teaching dossier example

Teaching Dossier∗

Douglas StebilaDept. of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario, Canada

[email protected]

2008 March 16

Contents

1 Teaching philosophy statement 2

2 Teaching responsibilities 3

3 Teaching strategies 4

4 Preparation for teaching 6

5 Evaluation of teaching 7

6 Future teaching goals 8

A Teaching materials 10A.1 Course outline, Linear Algebra (MATH 136) . . . . . . . . . . . . . . . . . . . 10A.2 Sample lecture notes, Linear Algebra (MATH 136) . . . . . . . . . . . . . . . 11A.3 Sample assignment questions, Linear Algebra (MATH 136) . . . . . . . . . . 12

B Letters from colleagues 13B.1 Observations from Certificate in University Teaching program . . . . . . . . 13B.2 Letter from Chair of Department of Combinatorics & Optimization, Uni-

versity of Waterloo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

∗Teaching dossier originally submitted for the Certificate in University Teaching at the Centre for Teach-ing Excellence, University of Waterloo.

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Teaching Dossier Douglas Stebila

C Course evaluations 16C.1 Evaluation summary – Spring 2006 . . . . . . . . . . . . . . . . . . . . . . . . 16C.2 Evaluation summary – Spring 2007 . . . . . . . . . . . . . . . . . . . . . . . . 17C.3 Evaluation comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18C.4 Student comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1 Teaching philosophy statement

As much as an instructor can explain and encourage, I believe learning is ultimatelydriven by students, who must learn material by and for themselves. In mathematics,this is particularly true, for students must practice the techniques they learn in class andapply them to new problems. My goal as a teacher, then, is to provide strong supportfor student-driven learning. I believe instructors should support student learning by un-derstanding and meeting students’ varied goals, teaching with clarity and structure, andcreating opportunities for student participation and interaction.

An instructor must understand students’ varied goals in order to effectively motivatelearning. In each class, students come from a variety of backgrounds, disciplines or sub-disciplines, and have different goals; all of these factors play a role in students’ motivationand efforts. I believe that students need to see how the course material is relevant to aproblem or subject that they care about, or else it will be difficult to sustain their interest.A common linear algebra course will, for example, be approached differently by com-puter scientists (who are interested in computer graphics applications), actuaries (inter-ested in optimization), and pure mathematicans (intrigued by more abstract properties).When I teach, I try to find out the topics in which my class is interested by asking studentstheir interests at the beginning of the term and then design assignment problems, shortexamples, and even entire lectures on relevant applications of interest to the class.

In lectures, an instructor must clearly present his/her ideas and place them structurallyin context in order to remove barriers to student-driven learning. Mathematics is a scarysubject for some students, so minimizing notation and jargon is useful in providing clar-ity to these students. Because students have different learning styles – some are globallearners who like to see the big picture, while others are sequential learners who like tosee one bit at a time – it is important for instructors to provide structure that adapts toboth styles. Global learners like to see connections to other aspects of the course and toother subjects, whereas sequential learners like to see course material that follows fromone topic to the next. I structure my lectures to clearly organize the material, alwaysmarking “Definition”, “Theorem”, “Proof”, or “Example” wherever appropriate, and try

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to draw connections between the material at hand and previous topics in this or othercourses.

Student participation is the most important part of the learning process. The purposeof learning mathematics is to develop tools that can be used to solve new problems, bethey theoretical or practical. Student participation in class helps students integrate newideas into their knowledge base and helps the instructor gauge success. My best mathteacher, a high school instructor named Mr. Bruce White, taught me math in an interac-tive, problem-solving environment. Students discussed and presented at the board theirsolutions to problems, and these problems were motivation for and illustrative of the lec-ture material. In presenting their ideas, students had to organize and critically evaluatetheir arguments. Moreover, Mr. White found a way to make mathematics a social activ-ity, thereby motivating student participation. I try to do this in my teaching by designingpoints of interaction into lectures and using tutorial time to get students to present theirsolutions to problems.

