Using Open Pedagogy in an Upper Division

Open Pedagogy The Artifact Artifacts and Reflections

Using Open Pedagogy in an Upper Division Mathematics Course Andrew Misseldine Southern Utah University

23 February 2018

Andrew Misseldine

Open Pedagogy in Math


Past OER Experiences Open Pedagogy Renewable Assignments

Past OER Experiences For the last two and half years, I have been using OER in my mathematics courses as SUU including:

Andrew Misseldine




Past OER Experiences For the last two and half years, I have been using OER in my mathematics courses as SUU including: Intermediate Algebra (Math 1010),

Andrew Misseldine




Past OER Experiences For the last two and half years, I have been using OER in my mathematics courses as SUU including: Intermediate Algebra (Math 1010), Contemporary Mathematics/Quantitative Reasoning (Math 1030),

Andrew Misseldine




Past OER Experiences For the last two and half years, I have been using OER in my mathematics courses as SUU including: Intermediate Algebra (Math 1010), Contemporary Mathematics/Quantitative Reasoning (Math 1030), College Algebra (Math 1050),

Andrew Misseldine




Past OER Experiences For the last two and half years, I have been using OER in my mathematics courses as SUU including: Intermediate Algebra (Math 1010), Contemporary Mathematics/Quantitative Reasoning (Math 1030), College Algebra (Math 1050), Calculus I (Math 1210),

Andrew Misseldine




Past OER Experiences For the last two and half years, I have been using OER in my mathematics courses as SUU including: Intermediate Algebra (Math 1010), Contemporary Mathematics/Quantitative Reasoning (Math 1030), College Algebra (Math 1050), Calculus I (Math 1210), Calculus II (Math 1220),

Andrew Misseldine




Past OER Experiences For the last two and half years, I have been using OER in my mathematics courses as SUU including: Intermediate Algebra (Math 1010), Contemporary Mathematics/Quantitative Reasoning (Math 1030), College Algebra (Math 1050), Calculus I (Math 1210), Calculus II (Math 1220), Linear Algebra (Math 2270),

Andrew Misseldine




Past OER Experiences For the last two and half years, I have been using OER in my mathematics courses as SUU including: Intermediate Algebra (Math 1010), Contemporary Mathematics/Quantitative Reasoning (Math 1030), College Algebra (Math 1050), Calculus I (Math 1210), Calculus II (Math 1220), Linear Algebra (Math 2270), and Abstract Algebra (Math 4220).

Andrew Misseldine




Past OER Experiences For the last two and half years, I have been using OER in my mathematics courses as SUU including: Intermediate Algebra (Math 1010), Contemporary Mathematics/Quantitative Reasoning (Math 1030), College Algebra (Math 1050), Calculus I (Math 1210), Calculus II (Math 1220), Linear Algebra (Math 2270), and Abstract Algebra (Math 4220). Although the successes I will discuss here arise from mathematics courses, this research is discipline-independent and is transferable to non-mathematical courses. Andrew Misseldine




Past OER Experiences Throughout that time, my students have seen the many benefits of OER including:

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Past OER Experiences Throughout that time, my students have seen the many benefits of OER including: cost savings (my students collectively have saved about $45,000 during this time),

Andrew Misseldine




Past OER Experiences Throughout that time, my students have seen the many benefits of OER including: cost savings (my students collectively have saved about $45,000 during this time), improved student performance (my students from OER sections have performed 7% better than my non-OER sections),

Andrew Misseldine




Past OER Experiences Throughout that time, my students have seen the many benefits of OER including: cost savings (my students collectively have saved about $45,000 during this time), improved student performance (my students from OER sections have performed 7% better than my non-OER sections), and increased student pass rate (my OER sections have 20% fewer failing students).

Andrew Misseldine




Past OER Experiences Throughout that time, my students have seen the many benefits of OER including: cost savings (my students collectively have saved about $45,000 during this time), improved student performance (my students from OER sections have performed 7% better than my non-OER sections), and increased student pass rate (my OER sections have 20% fewer failing students).

Andrew Misseldine




Open Pedagogy This discussion is not about the benefits of using OER. Open Education is much more than just free textbooks.

Andrew Misseldine




Open Pedagogy This discussion is not about the benefits of using OER. Open Education is much more than just free textbooks. David Wiley “Using OER the same way we used commercial textbooks misses the point. Its like driving an airplane down the road. Yes, the airplane has wheels and is capable of driving down on the road (provided the road is wide enough). But the point of an airplane is to fly at hundreds of miles per hour – not to drive. Driving an airplane around, simply because driving is how we always traveled in the past, squanders the huge potential of the airplane. So what is the analogous additional potential of open educational resources, compared to commercial textbooks and other commercial resources?” Andrew Misseldine




Open Pedagogy

Open Pedagogy An open pedagogy is any method and practice of teaching that encourages or requires students to use the five R’s of OER: Retain, Reuse, Revise, Remix, Redistribute.

Andrew Misseldine




Open Pedagogy

Open Pedagogy An open pedagogy is any method and practice of teaching that encourages or requires students to use the five R’s of OER: Retain, Reuse, Revise, Remix, Redistribute. As part of a Curriculum Innovation Grant (CIG) from SUU’s Center of Excellence for Teaching and Learning (CETL), I have started to implement open pedagogical methods in my mathematics courses, starting with Abstract Algebra (Math 4220) Fall 2017.

