Background ritical thinking dates back more than 2,000 years at the birth of Western civiliza- C tion. Socrates’ dictum “The unexamined life is not worth living” subsumes the ultimate value of critical thinking in human life. Plato’s Dia- logues epitomizes not only a method Visual Mapping to but also a way of living that is still relevant to our time.1 Critical think- Enhance Learning and ing skills involve the processing of in- formation through analysis, synthesis, interpretation, explanation, evaluation, Critical Thinking Skills generalization, abstraction, application, comparison and contrast.2 Critical thinking skills are, like common sense, not very common. Studies indicate that 70% of high school graduates are defi- cient and only 28% of four-year college graduates possess excellent skills. Yet, it Héctor C. Santiago, OD, PhD, FAAO is considered to be the most important asset sought by human resource profes- sionals.3 Across the globe, many university edu- cators use the lecture format assisted with PowerPoint slides as the main delivery method. More than a genera- Abstract tion of students has suffered “death by PowerPoint,”a term describing the use Visual mapping allows the learner to explicitly explore, analyze, synthesize and of slides cluttered with text, often with share ideas.This paper reviews mapping tools suited for brainstorming and pic- irrelevant embellishments, leading to turing the thinking process (mind mapping), exploring the structure of knowl- student boredom and little meaning- 4,5 edge (concept mapping), developing premises, counter arguments and conclusions ful learning . Although these presen- around a contention (argument maps), exploring the learner’s own thinking pro- tations can be improved, there is an cess (®Thinking Maps), seeking the inter-relation among variables (general sys- inherent limitation to these traditional methods. Lectures and text slides are tems thinking) and developing simulation models (system dynamics).The paper inevitably linear representations that also presents the evidence on the effectiveness of these tools in promoting recall, hide the rich inter-relations among the comprehension and general critical thinking skills. concepts. As Davies explains: “This par- Key Words: critical thinking, recall, comprehension, visual map, mind map, adoxically usually results in less mean- concept map, thinking map, systems thinking, system dynamics ingful learning, not more. It results in linearity rather than connectivity out of which genuine understanding arises … It also fosters a lack of engagement critical to the development of mean- ingful understanding … To meet as- sessment demands, students begin to Dr. Santiago is a Professor at the Inter American University of Puerto Rico School of Optometry. rely on memorization techniques and cramming, not meaningful activities to ensure engagement and learning, and ultimately — via a transformative learning cycle — expertise.”6 David Ausubel, an educational psy- chologist, saw the primary responsibil- ity of the educator as the presentation of learning materials in a meaningful

Optometric Education 125 Volume 36, Number 3 / Summer 2011 form, not as a list of facts. He indicated an interlinked network. Furthermore, of these bigger branches grow smaller that educators must find procedures al- note-taking emphasizes the verbal com- branches detailing the information. lowing the learners to tie new knowl- ponent (a left-brain process) while ig- Each branch line should contain only edge into their prior cognitive struc- noring imagery (a right-brain process). one keyword. Ideally, lines closer to ture. He proposed visual mapping as a He concluded that mind maps tap into the center should be thicker than those tool par excellence to promote mean- the natural nonlinear thinking process. far from the center. The use of images ingful learning.7 His view on mean- He also concluded that mind maps po- tagged to the branches is encouraged. ingful learning has been supported by tentiate learning by using both left and The use of color, especially for grouping research on the organization of knowl- right brain capacities. and encoding is also recommended. edge by experts as compared to nov- McClain proposed the use of mind Although mind maps can be produced ices: “Studies in areas such as physics, maps in optometric education. In par- using paper and color pens or pencils, mathematics, and history also demon- ticular, she recommended that students several companies have developed mind- strate that experts first seek to develop be given a skeletal map (with blank mapping software that facilitates draw- an understanding of problems, and this terms) at the beginning of the lecture. ing and allows saving of the maps. The often involves thinking in terms of core Students would be required to fill the original organic version of mind maps is concepts or big ideas such as Newton’s blanks as they listened to the lecture. ©IMindMap. Mind Map is a registered second law in physics. Novices’ knowl- She indicated that mind maps would trademark of the Buzan Organization edge is much less likely to be organized allow teachers to stay on task, allow stu- Limited 1990 (www.thinkbuzan.com). around big ideas; they are more likely dents to add their personal ideas to the An alternative and less organic version to approach problems by searching for topic, and increase comprehension.11 of mind maps allowing for multiple correct formulas and pat answers that words and phrases have been developed fit their everyday intuitions.”8 Paykoc et al. described the successful use of mind maps by faculty members in by ©MindJet (www.mindjet.com). Free Marzano completed a meta-analysis of the process of brainstorming curricular versions of mind maps software include research on instruction and strategies changes. The map was projected to the ©SciPlore (http://www.sciplore.org/ that significantly affect student achieve- group and the progress of the discussion software/sciplore_mindmapping/) and ment. Nonlinguistic representations, was reflected in the mind map.13 ©FreeMind (http://freemind.source- questions, cues and advanced graphi- forge.net/wiki/index.php/Download). cal organizers were among those that The construction of mind maps follows These programs permit the attachment 12 were correlated with effective learning.9 specific guidelines. The map itself has of documents, images and Internet links Prince reported that activities that pro- an organic appearance, similar to a tree to the branches of the maps. mote student engagement like thinking with a trunk, branches around the trunk and smaller branches outgrowing from Figure 1 is an organic mind map (©IMi- about their own learning (metacogni- ndMap) based on an optometric case tion) and explicit instruction in prob- the main branches. (Figure 1) The map 14 is started with an image at the center of scenario. The case was a 9-year-old lem-solving enhance student learning student who came with his mother com- outcomes.10 the page (landscape mode) represent- ing the core idea. Branches are drawn, plaining about poor academic achieve- This paper reviews visual tools beginning at the top right of the page ment that started in the third grade. that can potentially increase and following a clockwise direction. Diagnostic hypotheses included a visual students’comprehension, meaningful The branches contain keywords that problem (related to refractive error, bin- learning and critical thinking skills. are subheadings of the main topic. Out ocular or accommodative dysfunction), Although most tools have received ex- a developmental (information-process- perimental corroboration of their ef- fectiveness in schools, undergraduate, Figure 1 graduate and medical education, there A Buzan organic mind map (®IMindMap Software, www. is still very limited use in optometric ThinkBuzan.com) of an optometric case scenario of a third- education.11 It is hoped that this paper grade boy failing in school. The map is read clockwise, starting will stimulate further study, experi- at the top right. It shows the hypotheses derived from the case mentation and implementation in our history, diagnoses corroborated or