Provisions Fellows Present on Critical Thinking

Our last Provisions session of the year included presentations from this year’s Provisions fellows on the topic of Teaching Critical Thinking.  Our three fellows for the year were Stephanie Bennett, Associate Professor of Sociology, James Allen, Professor of Educational Psychology, and Amina Eladdadi, Assistant Professor of Mathematics.

Dr. Bennett began her presentation with an overview of the year-long fellowship.  The fellows met bi-weekly and provided a bibliography and other resources for faculty, which included the four common texts that all of the fellows read in addition to those that they read of their own interest.  Dr. Bennett pointed out that even after this year-long fellowship the fellows are just beginning to understand the topic and how to incorporate it into their classes.  To that tune, she provided us with the mottos that they came up with, which are “change just one thing” and “less is more.”  Dr. Bennett explained that these slogans speak to the idea that it is more worthwhile to change and integrate new strategies slowly, and that everything does not need to be revamped right away; she explained that it is best to start small, and that introducing more critical thinking strategies is not something that has to be done radically and all at once.  Additionally, they believe that “less is more” is best practice as critical thinking lends itself to more in depth learning and less base-level learning, which in turn lends itself to a stronger base for a transfer of skills.

Dr. Bennett noted that the fellows came to a few universal conclusions in regards to critical thinking: that questions are important, that a collaborative work environment is imperative, and that teachers must make skills transferrable.  After describing a personal experience from her own classroom, Dr. Bennett concluded that she found collaboration was a good start, but that she needed to begin with this earlier in the semester and institute these more transferable techniques in class more often, instead of just making it a one-time thing.

Dr. Eladdadi’s presentation focused on her experience with teaching critical thinking through problem solving, and the idea that problem solving is only one skill involved with  critical thinking.  She explained how often, critical thinking is confused with problem solving and higher-order thinking, but that critical thinking involves many skills working in conjunction with one another, including reasoning, evaluating, analyzing, decision making, and problem solving.  She discussed George Polya’s four-step model of problem solving (read & understand, devise a plan, carry out the plan, and looking back), and came to the conclusion that in her personal practice, it was the guiding questions that were the missing piece in her pedagogical strategy, and that she needed to help create that stepping stone bridge between theory and practice for her students to help direct them towards thinking more critically.  Here is a slide from Dr. Eladdadi’s PowerPoint that illustrates various guiding questions that line-up with and fit into Polya’s model:

Picture1

Dr. Eladdadi then talked about how this adapted type of problem solving strategy, with guiding questions that help elicit that overlay of skills from students (as opposed to a very linear process of evaluation linked to solely problem solving), introduced and used to approach mathematical problems with real world applications, truly led to that all-important transferability of skills.  As with Dr. Bennett, Dr. Eladdadi also came to the conclusion that critical thinking is very closely linked to collaboration and that she needs to start using this adapted problem-solving method earlier in the semester.

Dr. Allen’s main point in his presentation was that the focus needs to be on the facilitation of critical thinking as opposed to the teaching of critical thinking.  He argues that it’s not what we “do” to students but what opportunities we give them to do things for themselves.  Dr. Allen stated that students are not learning for class, but instead they are learning for the transferability of skills in the discipline, across the discipline, and for life, both personally and professionally, which should be the goal of all education.

A main strategy linked to facilitating critical thinking that Dr. Allen pointed out is the importance of questions.  He stated that there is a lot of literature on the role of instructor generated questions, but not on student generated questions, where the latter is more beneficial for the student.  Dr. Allen discussed the Questioning Formation Technique and the Reciprocal Questioning strategy and their role in keeping students motivated and cognitively engaged, as well as how these questioning strategies can work positively when students are collaborating with their peers.  In the end, Dr. Allen concluded that facilitating critical thinking in such a way that helps students learn how to generate questions, learn how to do for themselves and how to collaborate with their peers, fosters an environment in which transferable skills will develop and in turn produce self-regulated learners.