Andrew Misseldine




Open Pedagogy #1: Use OER materials

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Open Pedagogy #1: Use OER materials This open pedagogy maybe goes without saying, but using open materials for course instruction is an open pedagogy.

Andrew Misseldine




Open Pedagogy #1: Use OER materials This open pedagogy maybe goes without saying, but using open materials for course instruction is an open pedagogy.

This is the one open pedagogy I was already using for my classes, including Abstract Algebra. Namely I was using Thomas Judson’s text Abstract Algebra: Theory and Applications. http://abstract.ups.edu/

Andrew Misseldine




Open Pedagogy #2: Create OER materials

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Open Pedagogy #2: Create OER materials As part of my course preparation, I create detailed, typed lecture notes which I use during lecture and share with students through the university LMS.

Andrew Misseldine




Open Pedagogy #2: Create OER materials As part of my course preparation, I create detailed, typed lecture notes which I use during lecture and share with students through the university LMS. I have modified these lectures notes and licensed them under a CC-BY-SA License. They are now shared openly through my faculty website in the Open Web instead of behind a password-protected LMS. Andrew Misseldine




Open Pedagogy #3:. . . A Personal Story First

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Open Pedagogy #3:. . . A Personal Story First Perhaps the most transformative courses I took as an undergraduate was a Combinatorics course (the mathematics of counting really “hard” things).

Andrew Misseldine




Open Pedagogy #3:. . . A Personal Story First Perhaps the most transformative courses I took as an undergraduate was a Combinatorics course (the mathematics of counting really “hard” things). The class was very small and we got to each other and the professor very well.

Andrew Misseldine




Open Pedagogy #3:. . . A Personal Story First Perhaps the most transformative courses I took as an undergraduate was a Combinatorics course (the mathematics of counting really “hard” things). The class was very small and we got to each other and the professor very well. As part of the course, we had to complete a term-project. I had a strong background in computer programming (I was a computer science major before switching to mathematics), so I decided to write a Java program to implement a combinatorial algorithm we learned about a very niche problem know as the Rook Polynomial.

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Despite my programming background, this task turned out to be very challenging to me.

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Despite my programming background, this task turned out to be very challenging to me. I learned so much about programming,

Andrew Misseldine





Despite my programming background, this task turned out to be very challenging to me. I learned so much about programming, so much about rook polynomials,

Andrew Misseldine





Despite my programming background, this task turned out to be very challenging to me. I learned so much about programming, so much about rook polynomials, so much about mathematics in general,

Andrew Misseldine





Despite my programming background, this task turned out to be very challenging to me. I learned so much about programming, so much about rook polynomials, so much about mathematics in general, and so much about myself while working on this computer program.

Andrew Misseldine





Despite my programming background, this task turned out to be very challenging to me. I learned so much about programming, so much about rook polynomials, so much about mathematics in general, and so much about myself while working on this computer program. Because of stories like mine and other hard data, the LEAP Initiative identifies Project-Based-Learning as a High-Impact Educational Practice.

Andrew Misseldine





I put my heart and soul into my program. I fell in love with the topic, a strong passion I still have to this day.

Andrew Misseldine





I put my heart and soul into my program. I fell in love with the topic, a strong passion I still have to this day. I was truly motivated to make my best effort toward this computer program, which caused me to grow so much as a student, as a mathematician, and as a citizen.

Andrew Misseldine





I put my heart and soul into my program. I fell in love with the topic, a strong passion I still have to this day. I was truly motivated to make my best effort toward this computer program, which caused me to grow so much as a student, as a mathematician, and as a citizen. Unfortunately, the common model for Project-Based-Learning does not generally lead to this level of motivation and enthusiasm in students as this project did to me.

Andrew Misseldine





I was so proud of my program. So proud that I wanted to share it with the world, but I couldn’t.

Andrew Misseldine





I was so proud of my program. So proud that I wanted to share it with the world, but I couldn’t. The OER movement that exists today was absent at that time. Open Licensing through Creative Commons or other organization is virtually unknown to my peers and me.

Andrew Misseldine





I was so proud of my program. So proud that I wanted to share it with the world, but I couldn’t. The OER movement that exists today was absent at that time. Open Licensing through Creative Commons or other organization is virtually unknown to my peers and me. I felt that I had created a masterpiece but had no way to share it. I was truly disappointed that I had to figuratively “throw away” all my hard work when I knew it could benefit others.

Andrew Misseldine





I was so proud of my program. So proud that I wanted to share it with the world, but I couldn’t. The OER movement that exists today was absent at that time. Open Licensing through Creative Commons or other organization is virtually unknown to my peers and me. I felt that I had created a masterpiece but had no way to share it. I was truly disappointed that I had to figuratively “throw away” all my hard work when I knew it could benefit others.

Andrew Misseldine




Open Pedagogy #3: Renewable Assignments

Andrew Misseldine




Open Pedagogy #3: Renewable Assignments Disposable Assignments A disposable assignment is one where students have little motivation to prepare and faculty have little reason to retain, that is, those assignments which after the assessment is made and the grade assigned serve no other purpose.

