Editor’s Note: This paper focuses on reflection, interaction, and feedback, not only to reinforce learning, but to raise learning to higher levels of critical reflective thinking. It demonstrates the value of interaction and learning communities to enhance quality and effectiveness of online learning, especially in problem solving and critical thinking skills.

The Role of Critical Thinking
in the Online Learning Environment

Kelly Bruning

Abstract

Research indicates that critically reflective learning provides students with an opportunity to evaluate concepts learned and apply them to their experiences, contemplating its affect on future learning. This process occurs in a learning community where student interaction and feedback fuels the learning process leading to a higher level of critical reflective thinking for the learner. The challenge for online instructors is how to incorporate critical thinking in the online environment in an effective manner. This paper addresses the issue of critical thinking and how it is applied in an actual online environment through an interactive exercise created by the instructor. The exercise not only fuels student learning but also creates a learning community in which students interact and share ideas. The BUS105 Create-A-Problem exercise described in this paper incorporates critical thinking in the online environment to meet the goals of developing reflective critical thinking in students and to nurture and online learning community that can be used as a model for other online instructors.

KeyWords: Critical Thinking, Online Learning, Reflective Learning, Critical Thinking Exercise,
Business Math Critical Thinking
 

Learning Challenge

The challenge to the instructor was to develop a course that provided the fundamental knowledge on the concepts. The second was to provide usability and functionality of navigating the course. An interaction component among students needed to be incorporated into the course to foster a learning community. The instructor wanted to reinforce concepts but was faced with the challenge of how to post questions to the discussion board and encourage interaction with other learners. The last challenge was to incorporate Northwestern Michigan College's core general education outcomes into the curriculum.

Northwestern Michigan College has a campus-wide movement to incorporate five core general education learning outcomes in all classes. They are summarized as follows:

• The ability to problem solve.

• The ability to communicate with other learners.

• The ability to use the English language in communication.

• The ability to read and summarize.

• The ability to apply critical thinking concepts to course concepts.

It is the goal of Northwestern Michigan College to incorporate as many of these core competencies across the curriculum. Not only did the course need to be designed with functionality and usability in mind but it also needs to incorporate as many general education outcomes as possible. The challenge to the instructor was to gain an understanding of the online learning platform and to think of ways to incorporate the educational learning outcomes as possible. Two specific areas needed special attention: establishing interaction among students and implementing critical thinking. Critical thinking is defined in the learning outcomes handout distributed to faculty members at Northwestern Michigan College as "The ability for the student to use independent thinking and incorporate concepts learned to problem solve a realistic situation."

The unique challenge of incorporating the outcomes in the online learning environment is the lack of face-to-face communication and real time conversation. In a traditional classroom the learning community is created through natural socialization of students and designing assignments in which students work in groups. The critical thinking is stimulated when the instructor asks open-ended thought provoking questions in which student need to tap into their analytical thinking skills and apply the knowledge to the problem. Since students in the online platform work independently through the computer technology medium, the instructor needed to create a way to promote interaction among students similar to group learning in the face-to face course. The instructor also needed to create critical thinking exercises in which course concepts were reinforced but that students could also relate to.

Key Issues

Numerous authors have proposed definitions for critical thinking relative to their own disciplines. One of the earlier teams to write about critical thinking viewed it as a composite of knowledge, skills, and attitudes (Watson & Glaser, 1964). This team went on to develop the Watson-Glaser Critical Thinking Appraisal tool which is presently used by researchers of critical thinking in nursing (Hartley & Aukamp, 1994; Pless & Clayton, 1993). This tool measures skill in performing inference, recognition of assumptions, deduction, interpretation, and evaluation of arguments, all of which are used during the process of reflection. In fact, some theorists believe critical thinking is a cognitive process grounded in reflection (Jones & Brown, 1993).

In general, critical thinking is the method of evaluating arguments or propositions and making judgments that can guide the development of beliefs and taking action (Astleitner, 2002). Glister (1997) regarded critical thinking as the most important skill when using the Internet (p. 87). Reinmann-Rotmeier and Mandl (1998) as cited by Astleitner (2002), found in a Delphi-study, that experts from economy and education nominated critical thinking as the most important skill in knowledge management (p. 33). Kraak (2000) as cited by Astleitner (2002), saw critical thinking as "an important, perhaps the most important of all present time educational tasks" (p.53).