To listen to a podcast of the session, click here!

PROVISIONS FELLOWS: Request for Proposals

Faculty are invited to apply to the new Provisions Fellows Program for the 2014-2015 year. The Provisions Fellowships are unique professional development grants in three ways:

1) The Fellowships focus on teaching and learning;

2) The Fellowships emphasize collaborative inquiry around an identified theme;

3) The Fellowships support interdisciplinary exploration rather than individual disciplinary expertise and research.

I. Objectives

Provisions Fellows will engage in a year-long collaborative project committed to the Scholarship of Teaching and Learning (SOTL). The Fellowship supports pedagogical research, teaching excellence, clear outcomes, and documented assessment. Each academic year will focus on a different theme. The theme for the 2014-2015 Academic year is “Teaching First Year Students.

II. Fellow Activities

  •          Create a reading list focused on “teaching first year students” in consultation withother Fellows.
  •          Meet regularly throughout the Fall 2014 semester to discuss reading. (Schedule to be determined by the Fellows.)
  •          Contribute regularly (biweekly) to the Provisions blog to document process, discussion, and progress.
  •          Develop and implement one or more innovative assignments, activities, workshops and/or lesson plans informed by the reading and discussion.
  •          Document the outcomes of innovation and produce a “toolkit” of research,pedagogical resources, sample assignments, and student examples to publish on the Provisions blog in support of faculty/staff professional development.
  •         Present at the final Provisions session of the year to celebrate and publicize results of collaborative research and innovation.

III. Fellowship Award

  •          Year long professional development opportunity for two faculty members. (Individual applicants will be selected by the Provisions Steering Committee.)
  •          Fellowship is equivalent to reassigned time for one course. The reassigned time can be taken at any time during the Fellowship (Spring or Fall) in consultation with the faculty member’s Department Chair.
  •          An additional $700 will be available to each Fellow to support attendance and/or participation in a conference or workshop germane to the common inquiry question.

 IV. Proposal Criteria and Format: (Maximum: 500 words)

  1.       Describe your interest in this year’s inquiry theme: “Teaching First Year Students.”
  2.       Identify your pedagogical questions, attempts, or challenges in regards to the theme, and provide one specific example/case that illustrates the direction of your future inquiry.
  3.       Provide evidence of past successful collaborative work in any venue. (e.g., professional, Saint Rose projects, committees, etc., or other contexts you deem relevant.) What skills or attributes will you bring to this work?
  4.       In addition, please note any other reassigned time/professional development support you’ve received for 2014-15.

 V. Schedule for Provision Fellows Program

  1.       Proposals are due Friday, 4/18, 4:00 p.m.You must submit a hard copy proposal as well as an e-mail attachment in Microsoft Word to Chris Miller at millerc@strose.edu.
  2.       Proposals will be reviewed by Provisions Steering Committee with recommendations made to the Provost/VPAA. Fellowships will be announced by the end of April.
  3.       Spring/Summer 2014: Provisions Fellows will create a common reading list identifying significant research in the Teaching of Critical Thinking.
  4.       Fall 2014. Fellows will meet regularly as a collaborative faculty learning community to research the common topic of “Teaching Critical Thinking” and develop curricular innovation ideas for implementation in Spring 2014.
  5.       Spring 2015: Curricular innovations implemented by each Fellow on an individual basis. Collaboration among Fellows will continue during this period (e.g. visiting each other’s classes; exchanging ideas; developing and consolidating ideas, research and assessment information).
  6.       Spring 2014-15 Provisions series culminates with the results of the collaborative research and innovation
  7.       Pedagogical “toolkit,” with documentation and reflection materials developed as part of the Fellowship posted to Provisions blog by end of June 2015.

Here you can download the Provisions Fellows Proposal Signature Sheet

 

March Provisions: Teaching [Toward] Common Core

The topic for this month’s Provisions session was “Teaching [Toward] Common Core.”  Our two presenters were Aviva Bower, Associate Professor of Educational Psychology, and Joseph Eppink, Associate Professor of Music.

