7: Create a set of data points that satisfies the following conditions:
� The set includes 8 data values.
� The range of the data set is 20.
� The median is equal to the mean.
Show that your data set satisfies the conditions.

Logical reasoning is fundamental to success in mathematics in general and problem solving in particular. Inductive reasoning uses easy to understand cases to identify patterns and it can also be used to establish relationships between mathematical objects. Deductive reasoning uses mathematical definitions, axioms, rules and theorems to draw conclusions. Deductive reasoning is fundamental to critical thinking. Geometry problems may be used as tools to develop deductive reasoning [14]. I believe that both must be used and explicitly discussed with students.

Critical Thinking: evaluating information

Critical Thinking: evaluating information

This problem can be solved using ratios because the ratio of the weight of bricks to the number of bricks will be a constant proportion.

This is an excellent question because ratios and proportion can be applied to many routine problems encountered in everyday life. Ratios allow you to compute unit prices, projected cost, projected weight and volume, quantity of cooking ingredients, and solve many other common problems.

I am going to spend a little more space on the preliminary explanation because ratios are so useful.

For example, when shopping for the best value of a particular item, ratios will allow you to compare unit prices between items sold in different quantities.

Suppose you are shopping for a particular kind of breakfast cereal. If you are comparing the prices for boxes with different quantities (say, a 48 oz versus 35 oz box), ratios will allow you to compute prices per ounce.

Suppose you are shopping for small bundles of firewood. If you need to compare the prices for different quantities (say. 75 ft³ versus 1.5 ft³), ratios will allow you to compute prices per ft³.

         A direct proportion between two variables means that one variable is a constant multiple of the other variable.

         The terms “proportional relationship”, “direct variation” and “direct proportion” all mean the same thing. The terms are interchangeable.

         The equation for a “proportional relationship” ALWAYS looks like this:

         k is a constant. It is called the “constant of variation”.


      I’m going to rearrange that equation so it looks like this:

         In other words, a direct proportion means that DIVIDING the value of ONE VARIABLE BY THE value of the OTHER variable is a CONSTANT value (k, the constant of variation ). (I’ll apply this idea to your problem shortly).

         For example. if you have a job and are paid by the hour, your pay is proportional to the number of hours you work.

             The more hours you work, the higher your pay.

             The fewer hours you work, the lower the pay.

             However, your total pay divided by the total number of hours you work is a constant value.

             If your rate of pay is $25 per hour and you work 10 hours, you will earn $250.

             $250 ÷ 10 hours = $25 per hour

             If your rate of pay is $25 per hour and you work 1000 hours, you will earn $25,000.

             $25,000 ÷ 1000 hours = $25 per hour

             Pay divided by hours always EQUALS the same number, the CONSTANT of variation. In this example the constant of variation is 25. The constant of variation (25) will not change, regardless of the number of hours you work.

         The equation for computing the weight of one brick in your problem statement is the same equation discussed in the preceding paragraphs. It will look like this:

             (weight of bricks) = k * (number of bricks)


             You need to calculate k, the constant of variation. That is the answer to your question.


             The constant of variation brick is:

             (weight of brick) / (number of bricks) = k

             Since the problem statement presents ¾ of a brick with a weight of ¾ pound:

             (¾ pounds) / (¾ of a brick) = k

             (¾ pounds) / (¾ of a brick) = 1

             k = 1


         The final equation is:

             (weight of bricks) = k * (number of bricks)

             (weight of bricks) = 1 * (number of bricks)

         For the sake of simplicity, let w = “weight in pounds” and n = “number of bricks”:

             w = 1 * n

             when n = 1

             w = 1 * n

             w = 1 * 1

             w = 1

1 brick weighs 1 pound

Math and Problem Solving Worksheets

Math and Problem Solving

Here you will find everything your child need to improve your child’s math skills. There are no formulas and definitions, your child will not memorize. There is an opportunity for your child to think, reason, and argue to convince his opinion.

Do not force your child with correct answers. He has his own logic, and you have no other way to get to know it patiently and kindly to support his version.

FUNtastic math worksheets focus on the development of critical thinking, cognitive skills, reasoning, and problem solving. as well as lead your child to analyze and evaluate the results and become detail-oriented .