ruled-out through testing, schools and colleges of optometry. one additional diagnosis and the final management of the case. Software-derived map used with permission. Picturing the Thinking Process: Mind Maps Mind mapping is the graphical repre- sentation of text content. It has been proposed as a technique to brainstorm and summarize information as well as a study method. The originator and main proponent of mind mapping is Tony Buzan.12 He argued that typical note- taking is linear, while thinking involves Optometric Education 126 Volume 36, Number 3 / Summer 2011 ing) disorder and learning disability. than just a single word) at the branches, A study showing no advantage of mind Case history showed that the boy start- allowing for clearer and easier map in- mapping in college students was com- ed having problems in the third grade, terpretation. Faculty and students can pleted by Shuttleworth using a within- had no word recognition problems, and develop these mind maps from case sce- subjects design. Initially, subjects stud- had good handwriting, ruling out both narios to share their clinical decision- ied a text using their preferred study the information-processing disorder making process. technique. They completed a multiple- and the learning disability. He claimed choice and fill-in-the-blank factual test. that his eyes got tired frequently, he did Evidence for the Then, they were trained in mindmap- not have double vision, had headaches Effectiveness of Mind ping study technique and used it while in the afternoon and reported having Mapping to Enhance studying a second equivalent text. They passed a recent vision screening (distant Learning completed a second factual test. Test re- visual acuity test). Tests revealed a low sults were not significantly different for refractive error requiring no correction, Farrand et al. conducted a study on the mind mapping technique compared convergence insufficiency, as well as the efficacy of mind mapping toen- with their preferred study technique. accommodative insufficiency and infa- hance performance in a fact-recall test No motivational differences were found cility. Additional tests revealed a sacca- by medical students. As an additional in this study. However, some partici- dic (oculomotor) dysfunction). The boy variable they asked students to self-rate pants found that the 20-minute study was scheduled for vision therapy. their motivation. In the study, a con- period was too short for the mind map- 16 The map illustrates an obvious issue of trol group used their preferred study ping procedure. traditional organic mind maps: They technique (keywords, re-reading the Abi-El-Mona and Adb-El-Khalick com- are typically difficult to interpret by an text or underlining keywords). The pared the performance of two groups outsider without proper help from the experimental group was instructed to of eighth-grade students on a multiple- developer. use mind mapping. Both groups were choice test based on national standards. immediately tested with a 15-question Figure 2 shows a second modified mind The experimental group spent one factual test. They were also tested a month in mind mapping techniques map, using ©Mind Manager Software, week after the initial exposure. In gen- of a clinical case scenario of a patient while the control group spent a month eral, students allowed to use their own in a note summarization technique. visiting an optometrist with a red and study techniques were more motivated 14 The mind mapping group scores were itching left eye. The map depicts the than those told to use mind mapping. clinician’s thinking process, including significantly higher than the note sum- However, the mind mappers had better marization group. This was true for the generation of hypotheses during the performance than non-mappers on the case history, the evaluation of the hy- students independently of their previ- immediate recall test (13% more) and ous scholastic achievement. The ex- potheses during the examination, and in the long-term recall test (24% more) the final diagnosis and management perimenters also compared mind maps when results were adjusted for motiva- developed at the beginning of their of the case. The look of the map is less tion.15 organic, but it depicts phrases (rather training to those at the end of the train- ing. Students with higher conceptual understanding displayed more accurate Figure 2 links, more colors and more links to mi- A modified mind map using ©Mind Manager Software nor concepts than other students. This accompanying an optometric case scenario showing the case history study had two significant differences to findings, the initial diagnostic hypotheses developed during the the previous two studies. First, partici- case history, the examination findings confirming or ruling out pants had a significantly greater mind the diagnoses, and the treatment and management of the case. mapping training period (one month). It summarizes the clinical decision process during the optometric Second, the experimenters required examination. Used with permission. participants in the control group to use a particular technique (note summari- zation) rather than their own preferred study technique. This study shows that mindmapping has an advantage over note summarization when participants have significant (one month) experi- ence with the techniques.17 An issue related to mind mapping is the development of rubrics with good con- struct validity and inter-rater reliabil- ity to evaluate mind maps. D’Antoni, Zipp and Olson developed the mind map assessment rubric (MMAR) us- ing weighted scores that include con-

Optometric Education 127 Volume 36, Number 3 / Summer 2011 cept-links, cross-links, hierarchies, ex- example, in Figure 3, one proposition is fined process to build concept maps as amples, invalid components, pictures “geometric optics implies light as a ray.” follows: and colors. In their study, first-year Concept mapping is the systematic de- 1. Find a focus question or concept. medical students received a 30-minute velopment of the structure of knowl- Identify 10-20 concepts that relate presentation on mind mapping tech- edge related to a main concept, tying to the main concept and place it niques. Immediately after the training, themain concept to subsidiary concepts around the main concept. they were allowed 30 minutes to read a via links. 2. Arrange the concepts so that the text passage from the Graduate Record There are two main characteristics that Examination. They were also asked to broader ones occupy the top of the differentiate concept maps from mind map. draw mind maps of the passage. Three maps: different examiners evaluated the maps 3. Continue and add concepts as Hierarchical: using the MMAR. The results showed 1. Concept maps are needed. high and significant inter-rater reliabil- hierarchical with the most impor- ities for pictures (0.86), colors (0.73) tant concept shown first, usually 4. Connect concepts by line links. and total score (0.86). The inter-rater at the top of the map. Subsidiary Name the links to define the rela- reliabilities were moderate and signifi- concepts are placed below the main tionship between the two linked cant for cross-links (0.58) and examples concept. Tertiary concepts derived concepts. (0.53). The inter-rater reliabilities for from secondary concepts are placed 5. Modify the structure of the map as concept-links and hierarchies were not below secondary ones. This process you add, delete or modify concepts significant.This study indicates that the continues as needed. In mind map- or links and as you gain insights.20 MMAR is an inter-rater reliable rubric ping, the main idea is placed at the center of the map and all other The Institute for Human and Machine for mind maps. Furthermore, the rubric Cognition, affiliated with the Florida can also be applied to concept maps18. ideas are outgrowths of the main idea with no obvious hierarchy. University System, developed specific In summary, the evidence indicates software for concept mapping, ®IHM- that mind maps are potentially useful 2. Explicit naming of links: Concept CCMap Tools, a free Web-based pro- techniques that can