Andrew Misseldine




Open Pedagogy #3: Renewable Assignments Disposable Assignments A disposable assignment is one where students have little motivation to prepare and faculty have little reason to retain, that is, those assignments which after the assessment is made and the grade assigned serve no other purpose. David Wiley “These are assignments that students complain about doing and faculty complain about grading. They’re assignments that add no value to the world after a student spends three hours creating it, a teacher spends 30 minutes grading it, and then the student throws it away. Not only do these assignments add no value to the world, they actually suck value out of the world.” Andrew Misseldine





Renewable Assignments A renewable assignment is an assignment which is created and shared openly by students, thus adding value to the world (value outside of their classroom)

Andrew Misseldine





Renewable Assignments A renewable assignment is an assignment which is created and shared openly by students, thus adding value to the world (value outside of their classroom)

Andrew Misseldine





Renewable Assignments A renewable assignment is an assignment which is created and shared openly by students, thus adding value to the world (value outside of their classroom) Besides making our students creators of knowledge and not just borrowers of it, renewable assignments have been shown to improve the quality of student work because students work harder and better since they value the artifact they plan on creating.

Andrew Misseldine



Project Proposal Progress Interview Showcase/Reflection

Create an Artifact In the past I have been guilty of using disposable assignments for my classes.

Andrew Misseldine




Create an Artifact In the past I have been guilty of using disposable assignments for my classes. While re-inventing my Math 4220 course, I created a renewable assignment which asks students to create an artifact:

Andrew Misseldine




Create an Artifact In the past I have been guilty of using disposable assignments for my classes. While re-inventing my Math 4220 course, I created a renewable assignment which asks students to create an artifact:

Andrew Misseldine




Create an Artifact In the past I have been guilty of using disposable assignments for my classes. While re-inventing my Math 4220 course, I created a renewable assignment which asks students to create an artifact: such as a paper, webpage, video, computer program, lecture notes, etc.

Andrew Misseldine




Create an Artifact In the past I have been guilty of using disposable assignments for my classes. While re-inventing my Math 4220 course, I created a renewable assignment which asks students to create an artifact: such as a paper, webpage, video, computer program, lecture notes, etc. which will be used by future students or others in their studies of abstract algebra and should supplement the already existing materials available to students (that is, it should fill a need not already met). In other words, this artifact should add value to our world beyond our classroom.

Andrew Misseldine




Create an Artifact In the past I have been guilty of using disposable assignments for my classes. While re-inventing my Math 4220 course, I created a renewable assignment which asks students to create an artifact: such as a paper, webpage, video, computer program, lecture notes, etc. which will be used by future students or others in their studies of abstract algebra and should supplement the already existing materials available to students (that is, it should fill a need not already met). In other words, this artifact should add value to our world beyond our classroom.

Andrew Misseldine




Create an Artifact

There are four important parts to this project:

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Create an Artifact

There are four important parts to this project: Project Proposal (15 points)

Andrew Misseldine




Create an Artifact

There are four important parts to this project: Project Proposal (15 points) Progress Interview (25 points)

Andrew Misseldine




Create an Artifact

There are four important parts to this project: Project Proposal (15 points) Progress Interview (25 points) Showcase (100 points)

Andrew Misseldine




Create an Artifact

There are four important parts to this project: Project Proposal (15 points) Progress Interview (25 points) Showcase (100 points) Reflection (60 points)

Andrew Misseldine




Create an Artifact

There are four important parts to this project: Project Proposal (15 points) Progress Interview (25 points) Showcase (100 points) Reflection (60 points) This project was worth 20% of student’s final grade (additionally three exams were worth 20% each and homework was worth 20% collectively).

Andrew Misseldine




Project Proposal Prompt: Students will choose a topic of interest related to abstract algebra, will identify a need or a way for their project to contribute to the outside world, create a plan to solve their problem and create their artifact, and, if desired, form groups and decide how to distribute the labor.

Andrew Misseldine




Project Proposal Prompt: Students will choose a topic of interest related to abstract algebra, will identify a need or a way for their project to contribute to the outside world, create a plan to solve their problem and create their artifact, and, if desired, form groups and decide how to distribute the labor. Students will fill out a proposal form. This is due Week 7 of 15 week semester (about half-way).

Andrew Misseldine




Project Proposal Prompt: Students will choose a topic of interest related to abstract algebra, will identify a need or a way for their project to contribute to the outside world, create a plan to solve their problem and create their artifact, and, if desired, form groups and decide how to distribute the labor. Students will fill out a proposal form. This is due Week 7 of 15 week semester (about half-way). The assignment is pass/fail. If the proposal is incomplete/inadequate, it is returned to the student(s) with a resubmission date and a request for appropriate correction.

Andrew Misseldine



Andrew Misseldine





Progress Interview Prompt: This is a formal meeting between all members of the group and the instructor and will take place outside of class time in the instructor’s office. The group should come to receive feedback, guidance, correction, and assistance. Likewise, the group should be prepared to ask questions, request advisement, and answer questions from the instructor.

Andrew Misseldine




Progress Interview Prompt: This is a formal meeting between all members of the group and the instructor and will take place outside of class time in the instructor’s office. The group should come to receive feedback, guidance, correction, and assistance. Likewise, the group should be prepared to ask questions, request advisement, and answer questions from the instructor. It is scheduled for a time outside of regular class to take place between Week 10 and Week 12 (about 20-30 minutes). The professor and all group members are in attendance.

