October 1, 2008
Identifying and Describing Tutor Archetypes: The Pragmatist, the Architect, and the Surveyor
By Harootunian, Jeff A Quinn, Robert J
Abstract: In this article, the authors identify and anecdotally describe three tutor archetypes: the pragmatist, the architect, and the surveyor. These descriptions, based on observations of remedial mathematics tutors at a land-grant university, shed light on a variety of philosophical beliefs regarding and pedagogical approaches to tutoring. An analysis of these archetypes is beneficial not only to tutors and tutor supervisors but also to mathematics instructors at all levels. By considering these archetypes, tutors and instructors should recognize their personal strengths and the areas in which they could improve. Supervisors should encourage balanced approaches that incorporate the strengths of each of these archetypes. The authors hope this discussion will serve as a stepping-stone for future research in this critical area. Keywords: mathematics, remediation, tutoring
The difficulties U.S. high school students face as they learn mathematics are well documented (National Center for Education Statistics 2005). When students enter college, those problems persist. Many students begin their first year of college with weak mathematical backgrounds (Povey and Angier 2004). According to the 2000 National Report Card, 35 percent of high school graduates fail to meet basic, entry-level college math skills requirements (Haycock 2002). Consequently, a considerable proportion of students entering college lack basic math skills, thereby making their college mathematics courses more challenging (Adelman 1999). Ultimately, in most universities, undergraduates are expected to attain some level of mathematical proficiency to pass core math requirements.
Tutoring is an approach that has been used with growing regularity over the past twenty-five years (Falchikov 2001). Students with increasingly diverse backgrounds are now seeking tutoring services to attain a wide variety of economic, social, and personal goals (MacDonald 2000). Because tutoring can reduce the risk of failing college algebra, it should be considered a potentially effective intervention for undergraduates struggling with mathematics. Despite its proliferation, research related to tutoring styles and efficacy remains limited.
In this article, we identify and describe three tutor archetypes: the pragmatist, the architect, and the surveyor. The anecdotal descriptions of these archetypes shed light on their philosophical beliefs and pedagogical approaches. These descriptions are based on observations and anecdotal evidence gathered at a land-grant university in the southwestern United States. We observed three tutors working under the auspices of the academic skills center at this university as they led sessions to support undergraduate students enrolled in remedial mathematics courses. Typically, three to five tutees participated in each session. Tutor interviews and journals provided additional sources of information that shaped our interpretations. The following archetype constructions are our personal perceptions and are presented with the intention of educating and informing tutoring practice.
The pragmatist views tutoring as a series of organized events. She asks a variety of "why" questions designed to help tutees focus on the steps needed to solve the problems. Order and structure are strong characteristics of her tutoring sessions. She often refers to the steps needed to solve math problems. The following are representative examples of prompts she uses:
* We just went over what a reduced polynomial is.
* Keep this in mind because you might see it on a test.
* Today we are going to go over the generic graphs.
* Today we are doing a tool kit.
* What do we know about the volume of a box?
* What does the word problem tell us?
* Did you write that down?
* What is next that is important to know about this?
* The first thing I want you to do is . . .
She states the intention and typically summarizes the outcomes. Although these are not the only types of statements she makes, much of her dialogue flows in this manner. Math and science are "concrete and they make sense. . . . I like to understand how and why things work and I like factual information . . . math and the sciences seem practical and useful to me." She is disciplined when it comes to education, takes pride in school, and thus performs well. She stresses cultivating a strong work ethic coupled with a high level of academic skills development. She even indicates that success in math comes from consistent practice and development of communication skills. She stresses the importance of worksheets and practice. She believes worksheets provide her tutees "with a resource sheet for a specific type of problem which is useful in studying and moving forward in math."
She favors questions that have a direct answer. The responses need to be quick, be to the point, and satisfy a practical purpose. Her questions focus on content and definition of terms. Once an appropriate answer is given, the goal is to move on, with little time invested in deriving deeper meaning. The following excerpt is indicative of a pragmatist's stance on questioning:
How do you learn? [Y]ou do it. They ask questions and in five seconds, I know it. I know the answer. I think that is the tutor brain. It's better when I know what they already know. They have to turn to their own resources to call up whatever it is inside their brain; dig up what they have. When they completely understand, I am the best tutor alive . . . as I was somehow able to figure out the steps to solve the problems.