enhance learning. mapping requires that the links be- gram. Students can develop their con- Well-motivated students with signifi- tween concepts are named explicit- cept maps, work collaboratively, and cant mind mapping practice are the ly through verbs such as “includes,” share them. The program allows map- most likely candidates to benefit from “is part of,” etc. Naming of the pers to attach documents, images and its use. links allows for an easier and more Web site links to their maps (http:// accurate interpretation of the map. cmap.ihmc.us). Mind maps do not name the links Exploring the Structure of An excellent and sophisticated group Knowledge: Concept Maps and the nature of the relationship is implicit. of concept maps was developed by the Concept maps are the brainchildren of NASA Ames Research Center. The Joseph Novak, a noted American edu- While mind maps do not impose con- maps are related to the exploration, 21 cator. Originally, he developed them as straints on the order of ideas, concept geology and climate of Mars. The a tool to document the changes in the maps require more rigorous thinking, elements of the maps provide links to cognitive structure of children taking analysis and implementation. documents, photographs, diagrams basic science lessons. Novak was a dis- Novak and Gowin describe a well-de- and films related to the topic at hand. ciple of David Ausubel, who argued: “If I had to reduce all of educational psy- Figure 3 chology to just one principle, I would A concept map related to optics using IHMC ®CMap Tools software. say this: The most important single Software used with permission. factor influencing learning is what the learner already knows. Ascertain this and teach him accordingly.”19 Concept maps allow explicit record- ing of what the learner knows and how this knowledge evolves through time. Figure 3 is a concept map of classical optics. A concept can be an object, idea or event. It is usually represented by a noun such as “chair,” “disease” or “op- tics.” Concepts are related to one an- other through links, which are usually verbs. Two or more concepts related through links become propositions. For

Optometric Education 128 Volume 36, Number 3 / Summer 2011 These concept maps convey the power were shown in an elementary physical maps had significantly better quality. of Web-based concept maps to display science course by students who were However, the mapping scores were not scientific information.22 trained in concept mapping.29 Univer- significantly correlated to residents’ in- 37 Although the basic knowledge about sity chemistry students who had signifi- training board exams. the construction of concept maps can cant concept mapping training outper- On the other hand, a smaller number of be explained in minutes, mastery re- formed control groups in their ability studies shows limited or no advantage to form concepts and relationships dur- quires significant practice. Daley et al. 30 of concept mapping over other proce- described the development of concept ing structured interviews. Zittle dures. For example, Schmid and Telaro mapping proficiency of nursing - stu found that, for a population of college divided high school Canadian students dents, finding significantly better maps students, concept mapping is more ef- of low, medium and high academic at the end of a semester of a clinical fective, but only when the learner has ability into a treatment group (concept 23 to actively construct the maps, rather course. Rendas, Fonseca and Rosado- 31 mapping) and a control group (no con- Pinto used computer-generated con- than examining pre-built one. Chang, cept mapping). Students’ performance cept maps as a problem-based learning Sung and Chen had an opposite con- was determined using achievement tool for medical students. The main clusion for elementary school children: tests. The post-test also included a test strategy was the presentation of clini- Students who were required to develop measuring the ability of students to use cal cases along with incomplete mind full-fledged maps performed worse than cross-linking. They found that concept students who were required to correct a maps, where students had to provide 32 mapping was only significantly bet- the missing concepts. They reported map provided by the experimenters. ter in the low academic ability group better quality maps at the end of their This result suggests that active concept and only in the concept-linking test.38 problem-based training.24 map construction only benefits the Spaulding obtained a similar result, learning performance of students who mainly that concept mapping only Evidence for Concept have achieved a significant level of mas- benefitted lower ability science high Mapping Effectiveness in tery. Coleman found that requiring stu- school students.39 No advantage of dents to use higher level learning strate- Enhancing Learning and concept mapping over outlining on a gies (such as evaluating, comparing and high school biology course was found Critical Thinking Skills contrasting) enhances their concept 40 33 by Lehman, Carter and Kahle. Rewey Vacek considers concept mapping a mapping advantage even further. et al. found that concept mapping im- fundamental tool in developing criti- There is also evidence that concept proved free-recall performance only in cal thinking in nursing education.25 mapping enhances free recall by college low ability students using a cooperative Many (but not all) studies show that students when the material is presented learning situation.41 34 concept mapping enhances problem- in a concept map versus ordinary text. Like mind mapping, one subsidiary solving skills or course achievement This is especially true of propositions at issue is the development of reliable of students. Esiobu and Soyibo found the top of the map, i.e., superordinate 35 rubrics for the assessment of concept that Nigerian secondary school stu- concepts. maps. Novak and Gowin proposed dents trained in concept mapping and Gonzalez et al. trained a group of medi- the first rubric based on the valid- re a technique called Veediagramming cal students in concept mapping. They lationships, hierarchy, cross-links and outperformed students in a conven- practiced their skills with the help of examples.20 West et al. obtained inter- tional environment (lecturing without a mediator during case presentation rater reliabilities ranging from 0.51 concept mapping) when tested using sessions. A control group of medical to 0.88.37 Srinivasan et al. reported a multiple-choice achievement tests. The students followed the traditional case study involving internal medicine resi- difference was quite robust, five- stan 26 discussion sessions. All students took dents, pediatric residents and fourth- dard deviations (SD). Bascones and multiple-choice examinations and year medical students. They produced Novak reported a study of secondary problem-solving exams (based on clini- concept maps related to diabetes (us- school physics students in Venezuela cal scenarios). The students receiving ing 61 concepts) and asthma (using 56 where students trained in concept map- concept mapping training performed concepts). The authors concluded that ping outperformed students without significantly better than the traditional good reliability required 4-5 repetitions concept mapping training in tests mea- students in the problem-based exam of the maps. This study is unique due suring problem-solving skills. In anoth- but not in the multiple-choice exams. to the high number of concepts used er study, high school physics students This was particularly true for lower- by the participants and that the partici- in the United States showed significant achieving students.36 West et al. trained pants were constrained to use the con- advantages in achievement tests when medical residents in concept mapping cepts provided by the experimenters using concept mapping throughout a techniques and immediately after asked rather than their own.42 course as opposed to using single-shot them to develop a concept map on the In general, these studies seem to in- concept mapping at the end of the topic of seizures. The residents