Andrew Misseldine




Progress Interview Prompt: This is a formal meeting between all members of the group and the instructor and will take place outside of class time in the instructor’s office. The group should come to receive feedback, guidance, correction, and assistance. Likewise, the group should be prepared to ask questions, request advisement, and answer questions from the instructor. It is scheduled for a time outside of regular class to take place between Week 10 and Week 12 (about 20-30 minutes). The professor and all group members are in attendance. The assignment is pass/fail. If the progress is unsatisfactory, students are offered correction and a follow-up interview is scheduled. Andrew Misseldine




Progress Interview 1 2 3

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What progress have you made on the project? What have you learned about the topic? What achievements do you believe you have already accomplished? What challenges have you faced? How has the project developed in comparison to the proposal? Are there any necessary course corrections? Does the scope of the project need to be broadened or restricted based upon your current understanding? How effectively has the group collaborated, if applicable? Any other follow-up questions based upon student answers and comments. What further assistance can I offer you? Andrew Misseldine




Showcase Prompt: This showcase is an opportunity for you to exhibit the artifact you have created. Additionally, you should summarize what you have learned about your topic, summarize the development of the artifact, summarize the overall progress you have made throughout this project, explain how your artifact will improve the mathematical community, and provide an appropriate demonstration of the artifact.

Andrew Misseldine




Showcase Prompt: This showcase is an opportunity for you to exhibit the artifact you have created. Additionally, you should summarize what you have learned about your topic, summarize the development of the artifact, summarize the overall progress you have made throughout this project, explain how your artifact will improve the mathematical community, and provide an appropriate demonstration of the artifact. It is scheduled during class during Week 14 (5-10 minutes).

Andrew Misseldine




Showcase Prompt: This showcase is an opportunity for you to exhibit the artifact you have created. Additionally, you should summarize what you have learned about your topic, summarize the development of the artifact, summarize the overall progress you have made throughout this project, explain how your artifact will improve the mathematical community, and provide an appropriate demonstration of the artifact. It is scheduled during class during Week 14 (5-10 minutes). The showcase is graded by the following rubric: attendance, time, development story, mathematics learned, share, demonstration.

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Reflection Prompt: Each student individually will submit a written, personal reflection about the creation of the artifact and their learning and growth throughout its creation. There will be three themes that student should be expected to express in their reflections: the development story, the mathematics learned, and the method of sharing.

Andrew Misseldine





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Reflection Prompt: Each student individually will submit a written, personal reflection about the creation of the artifact and their learning and growth throughout its creation. There will be three themes that student should be expected to express in their reflections: the development story, the mathematics learned, and the method of sharing. It is due the last day of class (about a week after the showcase).

Andrew Misseldine




Reflection Prompt: Each student individually will submit a written, personal reflection about the creation of the artifact and their learning and growth throughout its creation. There will be three themes that student should be expected to express in their reflections: the development story, the mathematics learned, and the method of sharing. It is due the last day of class (about a week after the showcase). Additional to the three criteria mentioned above, students include their complete bibliography at the end of this reflection paper as it might inappropriate to include in the artifact itself.

Andrew Misseldine



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Student Artifacts: Part 1 Student Artifacts: Part 2 My Reflection

Math 4220 - Fall 2017

My Math 4220 - Abstract Algebra I - Fall 2017 course consisted of students that separated into 10 groups for this project.

Andrew Misseldine




Math 4220 - Fall 2017

My Math 4220 - Abstract Algebra I - Fall 2017 course consisted of students that separated into 10 groups for this project. Their creativity blew me away. I am very proud of the wonderful artifacts they made.

Andrew Misseldine




Math 4220 - Fall 2017

My Math 4220 - Abstract Algebra I - Fall 2017 course consisted of students that separated into 10 groups for this project. Their creativity blew me away. I am very proud of the wonderful artifacts they made. They created computer programs, instructional/supplementary course materials, maps, games, and original research!

Andrew Misseldine




Math 4220 - Fall 2017

My Math 4220 - Abstract Algebra I - Fall 2017 course consisted of students that separated into 10 groups for this project. Their creativity blew me away. I am very proud of the wonderful artifacts they made. They created computer programs, instructional/supplementary course materials, maps, games, and original research! Pseudonyms for used for these students’ names.

Andrew Misseldine




Computer Programs

Three groups created computer programs based upon algorithms we learned about abstract algebra.

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Computer Programs

Three groups created computer programs based upon algorithms we learned about abstract algebra. Their experience writing their programs were similar to mine.

Andrew Misseldine




Computer Programs–Ruth’s Story Ruth was one of these students working on a computer program for abstract algebra.

Andrew Misseldine




Computer Programs–Ruth’s Story Ruth was one of these students working on a computer program for abstract algebra. Ruth “The idea for this project was conceived early in the semester while sitting in class. On this particular day we had been discussing the finer points of [permutations]. I recalled trying to utilize Wolfram Alphas [cycle] product capabilities [before], and failing because the method of calculation . . . was unclear. This memory caused me to think that maybe I could design a [permutation] calculator that would be easy [to use]. . . ” Ruth discovered a need that would have benefited her and certainly would benefit other students. Andrew Misseldine




Computer Programs–Ruth’s Story Ruth was one of these students working on a computer program for abstract algebra. Ruth “The reason I believed I could pull this off stemmed from the fact that earlier that week I become comfortable using . . . arrays in [compute programming]. . . . [S]ince a permutation cycle could be thought of as an array of numbers, I figured writing a program for the product of two or more cyclic permutations would be simple. . . . I should have known this idea was too good to be true.” Ruth found an interdisciplinary connection between this course and her other coursework and interests.

