## Critical Thinking and Problem Solving

“What was I thinking,” one of my Calculus students exclaimed when I pointed out the mistake he made while solving an applied math problem on free-fall motion that required both synthesis and analysis. “Well, I am glad you’re thinking at all, that’s a good place to start,” I replied with a sense of humor. Students do not develop problem-solving abilities, nor they become critical thinkers overnight. Critical thinking and problem solving are acquired skills that require instruction and practice, as well as time, involvement and devotion from both the students and instructors alike.  Although the National Council of Teachers of Mathematics (NCTM) recommends that elementary and secondary mathematics instructions address problem solving, quantitative reasoning and critical thinking, many of us at the College level still struggle to engage students in critical thinking and problem solving activities.  In this blog, I briefly reflect on how problem solving and critical thinking in mathematics – or any discipline for that matter – are intertwined.

Many students come to college ill-equipped to problem solving in mathematics as well as in other disciplines. Problem solving requires critical thinking and both are fundamental to learning mathematics. In fact, students must learn how to think critically to be able to acquire mathematical knowledge through problem solving.  This is why NCTM advocates that mathematics instruction should include problem solving, quantitative reasoning, and critical thinking.  The Principles for Mathematics Curriculum and Assessment (2009) states:

“… Students should have frequent opportunities to formulate, grapple with, and solve complex problems that require a significant amount of effort. They should then be encouraged to reflect on their thinking. Problem solving is an integral part of all mathematics learning.” (http://www.nctm.org/standards/content.aspx?id=23273)

While critical thinking has several definitions depending on the discipline, there is a strong consensus that critical thinking is the ability to use knowledge to conceptualize, apply, analyze, and synthesize information to successfully solve problems (http://www.criticalthinking.org/). Hence, for the students to be critical thinkers, they need to be able to both analyze and synthesize information.  Mathematics can be either analysis or synthesis, and sometimes both depending on the math topic. Nonetheless, both require critical thinking in problem solving.

Many problem-solving models have been developed. Some of these models are specific to a given discipline while others are all-purpose models. Two models that are worth noting are the Polya’s and Wallas’ problem-solving models. In his best-selling classic How to Solve It (Princeton University Press, 1945), George Polya (1887 – 1985), a Hungarian mathematics educator, identifies the four main steps that form the basis of any problem solving. These steps are: understanding the problem (identifying what is being asked), devising a plan (formulating a set of strategies), carrying out the plan (executing the selected strategies), and looking back (checking and interpreting the results). Polya also argued that a mathematics problem should not end just because the answer has been found, instead, there should be a constant probing related to the problem. This practice not only helps the students to develop critical thinking skills, but also allows them to increase their confidence, inspire and engage them in the subject.

When I first started reading Diane Halpern’s (2014) text Thought and Knowledge: An Introduction to Critical Thinking, 5th ed. (Psychology Press), suggested to us by our colleague and provision fellow Prof. James Allen, I skipped straight to Chapter 9 on Development of Problem-Solving Skills. Halpern describes how psychologists think of the word problem as “a gap or a barrier between where you are and where you want to be.”  She also gives a nice visual illustration of a “problem” in Fig.9.1 p. 453: one long rectangle/box divided by a vertical line into two blocks “X” and “Y” – you are at “X” (box left of vertical line) and want/need to get to “Y” (right box), how do you that? Well, you may be tempted to say, “Jump over that line!” – I can assure you that the “line” is so high for some students, that the “line” is the “problem” – Got the picture? …… Good!!

Halpern examines the stages in the model of problem solving proposed by the English psychologist Graham Wallas (1858 – 1932), which is commonly known as the model of the process of creativity. These four stages are: preparation (definition of issue, observation, and study), incubation (step back from the problem and let the mind contemplate and work it through), illumination (the moment when a new idea finally emerges), and verification (checking it out).  Halpern argues that the incubation is the most difficult stage and the least understood and therefore devotes a whole section of this chapter to it.

Notwithstanding the many stages in the model, it all begins by looking for a clear statement of the problem, and defining it as accurately as possible.  Getting the student to interpret the problem is the first important step in successful problem solving. Once the problem is well stated, students will be engaged to think critically about the solution – hopefully!