com- course.27 However, even students us- dicate that concept mapping may en- pleted three one-hour education ses- hance learning, recall and problem- ing concept mapping at the end of the sions on the same topic and were asked course had significantly better achieve- solving skills, most especially with to develop a concept map again. Using students with lower abilities. They also ment than those who did not use con- their rubric, they found that the second cept mapping at all.28 Similar results Optometric Education 129 Volume 36, Number 3 / Summer 2011 suggest that learners should achieve a The method is based on eight map Figure 5 shows an optometric example significant level of mastery in the con- templates that purportedly represent of a double-bubble map where two re- struction of concept maps to reap their distinct thinking skills: defining, de- fractive errors (myopia and hyperopia) full benefits. Finally, they indicate that scribing, comparing and contrasting, are compared. The central bubble iden- concept maps can be evaluated and classifying, dividing into parts, se- tifies them as concepts related to refrac- graded reliably. quencing, establishing cause/effect and tive error (common characteristic). The determining relationships. (Figure 4) peripheral bubbles show the unique, Visual Organizers for As generic templates, they can be ap- contrasting characteristics of each one. Metacognition: Thinking plied across disciplines and grades.45 The construction of this simple map Maps Rubrics for teachers and students have requires a sound knowledge of the con- been developed.44,46 These tools have cepts. The details can be modified as One of the goals of critical thinking is been implemented in more than 5,000 the learner gains sophistication. learners’ awareness of their own think- schools in the United States, New Zea- ing process (metacognition). One of 47 It is not difficult to imagine other uses land, England and Singapore. The of the double-bubble map, such as the most powerful tools for develop- process can be done as paper and pen- ing metacognition are the ©Think- comparing and contrasting the signs cil tasks or with the help of specifically and symptoms of two ocular diseases. ing Maps, a brainchild of David Hy- designed software (www.thinkingmaps. erle.43,44 Other maps can also be applied to op- com). tometric subjects. For example, the multi-flow map can be used to depict Figure 4 the risks (antecedents) and the conse- ®Thinking Maps (Thinking Maps, Inc.) are a powerful set of quences of a particular disease. metacognitive visual organizers developed by Dr. David Hyerle. Used with permission. Spiegel indicates that one of the benefits of the practice of thinking maps is that students may become teachers, as they share their maps with their classmates, creating a sense of empowerment.48 Evidence for the Effectiveness of Thinking Maps in the Improvement of Learning The research literature on thinking maps is mostly related to school chil- dren in the area of reading and lan- guage skills. For example, Blount tested a group of 17 fourth-grade students, all below grade level in reading perfor- mance. During the first two weeks they Figure 5 had a typical teaching unit. After fin- The compare and contrast visual organizer used for the concepts of ishing a teaching unit, they completed myopia and hyperopia. a multiple-choice test. They also wrote an essay related to the unit. During the second two weeks, they had a different teaching unit. Students were familiar- ized with the flow, bubble and double bubble maps. They were requested to apply these maps to the material taught in the teaching unit. At the end, like in the previous unit, they completed a multiple-choice exam and wrote an essay related to the new teaching unit. There were increases in the performance on the second test as compared to the first test in main ideas, details, sequenc- ing and inferences.49 Unfortunately no statistical tests were conducted to verify if the differences were significant. Manning describes the experience of a

Optometric Education 130 Volume 36, Number 3 / Summer 2011 school for learning-disabled children teachers and students agree or strongly the law, expert opinions and examples in Massachusetts. The thinking map agree that the tools are easy to use. In- among others. Finally, the reasons, ob- tools were applied in all school subjects terestingly, administrators had lower jections and evidence basis should be and all grades in this school. Students opinions of their effectiveness in - fa evaluated (accepted, rejected or in some were required to take the Massachusetts cilitating learning (58%) or ease of use difficult cases undecided). At the end, Comprehensive Assessment System (42%).52 the evaluator must decide, if in light of Retest, which includes Language Arts In general, the literature indicates that all the evidence, the primary conten- and Mathematics. Within a year, the these tools are effective, particularly tion should be accepted, rejected or left passing rates in English Language Arts unresolved until better evidence is ob- with students having lower achieve- 53 increased from 17.3% before introduc- ment. They help organize the learners’ tained. tion of the thinking mapping tools to thinking, providing a platform for bet- As an example, Figure 6 depicts an ar- 68.3% after their introduction. Math- ter comprehension. Most importantly, gument map on the ethics of assisted ematics passing scores increased from learners enhance their own apprecia- euthanasia using ©Rationale software. 11.5% to 45.6% during the same pe- 45 tion of their thinking processes (meta- This contention was considered to be riod. cognition). the most important ethical issue during Worsham and Austin conducted a study the second half of the 20th century.54 with 139 high school students with low Facilitating Judgments: Reasons based on religious values, com- Scholastic Aptitude Test (SAT) verbal Argument Mapping passion, professionalism and the laws scores. The control group (52 students) are presented on the argument map. As Argument mapping is a graphical rep- received no mapping training while the the map is developed, the student must resentation of a contention where argu- experimental group (87 students) spent research questions such as: ments can be explicitly presented for 20% of their English class developing and against the contention. Argument • What do religions have to say about their mapping skills. The experimental mapping is especially useful in the dis- assisted euthanasia? group had significantly higher achieve- cussion of complex and sometimes con- ment in all verbal measures of the SAT • What does the professional organi- troversial issues such as those presented (vocabulary, reading comprehension zation (American Medical Associa- in an ethics course. and total score).50 tion) consider ethical? An argument map starts with a con- Ball conducted a study on the effects of • Is assisted euthanasia legal? tention. The rest of the argument map the use of thinking maps visual tools on strives to answer why the contention • What are the personal and profes- performance in a standardized reading should be accepted or rejected. A rea- sional consequences of assisted eu- test. The subjects were college students son is a statement supporting a conten- thanasia? taking a reading course. All groups re- tion. An objection refutes a contention, • Are there reasonable alternatives to ceived training in thinking skills such a reason or another objection (rebut- assisted euthanasia? as descriptors, contrasting, compari- tal). The evidence basis for the reasons sons, analogies, cause/effect and clas- These questions require that students and objections can be added to the ar- sification. The experimental group also conduct a thorough search on the his- gument map. Evidence basis may be received training in the use and applica- torical context of the issue, the impact data from experiments, publications, tion of the visual mapping tools while of religious beliefs, the professional a known statistic, personal experience, the control groups did not receive this stand of the medical profession, the ap- second training. All students were tested with the Stanford Diagnostic Figure 6 Reading Test Form G at the beginning Argument map regarding assisted euthanasia developed in of the course and with the Form H at an ethics course with ®Rationale software. Software used with the end of the course. This test provides permission. data on reading comprehension, vo- cabulary, fast reading, phonetic analy- sis, structural analysis, word parts and skimming/ scanning performance. The experimental group (using the maps) had significantly better performance than the control group (no map use). Further analysis revealed better perfor- mance in all areas except phonics and scanning.51 A study in England in a school system using these visual tools found that 77% of teachers and 62% of students agree or strongly agree that these tools help students learn. Sixty-six percent of