Dr. Bower began the session by focusing on who created the Common Core State Standards (CCSS) and, consequently, the issues that have arisen as a direct result of this group of creators.  Dr. Bower pointed out that the list of those who created the CCSS includes for profit organizations and those who will benefit financially from the tests, textbooks, and the curricular materials and “coaching” associated with the CCSS.  She noted that those who would have had the most to contribute, such as educators and families, were left out of the equation.  Dr. Bower stated that good teachers who “consider students’ emotional needs, cognitive abilities, and social development will always find a way to transform an inappropriate curriculum, but when the curriculum is tied to high-stakes testing, teachers take that scripted curriculum and subject children to what [she is] calling “the literacy of obedience.”

One of the main issues with the CCSS that Dr. Bower delved into is that they are developmentally inappropriate, where students are lacking transactional reading and writing experiences and are not being asked to draw on their own experiences and knowledge.  Dr. Bower asserted that doing what a script tells you is never going to teach children, and the way in which instruction and assessment is being boiled down to “tell me what the text says within the four walls of the page,” and “show me two details,” is sucking writing and reading dry of curiosity and passion.  Dr. Bower focused specifically on CCSS and the elementary grades, and provided examples as to how teachers are being pressured to teach using developmentally inappropriate abstractions (in an effort to reach the standards), which then leaves young students with nothing concrete to hold on to.  Essentially, Dr. Bower argues that both children and teachers suffer when testing begins to dictate pedagogical and curricular decisions.

Dr. Bower believes that one way in which teachers can help turn it around is by making what they are given developmentally appropriate and enjoyable.  You can take a look at Dr. Bower’s PowerPoint presentation here: The Common Core.

Dr. Eppink began his presentation by explaining the daunting task of trying to “do it all.”  He stressed how music education used to be more hands on, but how now, music educators are being handed new material to be covered and new goals to be reached, such as producing reading, writing, and speaking grounded in text, which has never been part of their job before.

For Dr. Eppink, the struggle lies in figuring out a way to get all of the new material covered and hit all of the new required tasks without cutting any of their existing material and activities.  To show how such a thing is possible, Dr. Eppink demonstrated the ways in which music educators could incorporate things like vocabulary into a hands on game for an elementary music class using Gene Baer’s Thump, Thump, Rat-a-Tat-Tat.  The book was used in an activity involving movement and music-makers to give the “kids” (his participants) a concrete example of the vocabulary words “crescendo” and “decrescendo.”  The group separated into two, standing apart while facing each other, and while reading the book, “students” were asked to keep a steady beat using a shaker-instrument while walking towards the other group.  Dr. Eppink asked the students to estimate the half-way point (using the book as their guide), and the activity allowed them to be able to physically hear when the sound of their instruments were approaching their loudest, at their loudest, and growing fainter, a.k.a. a hands on experience with these two aforementioned vocabulary terms.

Ultimately, Dr. Eppink feels that when we work within the chaos, we may not have all the answers, but what we can do is begin to incorporate small parts of the new standards into our existing pedagogical practices.

Critical thinking: Who’s asking the questions?

During the last few months I have been reading a considerable amount of literature on critical thinking. Although I’ve reviewed theoretical perspectives and research on the topic to gain a deeper and broader understanding, I have focused my attention mostly on pedagogical strategies that teachers can initiate in their classrooms to promote the critical thinking skills of their students. In the article Critical thinking: Why is it so hard to teach? Willingham (2007) argues that due to lack of scientific rigor, there is not strong support for many of the critical thinking programs that have been developed to help students to be better critical thinkers. However, from my review of the literature I believe that there is good research based on sound theoretical principles of learning that support effective pedagogical strategies that focus on various ways to use questions to promote deeper critical thinking skills among students. These questioning strategies have been shown to help students become more thoughtful, reflective, motivated, and self-regulated learners. It is this last point that I want to particularly emphasize in this article, i.e., how to get students to be motivated and self-regulated learners by constructing their own questions rather than responding to teacher-generated questions. But first, a little background on the use of questioning to promote the critical thinking skills and learning of student.