2 Teaching responsibilities

Lecturer. I have been an instructor for a multi-section first-year course in Linear Alge-bra for math majors (MATH 136) for two terms (Spring 2006, 100 students; Spring 2007,116 students) at the University of Waterloo. Although the course syllabus (Appendix A.1)was set by the course coordinator, I was responsible for designing lecture material for mysection, helping develop assignment material, supervising graduate teaching assistantsand undergraduate markers, developing exam questions, marking midterm and final ex-ams, and holding office hours.

Teaching assistant. I have also been a graduate teaching assistant for two upper-yearcourses, one in Graph Theory (CO 342, Fall 2004, 73 students) and one in Quantum Com-puting (CO 481, Winter 2007, 37 students), both at the University of Waterloo. For GraphTheory, I held office hours and marked assignments. For Quantum Computing, I helpeddevelop assignment solutions, maintained the course website, marked assignments, andheld office hours; my efforts in this course were recognized by my department chair whoconsidered me for an Outstanding Teaching Assistant award (see Appendix B.2).

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3 Teaching strategies

Review previous lecture at the beginning of each class. At the beginning of each lec-ture, I spend two to three minutes reviewing the major topics from the previous lecture,restating important theorems and definitions. This serves a number of purposes. By do-ing this at the start of each lecture, it provides a consistent start to each lecture and is acue for students to focus on the lecture. Since the review only covers previous material,no new content is missed if there are small disruptions from students entering late. It alsohelps place the previous material in context for the present lecture. While every instructorwould like their students to be reviewing their notes and text in between lectures, I amrealistic about the fact that most students will not, and providing a review helps studentsremember what was important from last time. A sample lecture review is included at thebeginning of the sample lecture notes in Appendix A.2.

Minimize notation and organize presentation. When I first taught Linear Algebra, Idiscovered that many of these first year students had problems with notation I used evenafter I explained it many times – students couldn’t remember the difference between ∈,⊆,and ≤ (for subspaces). As a result, I now try to minimize the use of notation in lectures,preferring to spend an extra few seconds writing out “is a subspace of” rather than usingthe less-common notation ≤, for example. I recognize that students copy almost directlyfrom the blackboard to create their notes in most math classes, so I explicitly indicate foreach item what it is – a definition, theorem, proof, example, fact, or corollary. I consis-tently structure my lectures to lead from motivation to definition to theorem to proof toexample, providing a standard progression typical of mathematical thinking; the samplelecture notes in Appendix A.2 illustrate such a progression.

Design points of interaction into lectures. When I prepare my lecture notes, I explicitlymark places where I can ask questions of the class. Rather than making generic querieslike “are there any questions?”, I instead look for places where I can ask students tocomplete equations, recommend techniques for trying to solve a given problem, or asktrue/false questions to gauge student understanding. When I first started lecturing, Inoticed that I had a hard time doing this on an ad hoc basis, so I adopted the practice ofexplicitly designing these points of interaction into lectures, an example of which is givenin Appendix A.2. I also had a tendency to only wait a couple of seconds and then answerthe question myself if no answer was forthcoming; I am now much better at waiting forstudent replies, even if it results in 5-10 seconds of unusual silence. I have found thatthese points of interaction become natural times for students to ask their own questions,

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and are much more likely to ask a question at one of these times rather than at an “anyquestions?” prompt.

Describe non-trivial, relevant applications of theoretical material. While some stu-dents enjoy the abstract beauty of mathematics, many see it as a tool to accomplish othertasks. For these students, I try to provide relevant applications of the theoretical material.Like many lecturers, I include simple application-oriented examples into lectures andassignments. However, I also try to go into greater depth with applications and showhow they are non-trivial uses of the theoretical material. For example, in my first-yearLinear Algebra course, I spend two lecture hours on error-correcting codes as an appli-cation. While not part of the standard course syllabus, I think it is an excellent exampleof important properties of linear algebra. It illustrates basic techniques such as matrixmultiplication and linear independence, but is also dependent on the deeper notion ofkernels of linear transformations, which is a new topic to the students in the class.