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UI Critical Thinking Handbook: Chapter Two - Applications

Chapter Two: Characterizing Critical Thinking

I begin the theoretical part of this chapter by examining the meanings of 'critical' and 'thinking'. After a systematic review of various definitions of 'critical thinking', I serve up the definition that will underpin the remainder of the handbook. I close by supplying an organized list of skills that figure into the process of critical thinking. In the applications part to follow, I offer teaching points and instructional tips related to an understanding of critical thinking and its attendant skills, along with an annotated bibliography of various books that concern critical thinking and critical thinking pedagogy.

  1. Introduce and use the technical terms. Critical thinking, like most subjects, has its own technical terminology. Don’t shy away from using it in the classroom. It serves a number of valuable purposes. First, terms like "argument", "conclusion", and "valid" are introduced to mark distinct conceptual boundaries that you must respect if you are to do a competent job of assessing pieces of reasoning. Second, they fit together into a coherent fabric that should be delivered as one complete bolt and not as a collection of random swatches. Finally, when you use the terminology, you signal to the students that you are talking about critical thinking again. The more they hear these terms, the more ingrained the concepts become, and the more likely it is that they will emerge from your classroom with skills that can be taken and used in other classes.
  • Clearly state the goals of critical thinking instruction. It is crucial to state the goal of this exercise in terms that appeal to the students, and to do this early. For instance, indicate that critical thinkers—i.e. those who can spot arguments, assess them, and respond with understanding—are in control of their own belief systems; they are not (often) victims of big advertising budgets and fallacious appeals, and so are not at great risk from false beliefs. Related to this is the fact that they should walk away from the experience with what amounts to a BS detector, i.e. a set of concepts and skills that will enable them to spot bad arguments when they are confronted by them or are considering them. It is a cognitive tool that they can use to great effect in most of their classes in their lives outside the classroom. It isn't often that one has a chance to acquire such a tool.
  • Don't go overboard. Of course, critical thinking is not a silver bullet—it has not cured cancer (yet), it will not eliminate falsehood, and it will not enable all of our students to get a 4.0 GPA. Don’t overstate the value of it, as students will see through this as if it were glass. Further, it is the sort of thing that should be used wisely. There are situations when deep criticism might be nice, but is not possible because of limits on time or energy. Further, there are times when you should wait to assess arguments, or perhaps knuckle under for the greater good. Nevertheless, on balance, the ability to think for yourself is a good thing—it empowers people, returning control over the life to the one who lives it.
  • Spend time describing and defending your definition of "critical thinking." Be open about how you choose to define critical thinking. Definitions can be constraining, but they can also be useful as a touchstone for the students. It also helps to use the definition to create a framework for instruction that informs the pedagogical moves you make in class; that is, use the definition to motivate a conceptual framework, and then use the framework to set up the way in which you introduce the critical thinking skills over the course of the year.
  • Critical thinkers aren't (necessarily) jerks. Emphasize the fact that you can be a critical thinker without being a critical person. Many students do not like the thought that their education might transform them into their parents, i.e. hypercritical people who can’t take it easy about anything. (Or so I’m told.) Criticism of the relevant sort is criticism of an argument relative to a standard. It is not of people or their ways. Critical thinking is about building oneself up—strengthening the hold one has on one’s own beliefs—and not about running other people down.
  • Be mindful of opportunities to mention critical thinking. You may set aside class meetings to focus on critical thinking, but you should not restrict your discussion of it to those days. There are many skills that count as critical thinking skills---see the Theory section of this chapter for a short list---and they are often employed by students and instructors in exercises, discussions, and other contexts where the focus is not on critical thinking. Mentioning the connection between the work done in these contexts and critical thinking is crucial to the goal of creating critical thinkers, i.e. people who can intuitively launch into argument analysis when the need arises. It is also worthwhile to note when critical thinking is not particularly helpful. Reinforcement, both positive and negative, is a necessary part of enabling students to internalize these skills and then apply them efficiently both in your class and outside of it. (Unfortunately, they may not be reinforced much outside of your class, so there is a burden available, should you choose to shoulder it.)
  • Study the skills list and emphasize them when and where appropriate. This is a development of (F). Read the list of skills in the theory section, and supplement it with other skills you regard as important. Whenever you find yourself and your class in one of the three critical thinking stages, have your teaching involve those skills that are relevant. You should mention them, model them, and walk the students through application of them. The more explicit emphasis you give to these skills, the more ingrained they will become in the minds of your students. (For more on this, see the discussion of rubrics in the Application section of Ch. 8.)
    1. Work on the big picture. Students need to learn the value of critical thinking first hand. Most have done it from time to time, but they likely have not done it systematically or put much thought into when they should do it. Put students in positions to determine where critical thinking is necessary. Work on assessing problems and asking questions. Here are some ideas for how this might be done:
    1. Have students come to class with two or three questions about the readings. If the reading is one that contains reasoning and a conclusion—this could be a fictional piece, of course—then have them identify the conclusion and ask questions about the reasons offered for that conclusion. Have them submit the questions, evaluate them, and return them.