Critical thinking occupies a special place in the hearts of adult educators, particularly because of its connections to the democratic tradition that informs the field. At the heart of a strong, participatory democracy is citizens' capacity to question the actions, justifications, and decisions of political leaders, and the capacity to imagine alternatives that are more fair and compassionate than current structures and moralities. Such capacities develop as we learn to think critically. Encouraging critical thinking in adults is therefore integral to the democratic project. It is also true that critical thinking seems to hold the promise of constituting a universal theory of adult learning and, by implication, a template for adult education practice (Brookfield, 2001). If critical thinking is a uniquely adult learning process, then fostering critical thinking becomes, by implication, a uniquely adult educational process. Critical thinking can be analyzed in terms of both process and purpose, although these two elements are inevitably intertwined.

As a process, critical thinking involves adults in recognizing and researching the assumptions that undergird their thoughts and actions (Brookfield, 1987). Assumptions are the taken-for-granted beliefs about the world and our place within it that seem so obvious to us that they do not seem to need to be stated explicitly. Assumptions give meaning and purpose to who we are and what we do. In many ways we are our assumptions. So much of what we think, say, and do is based on assumptions about how the world should work and about what counts as appropriate, moral action. Yet frequently these assumptions are not recognized for the provisional understandings they really are. Ideas and actions that we regard as commonsense conventional wisdoms are often based on uncritically accepted assumptions. Some person, institution, or authority that we either trust or fear has told us that this is the way things are and we have accepted their judgment unquestioningly (Brookfield, 1987). When we think critically, we start to research these assumptions for the evidence and experiences that inform them.

Proposed Solution

Goals

1. Provide general education on concepts in the course design achieved through "helpful hints."

2. Design the course with Web usability and functionality issues in mind.

3. Incorporate as many educational outcomes as possible.

4. Foster a learning community within the classroom.

5. Create critical thinking opportunities that are fun and relevant to the student.

Strategy

• Weight course assessment tools according to importance in calculating student grades. Create-A-Problems are 20% of the student grade.

• Describe the course requirements as detailed as possible in syllabus with additional online areas that are repetitive to provide easy access to reminder information.

• Require an orientation to the course.

• Instructor comments on create-a-problems to learners via e-mail to provide positive reinforcement.

• Several core educational outcomes are incorporated throughout the course.

Required Resources

There are no other required resources for this project. The instructor must be knowledgeable in online course tools ad techniques and well as Web design. The instructor has taken Web design courses as well as courses in online teaching and training.

Providing General Knowledge

The goal of providing general knowledge to students in BUS105 was the development of "Helpful Hints" for each section of the chapter. Helpful hints provide students with brief notes on the section concepts. It is a form of mini-lecture that provides students with information and analysis of key concepts of each unit. Students were also assigned homework from their textbook. A one page summary sheet of their answers was submitted to the instructor via the instructor's drop box.

Usability and Functionality

The Blackboard platform provides a general "shell" for the course. The command buttons are all the same. It serves as a template for designing the course and provides standardization of usability and functionality of all online courses that use the Blackboard platform. To further enhance usability and functionality, the eleven chapters were divided into five modules. The components needed to complete each module were then nested within the module folder. In essence, a hierarchical filing system was developed by the instructor so that each module was self-contained. Components of each module consisted of the following: (a) helpful hints; (b) homework assignment (c) homework assignment solutions (time released after submission of the homework); (c) quizzes for the chapter in the module; and (d) create-a-problem examples.

The concept of nesting the chapters into a hierarchical file structure was developed so that students could easily find the components of the course that pertained to specific units assigned. It also provided a neat visual for students in which they would not feel overwhelmed seeing 11 different folders for each unit, in addition to a quiz folder, a create-a-problem folder, homework folder, homework solution folder, etc. The students see four folders which has been cited in student evaluations to alleviate fear of navigating the course.