Both critical thinking and problem solving are intertwined and similar in a way that they both involve steps and processes to tackle thought-provoking challenges such as applying solid reasoning, understanding the interconnections among systems, framing, analyzing and synthesizing information. So, when students participate in problem solving in mathematics or for that matter any other discipline, they are engaged in critical thinking in their analysis of the problems and in the synthesis and application of previously learned concepts. Moreover, students’ critical thinking abilities are improved when the solutions require knowledge and problem solving skills from more than one discipline such as physics, business, psychology, sociology, etc., and when the problems are ill- defined, as is the case for most real-world problems.

Problem solving and critical thinking are not only vital skills in all academic disciplines, but also life skills that students will continue to use throughout their lives. It is important that our students are challenged in ways that engage them in critical thinking and be metacognitive, that is, that they think about their thinking.

In summary, I liked reading a couple of chapters from Diane Halpern’s text, which I highly recommend to anyone interested in integrating critical thinking into the classroom.

Likewise, I enjoyed re-visiting George Polya’s classic How To Solve It, which I have previously read (many times in French) during my undergraduate studies.  Finally, I would like to close this blog with one of Albert Einstein’s remarkable quotes: “The value of a college education is not the learning of many facts but the training of the mind to think“

Reference:

## The Process of Learning about Critical Thinking

By Dr. Stephanie Bennett, Department of Sociology and Provisions Critical Thinking Fellow

Throughout the summer, last semester, and this semester, I have been delving into the academic world of critical thinking.  I found that the process could get overwhelming very quickly.  I started on a journey that took me into a variety of areas.  I choose for the group, Richard Paul’s Critical Thinking: What every person needs to survive in a rapidly changing world.  Amina Eladdadi brought to the group Hunter’s A Practical Guide to Critical Thinking.  Paul and Hunter’s book brought me into Philosophy.  Jim Allen brought to the group Halpren’s Thought and Knowledge which revealed the Educational Psychology of critical thinking.  All us Provision Fellows read the Bean book Engaging Ideas which opened me up to understanding how to bring about critical thinking thru writing exercises.  From these core books I have found that Critical Thinking is truly interdisciplinary and that I could learn from all.

So after being overwhelmed with new ideas, new fields of study, and new ways to look at the issue I began to hone in my needs.  My need was how to get all this information into my understanding and bring it to a usable place for my students.  This led me into some more interdisciplinary work.

I found an author Elizabeth Barkley who just so happens to be a Professor of Music.  Barkley’s book Student Engagement Techniques: A Handbook for College Faculty was really good for me.  The book illustrates real class engagement techniques that have been tried in real classes with success that have been selected from various sources. One specific example I liked was to set up book clubs for classes.  Allow students to collaboratively work on book with faculty guidance and then present an end of the year report.  I have sent students off to do book reports in groups, but I found with a little honing, I could get better outcomes.  The book is filled with several examples all providing step by step instructions.  I found it to be a great resource for transitioning from the wealth of knowledge I had gained to being able to translate it into my classrooms.

The topic for this month’s Provisions session was “Teaching Graduate Students.”  Our two presenters were David DeBonis, Associate Professor of Communication Sciences & Disorders, and Sev Carlson, Dean of the School of Business.

Dr. Carlson was the first to present, and he focused on revisions in the MBA curriculum.  His first major point was that getting a master’s in finance involves an extensive list of finance courses, a master’s in accounting involves an extensive list of accounting courses, yet with an MBA, the course requirements include a little bit of everything (i.e. finance, accounting, human resources, management, etc.), where with this more generalist approach, a person can work in any business.  As a result, Dr. Carlson explained how when one professor wants to revise their curriculum within the MBA program, they have to engage all the faculty because the curriculum is so integrated.  Therefore, electives are where faculty has a lot more ability to do what they want to do how they want to do it, or in other words, where MBA curriculum revision has really taken place.  Dr. Carlson then explained the way in which Saint Rose’s MBA program has set up the additional courses to be linked with the required ones to offer certificates, where students may come in for an MBA, and by choosing the right electives and a couple of extra courses, they will graduate with an MBA and a certificate.  This set-up has a number of benefits, according to Dr. Carlson.  First, students are able to self-lengthen the program, where some will want the specialty while others are not forced to.  Secondly, outsiders have the opportunity to come in and take the courses required for a certificate, and this might very well result in new MBA students.  Dr. Carlson concluded by saying that faculty have been talking to other parts of campus are there other areas where this same type of certificate set-up might make sense.