Optometric Education 131 Volume 36, Number 3 / Summer 2011 plicable federal and state laws, the avail- are also online collaborative argument nia Critical Thinking Skills Test at the ability of alternatives such as hospice tools for debate such as TruthMapping beginning of the course and a second care, and current outcomes in states (www.truthmapping.com). version at the end of the course. The that allow assisted euthanasia among test itself has 34 items for testing the others. Evidence of Argument student’s skill in analyzing, evaluating, Weinstein proposed a useful model for Mapping to Improve Recall drawing inferences, deducting and us- resolving ethical dilemmas.55 The four and Critical Thinking Skills ing inductive arguments. The difference steps of his model are: between the post-test and the pre-test Dwyer et al. have argued that argu- was an indication of the critical think- 1. Obtain the objective facts about ment maps decrease the cognitive bur- ing skills gains. Results showed that the situation. den by combining the text (reading) students had the equivalent of 0.45 SD 2. Identify the values (personal and and structure of the argument. They improvement in these skills.This result societal) involved in the situation. hypothesized that argument mapping compared favorably with gains of 0.19 would significantly increase compre- SD with a standard course (without the 3. Describe the options to the dilem- hension and memorization of an argu- use of the mapping software).61 ma. ment compared to a pure text reading. Van Gelder et al. used an argument 4. Based on the values, make a judg- In an experiment, they presented writ- mapping software in a one-semester ment of the best option. ten (text only) arguments compared to arguments maps to groups of university undergraduate critical thinking course. In this model, the best option is the one students. Students’ reasoning ability They hypothesized that students would that satisfies the most important values. was initially assessed with the Differ- have significant gains in their criti- The method can be best applied using ential Aptitude Test. Six experimental cal thinking scores as measured by the an argument map. groups were tested using a multifactori- California Critical Thinking Skills Test Halpern has described a set of skills al design with two levels of complexity (CCTST). They also hypothesized that necessary for the construction of argu- (arguments with 30 propositions and the gains would be significantly corre- ment maps:56 50 propositions) and three conditions lated to deliberate practice measured objectively and subjectively. For exam- 1. identification of the premises (rea- (text only, black-and-white maps, and color maps). Subjects were tested for ple, one objective measure of deliber- sons), counter arguments and con- ate practice was the actual (measured) clusion comprehension by being asked whether a subset of the propositions supported number of hours using the software. An 2. developing strong arguments that or denied the main argument claim. example of a subjective measure would show good thinking and commu- Each subject also received a fill-in-blank be a self-reported estimate of number nication skills memory test. of completed practice exercises. The re- sults showed a gain of 0.8 SD in criti- 3. judging the credibility of the in- The results indicated that there was no formation, including knowing the cal thinking skills as determined by the difference in the comprehension level difference between the pre-training and source of the information and its across all experimental groups. Howev- validity post-training scores on the CCTST. er memory performance was better for The gain of 0.8 SD through the one- 4. understanding the difference the smaller (30 proposition) complexity semester software-assisted course was among opinions, reasoned judg- in the text-only, black-and-white map equal or better than the gain achieved ments and facts. and the color map conditions. Also, by students after three years of college Kee and Bickle provide an example of both the black-and-white and color undergraduate education. The gains argument mapping applied to epide- map conditions were superior to the were significantly correlated to the ac- miology.57 While argument mapping is text-only condition. No difference was tual number of hours spent using the best suited for issues related to the issue found between the black-and-white software and the number of activities of validity or truthfulness of a conten- and the color map condition. In short, related to the use of the software. The tion, clinical decision-making is best argument maps produced better recall correlations were moderate (0.31 and assisted through similar methods, such than text-only arguments. Subjects in 0.27 respectively). Gains were also as hypotheses mapping or analysis of this experiment were only allowed a significantly correlated with the self- competing hypotheses.58,59 10-minute presentation of the maps. reported amount of effort spent on the It is possible that longer presentations subject (0.19).62 Argument mapping and decision- by subjects experienced in argument making can be facilitated by the use of mapping techniques may lead to better Guzetti et al. performed a meta-analysis software. ©Rationale is a commercial comprehension.60 of experimental studies and found that product that provides useful tutoring student argumentation had the great- support for students and educational Butchart et al. used computer-assisted est effect on correcting misconceptions, guidelines for educators (http://ratio- mapping software in a 12-week under- a 0.80 SD effect compared to student nale.austhink.com/). Compendium is graduate course. The course included a discussion, 0.51 SD, or simple activa- a free argument mapping tool useful one-hour lecture and a two-hour tuto- tion of prior knowledge, 0.08 SD.63 for group deliberations (http://com- rial session per week. Participating stu- dents took one version of the Califor- Alvarez-Ortiz completed a meta-analy- pendium.open.ac.uk/institute/). There sis of the impact of philosophy, critical