  • Have the students provide one or two sentence summaries of the point of readings written to press a point. This could be done in a free write at the beginning of class, or it could be handed in when they arrive in class. Work on identifying the conclusion first, and then work on identifying the conclusion and the reasons.
  • Have the students tell you if a reading contains critical thinking, or if they feel the need to think critically about a reading. Once they are familiar with what it is, through your presentation of the definition, lead a discussion devoted to identifying contexts in which (i) producers of text or speech engage in critical thinking (e.g. columns, op/ed pages, editorial cartoons, speeches, debates, etc.), or (ii) consumers of text or speech should engage in critical thinking (e.g. watching television, watching or reading advertising, reading newspapers or magazines, etc.).
  • Work on your own collective definition of 'critical thinking'. You should work out the definition of this term that you find most helpful, either by becoming comfortable with one of the definitions in the theoretical part of this chapter or by working up your own. This could be done collectively in the context of a class discussion.
    1. Have the students develop their own definitions, in a 10 minute free write before this discussion. Ask them to muse on the meaning of the term and work toward expressing what they understand by it. In discussion after this exercise, work with what they have developed by asking for illustration and defense. Be sure to do this in light of the meanings of the specific terms. (This is perhaps best done in classes where critical thinking as a topic is part of the stated content of the course, e.g. Core Discovery courses.)
  • This could be done as a before/after exercise---early in the first part of the course and late in the latter part. Alternatively, it might be done early if the students are familiar with the term, or late as a way of checking to make sure that the goals associated with critical thinking skills instruction have been achieved.
  • Ask your students occasionally if and how critical thinking is appropriate in non-obvious contexts. If you have made a commitment to teaching critical thinking skills, you will select texts for the purpose and set aside class time to accommodate lecture and discussion. However, if critical thinking instruction is only a part of your pedagogical efforts, there will be other course modules that are not designed with it in mind. However, it is not a good idea to hermetically seal critical thinking instruction inside independent modules. One way to avoid this is to bring it up from time to time when you are working with different texts and doing different things. You might make a point of working this into your lectures or into the discussions that you facilitate. This can be done when the lecture or discussion is evaluative or because the text you're studying can be read in an evaluative way. Alternatively, you might try to locate the text you are studying in a different context for the purpose of motivating a bit of critical thinking. (E.g. "What sort of life does this novel recommend as the good life, and does it defend that recommendation?")
  • Prepare a handout that introduces the principal critical thinking skills. Early in teaching critical thinking, you should introduce your students to the principal skills that will be involved in the process. Consider an analogy with soccer---in order to learn how to play, you must learn to dribble, pass, trap, shoot, etc.; however, before learning the nuances of each of these, you must first learn what they are, how they are related to one another, etc. The same is true of critical thinking, and a handout can help your students make progress toward awareness of the skills that figure into the process. If one is to work on these skills, one must know what they are; further, knowledge of them can help a student new to the study of critical thinking know when they are engaged in the process or when it is appropriate.
  • Use the Socratic method when teaching the skills. You will likely want to model critical thinking in class, calling attention to the process while you do it. Once the students are familiar with the skills and their employment, you can work through a critical thinking example by asking the students to identify the necessary skills and indicate how they are to be employed. You might prefer to have the students do this themselves in groups.
  • Develop goal formulation skills. What are the goals of those who engage in critical thinking? Often text or speech, containing the output of critical thinking, is produced as a means of achieving these. Ask students to take essays or readings and contextualize them; that is, ask them to determine what purpose they might have been produced to serve. This can be done through short essays, or through group work. It is often done to positive effect in synthetic circumstances, that is, circumstances in which students are asked to bring together a number of different writings.
  • Have students consciously reflect on the criteria and standards they select and apply. During the criteria identification and option evaluation stages, encourage students to reflect consciously on the standards they identify and how they use them. Are the standards context-specific? Are they drawn from the specific subject matter used? Again, this should be a point of emphasis during discussion, but it can also be part of a written exercise. For instance, you might make an argument, or pull one from a text, and then ask them to write a two-part reaction. In the first part, they are to evaluate it, and in the second, they are to comment on the standards they used in the first part and why. This will help students develop an explicit understanding of the stages of the critical thinking process, an understanding that will support them as they apply these skills on their own in other circumstances.
  • Create "self-reflective" groups. Break the students up into groups to solve a problem or analyze and evaluate an argument. Designate one person the "reporter" for the group, but instead of having this person report results, have them comment on the way that the group worked. For example, how did they identify possible solutions? By consensus? How did they evaluate these? How did they test these? Etc. Thus, these are process reporters and not product reporters.
  • Call attention to places where critical thinking is not in evidence and explain why. Have the discussion mentioned in A.3 include some mention of contexts in which critical thinking is not generally found, and why not?
  • III. Annotated Bibliography of Readings Available at the UI Library or via ILL