Communication and dialogue may not engage the tutees as much as it should in the pragmatist's sessions:
I try to explain what or where the problems are coming from and go from there . . . dialogue is [happens] between the students but mostly involves me talking and asking them what they think. [U]sually they respond with short answers or with other questions . . . sometimes I just get stares as they all look blankly to me.
One can infer that the blank stares the tutees give the pragmatist are a product of her tutor-centered approach.
The pragmatist prefers that a problem have an obvious utility and a precise, desired result. Consequently, she stresses the pragmatics or the "whys" of the problems. Thus, in most cases, her tutees' responses are a direct echo of her expected answer or a vague indication of not knowing. The pragmatist feels: "We [tutors] are for facilitating learning . . . we fill in the gaps in their understanding and allow them to get from us what they need." The pragmatist strives to create a supportive and caring learning environment; however, she does this by providing critical analysis for her tutees rather than allowing them to make their own analysis and connections. She is thoughtful, articulate, and has the welfare of her students at heart. This sets in motion an intriguing paradox. At first glance, a precise response from her tutees might indicate that they understand; yet, in her desire to obtain a fixed answer, she leaves little room for tutees to engage in critical reflection during the learning process. Regarding this dilemma, she said:
[T]hey seem to want to skip over that part and get straight to the answer and then when they get to the next problem, they can't get it. There is not enough time to get the critical analysis part. I'm doing the critical analysis, they follow, but don't absorb it . . . as a result, the problems need to be done over and over again until it finally clicks what they are doing and that they are actually doing the same thing in each problem. . . . They don't realize that if they did the critical analysis in the first place, everything else would go faster.
In conclusion, the pragmatist demonstrates a consistent and systematic approach in each session. She feels that "one should memorize all material needed . . . practice a lot, and develop good studying [habits]. . . . Deductive reasoning and analytical skills are key." However, some aspects of her caring ethic may have an unexpectedly detrimental effect. She noted, "I can't understand why they can't learn . . . they have the attention span of about five seconds." Yet, as the semester progressed she came to understand the relationship between her willingness to take on every aspect of her tutees' learning and getting only precise, expected outcomes. She realized that providing everything for her tutees was not effective and should be reconsidered.
The architect views the study of math as finding pieces of information that create the steps necessary to solve a particular problem. He typically strives for his tutees to gain an understanding of the problem first through a series of spontaneous questions. Thus, we find him frequently making statements to the tutees that are related to taking in and identifying the component parts of a problem. When asked what skills the tutees need most, he replied, "they need more help visualizing problems. They can't see the equation and the problem, and see what parts fit where." To this end, he uses diagrams to help tutees make connections between algebraic formulas and geometric concepts.
When it comes to questioning, he has a master plan. Each question he poses is carefully crafted to cause his tutees to take certain steps when solving a problem based on continual increments of thinking. Consequently, we see the architect building the tutee's understanding through a carefully crafted set of questions with a new level of inquiry added with each tutee response. He views the steps as integrally linked to the particular type of questions that he is likely to ask. For example, when he presents a tutee with a math problem, he typically strives for the tutee to gain a visual understanding of the problem through a series of spontaneous questions. Through questioning, he gradually builds his case: I might tell them . . . it looks better [with] each wrong answer [response]. With a new question . . . I direct him closer to the answer we were looking for. The tutor should not give answers immediately but rather provide questions that lead the tutees to their own conclusions. The questions should relate to information they already know and not give information the tutee would not have come up with on his or her own. The question should also follow one's own thought process. The response is important for the tutor to judge how further questioning should proceed, and it gives a lot of insight as to how well the tutee is understanding and thinking about the problem. . . . Get them to the right answer but make sure they are able to communicate their answer back to the tutor.
He is like a project foreman who highly values input from his coworkers, the tutees, as they work together on a problem. Like the foreman, he sees a key aspect of his role as being responsible for pulling together the final outcome.