Developing a Learning Community

Developing a learning community requires student interaction. The instructor was challenged with a way of promoting student interaction in a mathematics course where most solutions required only one answer. To post a question to the discussion board where students replied independently with only one answer did not meet the interaction goals desired by the instructor. Students could not really reply or build upon the previous discussion thread because only one solution is arrived at. It was the decision of the instructor to attempt to incorporate student interaction with the creation of a critical thinking exercise. This concepts is further addressed in the critical thinking section of this paper.

Incorporating Educational Outcomes

The problem solving educational outcome was in place due to the problem solving required in a mathematics course. The instructor felt that the communications core competency could be achieved by creating the interactive learning community. The writing component could be achieved through writing story problems on mathematical problems. The critical thinking could also be stimulated in the formulation of mathematical story problems using course concepts.

Critical Thinking Component

A critical thinking exercise was developed with the following goals in mind:

(a) apply the mathematical concepts learned using analytical skills

(b) have the exercise relate to the student in order to provide student interest;

(c) the ability to share the critical thinking exercise with fellow learners on the online platform to stimulate student interaction and develop a learning community.

The concept of the Create-A-Problem exercise was as follows:

• Students create a problem using the chapter concepts. This allowed the students to relate the problem to their life and incorporate the fundamentals of problem solving into a story problem that another student would answer.

• Students also create the detailed solution key to the problem. This also stimulates problem solving. It also prepares the student to address concerns of the student answering their problems.

• The students are paired up as partners by the instructor. The pairing changes each week to allow students to interact with each other forming a learning community.

• If Smith is paired with Jones. Smith posts the Create-A-Problems questions to Jones via the discussion thread in the course room. Jones then has a few days to prepare the answers. Jones post to the link, his solutions to Smith's problems. Smith now has the responsibility of correcting Jones' answer sheet providing feedback on incorrect problems. After a mutual understanding by the partners of the problems is met, Smith also has the responsibility of providing positive feedback to Jones on his problem solving. In this scenario, Jones in turn, is submitting his Create-A-Problems to Smith to answer and also following the sequence.

• If the partner does not post the Create-A-Problems by the due date, the student is free to answer anyone else's Create-A-Problems in the class. This alleviates the problem of students not receiving their questions from their partners on a timely basis. The partner that failed to post on time receives a markdown grade on the Create-A-Problems for not meeting the deadline.

• An example of acceptable Create-A-Problems for each unit is available to students so that they understand the expectations of the caliber of Create-A-Problems expected by the instructor. The examples were written by prior students using the rubric that appears in the following paragraph. The create-a-problem examples provided to students are based on the rubric for the problems and incorporate concepts addressed in the research cited in the literature review of this paper regarding critical thinking theory.

• The Create-A-Problems comprise 20% of the student’s total grade. This gives the student the incentive to participate in the process and to formulate good, sound, problems that follow the rubric in the course room. In addition, the instructor provides feedback to individual students regarding their Create-A-Problem assignments.

Table 1. Rubric
 

Each create a problem within the set that is worth a total of fifteen points. Students receive a rating of 1-5 on the comprehensive concept of the problem. They receive a 1-5 on preparing the solutions to the problems, and they receive a 1-5 for responding and providing feedback to their partner. Late postings to the course discussion board are not be accepted for credit. If the student partner does not post to the discussion board by the due date on Wednesday evenings, students are free to answer questions posed by another learner in the classroom. This solves the problem of students not receiving their create-a-problems because their partner did not post them.

Example Problems

Section 3.1

(1)  Write 1.5 as a percent. Comp. Level 1

(2) After sharing a lemon pie with my family, there is 1/8 of a pie left. What is the percent of pie left? Comp. Level 4

(3)  My brother ate 1/4 of a pie and I ate 1/8 of a pie. How much of the pie is left?
      Comp. Level 5

Appropriate Solution for (3) above that would score a 5 for solution detail:

1)    Convert 1/4 and 1/8 to like fractions. 8 is the common denominator.

2)    2/8 + 1/8= 3/8 is consumed. 5/8 remain.

3)    To find the percentage of pie convert 5/8 into a decimal by dividing the numerator by the denominator. 5 divided by 8 = .625

4)    To find the percentage move the decimal point 2 placed to right and add percent sign. 62.5% of the pie is consumed.