    What follows is a bibliography of various books on critical thinking. A good many of these are located in the library, but some are only available via ILL. (The ILL books are marked as such.) The materials are listed alphabetically by author's name.

    1. Learning Through Problem Solving. Daniel Apple, et al. (Eds.). This book contains many examples and problems in mathematics that could be used for teaching a variety of critical thinking skills. (Or, alternatively, it could teach problem solving skills that will come in handy as a part of the suite of critical thinking skills you might want your students to acquire.) It is pitched mainly at college instructors, but still worth a look if you teach math.
  • Teaching for Thinking. T.G. Aylesworth. An older book, from 1969. It is similar to Hullfish & Smith, although with more examples. Thee are several "Helping Learners to. " chapters devoted to topics like identifying problems, formulating hypotheses, testing hypotheses, and drawing conclusions.
  • (ILL) Metaphors and Symbols: Forays Into Language. Roland Bartel. A book-length study of the role of metaphor in society and literature. Consideration of metaphor at a number of levels, including the semiotic and semantic. This book would be useful for one interested in a project on critical thinking in literature studies or, more specifically, a project that involved investigation of conversational implicature.
  • (ILL) Developing a Thinking Skills Program. Barry Beyer. A very good reference volume for this class. If this were still in print, I would consider using it as a book for this class. This includes model programs, curriculum suggestions, strategies, grade level keys, consideration of thinking skills that could be taught, etc. Definitely worth a look whatever your project.
  • (ILL) Improving Student Thinking. Barry Beyer. Now this could have been a textbook for this class---indeed, I will use this when I teach the class again. The book is organized into four parts: "Providing a Thoughtful Classroom," "Making Thinking Visible and Explicit," "Guiding and Supporting Student Thinking," and "Integrating Instruction in Thinking and Subject Matter." There are several chapter in here that you should look at, e.g. Chs. 2, 4, 5, 7, 8, 9, & 10. Definitely look at this book.
  • Inquiry in the Social Studies Classroom. B.K. Beyer. This is a must see for social science teachers. It includes a very nice introductory chapter, "The Nature of Inquiry", which is worthwhile for anyone. It includes a lot of examples. Furthermore, the theory and practical applications are well integrated.
  • (ILL) Practical Strategies for the Teaching of Thinking. Barry Beyer. Another excellent reference volume. This isn't as focused on the practical issues of course design as Developing a Thinking Skills Program. but it is still useful. The focus here is more theoretical, and so dovetails nicely with the work we'll do during the first two week. This contains a number of sections that are relevant to the goal of introducing critical thinking skills in the classroom; Chapter One is especially good. Definitely worth a look, perhaps during the first couple of weeks.
  • (ILL) Teaching Thinking Skills: A Handbook. Barry Beyer. This dovetails nicely with the other Beyer books. There are chapters on identifying thinking skills and designing and teaching them. There are also sample materials and reports from teachers who have implemented the teaching of thinking skills into their classrooms. Highly recommended.
  • Asking the Right Questions. M. Neil Browne & Stuart M. Keeley. This book outlines a question-based approach to critical thinking instruction. This treatment seems to dovetail nicely with the approach I've recommended in our class -- see Chs. 3, 4, 5, 7, and 11. There is good discussion of issues relevant to non-deductive arguments, with science applications -- see Chs. 8, 9, and 10. Well worth a look.
