Teaching Reflective Commentary Portfolio Mathematics Research Paper

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Convergent questions seek one or more very specific correct answers, while divergent questions seek a wide variety of correct answers. Convergent questions apply to Bloom's lower levels of Knowledge, Comprehension, and Application

and may include questions like "Define nutrition," "Explain the concept of investing," and "Solve for the value of X." Divergent questions apply to Bloom's higher levels of Analysis, Synthesis, and Evaluation; are generally open-ended; and foster student-centered discussion, thereby encouraging critical thinking. For example, "Describe the qualities that make a person successful," "Create an office design to facilitate group interaction," and "Describe how sun spots might affect tree growth" are all divergent questions. (162)

So, not every question even needs to lead the students through the same pathway. In the above example, a false-factor could be thrown into the mix, simply to force the student out of any developing routine when analyzing the problem.

The third suggested step to bringing about critical thinking in accounting is to have the students practice various techniques before assessing those techniques. Fink (2003), a leading educational writer, addresses this by creating two steps to consider when creating preparatory learning activities:

First, activities should be chosen from each of the following three components of active learning: Information and Ideas, Experience, and Reflective Dialog. Information and Ideas include primary and secondary sources accessed in class,

outside class, or online; Experience includes doing, observing, and simulations; Reflective dialog includes papers, portfolios, and journaling. Second, whenever possible, direct kinds of learning activities should be used. Examples of direct activities include doing in an authentic setting, direct observation of a phenomenon, reflective thinking, service learning, journaling, and dialog in or outside of class.

The key is to select an activity that fits the lesson and the teacher's teaching preferences. For example, when teaching forecasting in a college level setting, a trip to the math computer lab and working with a forecasting program would allow the students the opportunity to practice the skills in a more realistic and less theoretical setting.

Computer simulation programs have become the ultimate in helpfulness in giving students a realistic application. According to a study conducted by Igor Batista and Edgard Cornachione (2005), the following results were achieved once students began using a business simulation program:

As can be seen, when the students used the program, their overall comprehension and application skills improved by roughly 50% in every area. In fact, by the end of the simulation, 81% of students were able to create other types of business applications. It is this ability that will allow the students to stand out and perform well in the real world.

Step four is by far the most vital to true quality teaching, and will be further addressed later in this essay in greater detail. This step is to review, refine, and improve a course. Courses should never be stagnant, but rather through the use of constant reflection and student surveys be improved and updated. According to Duron:

Teachers should strive to continually refine their courses to ensure that their instructional techniques are in fact helping students develop critical thinking skills. To accomplish this, teachers should monitor the classroom activities very closely. To track student participation, a teaching diary can be kept that identifies the students that participated, describes the main class activities, and provides an assessment of their success. Other reflective comments can also be tracked in this journal and can be very useful when revising or updating instructional activities. (163)

Along with journaling, another very powerful tool to ensure the course is teaching critical thinking is through student surveys. While some students may be put off by being forced to do more than simply listen to lectures, others will give honest feedback at how the activities assisted in further understanding the material being taught. Furthermore, the surveys need not be given in a survey form. Angelo and Cross (1993) suggest using indirect techniques such as giving students a two-minute paper where they are asked to identify the most important points learned within a certain lesson.

The final step to creating critical thinking in any skill, including accounting courses, is to provide feedback to students through assessment. Even though the simpler approach, and an understandable one given class sizes, is to assign a certain number of problems, mark the incorrect problems, and move on to the next paper, this does not offer the students a chance to reflect or improve. During my time as a student, I have had the opportunity to tutor multiple entry level accounting students and the one area that most are lacking is feedback. The students strive to improve in the course, but do not understand how. Thankfully, tutors have much more time to devote to feedback and can offer the necessary advice and guidance that a busy professor cannot. A simple way for teachers to start offering feedback is to use more word problems or problems with extended analysis. Encourage the students to write out all steps so that you can correct any and all incorrect steps while grading as a means of pointing the student back into the right direction.

Teaching Techniques

While preparing lessons, teachers should also come to grips with the reality that simply standing in front of a classroom will not merit a very responsive or well-informed class. Even more so, simply teaching out of a textbook will not ensure proper learning. Instead, instructors should integrate the lecture approach with a small group interval offered. For instance, a professor could lecture for the first class during the week, and end the lecture giving the students further reading for the following lesson and an extended word problem. During the next class, the instructor selects students to verbally work out the word problem with the guidance of the instructor at the board. Finally, the third session for the week is with smaller groups of students meeting with student aids and working on problems that extend slightly outside of the box of the textbook lesson, allowing the students to apply the principles in a different way. This example of teaching style is becoming more widely adopted by many universities as a means of ensuring that accounting students are prepared for the real world (Ainsworth, 1994). As can be seen, within a single week's worth of course lessons, students are taken entirely through the Bloom's Taxonomy and will reach the final desired stage.

This technique may seem overly complex or difficult to employ in the classroom, however, textbooks are now integrating Bloom's taxonomy in order to encourage use by professors. In a paper written by Ronald Davidson and Bruce Baldwin (2004), it was found that between the years of 1934 and 2004, the problems at the end of chapters have consistently went through the various components of Bloom's taxonomy, even before his published theory emerged. In other words, a properly prepared professor need only utilize the material at the end of each course chapter in order to ensure that the goals of Bloom's taxonomy are reached by his students.


The greatest improvement by which a teacher can make to their curriculum is through self-reflection and improvement. One technique that many professors are using to improve their teaching style and approaches is microteaching (Jiannong, 2002). The first step in this approach is to videotape ones self teaching a class. Often there is no greater critic of ones work than ones self and many mistakes can be caught and corrected by simply reviewing the tape. The next step is to be critically reviewed by a peer or professor. While every teacher's learning style is different, seasoned teachers can offer excellent advice that will assist in improving overall teaching style. A critical review by a teacher does not need to be long or time consuming, but can rather ask some very basic questions. Below is an example of a teaching review from one of my own lessons:

As can be seen in the image, the observer is an established professor. The evaluation does not simply address speaking and presentation style, but also the response of the students and the comparative quality and effectiveness of the teacher's overall objectives. In this example, improvement was suggested with regard to the methods of having the students complete problems on the white board. Instead, it is recommended to have the students complete the problems in groups. Whereas videotaping ones self will produce an improvement in overall presentation, it is these evaluations that will improve the overall quality and effectiveness of the lessons.

Intended Learning Outcomes in Accounting

It is an established fact that there is a learning gap with accounting students (Baker, 1987). Students leave accounting with only basic knowledge of the theories and are typically unable to effectively evaluate and process problems in the real world. This lack of flexibility is caused directly by a lack of higher thinking objectives within the classroom setting. In order for teachers to ensure their students reach that higher level of analytical ability, the…[continue]

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