Use regular assignments to reinforce lecture material. For first- and second-year courses,I like to assign students weekly problem sheets to allow them to practice the coursematerial. In upper-year courses, I still believe students should do regular assignments,though not necessarily every week as upper-year assignments may have more advanced,in-depth problems requiring more time to complete. I prefer smaller, frequent assign-ments instead of larger, infrequent assignments, because infrequent assignments meanthat students who do not study the material at their own initiative will fall behind with-out practice. A weekly assignment from my first-year Linear Algebra course is includedin Appendix A.3.

Students present solutions in tutorials. In high school, one teacher used problem solv-ing sessions in which students presented their solutions to the rest of the class. I foundthis an incredibly valuable way of developing my knowledge and mathematical commu-nication skills. In a review session for my Linear Algebra course, I provided students witha problem sheet ahead of time and then had volunteers present their solutions. AlthoughI was concerned that students would be unwilling to get up in front of their peers, I waspleased to find I had no trouble getting students to volunteer, and even weaker studentswho were not certain about their solutions were willing to give it a try. In future courses,I would like to extend this to be a required component of the course, with students pre-senting and discussion solutions to problems in tutorial sections. This proposed activitywas the focus of a paper I wrote for the Certificate in University Teaching (described inthe next section).

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4 Preparation for teaching

Between Fall 2004 and Winter 2008, I participated in the Certificate in University Teaching(CUT) program offered by the Centre for Teaching Excellence (CTE, formerly TRACE) ofthe University of Waterloo. There are three courses required for the program. I completedthe program in Winter 2008.

Preparing for University Teaching (GS 901) requires participation in 6 teaching work-shops (each averaging 1.5 hours in length) and the submission of 4 short (2-3 page) re-sponse papers. For this course, I attended workshops on course design, learning styles,professionalism in the classroom, presenting versus lecturing, voice projection, and teach-ing large classes. In the learning styles workshop, for example, we studied the Soloman-Felder Index of Learning Styles, which describes four learning scales and how studentscan have different preferences on these scales. I use what I learned in this workshop totry to strike an appropriate balance between visual and verbal learning in lectures and toorganize information for both sequential and global learners.

Preparing for an Academic Career (GS 902) requires the preparation of a teaching dossierand research paper. For each of these, one attends a workshop and subsequent consulta-tion session before submission. I first prepared this teaching dossier for this course. Myresearch report was entitled “Improving formal reasoning in mathematics through tutori-als.” I learned about comprehension tests, which are questions designed to help studentsimprove formal reasoning and skills at proof validation. In my report, I discussed myproposal for small (30-student) tutorials in which students presented their solutions tocomprehension test-style questions and discussed them with their peers. I look forwardto trying out this proposal in a future teaching opportunity.

Teaching Practicum (GS 903) consists of three observed teaching events. For each obser-vation, a trained staff member from the CTE office attends the event and provides writtenfeedback consisting of aspects to maintain and targets for change and improvement. Myteaching observations were completed in Spring 2006 when I was teaching Linear Alge-bra (MATH 136). I have included some comments from these teaching evaluations inSection 5 and additionally in Appendix B.1.

In addition to the certificate program described above, I attended teaching assistant train-ing in the Faculty of Mathematics at the University of Waterloo upon starting my PhDprogram. I have subsequently participated in this training session as a senior graduatestudent, offering advice to new graduate students on how to be a good teaching assistant.

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5 Evaluation of teaching

Student evaluations. As an instructor, I have had my teaching observed by facultymembers from my department and trained observers from the Centre for Teaching Ex-cellence at the University of Waterloo. Additionally, my students have completed courseevaluation forms. On quantitative criterion, students ranked me better compared withother instructors of the same course, and I have demonstrated improvement over multi-ple terms of teaching. Students’ qualitative comments are consistently positive.