  • Education for Effective Thinking. W.H. Burton, et al. This is an introductory text in critical thinking skills from 1960. It includes the following parts: "Reflective Thinking: Definition, Description, and Attitudes Necessary", "The Thinking Process", and "The Teaching Process & Learning to Think." It includes exercises and examples for teachers in a wide variety of areas: general mathematics, elementary education, language arts, social science, mathematics, natural science, etc. It is worth a look, although perhaps you would want to look at it after you have put your own framework in place.
  • Thinking in the Classroom. P. Chance.(1986) A survey of the various thinking education movements out there: Philosophy for Children (see "Links"), Odyssey, Productive Thinking Program, etc. Chance discusses each in detail, remarking on the upside and downside of each. The book opens with a good introductory essay on the Thinking Movement.
  • (ILL) Questioning: A Path to Critical Thinking. Leila Christenbury and Patricia Kelly. This short pamphlet contains a discussion of Socratic technique, i.e. use of well-designed questions to encourage students to think on their own. Contains tips on methods of effective questioning.
  • Patterns of Thinking. J.H. Clarke. This is a relatively new (1990) discussion of critical thinking for the teacher. It is also relatively theoretical. The sections are: "Teaching Thinking", "Frames for Inductive Thinking", "Frames for Deductive Thinking", and "Beyond Graphic Organizers." There are several chapters in each section, and there are examples in each chapter.
  • Writing to Learn Mathematics and Science. P. Connolly, et al. (Eds.). This is a collection of essays. It includes the following parts: "Defining Problems, Seeing Possibilities", "Writing as Problem Solving", "Classroom Applications: What Works and How", "Programmatic Policies & Practices", and "The Context of Learning". If you are a teacher of math or science, look at this book.
  • Imagine That. David Considine, Gail Haley, & Lyn Lacy. This is a book designed for use in the teaching of literature, especially at the elementary level. There are many suggestions for specific lessons. This is worth a look if you plan to teach art or literature to younger kids.
  • Building Social Problem Solving Skills. M.J. Elias, et al. (Eds.). This book has to do with "areas of self-control, social awareness, group participation, and interpersonal decision making." It includes the following parts: "Conceptual Foundations of Social Problem-Solving", "The Social Problem-Solving Approach in Action", "Key Elements of Program Implementation", "Guidelines for the Practitioner", and "Adapting the Social Problem-Solving Approach to Diverse and Changing Settings." If you teach a social science course, this might be worth a look. It is focused on the classroom.
  • Understanding Arguments, by Robert Fogelin & Walter Sinnott-Armstrong. This is a lengthy, philosophical introduction to argument analysis. It includes sections on rhetoric, logic (propositional, categorical, and quantificational), inductive reasoning, analysis, and the fallacies. I use this as the text in my Critical Thinking class, and I am very pleased with it. Much of what you read in the Handbook is influenced by the material in this book.
  • (ILL) Activities to Promote Critical Thinking. Ed. by Jeff Golub. A definite must-see. The essays are short, but many are relevant to the work we'll do in here. Here is a list of essays that you might want to skim (at least): 1.6, 1.7, 1.8; 2.1, 2.3, 2.4; 3.1, 3.4, 3.5, 3.8; 4.2, 4.3, 4.4; 5.3, 5.4. Among other things, there are ideas for using debate, mock trials, math writing, and philosophy in teaching critical thinking to students at a variety of levels.
  • Thinking Skills Instruction: Concepts and Techniques. Marcia Heiman and Joshua Slomianko (Eds.). This is a collection of essays that cover a wide range of topics. They also cover the spectrum from theoretical to practical. All the big names of the critical movement are in here. You might want to take a look and see if any of the titles relate to the work you're doing.
  • (ILL) Critical Thinking Skills. M. Heiman & J. Slomianko. This is a long (

    43 page) pamphlet on the nature of critical thinking. It includes three parts: "What Is Critical Thinking?", "Efforts to Improve Students' Thinking Skills", and "Improving Students' Critical Thinking Skills: Some Exercises". There are 20 pages or so of exercises. It's worth a look.