## Teaching Graduate Students – Provisions Session this Tuesday, 2/11!

Don’t forget to stop by Standish A/B this Tuesday, 2/11 at 12pm for our next Provisions session on “Teaching Graduate Students.”  Our three presenters will be David DeBonis, Associate Professor of Communication Sciences & Disorders, Sev Carlson, Dean of the School of Business, Jennifer Childress, Associate Professor of Art Education.  In preparation for Tuesday’s session, here is a brief look into the conversation that surrounds teaching graduate students.  Leonard Cassuto, a professor of English at Fordham University, writes regularly about graduate education for the Chronicle of Higher Education, and below you will find a survey of some of the articles he has written.

In “Student Centered Graduate Teaching,” Cassuto wonders how most academics dream of teaching doctoral seminars, yet so little time is spent thinking about how to do it well.  Cassuto details his own experience, his excitement and anticipation for the day that he would get to teach graduate students, his belief that graduate teaching “looked like the pinnacle of professional existence,” and how when the opportunity did arise, he felt “lucky rather than entitled.”  What Cassuto sees as ironic is that he was chasing something he knew little about: he had “no particular ideas about how to do it,” nothing special he wanted to try, and no distinct pedagogical vision for those courses.

Cassuto believes that there is little scholarship on how to teach graduate students due to the fact that it’s possible to teach a graduate seminar without doing much work, where “most graduate students are heavy lifters, and they usually carry the load if you don’t step forward to do it.”  He argues, however, that such professors are “abdicating their responsibility to plan and shape a course around the educational needs of their students.”

Cassuto states that graduate students learn the same way that other students do: through what educators label “retention” and “transfer,” and argues that student-centered learning has not, for the most part, reached graduate school yet.  Cassuto points out that most graduate seminars squeeze too much information into a brief time, and that many professors in graduate school want to cover “content” and consider anything else to be a distraction.  Cassuto understands that graduate students have to read a lot to learn their fields, and that nothing is going to change that, but he believes more work needs to be done on the professor’s part to allow them to be able to work with what they’ve read, leaving enough time not just to “cover” material but also for students to practice doing things with it.

In “OK, Let’s Teach Graduate Students Differently. But How?,” Cassuto writes that graduate programs should prepare students for an “array of positions outside the academy,” where right now many graduate programs are only designed “to produce more professors.”  Cassuto states that to move students away from thinking about their possible futures in purely professorial terms, graduate-seminar leaders must “teach from unconventional stuff.”

Cassuto quotes Edward Balleisen, an associate professor of history at Duke University, whose ideas aim to reconceive the boundaries defining discipline and authorship: “imagine interdisciplinary seminars around a given theme,” in which graduate students would work “with grad students from other disciplines, as well as professional students.”  Cassuto explains that such courses would allow graduate students to imagine their work outside of the contexts of their own specialties: “in fact, the central virtue of the whole approach lies in its endorsement of a move away from the sort of niche specialization that creates scholars whose work is far deeper than it is wide.”

Cassuto writes that we need to connect the way we teach to what our students will actually be doing with their degrees.  In “Making a Public Ph.D.,” Cassuto considers the possibility of training history graduate students to enter into the field public policy.  For the graduate educators who would design such programs as the one he considers, he believes those various needs point to two main structural guidelines:

• “Professors need to identify specific employment goals for graduate students and work backward to structure a curriculum. That may seem obvious, but it’s not what we usually do. In a world of esoteric graduate seminars, the student’s foot is much more often forced to fit the professor’s already-designed shoe.”
• “Faculty members would have to actively intervene in graduate students’ training in order to equip them to pursue those career goals themselves. The intervention ‘needs to be specific, targeted, and early.’

Check out the Chronicle of Higher Education online to check out Cassuto’s reports of other graduate programs.  See you Tuesday!

## Comments on Diane Halpern’s (2014) Thought and Knowledge: An Introduction to Critical Thinking.

In my last blog posting I stated that from my perspective as an educational psychologist there are many educational and psychological factors that interact with one another and influence how I view critical thinking. These factors include: individual, group, and cultural differences among students; motivational levels and processes involved with learning; instructional practices and class activities initiated by the instructor; the quality of student-teacher relationships; and even influences of technology. I then discussed issues related to the cognitive development of students as they progress towards and enter college. Today I would like to focus on what we know about how humans think and acquire knowledge in a “critical” manner as discussed in Diane Halpern’s (2014) text Thought and Knowledge: An Introduction to Critical Thinking, 5th ed. (Psychology Press).