For the Linear Algebra course (MATH 136) that I taught in Spring 2006, students eval-uated my overall effectiveness as an instructor and the organization and coherence ofmy lectures substantially better than instructors of other sections of the same course thatterm, and my evaluations even improved from my Spring 2006 to my Spring 2007 teach-ing, as shown in the following table. In the Spring 2007 term, 93% of students rated meas an excellent or good overall instructor.

Evaluation criterion Response Me Instructors ofother sections

Spring 2006 Spring 2007 Spring 2006Organization andcoherence of lectures

Excellent 47% 60% 10%Good 40% 37% 37%Exc.+Good 87% 97% 47%

Instructor’s treatmentof students’ questions


Overall effectivenessas an instructor


(See Appendices C.1 and C.2 for a numerical summary of my course evaluations forSpring 2006 and Spring 2007, respectively, and Appendix C.3 for a comparison with otherinstructors for Spring 2006.)

As I indicated in my teaching philosophy, I believe it is important for an instructor toteach with clarity and structure. I was very pleased that most (80%) students thought thelevel of my explanations were “just right” and that the same number of students thoughtmy treatment of students’ questions was “excellent” or “good”. Students commented thatI “organized the material quite well” and that I give “clear lectures, effective communica-tion, [and] focus on what is important”.

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Student comments also reinforced some of my teaching strategies from Section 3. Onestudent commented that I gave “good summaries of previous class material,” referringto my technique of reviewing the previous class at the beginning of each lecture, andthat I “handle[d] students’ questions perfectly”. Another student commented that they“[enjoyed] the practical applications”, and one student described me as “By far, the bestinstructor I had during first year”. More student comments are included in Appendix C.4.

Observed teaching events. While completing the Teaching Practicum course for theCertificate in University Teaching (c.f. Section 4), I had some lectures observed by trainedobservers. Since my observed teaching events were spaced throughout the term, I wasable to incorporate feedback from early evaluations in my lectures and gauge my suc-cess. In an early observation, it was noted that my question asking strategies could beimproved. In preparing for subsequent lectures, I identified points in each lecture whereI could ask focused, specific questions. In a later observation event, I received feedbackthat I had addressed this area well:

“I liked how you asked a number of questions throughout the lecture in anattempt to engage students in the learning process. One of the things thatyou did during your lecture to facilitate student learning was to ask studentsto complete equations that you wrote on the board. . . . This really facilitatesstudent learning.”

The teaching observation report in Appendix B.1 gives an example of further commentson my teaching from the trained observer from the Centre for Teaching Excellence at theUniversity of Waterloo.

6 Future teaching goals

I would like to teach a variety of courses at different levels in a university setting. Ihave enjoyed teaching first-year courses and would like to continue teaching introduc-tory courses in algebra, combinatorics, discrete mathematics, and theoretical computerscience.

In future introductory math courses, I would like to try a new technique of using weeklytutorial sessions to have students present their solutions to problems. I have tried outthis technique in review sessions in previous linear algebra courses with some success.

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I would like to integrate it more tightly into future courses to provide students moreopportunities to interact with each other and the instructor. Over the course of the term,each student would have to present one problem (which they receive about a week inadvance) and would be evaluated on correctness (50%) as well as clarity and presentation(50%), contributing around 4% to the final grade.

I am also interested in teaching senior courses, especially in my area of research, cryp-tography, and in related areas such as quantum computing, error-correcting codes, andcomputational complexity theory. In particular, I would like to design and teach a fourth-year or graduate-level topics course on network security, first teaching the mathematicalstructures behind security protocols on the Internet today (e.g., the Secure Sockets Layer(SSL)) and then examining case studies of security successes and failures (e.g., the WiredEquivalent Protocol (WEP) for wireless security).