  • Varieties of Thinking. V.A. Howard. This is a collection of essays. It includes papers such as "Understanding Critical Thinking" and "Thinking on Paper: A Philosopher's Look at Writing". It is pretty theoretical and written primarily for scholars in the field, although there may be some things in here for your theory section.
  • Reflective Thinking. H.G. Hullfish & P.G. Smith. This is an older critical thinking textbook written for the teacher. The book includes chapters entitled, "A Theory of Learning for Teachers", "The Classroom as Reflective Continuity", and "Each Classroom May Be Reflective".
  • (ILL) Teaching Thinking Through Effective Questioning. Francis Hunkins. A book-length discussion of question-based approaches to the teaching of thinking. This volume contains information on the use of questions to lead, direct, and help students learn to think for themselves. Both this volume and the Christenbury pamphlet would be worth a look if you consider question-based approaches in the course modules you design.
  • Teaching Thinking Skills: English/Language Arts. B.F. Jones, et al.This is very useful if you are a teacher of literature, writing, grammar, etc. There is a bit of theoretical stage setting, but this is followed by exercises and worked examples, focusing on content and skills.
  • Teaching for Thinking. Keefe & Walberg (Eds.). This is a recent collection of essays, with pieces by many of the big names in the critical thinking movement. The sections are "Curriculum Development", "Teaching and Assessment", and "Perspectives". In the first of these, you will find the following essays: "Thinking Skills in the Curriculum", "Nurturing Thoughtfulness", and "A Rationale and Framework for Teaching Thinking Tactics". Well worth a look. (There is also a very helpful essay by Beyer in the last section.
  • Developing Decision-Making Skills. Dana Kurfman (Ed.). This is a collection of essays with a social studies slant. There are essays on thinking skills (1 & 2), decision-making skills at the elementary level (6), decision-making skills at the secondary level (7), and a model for the introduction of thinking skills instruction into the classroom (8). This is worth reviewing, particularly (1) and (2).
  • Thinking, Reasoning, and Writing. Elaine Maimon, Barbara Nodine, & Finbarr O'Connor (Eds.). This is a collection of essays, collected into three broad groups: thinking, reasoning, and writing (go figure). Within these, there are useful essays: a model of a mature thinker, a discussion of informal logic, and the use of fallacies to criticize arguments. The essays are more theoretical than practical, but it might be worth a look as you think about what skills to implement.
  • The Future of Thinking. J. Mason & P. Washington. The subtitle is "Rhetoric and Liberal Arts Teaching." It is mainly theoretical and should be of interest to teachers of composition. The last chapter, "The Future of Thinking", is a nice summary of the work in the book as a whole. It is mainly pitched at college instructors.
  • (ILL) Cultivating Thinking in English and the Language Arts. Robert Marzano. A short book that concerns four types of thinking and the role that the language arts can play in conveying them to students. These types include: contextual thinking, thinking that aids meaning construction, thinking that builds knowledge, and thinking that spurs higher-order learning. The discussions of cognitive structures and contextual thinking are worth a look. A more theoretical account, but one that could be useful in bridging the gap between some of the more theoretical discussions during the first two weeks and the practical concerns of the third.
  • Dimensions of Thinking. Ed. by Robert Marzano, et al. A good book on thinking in general that could serve as a companion volume to the Fogelin text. It addresses a variety of types of thinking in addition to critical thinking. The chapters on critical and creative thinking, thinking processes, and core thinking skills are particularly useful. Look at this during the first two weeks if you get the chance. The last chapter (Ch. 7) would be worth a look early in the third week for everyone.
  • Critical Thinking and Education. John McPeck. This could have been a textbook for this class. It includes chapters on the meaning of "critical thinking", informal logic and critical thinking (representing a view that is in some tension with my own), and also reading, testing, and the relation between these and critical thinking. This is primarily a theoretical treatment of these issues, but Ch. 6 does provide a few instructional models.
  • (ILL) Teaching Students to Think Critically. C. Meyers. This is subtitled, "A Guide For Faculty in All Disciplines." It is geared to the college teacher, but would be very useful for the high school teacher. The parts are: "Understanding Critical Thinking", "Steps in Teaching Critical Thinking", and "Building Commitment to Critical Thinking in College." The second part should prove especially helpful. It includes chapters such as "Structuring Classes to Promote Critical Thinking" and "Designing Effective Written Assignments". A must see.
  • Critical Thinking. Richard Paul. A big book that contains two large parts: "What is Critical Thinking?" and "How to Teach Critical Thinking". Some of this stuff is found in the handbook above and in the other stuff of which Paul is a part. There is a section entitled "The Contribution of Philosophy to Critical Thinking" that might be of some interest to people. Also, there is an appendix that includes the views of teachers on critical thinking, a glossary of terms, and sections on the relation of CT to science and to the language arts. This is primarily a theoretical treatment, but worth a look.
  • (ILL) Thinking Skills. B. Presseisen. A short (