Optometric Education 132 Volume 36, Number 3 / Summer 2011 thinking education and argument map- While cause/effect analysis is usu- ping on performance on critical think- ally linear and unidirectional, systems Figure 8 ing tests. Students in the control groups thinking analysis is based on feedback Top: Two typical unidirectional had a gain of 0.12 SD within a semester loops. In Figure 8, stress leads to con- relationships. Stress level without any specific training. In com- sumption of beer, the plus sign signify- affects consumption of beer, parison, philosophy students without ing that an increase in the level of stress while consumption of beer argument mapping training had a gain increases consumption of beer. (Also a affects stress levels. Bottom: of 0.26 SD while philosophy students decrease in the level of stress decreases A feedback loop is a more with significant argument mapping consumption of beer.) This is a typical accurate representation of the training had a gain of 0.78 SD.64 unidirectional relation that does not inter-relationship. In conclusion, argument mapping in- portray the whole story. However, con- creases critical thinking skills and argu- sumption of beer itself produces chang- ment recall when compared with stan- es in the levels of stress. The minus sign dard procedures. implies that increasing levels of beer consumption leads to decreases in the Seeking Inter- level of stress. This is also a unidirec- Relationships: General tional relationship. A feedback loop, as shown, portrays the whole relationship Systems Thinking more accurately. The most powerful of all visual- map Feedback loops can be reinforcing, ping tools derives from general systems where there is continuous growth or thinking. General systems thinking was decline in a variable. Feedback loops promoted by Peter Senge as one of the can also be balancing (like the one in characteristics of the effective learning Figure 8) where an explicit or implic- 65 organization. It hypothesizes that in it goal (level of stress) is maintained. most situations we are aware of single Some effects may take significant time A better, fundamental solution is avail- events, the tip of the iceberg, which are to be seen, and this is depicted by a de- able, but this solution requires more ef- occurrences manifesting deeper reali- lay in the feedback loop. fort and time (delay). In the meantime, ties. As we study the sequence of events System thinkers have found that many reliance on the symptomatic solution in time, we discover patterns of behav- has unintended and undesirable effects. ior just under the surface. These pat- situations can be explained through ge- neric templates called, appropriately, Consider the following two scenarios as terns reflect the hidden structure of the applications of this archetype. system: the beliefs, mental models and “system archetypes.” These archetypes culture of the organization.66 Effective are a combination of feedback loops Scenario 1 (Figure 9, middle) that can be applied across many fields, problem-solving requires that we dig Paul is a freshman optometry student. such as economics, psychology, science below the surface (events) and discover He is having serious difficulties keep- and sociology. As an example, Figure 9 the structure that perpetuates the pat- ing up with his classes and his grades (left) depicts the “shifting the burden” terns of behavior and the events we dis- are poor. As he ponders his future, he is archetype. A symptom creates a need cern from the outside. (Figure 7) very tense and stressed-out. He knows for a short-term, symptomatic solution. that he can have counseling and tuto- rial help through the Office of Student Figure 7 Affairs. However, he believes that this Systems Thinking allows recognition of the patterns below unique would detract from his study time and events. It also promotes the examination of the mental models, his busy schedule. On weekends, he can beliefs and culture that support the systems behavior. relax and enjoy drinking beer with his friends. He discovers that drinking beer on weekdays helps him to cope with the stress. His drinking habit increases every week. Soon, his grades plummet and he fails the semester. Paul’s symp- toms (stress) led him to a symptom- atic solution (drinking). This led to a temporary reduction of his symptoms. A more effective solution was avail- able through counseling and tutoring (fundamental solution), but this solu- tion would take more time to achieve (delay). Unfortunately, the symptom- atic solution (drinking) led to alcohol addiction (unintended consequences) Optometric Education 133 Volume 36, Number 3 / Summer 2011 which decreased the perceived need for In both scenarios, the best strategy Simulation Models: System the fundamental solution. would have been the application of the Dynamics Scenario 2: (Figure 9, right) fundamental solution. If the symptom- atic solution is ever applied, it should System dynamics applies general sys- Dr. Rogers has a healthy optometric be used only once or for a very short tems thinking via mathematical simu- practice and the number of examina- time. The power of systems thinking is lation models. These models allow the tions has been steadily increasing dur- the explanatory ability of the archetype, exploration of different scenarios based ing the past few years. However, the allowing exploration of the variables on the changes of the variables of the number of patients buying optical and feedback loops in the systems. It model. This allows students to design devices (eyeglasses and contact lenses) gives useful insights into optimal ways experiments and answer specific ques- from her optical dispensary has been to apply leverage so that the problems tions on their model: “The move from slowly but steadily decreasing. Dr. at stake are resolved satisfactorily.65 a static model in an inert medium, like Rogers may hire another optician and a drawing, to dynamic models in inter- send the current dispensing technician Other examples of archetypes: active media that provide visualization for additional training. However, this • Limits to growth (limits to suc- and analytic tools is profoundly chang- would take significant investment and cess): A process starts with a period ing the nature of inquiry… Students time. She decides to hire an advertising of increasing growth. After some can visualize alternative interpreta- agency and spend money on a campaign time, the growth slows down or re- tions as they build models… in ways with an emphasis on her dispensing verses due to a limiting condition. that introduce different perspectives on services. Initially she sees an increase in • Success to the successful: Two the problems. These changes affect the the number of sales in the dispensary, processes or activities compete for kinds of phenomena that can be con- but after a few months the sales drop sidered and the nature of argumenta- finite resources. The more success- 8 to old levels. She decides to invest ad- ful process gains an increasingly tion and acceptable evidence.” ditional funds on a stronger market- bigger share of the resources and System dynamics uses three basic ing campaign. Again, sales increase for eventually obliterates the weaker graphical units: stocks, flows and con- several weeks, and then drop again. In one. verters.67 Stocks are the nouns of sys- this second scenario, the problem was • Tragedy of the commons: Units tem dynamics and are symbolized by a the drop of sales at the dispensary. The rectangle. They represent variables that symptomatic solution was the hiring within an organization share com- mon finite resources or assets. The accumulate through time. Examples of an agency to launch an advertising are number of patients, clinic income, campaign. The fundamental solution more they use these assets, the big- ger the rewards as they develop knowledge, population and gasoline in was to increase the quality of services at car tank. Flows are the verbs of system the dispensary by hiring additional staff more activities. Soon, the return on the use of resources decreases, dynamics and they are symbolized by a and training her current staff. However, pipe, flow regulator and a spigot. The this solution would take more time to forcing them to request additional resources. Eventually, the resources direction of the actual flow is shown by take effect (delay). The advertising cam- an arrow at the end of the pipe. Typi- paign worked temporarily creating the diminish dramatically or are ex- hausted. cally, a flow can move toward a stock, perception that there was no need to increasing its accumulation, or move apply the fundamental solution. It led • Eroding goals: A version of a shift- away from a stock, decreasing its accu- to a dependence on an intervenor (out- ing the burden archetype, where a mulation. Examples are births, deaths, side advertising agency) and erosion in fundamental goal of an institution patients to clinic, patients leaving, ex- the capacity of her staff to resolve the is sacrificed in order to fulfill a penses and hiring. Converters are the problem. short-term gain. adverbs of the system and are symbol- ized by a circle. They represent variables

Figure 9 The “shifting the burden” archetype (left) and two examples of its application in psychology (center) and optometric practice management (right).