A majority of Halpern’s text focuses on ways to help college students develop critical thinking skills along specific critical thinking avenues such as: “Reasoning” (Ch. 4); “Analyzing Arguments” (Ch. 5); “Hypothesis Testing” (Ch. 6); “Understanding Probabilities” (Ch. 7); “Decision Making” (Ch.8); “Problem Solving” (Ch. 9); and “Creative Thinking” (Ch. 10). She also includes a well-organized Appendix (“Lists of Critical Thinking Skills”) that includes excellent summary charts for each chapter organized as follows:

 Skill Description Examples of Use A. B. C. . . . P.

[The number of skills for each chapter summary chart varies]

These summary charts in the Appendix alone make a valuable resource for any teacher who wants to promote critical thinking skills of students in their classes. However, what I wish to mainly discuss in this blog are the first three chapters of Halpern’s text in which she lays out the psychological foundations for the subsequent chapters.

Halpern’s introductory Chapter 1 (“Thinking”) begins the text by describing the relationship between “knowing” and “critical thinking.”  She acknowledges that one must have something to think about (e.g., content knowledge) before one can critically think about it, but she argues that knowing how to learn that knowledge and understanding how to critically think about that knowledge is more important than simply knowing the content. In addition, Halpern argues that for critical thinking to be of value, one must also be able to communicate, both orally and in writing to others, one’s critical thinking arguments, reasoned conclusions, and problem solving abilities.

Halpern defines acquiring knowledge as a mentally constructivist activity. A person constructs an understanding of something by imposing personal and cultural “meaning” to related bits of knowledge and experiences into organized cognitive schemas. However, one may or may not “critically think” about that acquired knowledge. According to Halpern, critical thinking is a mental activity that is effortful and consciously controlled. What makes critical thinking “critical” is the process of careful evaluation of knowledge based on a clear set of standards or criteria. So to think critically requires having an effortful attitude, content knowledge, and the skills to think critically to evaluate that knowledge.  Halpern summarizes this in the following equation (borrowed from Russell, 1960):

CRITICAL THINKING = ATTITUDE + KNOWLEDGE + THINKING SKILLS

Thus, if one wishes to develop students to think critically, not only must they be taught the content (knowledge), students must also be motivated to learn it (attitude) and be explicitly taught critical thinking skills via instruction that engages them to use critical thinking strategies and processes to learn the content knowledge. This is particularly important if we wish to have students be able to transfer and use this knowledge in the “real world” in critical and meaningful ways.

The four-part model that Halpern suggests for critical thinking instruction is as follows:

1. Explicitly teach critical thinking skills to students so that they explicitly learn the skills of critical thinking along with content knowledge.

2. Help students to develop the disposition (i.e., attitude) for effortful thinking and learning. This includes (a) a willingness to plan by becoming self-regulatory in one’s learning; (b) developing an open-mindedness and flexibility in one’s thinking; (c) being persistent on difficult academic tasks; (d) developing a willingness to self-correct, admit errors and change one’s mind based on additional evidence; (e) being mindful of one’s thinking rather than being on “auto pilot” for tasks; and (f) working with others to see if consensus can be achieved.

3. Teach for transfer of critical thinking by providing specific instruction, practice in a variety of contexts, and feedback, so that knowledge and critical thinking skills can be used in future, varied, and novel situations.

4. Help students to develop the metacognitive skills of (a) an awareness of their thinking, (b) the monitoring of their thinking, and (c) the regulation of their thinking.

In Chapter 2 (“Thinking starts here: Memory as the mediator of cognitive processes”), Halpern reviews current learning theory as it relates to what we know from research on memory and the acquisition, retention, retrieval, and transfer of knowledge. She begins by summarizing the relationship between learning, memory, retrieval and retention of knowledge [see: Figure 2.1 (Halpern, 2014, p.59)]. The level or quality of retention of knowledge is defined as to the length of time between when one first learns knowledge and when one is still able to retrieve it from memory in an accurate manner. The key to this relationship is how well knowledge is embedded into memory when it is learned. How well knowledge is established into memory is based on how well organized the knowledge is and how well it is related or connected to other knowledge in memory (referred to a cognitive schemas and associative networks). This relates to the importance of explicitly teaching critical thinking strategies to students as we teach specific content knowledge. Knowledge that is closely related and connected to other meaningful knowledge is more easily recalled for later use (i.e. transfer of knowledge).