He uses a particular problem-solving style well matched to his perspective of mathematics. One of his strongest characteristics as a tutor is his consistent emphasis of the steps involved in solving any math problem. To this end, he views the steps as integrally linked to the types of questions he is likely to ask. When his tutees attempt to solve a problem, he encourages them
to take pictures and take [them] apart. . . . What I have them do is [put the problem together without conceptualizing the image first]. . . . [I] pretty much write a whole plan for solving the problem without actually solving it.
He further elaborates that solving problems is an art. Tutees need to have a plan of action and think of their acquired knowledge and skills as a toolbox that can be accessed as needed. He works to supply his tutees with a toolbox of different techniques and formulas to consider when solving a problem. Thus, the architect frequently makes statements related to taking in and identifying the component parts of a problem and searching for the tools that unlock the problem-solving process. "[It is] based on what can we get and how can we use it," he said, referring to drawing on the tools available in the problem solver's toolbox. Regarding how he views this process, he stated, "[I] think of it as a flow chart for us to use."
He tends to "use the tutees' responses to determine their learning styles and abilities . . . and conduct sessions in a manner that best supports the tutee's specific needs . . . yet, at the same time, still allows for the necessary amount of information coverage needed." Moreover, he contends that by "knowing the specific strengths and weaknesses of the tutees, the tutor can avoid problems and subjects that he or she does not feel will be of much value to the tutees." He seeks challenges and looks for opportunities to gain greater rewards than simply good grades for both himself and his tutees. He summed up his personal philosophy of learning by saying, "My goal in classes is not to get good grades or pass tests, but to learn the material. By setting that as my goal, it then helps me achieve the grades and test scores I want."
Like a surveyor, this math tutor examines the mathematical terrain and creates maps, charts, and diagrams to provide his tutees with visual representations of the landscape. Using these visual aids clearly helps the surveyor's tutees gain a better conceptual understanding of the connection between math formulas and pictures. Moreover, this visual connection makes it easier for him to verify with his tutees how they arrived at their solutions or to further explore contradictory information from the textbook's perspective.
He is a global thinker. He demonstrates a strong tendency to view tutoring and learning as an exploration of the mathematical terrain. He typically does not have a structured tutoring format and lets his tutees' needs and questions guide the direction of the tutoring session. Although the surveyor seeks for his tutees to understand and carry out the necessary steps to successfully solve each math problem, he places a greater emphasis on assisting them to discover the correct aspects of math theory to apply to each problem. Not surprisingly, he concentrates much of his energies and talents on figuring things out. He is quite curious and welcomes math challenges. As a result, he likes to discover new and different routes to solving problems, as he demonstrates with his calm demeanor and willingness to approach each tutoring session as a new set of ideas that need to be understood.
His questions are open and spontaneous, created to fit the terrain of each learning situation. In addition, the surveyor engages the tutees in an articulate manner and strives for balance and conceptual understanding, often taking many steps to solve problems. Although questions related to taking specific steps and following procedures are important to his strategy, he devotes equal time to questions of process. Process and conceptual understanding are one of the hallmarks of his stance on learning math:
There is usually no way to demonstrate that any math skill or concept is easy with one broad stroke . . . uncovering the misconception might require a stepped approach; if the tutor can slowly work a concept to the point where a tutee has a sudden insight, the skill or concept will probably stick, and seem very much easier. The key here is letting them uncover the simplicity of the concept, or the ease with which a concept can be grasped if the correct approach is used and letting them . . . uncover the misconception themselves, with your help.
Although he did a solid job of providing a subtle blend of process and procedural questions, he did not see this as one of his tutorial strengths:
I have a ways to go on improving the question-andresponse aspects of my sessions. . . . Thus, my line of questioning often seems to fall fairly flat. . . . I'm not quick enough on my feet to think up questions that really engage the student. . . . I want to be able to use a line of questioning that will break a problem down, or back to a point when the tutee has some understanding . . . so far I have not been too successful.
This statement shows his humble approach, reflective nature, and openness to improving his practice.
He sees dialogue and communication as the real "meat" of a tutoring session. He feels that communication
occurs between tutees as the best learning tool that the tutees can possess. . . . Once I can get a tutee to start speaking about what they are understanding and how they understand it, I can see immediately where I need to go in my own explanations of the material. . . . As soon as the tutees begin to talk amongst each other, I immediately shut up and listen really hard. The worst thing that can happen in a session is for me to be up at the board, or over a book speaking endlessly, and acting almost as a teacher.