Andrew Misseldine




Computer Programs–Ruth’s Story Ruth was one of these students working on a computer program for abstract algebra. Ruth struggled to get here programmed calculator to work correctly. After about 2 months, she had great success but lots of short comings. Ruth “It seemed like I was constantly running into brick walls. I would struggle for hours or sometimes days trying to think my way around a problem. . . . Overall, I feel this project has been a beneficial experience for me. If nothing else, it drastically [stretched] my problem-solving abilities!” Her persistence paid off! Andrew Misseldine




Computer Programs–Ruth’s Story Ruth was one of these students working on a computer program for abstract algebra. Ruth “I feel [I] developed a solid understanding of permutations and cyclic notation because I had to explain them, on more than one occasion, to individuals that were not mathematically inclined. I have long believed that you learn the most about a subject when you have the opportunity to teach it.”

Andrew Misseldine




Computer Programs–Ruth’s Story Ruth was one of these students working on a computer program for abstract algebra. Ruth “The first instance of this was when I presented the idea for this project to my programming professor. As simply and clearly as possible, I had to explain how we viewed permutations in this class, how those permutations could be represented as cycle of elements, and then the daunting task of explaining how the algorithm worked for obtaining a product of permutation cycles.”

Andrew Misseldine




Computer Programs–Ruth’s Story Ruth was one of these students working on a computer program for abstract algebra. Ruth “I [explained] these concepts to the TA for my programming class as well as several of my class mates. I realized that the more people I explained it to, the better I got at explaining. Thus, I feel that I understand the concept of cyclic products on a much deeper level.” Because Ruth’s artifact ultimately had to be shared, she shared it early and often with others, leading to deeper learning she would not have experienced with traditional projects.

Andrew Misseldine




Computer Programs–Henry’s Story Henry was another one of these students (double major: math and computer science) working on a computer program for abstract algebra.

Andrew Misseldine




Computer Programs–Henry’s Story Henry was another one of these students (double major: math and computer science) working on a computer program for abstract algebra. Henry “After it all, I have certainly cemented a better understanding of the [abstract algebra] covered. The cool thing about programming is that in order to implement something in code you have to either know it really well or use a library that does it for you. Since only the mundane mathematical operations rely on the math library I used, I now have a much firmer grasp on [algebra]. . . . It is very cool to take these tools I have learned and see how they are actually applied. Algebra is an excellent tool for manipulating data.” Andrew Misseldine




Instructional Materials Two groups created supplementary materials to the textbook and lecture notes.

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Instructional Materials Two groups created supplementary materials to the textbook and lecture notes. One group created instructions how to created cubes and pyramids out of origami and then use these shapes to explore the symmetry groups of these solids. This project arose from an actual homework being discussed during office hours.

Andrew Misseldine




Instructional Materials–Mary’s Story

Mary was a student working on this origami project.

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Instructional Materials–Mary’s Story

Mary was a student working on this origami project. Mary “Being able to see these objects and hold them proved to be beneficial in my personal learning process. Learning how to use these objects to learn about cycles was amazing.”

Andrew Misseldine




Instructional Materials The other group created a peer-reviewed, solution manual supplement to the textbook.

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Instructional Materials The other group created a peer-reviewed, solution manual supplement to the textbook. They decided upon the exercises and concepts they individually struggled with the most throughout the semester (imagining other students would equally struggle) and they created detailed solutions and other commentary to explain their answers, thoughts, and methods.

Andrew Misseldine




Instructional Materials The other group created a peer-reviewed, solution manual supplement to the textbook. They decided upon the exercises and concepts they individually struggled with the most throughout the semester (imagining other students would equally struggle) and they created detailed solutions and other commentary to explain their answers, thoughts, and methods. Then the group members swapped their work and peer-reviewed each other. All the materials were then seamed together as a single document.

Andrew Misseldine




Instructional Materials–Sophie’s Story Sophie was a student (math ed major) working on the solution manual project.

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Instructional Materials–Sophie’s Story Sophie was a student (math ed major) working on the solution manual project. Sophie “This was a great and fun project to have the opportunity to do. I now have a better appreciation for the abstract algebra content. I believe that creating this artifact has taught me more than just abstract algebra. It has taught me how to find new ways of solving problems (or proofs) so that other students can understand what they are doing. Creating this artifact has in some ways taught me how to be a better teacher. I appreciate having the opportunity to learn all of these things.”

Andrew Misseldine




Map: History of Algebra One group created an interactive map showing the development and history of algebra up to the birth of abstract algebra.

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Instructional Materials–Carla’s Story Carla was a student (math ed major with geography minor) working on the map project. Carla “When this project was first introduced to us I knew that I wanted to create something outside of the box and something interesting to me. After thinking about it for quite a while I finally came up with a plan that I was, and still am, really excited about. I was . . . studying maps when I remembered [a professor] teaching us about how the geography of Europe, the Middle East, and China affected the way that math developed. . . ”

Andrew Misseldine




Instructional Materials–Carla’s Story Carla was a student (math ed major with geography minor) working on the map project. Carla “This got me thinking about a way that I could incorporate Abstract Algebra and Geography, since Geography is another of my passions. I came up with the idea of creating an online web application that displays the history of algebra using . . . ArcGIS . . . This idea was really exciting to me since the project incorporated many of my favorite things, studying peoples lives and history, geography and of course mathematics.”