Some of the strategies that Halpern suggests that promote learning and memory and that should be taught along with the content being learned are:

Attention – One must pay attention to begin to store information into memory. One must also understand that there are limitations to how much information one can effectively attend to at any one moment. Research clearly demonstrates that information is retained at a more superficial level when one is trying to multitask and process multiple stimuli at one time. Also, one is most attentive to information that is meaningful and relevant to the person. Sustained attention requires effort.

Monitor Meaning – When one reads, listens to a lecture, writes a paper, or solves problems, one needs to develop strategies to monitor their understanding of the text, lecture, paper, or problem so that it has meaning to the person. This is determined by being able to elaborate on the information that is being learned or demonstrated.

Distributed Learning – This means that one learns and remembers best if the time for learning information is distributed across time and multiple sessions rather than trying to learn information at one time in one session.

Organization – The better one organizes and creates relevant and meaningful connections between bits of knowledge the better knowledge is embedded in memory and the easier it is to retrieve.

Generate multiple cues for retrieval – The more ways and the more connections we can make between bits of information, the easier it will be retrieved at a later time. Halpern provides several mnemonic devices and strategies that students can learn to create retrieval cues including the use of imagery, peg-words, method of loci, acronyms and acrostics.

Awareness of non-cognitive factors – If one is physically exhausted, sleep-deprived, or in a state of anxiety, it is much harder to learn.

In Chapter 3 (“The relationship between thought and language”) Halpern illustrates the importance of being able to communicate one’s thoughts and thinking processes to another via language, that is, through oral and written forms of communication. She argues that the reason it is important to be able to both use and interpret language effectively is in order to comprehend knowledge fully. Oral and written language must be able to be used so that others can comprehend and understand what we want to communicate to them, but also so that we can comprehend and understand what others are trying to communicate to us.

Because of this emphasis on comprehension, Halpern discusses several strategies that can be taught to students to improve their abilities to comprehend what they read and hear from others. The following are two of the many comprehension strategies she discusses and provides illustrations.

1. Re-representation – If one can create a “model” that represents the knowledge and connections relating relevant bits of information together this model helps to re-represent the information and that promotes comprehension of the knowledge.

2. Questioning and Explaining –Being able to formulate good questions about the information read in a text or heard in a lecture and then being able to answer those questions helps to improve comprehension. Although this can be done in isolation, research by King (1989, 1992) has demonstrated that when small groups of students reciprocally ask and respond to each other’s questions the depth and breadth of knowledge is expanded. This is described by King (1994) as “reciprocal peer questioning.” King (1990) describes a specific manner to facilitate this by teaching students to use a set of generic question stems to formulate higher-order and critical thinking questions such as the following as they read.

Generic Question Stems*

• How would you use … to …?
• What is a new example of …?
• Explain why …
• What do you think would happen if …?
• What is the difference between … and …?
• How are … and … similar …?
• What is a possible solution to the problem of …?
• What conclusions can you draw about …?
• How does … affect …?
• In your opinion, which is best: … or …? Why?
• What are the strengths and weaknesses of …?
• Do you agree or disagree with this statement: …? Support your answer.
• How is … related to … that we studied earlier?

* [Source: King, A. (1990). Enhancing peer interaction and learning in the classroom through reciprocal questioning. American Educational Research Journal, 27(4), 664-489.]

Other comprehension strategies Halpern discusses to help students organize content include: Concept Maps, Linear Arrays, Hierarchies, Networks, and Matrices (such as the one illustrated in paragraph 2 at the beginning of this post).

In summary, I find Halpern’s text to be extremely informative in providing a firm theoretical foundation to helping students to develop critical thinking skills and providing very specific strategies to teach students specific skills to become better (more critical) thinkers.

Jim Allen, Professor of Educational Psychology, The College of Saint Rose

## Critical Thinking in Mathematics & Sciences

As a mathematician, I am trained to think critically since critical thinking is the “quintessence” for doing mathematics. As a Bio-mathematician, I am trained to be a multidisciplinary critical thinker with collaborative skills so that I can communicate – mathematically speaking – with my colleagues in the biological and medical disciplines, where I apply mathematical and computational theories.