Perhaps the most well known questioning strategy is the Socratic Method. I remember reading many years ago Plato’s Meno (380 B.C.E) describing how Socrates used questions to “draw out” knowledge and understanding of the world (specifically the concept of “virtue”) from his students (see http://classics.mit.edu/Plato/meno.html). More recently, and for many years, Richard Paul of The Critical Thinking Community has been encouraging teachers to use the Socratic Method during class discussions (for example, see http://www.criticalthinking.org/store/products/the-art-of-socratic-questioning/231). However, the major focus of the Socratic Method is that it is the teacher who primarily constructs and asks multiple questions to students to guide their learning during a class to help them become critical thinkers.

While Paul was writing about critical thinking and the Socratic Method, J. T. Dillon (1982, 1984, 1991) at the University of California was doing extensive research and writing on the use of questions by teachers in relationship to effective and ineffective classroom discussions. Dillon’s research (and other research cited by Dillon) suggests that in many cases the use of questions by teachers to promote effective discussion is in fact questionable and often ineffective. Dillon (1984) states: “A single, well-formatted question is sufficient for an hour’s discussion. The rule of thumb during discussion is not to ask questions but to use various alternative techniques … alternatives will foster discussion processes, whereas questions will foil discussion by turning it into a recitation (see Dillon, 1978, 1981, 1984)” (p. 55). Some of the “alternative techniques” that Dillon suggests include the instructor just responding to students with statements instead of more questions and just being silent (often referred to as “wait time” – see: http://www.sagepub.com/eis2study/articles/Budd%20Rowe.pdf).

The idea of not having teachers ask questions to promote critical thinking skills of students, but instead having teachers instruct students how to create, modify, and investigate their own questions, is discussed in detail by Rothstein and Santana (2012) in their book Make just one change: Teach students to ask their own questions. They discuss a questioning strategy they refer to as the Question Formulation Technique (QFT). The focus of this strategy is to help students develop their divergent, convergent and metacognitive thinking abilities.

As the name suggests, the method is very structured in its approach in teaching students how to formulate, modify, improve, and use questions to deepen their learning. There are seven basic steps of QFT where both the teacher and students work collaboratively in the process. The teacher is involved in facilitating the process by setting a “focus” for the questions, discussing with students a set of “rules” for the process of creating questions, monitoring students so that they follow the rules, and providing direction for using the questions to learn specific course content. However, it is ONLY the students who actually create questions about the content “focus,” with the teacher specifically avoiding ever posing any questions. Once a topic “focus” is provided by the teacher (usually a short phrase, such as “racial inequality” in a sociology class, or “being a self-reflective learner” in an educational psychology class), students generate as many questions as they can about the topic without editing, discussing, or responding to the questions. During this divergent thinking phase, students only generate questions and record them. In the next phase students categorize and label the questions as either closed-ended or open-ended questions, discuss the advantages and disadvantages of each and change closed-ended questions to open-ended questions and open-ended questions to closed-ended ones. This helps students to develop a metacognitive awareness of types and advantages of different types of questions. The next phase has students prioritize their questions and choose the three that they believe are the most important as related to the initial “focus” and state why they think these are the most important questions to ask. Through this process, students engage in convergent thinking to be able to effectively address the “focus” of the topic in terms of learning course content. Finally, the teacher asks students to reflect on the process of generating their questions, what they found of value through the process, and how it might be used and transferred in future studies, further helping students to be metacognitive about their thinking process.

In this manner, students not only become more metacognitive and self-regulated in their learning, they learn academic content more deeply, and have higher levels of engagement and motivation to learn. The major point is that these changes come about not because teachers are asking questions that students have little investment, but because students are the ones asking their questions that they generated through a thoughtful and critical analysis – they have become critical thinkers engaged in critical thinking.