The following solution for (3) above that would score a 1 due to lack of detail in solving the problem.

1)   62.5%

3.5 Appropriate level 5 concept:

Mr. and Mrs. Williams purchased a new home last year for $60,000. The value of the home has decreased in value 15% since last year. What is the value of the house now?

Appropriate level 5 Solution:

1)     First determine how much of a decrease the home is valued at. 100%-15%=85%

2)     Multiply the value of the home $60,000 by .85 (to convert % to decimal, move   the decimal place two places to the left and ad a .)

3)     60,000 X .85 = $51,000

4)     The home is now valued at $51,000.

Responding to partners questions via the discussion board:

No response                            0

Late response                          0

Incomplete response                 1

Constructive Feedback              5

*    Even if the answer sheet is totally correct, you must supply constructive feedback to your learning partner. (i.e. All are 100% correct, good job!)

Appropriate level 5 Feedback to question above.

(assume that the error was 8.5 (line 2 above) not .85 as it should be)

The error is in converting the percentage into a decimal.

To convert a percentage to decimal, move the decimal point 2 places to the left.

85% converts to a decimal .85
 

Process of Discussion Thread:

1) Step One- Student posts questions to assigned partner via the Discussion Thread.

 5.1. Teagan makes $ 2750.92 semi-monthly. Find how much she makes weekly, biweekly, monthly, and annually.

5.2 Everett sells insurance; he makes a 5% commission on all sales he makes. On Monday he sold $ 7500, on Tuesday he sold $ 405, on Wednesday he sold $ 13000, on Thursday he sold nothing, and on Friday he sold $ 3500. What did he make this week?

5.3 Deacon makes $ 75,176 annually. How much does he pay in Social Security Tax (6.2%), Medicare tax (1.45%), and what does he make after the deductions?

5.4 Riley makes $ 2017 monthly; she is single with 3 withholding allowances. What is her withholding tax?
 

2) Step Two: Student has three days to respond to the questions.

Teagan makes $ 2750.92 semi-monthly. Find how much she makes weekly, biweekly, monthly, and annually.
 

5.1 Teagan makes $1269.66 weekly, $2539.31 biweekly, $5501.84 monthly, and $66022.08 annually.
 

5.2 Everett sells insurance; he makes a 5% commission on all sales he makes. On Monday he sold $ 7500, on Tuesday he sold $ 405, on Wednesday he sold $ 13000, on Thursday he sold nothing, and on Friday he sold $ 3500. What did he make this week?

    Everett earned a gross pay of $635.25 this week.
 

5.3 Deacon makes $ 75,176 annually. How much does he pay in Social Security Tax (6.2%), Medicare tax (1.45%), and what does he make after the deductions?

    Deacon pays $4660.91 in Social Security tax, $1090.05 in Medicare tax, and earns $69425.04 after these deductions.
 

5.4 Riley makes $ 2017 monthly; she is single with 3 withholding allowances. What is her withholding tax?

    Found on the wage bracket method, her withholding tax is $161.
Found on the percentage method, her withholding tax is $160.65
 

3) Step Three: The partner responds to the solutions and provides feedback.

5.1

To find the monthly multiply the semi-monthly by 2.
$ 2750.92 x 2 = $5501.84

To find the annual multiply the monthly by 12.
$5501.84 x 12 = $ 66,022.08

To find the weekly divide the annual by 52.
$ 66022.08 / 52 = $ 1269.66

To find the biweekly, multiply the weekly by 2.
$ 1269.66 x 2 = $ 2539.31

5.2

Multiply Monday’s sales by the 5% commission rate.
$ 7500 x .05 = $375

Multiply Tuesday’s sales by the 5% commission rate.
$ 405 x .05 = $20.25

Multiply Wednesday’s sales by the 5% commission rate.
$ 13000 x .05 = $650

Multiply Friday’s sales by the 5% commission rate.
$ 3500 x .05 = $175

Add all the totals up. 375 + 20.25 + 650 + 175 = $1220.25

5.3

Take the amount he makes annually and multiply it by the 6.2% SST. $75,176 x .062 = $ 4660.91

Take the amount he makes annually and multiply it by the 1.45
Medicare tax. $ 75,176 x .0145 = $ 1090.05

Add the SST and the Medicare tax together.
4660.91 + 1090.05 = $5750.96

 Subtract the $ 5750.96 from his annual pay.
 $ 75,176 – 5750.96 = $69,425.04

5.4

Check chart for a single person who is paid monthly.