Optometric Education 134 Volume 36, Number 3 / Summer 2011 that do not accumulate through time. mixture of “faculty days for third year” affect stocks such as clinic income and Examples are birth rate, dispensing rate, and “faculty days for fourth year.” This number of patients through time. The new patients per year and consumption is a fairly complex model that incorpo- first set of inputs is the initial values of per capita. rates many of the main variables that the stocks (clinic income and number Consider the following example, close affect clinic income. The model can be of patients). The second set of inputs to the colleges and schools of optom- adjusted to add or delete variables or representsthe values of the converters. etry. One of the main challenges of represent them in alternative ways. The values of the converters can be set optometric institutions is to maximize The model allows us to experiment through sliders (Figure 11). The val- the income of their clinics while main- with changes in the values of the in- ues on the sliders can be changed into taining the breadth and quality of the put variables and determine how they a virtually infinite number of positions education. This helps maintain tuition within a range. costs as low as possible. A systems model allow us to critically examine the Figure 10 variables that impact clinic income and System dynamics model of a college optometry clinic developed experiment with scenarios as the values with ©Stella Software. Used with permission. of the variables change through time. These “experiments” allow us to deter- mine the best strategies for maximizing income. (Figure 10) The model of Figure 10, using iseesys- tems inc.’s ©Stella Software (available at www.iseesystems.com), depicts two main stocks: clinic income and number of patients. As shown at the bottom of the model, the “number of patients” at the clinic increases by the flow “patients to clinic” and decreases by the flow “pa- tients leaving.” The flow “patients to clinic” depends on two converters: new patients per year and thereturn patient fraction (the fraction of all patients at the clinic who return for an exami- nation within a year). As the model shows, because the income of the clinic is directly affected by the number of patients seen at the clinic, the “number of patients” stock at the bottom feeds into the “producing income” flow that increases the “clinic income”stock. The income flow is affected by the “exam in- come per patient” (cost of the eye exam Figure 11 per patient), the “dispensing rate” (frac- Sliders allow a continuous variation of the system parameters tion of patients who acquire eyeglasses, within limits for a college optometric clinic. Simulation allows us to contact lenses, low vision devices and determine which combination of parameters maximizes a critical other optical devices) and the “dispens- variable such as clinic income. Diagrams developed with ©Stella ing income per patient”(gross income software. Used with permission. from the sales of optical devices). This last variable depends on the “dispens- ing mark-up” (a number indicating the multiplying factor for the cost of optical devices to the patient) and the “dispensing cost per patient.” On the other hand, the “clinic expenses” flow is affected by the “cost of utilities,” “staff salaries,” “faculty salaries,” “dispensing cost,” and “interest expense” (assum- ing the institution is paying off a loan for the facility). In the depicted model, “faculty salaries” are affected by the

Optometric Education 135 Volume 36, Number 3 / Summer 2011 Figure 12 shows the effects of chang- lation dynamics, predator-prey systems, namics (computer simulation) training ing dispensing rate from 0.3 to 0.6 on impact of policies on drug trafficking, improved the ability of participants in clinic income during the first 25 years and epidemiology, among others.67 the last two, high-complexity, tasks. The of operation. The values of the other results suggest that full-fledged benefits converters are maintained constant. Evidence of Improvement are obtained through training on both For example, exam fee at $50, new pa- of Decision-Making Skills systems thinking and system dynamics tients per year at 6,000, return patient through Systems Thinking (computer simulation).68 fraction at 0.5, and dispensing mark- and System Dynamics Maani and Maharaj were interested in up (multiplying factor of sale vs. cost the variables related to decision-making of dispensed devices) at 2.0. The graph There are studies that indicate that performance and the sequence of sys- shows that a dispensing rate of 0.3 (30% systems thinking may enhance deci- tems thinking that would lead to better of patients acquiring optical devices at sion-making abilities, especially those performance. Ten business school grad- the clinic) will lead to increasing losses related to complex situations. For ex- uate students, versed in system think- throughout the years (if everything else ample, Dhawan, O’Connor and Bor- ing and system dynamics, participated remains equal). A dispensing rate of 0.6 man completed a study on 26 business in a computer simulation model of a will lead to a net cumulative gain at the school graduate students to determine company. Their objective was to maxi- beginning of the seventh year. Strategi- if systems thinking and system dynam- mize revenues, profits and market share cally, one can increase the dispensing ics training could improve the quality by manipulating variables such as total rate by training the dispensing staff, of their analysis of a business scenario. workforce and spending on marketing. providing better frame and lens options The scenario involved an information The results showed that better perform- to patients and counseling of patients technology company with revenue ers had higher levels of understanding by the optometrist. Besides the graphs, oscillations through time. They com- as shown by their models.69 the program can produce detailed tables pleted a pre-test and a post-test after by year of operation. 