Andrew Misseldine




Dihedra One student, named Emmy, created and playtested a card game based upon abstract algebra, called Dihedra.

Andrew Misseldine




Dihedra One student, named Emmy, created and playtested a card game based upon abstract algebra, called Dihedra.

Andrew Misseldine




Dihedra–Emmy’s Story Emmy was the student working on the Dihedra project. Emmy “My idea began as a hope to create a fun and simple way to become familiar with the axioms of group theory. I wanted to create something that would bridge the gap between numerical and familiar groups and those which were unfamiliar. Ultimately, I decided to create a card game out of the dihedral-four group. I chose that specific group because of how visually appealing and hands-on it was. This was a group that dealt with an object that I could actually create, and I felt that this would cater the game more to the general population. I also find that the visual and tactile approach helps me internalize otherwise difficult subjects.”

Andrew Misseldine




Dihedra–Emmy’s Story Emmy was the student working on the Dihedra project. Emmy “With the help of several people who agreed to play it with me, I learned what things would need to be stated in the rules, and how play would happen. I [realized] as I began to play it, how important it was to know the axioms of a group, and how they apply to the dihedral group specifically. Inverses are especially essential, and having a good solid understanding of those makes you very good at playing Dihedra. This was huge positive as this had been part of my original goal.” Emmy learned so much about groups and dihedral while playtesting the game, especially through the mistakes she had made. Andrew Misseldine




Dihedra–Emmy’s Story Emmy was the student working on the Dihedra project. Emmy “One of my favorite things about this game is that it’s entertaining and simple enough that those who play it could be learning about group theory without knowing they are. Most of the people I played it with were not people that do math for fun, but Dihedra was easy and visual enough to make it not seem like mathematics. It’s a unfortunate but very true that sometimes math has to be disguised to be perceived as fun.” Emmy is still developing and playtesting Dihedra as it as now become her EDGE (Education Designed to Give Experience) Project, a senior capstone project required for graduation based in SUU’s mission of experiential learning. Andrew Misseldine




Scholarship Three groups worked on creating original research/scholarship related to abstract algebra.

Andrew Misseldine




Scholarship Three groups worked on creating original research/scholarship related to abstract algebra. The first of these groups wanted to find a way to explain difficult abstract algebraic concepts to laypeople.

Andrew Misseldine




Scholarship Three groups worked on creating original research/scholarship related to abstract algebra. The first of these groups wanted to find a way to explain difficult abstract algebraic concepts to laypeople. The group created a script using conversational English meant to teach the axioms of group theory.

Andrew Misseldine




Scholarship Three groups worked on creating original research/scholarship related to abstract algebra. The first of these groups wanted to find a way to explain difficult abstract algebraic concepts to laypeople. The group created a script using conversational English meant to teach the axioms of group theory. Using this script, they taught three non-mathematicians about group theory and interviewed about the conversation.

Andrew Misseldine




Scholarship Three groups worked on creating original research/scholarship related to abstract algebra. The first of these groups wanted to find a way to explain difficult abstract algebraic concepts to laypeople. The group created a script using conversational English meant to teach the axioms of group theory. Using this script, they taught three non-mathematicians about group theory and interviewed about the conversation. The group then reported their findings. It is HARD to explain abstract mathematics! Andrew Misseldine




Scholarship–Arthur’s Story Arthur was one of the students working on this project. Arthur “When I heard that I would be required to ‘contribute’ to the mathematical community, my first response was denial. Then anger, depression (an overstatement, but one with comedic value), and finally acceptance as I dug into what I could do. I don’t think I’m a great mathematician I am an undergraduate and so I was stumped as to how I could figure out what I could do.” Confidence is built when someone accomplishes something they believed they could not do. Arthur’s confidence increased through this project.

Andrew Misseldine




Scholarship–Arthur’s Story Arthur was one of the students working on this project. Arthur “The problem that academia seems to have in general is how to best communicate ideas of a highly specific, technical, or theoretical sort to ‘lay people.’ ” Arthur found his need.

Andrew Misseldine




Scholarship–Arthur’s Story Arthur was one of the students working on this project. Arthur “I wanted the teaching to be more of a conversation. . . The first time went terribly, which was also a part of the goal, the hope was to learn what kinds of things go wrong when trying to quickly communicate mathematical ideas, as well as find key points to focus on to improve understanding.” Arthur recognizes the failure is part of research and part of learning.

Andrew Misseldine




Scholarship–Arthur’s Story Arthur was one of the students working on this project. Arthur “Over time I got much better, but I still never achieved my goal: to teach the group axioms to someone in under 10-15 minutes . . . I’d also like to find a more rigorous way to determine comprehension to make sure that the people I’m talking to are actually absorbing the information. I did however much more intimately internalize what a group is, the structure of it, how it operates, and different ‘concrete examples.’ ” Although Arthur did not achieve the goal his group set in the proposal, he learned much more from chasing a grand goal and falling short than from chasing a mediocre goal and obtaining it. Andrew Misseldine




Scholarship Another student, George (a double major: math and performing arts), took the unusual task of writing a mathematical poem, entitled “Idempotency” in order to explain difficult mathematical concepts in a beautiful way.