He possesses a methodical mind. He is slow in thought, yet his mild reserve produces a quiet strength. Consequently, being careful and thoughtful with questions and responses allows him to present an open tutoring environment in which tutees are noticeably comfortable and able to think. As a result, the tutees often work together with the surveyor as a small community in a shared learning experience.
In this communal problem-solving approach, he is rarely the center of learning. He sits among his tutees, verifying and conferring with them as a team. In addition, although board use is necessary at times, it is infrequent and reserved for times when students express confusion or multiple views and interpretations of how to solve a particular problem. In this respect, the surveyor sees the board as a tool for exploring a problem in depth, providing a common ground for tutor and tutees to share and discuss their thinking. Interestingly, the surveyor uses the board as a learning arena for himself. Often, while tutees are working on a problem, he works on the board drawing formulas and diagrams so that he might gain a clearer grasp of a problem that he is not completely sure how to solve or explain.
In conclusion, the surveyor is a steadfast worker. He carefully analyzes his experiences and derives new meaning from each experience. He demonstrates the willingness and unique capability to deeply analyze learning and thinking about mathematics and problem solving from multiple angles. His ability to effectively incorporate charts, graphs, and diagrams into the problem-solving process serves his needs and helps him engage his tutees in critical dialogue designed to help them in the discovery learning process.
Summary of the Archetypes
Each of the tutor archetypes displays a unique philosophy and style of tutoring. The approaches of the pragmatist, the architect, and the surveyor embody various strengths and potential challenges. The organizational skills and practicality of the pragmatist allow her to lead her tutees through mathematics in a structured manner, typically posing factual questions with simple answers. Although this helps her tutees with the problems under consideration, the lack of focus on critical reflection may prevent them from fully developing their problem-solving skills. The architect stresses the importance of understanding the problem first and then forming an appropriate plan for solving it. He values the input of his tutees as they draw closer to a solution and uses their responses to inform the questions he poses. He considers it important for tutees to develop a toolbox of potentially useful problem- solving strategies. The architect strives to achieve a balance between the learning styles of his tutees and the mathematical content that must be covered. The surveyor encourages a team approach to the problem- solving process, skillfully using charts, graphs, and diagrams to promote conceptual understanding in his tutees. He stresses the importance of engaging his tutees through dialogue, helping them to discover appropriate solution strategies. The surveyor must struggle with the difficult, ongoing task of achieving an appropriate balance between process and procedural questions. Discussion
Consideration of the tutor archetypes will not only benefit tutors and tutor supervisors but will also help mathematics instructors at all levels. A comparative discussion of the efficacy of these styles is not our intention, nor is it provided. Instead, tutors and instructors as well as their trainers or supervisors should carefully analyze these archetypes. Of course, each individual's unique personality traits will guide his or her instructional approach, including the view of mathematics and learning. After comparing tutors' and instructors' tendencies to those of the archetypes, individuals should be able to recognize their personal strengths. In addition, they should be able to recognize areas in which they could improve, gleaned from archetypes that differ from their own, and make appropriate adjustments. Similarly, trainers and supervisors should provide those in their charge with balanced approaches that incorporate the strengths of each of these archetypes. Because of the importance of improved performance in introductory and remedial college classes, particularly mathematics, continued research on tutoring and instructional styles must be undertaken. This discussion of tutor archetypes should serve as a stepping-stone for future research in this critical area.
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National Center for Education Statistics. 2005. The Nation's Report Card: National Assessment of Education Progress. http://nces .ed.gov/nationsreportcard/pubs/main2005/2007468.asp (accessed June 26, 2007).
Povey, H., and C. Angier. 2004. Some undergraduates' experience of learning mathematics. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education 4:57- 64.
Jeff A. Harootunian, PhD, is a mathematics instructor at Truckee Meadows Community College, Reno, Nevada. Robert J. Quinn, EdD, is a professor of mathematics education at the University of Nevada, Reno. Copyright (c) 2008 Heldref Publications
Copyright Heldref Publications Sep/Oct 2008
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