10 hours of systems thinking train- Plate completed two studies assessing the effectiveness of systems thinking in The above exercises brought into prac- ing. A second post-test was completed after an additional period of 13 hours the ability of students to develop causal tice management would allow students maps. The first study included 23 -un to make rational decisions about strat- of system dynamics training (computer simulation). The tests were designed to dergraduate college students on a topic egies to increase their practice success. within a political science course. Post- It is a high level, sophisticated environ- ascertain their ability to identify stocks and flows, propose a cause for the os- test maps (at the end of the course) ment that may be used to simulate their were compared to pre-test maps (at the own future practices. cillations, suggest solutions and predict the workforce of the company. The beginning of the course). At the end of System dynamics is not limited to busi- first two tasks are of low or medium the course the maps had more concepts, ness modeling. It can also be applied to complexity, while the last two tasks more link densities, more complex simple and complex modeling of scien- have high complexity. The researchers causal loops and were more similar to tific and social issues. For example, it found that systems thinking training expert maps. A second study compared can be used to model the dynamics of improved performance in the first two middle school children trained in sys- glucose regulation in physiology, popu- tasks but not the last two. System dy- tems thinking to children without such training. The group trained in systems thinking had maps with higher link Figure 12 densities, more complex causal loops Clinic income by year of operation for four dispensing rates: Curve and that were more similar to expert 1= 0.3, Curve 2 = 0.4, Curve 3 = 0.5 and Curve 4 = 0.6. Graphs maps.70 developed with ©Stella Software. Used with permission. LaVigne completed a meta-analysis of studies relating systems thinking and dynamic modeling to students’ learn- ing. She reported trends indicating that this training enhances the connections between curriculum and real-life expe- riences, clearer exploration of thoughts and mental models, and increased mo- tivation and engagement.71 Systems thinking and system dynamics are promising tools in optometric edu- cation. System dynamics is the most so- phisticated tool in our armamentarium. Several companies offer commercially available software for dynamic model- ing, training and specialized books:

Optometric Education 136 Volume 36, Number 3 / Summer 2011 • Isee Systems (http://www.iseesys- map of your entire course and 7. Consider using system dynamics tems.com) present it to your students on the models for practice management. • Ventana Systems: (http://www. first day of class. The map will be Students can develop a systems vensim.com) an expert, holistic representation model of their own future practices of the knowledge structure related and simulate scenarios to find out • Pegasus Communications(http:// to your course. It will serve as an which strategies are more likely to www.pegasuscom.com) anchor throughout the quarter or maximize their success. • The Waters Foundation, which pro- semester. You may refer back to the motes systems thinking education in map as you develop your topic. It References schools, offers via its Web site free will be a helpful tool as students 1. Gross R. Socrates way: Seven mas- modeling tutorial lessons as well conduct a systematic review when ter keys to using your mind to the as detailed lesson plans that can be studying for your examinations or utmost. New York: Putnam; 2002. adapted to college-level courses(www. the optometry boards. 2. Gabennesch H. Critical thinking: watersfoundation.org). 2. Train students in the use of mind What is it good for? (In fact, what mapping and concept mapping is it?). Skept Inq. 2006;30(2):3-4. Conclusion techniques. Initially, they may use 3. Chartrand J, Ishikawa H, Flander The evidence indicates that visual tools them for note-taking during their S. Critical thinking means busi- may help our students develop bet- own readings. Once proficiency is ness: Learn to apply the #1 work- ter recall, comprehension and critical established, they can be used for place skill. Available from: http:// thinking skills. It is important that note-taking during lectures. thinkwatson.com/downloads/Pear- the tools be used mindfully and judi- 3. Ask students to develop a concept son_TalentLens_Critical_Think- ciously. Mind mapping is most useful map of their knowledge about your ing_Means_Business.pdf. Accessed during brainstorming, note-taking and lesson topic before the beginning September 30, 2010. developing clinical scenarios. Concept and at the end of your lesson. The 4. Garber AR. Death by Power- mapping’s strength lies in forcing us beginning map will allow them to Point. April1, 2001. Available to organize knowledge hierarchically. explore their own knowledge base from: http://www.smallbusiness- Thinking maps are powerful templates before the lesson. The final map computing.com/biztools/article. allowing the learner to develop meta- will allow them to explore the ex- php/684871. cognitive skills. Argument mapping panded knowledge base and how it 5. Medina J. Brain rules: 12 principles is a critical thinking tool to formalize fits into their cognitive knowledge for surviving and thriving at work, premises, counterarguments and con- structure. You may want to period- home, and school. Seattle (WA): clusions. Systems thinking provides the ically review some of your student Pear Press; 2008. ability to observe the deep structure of maps for accuracy and understand- 6. Davies WM. Concept mapping, systems, transcend the simplistic linear ing. mind mapping and argument cause/effect relationships and apply the mapping: What are the differences language of archetypes across different 4. Ask students to use ©Thinking and do they matter? 2010. Avail- disciplines. System dynamics allows Maps tools around specific course able from: http://www.tlu.fbe. us to simulate the behavior of systems topics. For example, they may use unimelb.edu.au/teaching_staff/ and determine the effects of changes in the classification organizer to rep- seminar_series/documents/Sem- critical variables. resent anterior and posterior seg- 1CMMMAM.pdf. Accessed Sep- ment diseases. The sequencing tool tember 30, 2010. Davies proposed a convergence of map- may be used to depict the stages of 7. Arends R. Learning to teach. New ping technologies where students incor- certain ophthalmic diseases such as York: McGraw Hill; 2007. porate concept maps, mind maps and diabetic retinopathy. The cause/ef- 8. Bransford JD, Brown AL, Cocking argument maps. The concept maps will fect tool may be employed to rep- RR., ed. How people learn: Brain, be the core maps where students are resent the risk factors and effects of mind, experience and school. able to depict their present knowledge diseases such as glaucoma. Washington (DC): National Acad- structure. Some concepts will be linked emy Press; 2000. to mind maps elaborating their associa- 5. Ask students to develop case pre- 9. Marzano RJ. What works in tive structure. Other concepts may be sentations using mind mapping schools. Alexandria (VA): Associa- tied to argument maps as needed.6 or concept mapping. They can use free collaborative mapping software tion for Supervision and Curricu- One of the main objectives of this pa- such as ®IHCMapTools and post lum Development; 2003. per is to promote educational research their maps on the Internet. Docu- 10. Prince M. Does active learning activities of optometric educators as ments, drawings and Web site links work? A review of the research. J they apply these tools in their courses. can be attached to their maps. Eng Educ. 2004;93(3):223-31. In the meantime, the available evidence 11. McClain A. Improving lectures. J supports the implementation of certain 6. 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Optometric Education 139 Volume 36, Number 3 / Summer 2011