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A Teaching materials

A.1 Course outline, Linear Algebra (MATH 136)

MATH 136 LINEAR ALGEBRA I Spring 2007

Sect. Time Location Instructor Office Phone email001 11:30 MWF MC 4059 Hoffman, Peter MC 5058 x35564 phoffman@math

Mon. tutorial MC2065002 9:30 MWF MC 4021 Stebila, Douglas MC5136A x36895 dstebila@math

Mon. tutorial MC2065003 10:30 MWF MC 1085 Wu, Shengli MC5153 x36008 s3wu@math

Mon. tutorial MC2065

Prerequisites: MATH 135 or MATH 145

Textbook: Linear Algebra and its Applications (3rd edition), by David C. Lay (available in the bookstore).

Websites: Each section will have its own website. Your lecturer will provide the URL.

Calculators: Only the calculators provided by the Faculty will be allowed on midterm and final exams.

Tutorials: These begin on Monday, May 7.

Tutorial Centre is open for MATH 136, Mondays and Tuesdays, starting May 7th.

Assignments: There will be eight assignments to be handed in, with your name and ID# on it, please!Assignments will vary slightly from section to section, to account for individual lecturers’ preferences inorder and pace of course topics. The best 6 of Assignments 1 through 7 will be counted, as will Assignment8. Each counted assignment will be worth slightly less than 2% of your final grade in the course, totalling12%, plus the 3% for MATLAB work. These are due to be handed in on designated Wednesdays by 1 p.m.into the Drop Boxes outside the Tutorial Centre. Late assignments will not be graded, and will receivea mark smaller than any positive real number.

Solutions: Solutions to weekly assignments will be posted on your section’s web site at most one weekafter the due date.

Midterm Exam: There will be one common 90 minute midterm exam, taking place on Monday, June 4from 7:00 p.m. to 8:30 p.m. It will be worth 20% of your final grade in the course.

Final Exam: There will be a common 2.5-hour final exam held during the examination period.

Labs: MATH 136 has a lab component, where you will learn to use MATLAB. The MATLAB componentof the course is separate from, but complementary to, the lecture component. You will be scheduled intoan introductory lab slot. It is important that you attend this session to learn the basics of MATLAB.There will be one lab to be handed in, worth 3% of your grade in the course, which you will be expected tocomplete on your own time. This is due on Wednesday, July 18. You will not be tested on the MATLABcomponent of the course.

Grades: Final exam: 65%; Midterm Test: 20%; Assignments: 12%; Lab: 3%.

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A.2 Sample lecture notes, Linear Algebra (MATH 136)

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A.3 Sample assignment questions, Linear Algebra (MATH 136)

1. [5 marks] Let S = {a + bt2 + bt6 | a ∈ R, b ∈ R}. Show that S is a subspace of P6.Find a basis for S.

2. [7 marks] Define S : P2 → R4 by

S(p) :=

p′′(2)p′(0)p(1)

p(1) + p′′(−1)

,

where p′, p′′ are the first and second derivatives of the polynomial function p.

(a) [2 marks] Show that S is linear.(b) [2 marks] Find a basis for Ker(S), if the latter is not just {~0}.(c) [1 mark] Is S one-to-one? (That is, is it injective?) Why or why not?(d) [1 mark] Find a basis for the range of S.(e) [1 mark] Is S onto? (That is, is it surjective?) Why or why not?

3. [10 marks] Error-correcting codes. Let H =

0 0 0 1 1 1 10 1 1 0 0 1 11 0 1 0 1 0 1

. The following

four vectors form a basis for NulH :(1 0 0 0 0 1 1

)> (0 1 0 0 1 0 1

)>(0 0 1 0 1 1 0

)> (0 0 0 1 1 1 1

)>Let A be the 7× 4 matrix whose columns are the basis vectors above.

(a) [2 marks] Encode the messages (i) 1100 and (ii) 0101 using the encoding matrixA.

(b) [4 marks] For the received encoded messages (i) ~x = 0110011 and (ii) ~x =1001011, compute H~x. What does the value of H~x tell you?