    26 page) pamphlet that is mainly theoretical, but aimed at someone who will be taking on the challenge of teaching critical thinking. After the introduction, which includes a historical perspective, the parts are: "The Various Kinds of Thinking", "Influences on Thinking and Learning", and "The Teaching of Thinking".

  • Teaching for Thinking. Louis Raths, et al. This is subtitled, "Theory, Strategies, and Activities for the Classroom," which gives you an idea about its focus. A good book for applications. It leads with a theoretical chapter that discusses the various thinking operations and follows that up with applications. It also includes a chapter on applications at the elementary and a chapter on applications at the secondary level. This includes many examples. Definitely recommended.
  • (ILL) Education and Learning to Think. L.B. Resnick. This is a longer pamphlet (

    50 pages) that is primarily theoretical. The parts are: "Higher Order Skills: A Working Definition and a Historical Perspective", "The Nature of Thinking and Learning: Going Beyond the Routine", "General Reasoning: Improving Intelligence", "Thinking in the Curriculum", "Cultivating the Disposition to Higher Order Thinking", and then a summary.

  • Toward the Thinking Curriculum. Lauren Resnick & Leopold Klopfer (Eds.). This is a collection of essays. There are discussions of mathematical thinking (4 & 5), science (7 & 8), as well as reading and writing. If you plan a project on math or science, look at this.
  • Mathematical Thinking and Problem Solving. A. Schoenfeld. This is a collection of essays, pitched mainly at college instructors. The book is set up in sections, with each section consisting of an article followed by a comment and then a group discussion. Each section focuses on the teaching or learning of mathematics or mathematical techniques. One particularly useful section is entitled: "Classroom Instruction That Fosters Mathematical Thinking and Problem Solving." The discussions in particular are of value for secondary mathematics teachers.
  • Educating Reason. Harvey Siegel. This is a theoretical book that could be of use to you as you work on the first section of your project. It contains chapters entitled, "Three Conceptions of Critical Thinking," "The Justification of Critical Thinking as an Educational Ideal," and "Science Education". The first and second of these chapters is particularly relevant to all of us, and the third would be if you plan to develop a science curriculum.
  • (ILL) Thinking Through Language. vols. I & II, Barbara Stanford and Gene Stanford. These are textbook/workbook combinations. They are for use in the classroom at the advanced elementary/middle school levels. The include units on art, problem solving, science, the future, perception, analysis, analogies, etc. These look like what a critical thinking book would need to look like for that level of student. Definitely worth a look for ideas on specific tasks you might want to design for students.
  • Teaching for Thinking. R.J. Sternberg, et al. This is new (1996) and is relatively short. It is built around goals that you might want to set for students. It describes teaching strategies to enhance thinking. Among other things, it discusses "teaching for the test" and creative thinking. Worth a look.
  • Measuring Thinking Skills in the Classroom. R.J. Stiggins, et al. This is a 27-page pamphlet on assessment. This contains many charts and tables that you could copy and use in the classroom. Worth a look.
  • (ILL) Analytical Reading and Reasoning, Arthur Whimbey. This reads like a study book for the SAT or the GRE. Contains verbal exercises, including those for vocabulary and for reading comprehension. Contains a unit on reasoning that includes premise/conclusion exercises. Designed for use at the secondary level. Contains many exercises that you might look to as models.
  • Socratic Method and Writing Instruction. R. Whipple. This book is mainly theoretical, as opposed to "how-to". Still, there are some useful tips on how to use the Socratic method in the classroom. It is particularly of value to teachers of writing.