Being able to think critically is one thing, but teaching others to think critically is another matter. Critical thinking calls for many skills and abilities, and so does teaching it! I believe that teaching critical thinking in mathematics or for that matter any other discipline is essential in the development of successful students because critical thinking is becoming “the critical skill” that is highly sought after by all employers.

The ability to “think critically” is always listed as one of the main outcomes of undergraduate education. Some instructors teach this skill, together with the content of their discipline. However, most of the time the teaching of critical thinking skills is done so “indirectly” that students do not even pick up the signals of the “critical thinking skills” being taught implicitly.  The question then becomes, “how much of critical thinking skills should be taught directly along with the discipline content rather than implicitly with the content being taught? This brings up many other questions about teaching critical thinking skills that I briefly mention (though not answered) in the next sections of this blog.

I must say that it is not an easy task for me to promote critical thinking skills in my mathematics courses, even though mathematics is all about logic and evaluating arguments. Similarly, students seem to find it difficult to cultivate critical thinking abilities during their learning process; that is if they know at all that they are being taught something called “Critical Thinking.” So why is it so hard to teach critical thinking? Are instructors trained to teach critical thinking to their students? Does critical thinking vary from one discipline to another? These were a few of my pedagogical questions that I set out to explore during my 2013-14 Provisions Fellowship on Critical Thinking.

In this first blog, I focus on the last question that is: “does critical thinking vary from one discipline to another?” This is of great interest to me because I work on biological and medical problems where I utilize my mathematical and computational knowledge to solve some of the pressing health issues such as cancer. My interdisciplinary experiences taught me that biological/medical scientists and mathematicians think critically of course, but differently about the same phenomena despite that the common objective is to solve a problem, such as curing cancer.

In the field of mathematics, critical thinking and problem solving go hand in hand. In other words, the students must learn how to think critically for them to be able to acquire mathematical knowledge through problem solving. So, what is critical thinking? There are many definitions of critical thinking depending on which field you come from. As a Mathematician, where logical inquiries and deductive reasoning govern everything we do, I would interpret critical thinking simply as a “logical and active approach of thinking.”  This is only my interpretation of critical thinking within my field of mathematics. I am sure you will be able to find your own interpretation as well within your field. Try it!

Curious to learn more about how critical thinking is perceived by and used in other disciplines, I delved into the book titled “A Practical Guide to Critical Thinking: Deciding What to Do and Believe,” by David Hunter (Wiley Publisher, 2009).  First, I choose this book because it was sitting on my bookshelf for a quite sometime, and secondly, because it presents an interdisciplinary approach to critical thinking across disciplines which is of great interest to me. This book is primarily a textbook, which can be used for college courses on critical thinking and logic.

The author presents an interdisciplinary approach to critical thinking by giving examples from various subjects and fields of research such as business, education, and the physical and biological sciences. I found Hunter’s book to be well organized. Chapters include several sections discussing some aspects of critical thinking, summaries, examples, and exercises. Each chapter ends with four sections: from theory to practice, thinking critically – about ourselves, in the classroom and the workplace. As I was reading this book, I reflected on many aspects of critical thinking that I briefly summarize in this blog.

Hunter defines critical thinking, as “a reasonable and reflective thinking aimed at deciding on what to believe and what to do.” I don’t know why, but he starts every chapter with this same sentence. I did ask him and will let you know in my next blog if I ever hear back from him! He explains that for the critical thinking to be “reasonable thinking”, one must have reasons for their beliefs based on adequate epistemic reasons, which in turns requires reflection on the meaning of the concepts and claims.

Additionally, Hunter shows how different disciplines might approach the same phenomena using different conceptual frameworks. He explains that thinking critically within a given discipline necessitates reflecting on that particular discipline’s frameworks. He also describes that mastering a discipline requires mastering its key concepts, sources of evidence, and primary modes of reasoning in this order. For example, Hunter describes that while geologists and physicists are both interested in earthquakes, they think about this phenomenon differently.  Similarly, sociologists and psychologists are interested in family dynamics, they use different tools to describe, explain and investigate the family life. Another example is cancer and how it can be conceived by different disciplines.

In summary, this book was worth reading and definitely gives the readers many strategies that can help them to think critically at home, at work, in the classroom, and in life in general. The book ends with two appendices: one on mistakes that a good critical thinker should avoid, and the other on practical strategies the critical thinker should embrace in order to be more reflective and reasonable.