(c) [4 marks] For each received encoded message in the previous part, determinewhich bit of ~x, if any, has been flipped. Then correct the flipped bit (if neces-sary) to obtain ~x′ and solve A~m = ~x′ to determine the original message ~m.

More information on error-correcting codes can be found in the Case Studies on the websitefor the course textbook, which is linked to from the course website. Notes from the error-correcting codes lectures can also be found on the course website under “Lessons and Files”→ “Lecture Notes”.

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B Letters from colleagues

B.1 Observations from Certificate in University Teaching program

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B.2 Letter from Chair of Department of Combinatorics & Optimiza-tion, University of Waterloo

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C Course evaluations

C.1 Evaluation summary – Spring 2006

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C.2 Evaluation summary – Spring 2007

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C.3 Evaluation comparison

This section provides come context for the course evaluation information in Appendix C.1 for theLinear Algebra (MATH 136) course I taught at the University of Waterloo in Spring 2006. I haveselected 3 key characteristics (organization and coherence, treatment of students’ questions, andoverall effectiveness) and compared my evaluations (a) to other instructors of the same course (b)and other first year course instructors (c) for the same term.

1) Evaluate the organization and coherence of the lectures

Excellent Good Satisfactory Unsatisfactory Very poor(a) Me 47% 40% 11% 0% 2%(b) Other course instructors 10% 37% 34% 11% 8%(c) All first year instructors 33% 44% 14% 6% 2%

3) Evaluate the instructor’s treatment of students’ questions


8) Evaluate the overall effectiveness of the instructor as a teacher


Note: percentages may not sum to 100% due to rounding.

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C.4 Student comments

These comments were submitted on course evaluations by students in the Linear Algebra (MATH136) course I taught at the University of Waterloo in Spring 2006.

• “He provided many examples to apply the content taught, and was persistent to en-sure students understood the material. Positive [class atmosphere], as many peoplecame to this section because of the thorough notes the instructor gave.”

• “[Enjoyed] the practical applications.”

• “Very good lecture notes, easy to follow when reading them later.”

• “Moves through the material at a very appropriate pace, and provides insight intothe usefulness of the material.”

• “Good organization, explained things well, good summaries of previous class ma-terial.”

These comments were submitted on course evaluations by students in the Linear Algebra (MATH136) course I taught at the University of Waterloo in Spring 2007.

• “The instructor has been very helpful to the actual learning process. Instead ofpenalizing students who miss class, he posts required notes on the course websitewhich really helps on the occasional time I miss a lecture. Also, his course websiteis the most update and complete I have seen.”

• “I loved how he was so organized and he had excellent communication skills (oral& written).”

• “He was very clear, well paced, helpful and fun to listen to.”

• “Clear explanation, good visual presentation; only he let me feel that MATH 136makes sense to me.”

• “Very approachable, willing to answer questions, not intimidating.”

• “Keeps the class going at an excellent pace to keep students interested but not gettoo far ahead. Handles students’ questions perfectly.”

• “Awesome! I loved your class, you made it interesting and were very informative.”

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• “Explanation / examples in the lecture were great. Writing big on the board wasvery helpful for students at the back; organizing the blackboard was well done.”

• “Great communication with students, gave the impression that he was there becausehe wanted to be, not because he had to. Was obviously passionate of the coursematerial.”

• “Everything was done very well. Clear presentation, handled questions well, veryorganized, updated the UW-ACE website extremely regularly. By far, the best in-structor I had during first year.”

The following comments were submitted on the website RateMyProfessors.com and refer to theLinear Algebra (MATH 136) course I taught at the University of Waterloo in Spring 2006.

• “I thought I would never meet another great prof like Vanderburgh, until I tookMATH 136 with Stebila. = ) I nominated Vanderburgh for best teacher award, butnext year, Stebila has my vote!! Keep up the good work, you will be one of the bestlecturers at UWaterloo math!”

• “He is an awesome prof. He even posted all his lecture notes online in case youmissed any of his lectures. Very clear and makes sure you understand. Moderateassignments, and easy midterm.”

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