Andrew Misseldine




Scholarship Another student, George (a double major: math and performing arts), took the unusual task of writing a mathematical poem, entitled “Idempotency” in order to explain difficult mathematical concepts in a beautiful way. After writing the poem, George shared it publicly at an open-mic night at St. George Art Museum on 26 October 2017.

Andrew Misseldine




Scholarship Another student, George (a double major: math and performing arts), took the unusual task of writing a mathematical poem, entitled “Idempotency” in order to explain difficult mathematical concepts in a beautiful way. After writing the poem, George shared it publicly at an open-mic night at St. George Art Museum on 26 October 2017. He said that the crowd was small, consisting mostly of high school English nerds and hipsters, and, although the audience did not expect to learn anything about mathematics that night, everyone was entertaining and had a positive experience.

Andrew Misseldine




Scholarship Another student, George (a double major: math and performing arts), took the unusual task of writing a mathematical poem, entitled “Idempotency” in order to explain difficult mathematical concepts in a beautiful way. After writing the poem, George shared it publicly at an open-mic night at St. George Art Museum on 26 October 2017. He said that the crowd was small, consisting mostly of high school English nerds and hipsters, and, although the audience did not expect to learn anything about mathematics that night, everyone was entertaining and had a positive experience. Currently this poem has been submitted and is being reviewed by a journal for publication. Andrew Misseldine




Scholarship–George’s Story George was the student who wrote the poem “Idempotency.” George “[My project] chose me . . . to write about [it]. On the first day of class Dr. Misseldine mentioned the word which was one I didn’t know before. It stuck in my head and I knew I had to do something with it. So that is when I decided to [create my artifact]. This [artifact] would also have the larger part of showing a little bit of the beauty I find in mathematics.” George really felt like creating his artifact was his calling.

Andrew Misseldine




Scholarship–George’s Story George was the student who wrote the poem “Idempotency.” George “Idempotency is the idea that a repeated action only takes place the first time. I love the image of learning a lesson the first time. I also really love the concept of idemptency being the opposite of insanity, as insanity is doing the same thing over and over again and expecting different results. Idempotency is doing the same thing and expecting the same thing to happen. ” George really put his soul into his composition. What greater assignment can an instructor give or how more transformative can an assignment be than that? Andrew Misseldine




Scholarship The last group began working on undergraduate research in abstract algebra with me.

Andrew Misseldine




Scholarship The last group began working on undergraduate research in abstract algebra with me. Their artifact for this course was an abstract and an earlier draft of the pre-print.

Andrew Misseldine




Scholarship The last group began working on undergraduate research in abstract algebra with me. Their artifact for this course was an abstract and an earlier draft of the pre-print. This semester, these students are continuing the research project.

Andrew Misseldine




Scholarship The last group began working on undergraduate research in abstract algebra with me. Their artifact for this course was an abstract and an earlier draft of the pre-print. This semester, these students are continuing the research project. They have already presented the research at a regional conference and are scheduled to present at three more conferences.

Andrew Misseldine




Scholarship The last group began working on undergraduate research in abstract algebra with me. Their artifact for this course was an abstract and an earlier draft of the pre-print. This semester, these students are continuing the research project. They have already presented the research at a regional conference and are scheduled to present at three more conferences. We should have a research paper ready for publication at the end of the semester. Andrew Misseldine




Scholarship–Issac’s Story

Issac was one of my research students. Issac Looking back on all the experiences that I have had in working on this project, I can say that I have learned quite a bit about abstract algebra. I now have a better understanding of where else groups show up in abstract algebra. I also have learned what rings, fields, group rings, and Schur rings are. In addition, I also learned how to use [LaTeX] better than I did before. All of this I would not have learned about this semester had I not being doing this project.

Andrew Misseldine




My Reflection–What Went Right?

Overall, student feedback given through their reflections and through student evaluations was very positive. Creating their artifact became a transformative, high-impact experience for students.

Andrew Misseldine




My Reflection–What Went Right?

Overall, student feedback given through their reflections and through student evaluations was very positive. Creating their artifact became a transformative, high-impact experience for students.

As the professor, I was very pleased with student performance and learning outcomes.

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing.

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Even with only ten groups, the progress interviews were a big time commitment out of class (about 6 hours), although it did not take more time than I had planned for it.

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Even with only ten groups, the progress interviews were a big time commitment out of class (about 6 hours), although it did not take more time than I had planned for it.

Originally, two interviews per group was planned but abandoned after the time commitment was considered.