As discussed briefly in a previous blog (posted on February 7, 2014), another model of helping students learn to generate and ask their own questions to obtain a deeper understanding of a subject is one developed by King (1990, 2002) known as Reciprocal Questioning. King’s model teaches students to use a set of question stems that they can use to generate questions from lectures and then use their questions to reciprocally ask one another to develop a deeper and broader understanding of the content of the lecture (or to use during out-of-class study). Some of the question stems that King suggests for students to use are:

“What is the main idea of . . . ?”

“How does . . . affect . . . ?”

“What is the meaning of . . . ?”

“Why is . . . important?”

“What is a new example of …?”

“What do you think would happen if . . . ?

“What conclusions can I draw about . . . ?”

“What is the difference between . . . and . . . ?”

“How are . . . and . . . similar?”

“How would I use . . . to . . . ?”

“What are the strengths and weaknesses of . . . ?”

“What is the best . . . and why?”

These question stems help students develop a set of higher-order questions that allow them to investigate the content of the lesson in greater depth. By reciprocally asking and answering their questions with a small group of their classmates they also obtain a broader understanding of the content through discussion of different perspectives that each individual brings to the discussion.

I have used a modified version of this strategy with my classes where I provide and review the use of the question stems during the first class session and then have students develop a set of 3 or 4 questions that they generate from the class readings for use at the next class meeting (Allen, 2010, 2012). They then bring these sets of questions to class and in small groups (usually 4 students) reciprocally ask and answer each other’s questions before I lecture on the class readings. As students discuss the readings via their self-generated questions, I monitor each group and provide clarification when asked by the students. I have found students to be much more engaged in the discussion of the readings and much more motivated to digest the readings before they come to class. Once students have worked together for a few weeks they start to rely less on the question stems and develop higher-ordered questions on their own, often ones that relate to how they might apply and transfer the knowledge they are learning to situations in their professional and personal lives. In short, they learn to become more critical thinkers about what they read, personalize their learning, as well as become more self-regulated learners as they learn course content.

Reciprocal Questioning and the Question Formulation Technique are but two ways to help students take more control of their learning and develop critical thinking skills. They help us remember that critical thinking is a cognitively engaging “process” that is best facilitated when one generates their own understanding such as learning to know how to ask their own questions.

References

Allen, J. (2010). The sharing of Individual and Cultural Perspectives through Reciprocal Questioning. Paper presented at the XIV World Congress of Comparative Educational Societies, Istanbul, Turkey.

Allen, J. (2012). Improving students’ learning and motivation through reciprocal questioning. Paper presented at the Annual Meeting of the American Educational Research Association, Vancouver, Canada.

Dillon, J. T. (1978). Using questions to depress student thought. School Review, 87, 50-63.

Dillon, J. T. (1982). The multidisciplinary study of questioning. Journal of Educational Psychology, 74(2), 147-165.

Dillon, J. T. (1984). Research on questioning and discussion. Educational Leadership, 42, 50-56.

Dillon, J. T. (1991). Questioning the use of questions. Journal of Educational Psychology, 83(1), 163-164.

King, A. (1990). Enhancing peer interaction and learning in the classroom through reciprocal questioning. American Educational Research Journal, 27(4), 664-687.

King, A. (2002). Structuring peer interaction to promote high-level cognitive processing. Theory into Practice, 41(1), 33-39.

Rothstein, D. & Santana, L. (2012). Make just one change: Teach students to ask their own questions. Cambridge, MA: Harvard Education Press  (see http://rightquestion.org/publications/)

Willingham. D. T. (2007). Critical thinking: Why is it so hard to teach? American Educator, Summer, 8-19.

Provisions: Teaching [toward] Common Core – Next Tuesday!