Then look for the column with 3 withholdings.

 $ 161
 

Step Four: The "ah-ha!" Response. Critical thinking has taken place! Positive feedback is given and a learning community is nurtured.

Assessment Strategy

Student feedback regarding the Create-A-Problem critical thinking exercise has been quite positive. Students cite (in course evaluations) the ability to interact with other students, getting a new partner every week, and the freedom to create story problems that they can relate to as key assets of the course. They also state that the critical thinking exercises prepare them to solve he story problems that comprise the majority of the exams in business math.

Once students learn the sequence of what is expected, they look forward to a new partner every week and the ability to apply concepts learned into a fun challenging story problem that they can relate to. This is the goal of critical thinking, to stimulate the student's analytical and problem solving skills and apply concepts learned to solve realistic problems.
 

Insights

There are several insights I have regarding this project. First of all, I feel if I can develop a successful business mathematics course on-line, I can develop just about any course online. I have become more confident in developing and facilitation an online course. I have also learned how to develop a learning community by personalizing e-mail messages, giving frequent and feedback to students, and providing positive reinforcement. In addition, my BUS105 Business Mathematics Course has been used as an example in teaching other faculty how to incorporate the educational outcomes required by Northwestern Michigan College into the online curriculum.

The Create-a-Problem develop provides a means for fostering student interaction as well as critical thinking. In the future, I plan on using this exercise in my face-to-face course, using the Blackboard platform for students to interact to exchange their Create-A-Problems. The exercise was piloted in a face-to-face course, but the schedule of the course did not allow for frequent feedback among students (it took one week to develop questions, one week to exchange, one week to answer).

The course design is well received by students. Students make an effort to communicate to me how well they like the Create-A-Problems aspect of the course. The course is entering its one year anniversary this summer. Each class has had a capacity enrollment with a 10% attrition rate. One student commented: "I've always hated math and wasn't very good at it. The instructor has developed this class in a user-friendly ways and provides an opportunity for learners to interact with one another creating "cool" story problems that we as students can relate to. I never thought math class could be this fun. I've taken this class twice now. I am currently holding a 4.0 and hope to do well on the final exam to maintain that grade." This comment, I feel summarizes the success of the BUS105 course.
 

Conclusion

The instructor that recognizes the value of critical thinking will provide students with assignments that require in-depth critical thinking skills. Critical thinking is the process of taking learned theory and applying them in practice. This requires cognitive skills that require the learner to think of ways to take the concepts learned and apply them. It is considered by some researchers in the field to be on of the most critical aspects to be included in the online learning environment and the most important knowledge skill.

The role of critical thinking and reflective learning in the online environment is paramount. Critical thinking assignments provide an opportunity for learners to apply knowledge to practical application. Online instructors have the responsibility of providing this opportunity for educational growth to learners and must become creative in developing assignments and projects that foster that growth.
 

References

Astleitner, H. (2002). Teaching critical thinking online. Journal of Instructional Psychology, 29, 53-76.

Brookfield, S. (2001). Repositioning ideology critique in a critical theory of adult learning. Adult Education Quarterly, 52, 7-22.

Brookfield, S. Developing critical thinkers: Challenging adults to explore alternative ways of thinking and acting. San Francisco: Jossey-Bass, 1987.

Brookfield, S. (1995). Becoming a critically reflective teacher. San Francisco: Jossey-Bass, Inc.

Hartley, D., & Aukamp, V. (1994). Critical thinking ability of nurse educators and nursing students. Journal of Nursing Education, 33, 34-35.

Jones, S., & Brown, L. (1993). Alternative views on defining critical thinking through the nursing process. Holistic Nurse Practitioner, 7, 71-76.

Watson, G., & Glaser, E. (1964). Watson-Glaser critical thinking appraisal manual. New York: Harcourt Brace & World.
 

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