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes are a problem for the Progress Interview. Some possible solutions include:

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes are a problem for the Progress Interview. Some possible solutions include: the interview could be abandoned entirely (I do not recommend this as the guidance students received during the interview made a remarkable and noticeable improvement on their artifacts),

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes are a problem for the Progress Interview. Some possible solutions include: the interview could be abandoned entirely, larger groups could be required to keep the number of groups few (My students had groups from 1-3 students. Larger groups are possible, but only up to a limit),

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes are a problem for the Progress Interview. Some possible solutions include: the interview could be abandoned entirely, larger groups could be required to keep the number of groups few, some digital platform could be used to automatic or simplify the process (This would less the beneficial impact of the interview on the student as the professor could not as easily offer expect advice),

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes are a problem for the Progress Interview. Some possible solutions include: the interview could be abandoned entirely, larger groups could be required to keep the number of groups few, some digital platform could be used to automatic or simplify the process, students could possibly interview themselves (As students are not content experts, their advice would have limited benefit as compared to the professor), Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes are a problem for the Progress Interview. Some possible solutions include: the interview could be abandoned entirely, larger groups could be required to keep the number of groups few, some digital platform could be used to automatic or simplify the process, students could possibly interview themselves, teaching assistants could be used to spread the workload (This would be my preferred method for handling a larger class while preserving the benefits of the interview, in tandem with larger groups if Misseldine necessary).Open Pedagogy in Math Andrew



My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Even with only ten groups, the showcases were a big time commitment in class (two 50 minute class periods), which eats up valuable lecture time.

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Even with only ten groups, the showcases were a big time commitment in class (two 50 minute class periods), which eats up valuable lecture time.

How much time to be dedicated toward Showcase depends on the learning outcomes of the course, but demonstrating the artifact in some public setting is an important part of the students sharing their work.

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes again compounds this problem of time. Some possible solutions include: the showcase could be abandoned entirely (Sharing is important part of open pedagogy),

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes again compounds this problem of time. Some possible solutions include: the showcase could be abandoned entirely, larger groups could be required to keep the number of groups few (This can only go so far),

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes again compounds this problem of time. Some possible solutions include: the showcase could be abandoned entirely, larger groups could be required to keep the number of groups few, some digital platform could be used to automatic or simplify the process (This distances the students from their audience and requires more technical resources),

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes again compounds this problem of time. Some possible solutions include: the showcase could be abandoned entirely, larger groups could be required to keep the number of groups few, some digital platform could be used to automatic or simplify the process, all showcases (or some of the showcases) could be preformed out of class at some other venue (This has the advantage of making the showcase, perhaps, more public, but demands more time on the professor and students out of class). Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Despite the best efforts of students, not all artifacts are ready to be shared upon submission to the professor at the end of term. Student work might still be containing errors. The responsibility of finalizing the artifacts then might fall upon the professor (I am still back-logged from last semester on many artifacts).

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes again compounds this problem of time. Some possible solutions include: only share high-quality artifacts (This makes the project possibility become disposable again, defeating the whole point),

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes again compounds this problem of time. Some possible solutions include: only share high-quality artifacts, use students to peer-review each other’s work (This could be an excellent addition to the project, but require students to work on an earlier timeline),

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes again compounds this problem of time. Some possible solutions include: only share high-quality artifacts, use students to peer-review each other’s work, make students completely responsible for finalizing and sharing their own work (Less than perfect artifacts will be shared, but maybe that is okay or not),

Andrew Misseldine




My Reflection–What Could be Improved? Time is the biggest concern with this project: Progress Interview, Showcases, and Finalizing. Larger classes again compounds this problem of time. Some possible solutions include: only share high-quality artifacts, use students to peer-review each other’s work, make students completely responsible for finalizing and sharing their own work, Feel content in being back-logged (That’s how I always feel!).

Andrew Misseldine




My Reflection–Your Call to Action! My last concern is about venues for sharing student artifacts.

Andrew Misseldine




My Reflection–Your Call to Action! My last concern is about venues for sharing student artifacts. Ideally, students should share their work is a public, open venue where others might expect to be able to find it. For example, if a group creates a learning video as their artifact, it makes sense to publish it on YouTube.

Andrew Misseldine




My Reflection–Your Call to Action! My last concern is about venues for sharing student artifacts. Ideally, students should share their work is a public, open venue where others might expect to be able to find it. For example, if a group creates a learning video as their artifact, it makes sense to publish it on YouTube. Not all artifacts have such natural venues.

Andrew Misseldine




My Reflection–Your Call to Action! My last concern is about venues for sharing student artifacts. Ideally, students should share their work is a public, open venue where others might expect to be able to find it. For example, if a group creates a learning video as their artifact, it makes sense to publish it on YouTube. Not all artifacts have such natural venues. As the open pedagogy of renewable assignments is a high-impact learning practice, it then becomes the responsibility of the schools or the State of Utah to create such a venue or repository for students to publish their artifacts. Andrew Misseldine




My Reflection–Your Call to Action! My last concern is about venues for sharing student artifacts. Ideally, students should share their work is a public, open venue where others might expect to be able to find it. For example, if a group creates a learning video as their artifact, it makes sense to publish it on YouTube. Not all artifacts have such natural venues. As the open pedagogy of renewable assignments is a high-impact learning practice, it then becomes the responsibility of the schools or the State of Utah to create such a venue or repository for students to publish their artifacts. Andrew Misseldine




Send me a message! If you would like more information, please email me at [email protected]

Andrew Misseldine




Send me a message! If you would like more information, please email me at [email protected] or visit my website at http://people.suu.edu/andrew-misseldine/student-authorship

Andrew Misseldine




Send me a message! If you would like more information, please email me at [email protected] or visit my website at http://people.suu.edu/andrew-misseldine/student-authorship

Thank you for listening. Are there any questions?

Andrew Misseldine


Using Open Pedagogy in an Upper Division

Using Open Pedagogy in an Upper Division

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