Don’t forget to come and check out our next Provisions session on Tuesday, March 25th, on Teaching [toward] Common Core.  Our three presenters will be Aviva Bower, Associate Professor of Educational Psychology, Joseph Eppink, Associate Professor of Music, and Deborah Kelsh, Professor of Teacher Education.  In preparation for the session, here is a short summary of two articles, suggested by Dr. Kelsh, that highlight the current conversation of dissatisfaction with the Common Core.

In “The Problems with the Common Core,” Stan Karp claims that many supporters of the Common Core don’t sufficiently take into account how larger forces define the context in which the standards are being introduced and implemented, as well as the new teacher evaluations, higher stakes testing, and mass school closings, which seem to have come as a “package deal” with the Common Core standards.

Karp points out that too many standards projects have been efforts to move decisions about teaching and learning away from educators and schools, have often codified sanitized versions of history, politics, and culture that reinforce official myths while leaving out the voices and concerns of our students and communities, and have repeatedly been undermined by bad process, suspect political agendas, and commercial interests.

Karp claims that by very publicly measuring test results, “NCLB succeeded in creating a narrative of failure that shaped a decade of attempts to “fix” schools while blaming those who work in them,” where these scores put the spotlight on gaps among student groups, but the law used these gaps to label schools as failures without providing the resources or supports needed to eliminate them.  Karp claims that though a decade of NCLB tests showed that millions of students were not meeting existing standards, the sponsors of the Common Core decided that the solution was tougher ones.  Of the 135 people on the review panels for the Common Core, Karp notes that not a single one of them was a K–3 classroom teacher or early childhood professional, parents were entirely missing, and K–12 educators were mostly brought in after the fact to tweak and endorse the standards.

Karp approaches the legitimacy of the standards on a number of levels, i.e. questioning whether or not the Common Core is an educational plan or a marketing campaign, and ultimately argues that there is no credible defense to be made of the high-stakes uses planned for these new tests: “Instead, the Common Core project threatens to reproduce the narrative of public school failure that just led to a decade of bad policy in the name of reform.”  He believes that as schools struggle with these new mandates, we should defend our students, our schools, and ourselves by pushing back against implementation timelines, resisting the stakes and priority attached to the tests, and exposing the truth about the commercial and political interests shaping this false cure-all for the problems our schools face.

In “Martin Luther King Jr. and the Common Core,” Daniel E. Ferguson states that proponents of the Common Core have likened the struggle to implement it to the Civil Rights Movement, yet we must consider how these standards and the related testing are threatening students’ rights to education, not upholding them.  Ferguson argues that the Common Core’s strict interpretation of “close reading of a text” dismisses the notion that students’ own thoughts and experiences, and how they connect to a text, are integral to reading. Rather, student voices are silenced in their own classrooms, and literacy is reduced to the ability to navigate standardized tests.

In terms of the Common Core, close reading involves what can only be found within the “4 corners” of the text.  Ferguson argues, however, that there should instead be a focus on critical reading, which involves a close reading of both what lies within and outside of the text.  He fights the idea that reading instruction has overemphasized personal connections to texts at the expense of understanding the author’s meaning, which is assuming the two are diametrically opposed.  He argues that reading devoid of one’s own thoughts and realities—or the broader social context—is impossible, and that understanding what you read and your own world are inextricably linked.  He claims that “a curriculum that de-emphasizes students’ worlds is one that obstructs their making sense of the word,” and is thus an act of oppression.

Ferguson argues that forcing discussion of a text to remain “text dependent” may make it easier to test, but that it also forces out its entire social and historical context.  In contrast, critical literacy argues that students’ sense of their own realities should never be treated as outside the meaning of a text, because “to do so is to infringe on their rights to literacy.” In other words, he argues that literacy is a civil and human right, and that promoting a Common Core system of close reading “promotes a system that creates outsiders of students in their own classrooms.”

Critical Thinking and Problem Solving

By Dr. Amina Eladdadi, Mathematics Department

 “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.

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