{"id":3632,"date":"2021-07-31T21:11:34","date_gmt":"2021-08-01T01:11:34","guid":{"rendered":"http:\/\/blogs.ams.org\/matheducation\/?p=3632"},"modified":"2021-08-05T12:17:28","modified_gmt":"2021-08-05T16:17:28","slug":"outcomes-based-assessment-structural-change-in-calculus","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/matheducation\/2021\/07\/31\/outcomes-based-assessment-structural-change-in-calculus\/","title":{"rendered":"Outcomes-Based Assessment &#8212; Structural Change in Calculus"},"content":{"rendered":"<h2><span style=\"font-weight: 400\">by Rebecca Torrey<\/span><\/h2>\n<p><span style=\"font-weight: 400\">Associate Professor of Math<\/span><\/p>\n<p><span style=\"font-weight: 400\">Brandeis University<\/span><\/p>\n<h3><span style=\"font-weight: 400\">Traditional Grading Sends the Wrong Message<\/span><\/h3>\n<p><span style=\"font-weight: 400\">For many years I taught Calculus with a traditional structure, in which the students\u2019 grades were mostly determined by a few high-stakes exams (a final and a couple of midterms).\u00a0 In my classes, I would tell my students:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">How important it was to practice regularly;\u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">To carefully review their exams and the solutions;<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">That it\u2019s ok to get things wrong and learn from their mistakes;<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">That the idea that we can improve through practice applies in math just as it would in anything else they want to learn.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">But the structure of my class was giving them a very different message.\u00a0 The structure told them:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">You only <\/span><i><span style=\"font-weight: 400\">really <\/span><\/i><span style=\"font-weight: 400\">need to study three times during the semester: right before the midterms and the final;\u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Don\u2019t bother reviewing your work since you will rarely, if ever, get tested on those same problems again;<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">You can only do well in the class if you get all the problems (including the very hardest) right on the first try.<\/span><\/li>\n<\/ul>\n<p><!--more--><\/p>\n<p><span style=\"font-weight: 400\">It gets worse.\u00a0 Based on the compelling work of Claude Steele, we started reading out a statement before our exams that said:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">\u201cThis test has not shown any gender or racial differences in performance or mathematical ability.\u201d\u00a0<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">This statement was carefully crafted to be technically true &#8212; the test had never been given before, so it couldn\u2019t have shown any biases.\u00a0 We adopted this with the best of intentions: research had shown that making a declaration like this could, like a self-fulfilling prophecy, help to reduce stereotype threat.\u00a0 I hope it worked, at least for some students.\u00a0 But in practice I suspect our tests actually sent a message more like:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Somehow you have to divine our expectations about how to properly write your solutions out, which (for whatever reason) you\u2019re much more likely to do successfully if your gender and racial identities match those traditionally overrepresented in math.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">There were other ways my pedagogical structure was undermining my own messages.\u00a0 I told my students:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">We care primarily about your understanding of the math and communication of it.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">But our structure was saying:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">If you can write down some vaguely-related words and symbols, you can probably rack up enough points to pass the class.\u00a0\u00a0<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">Here\u2019s another one.\u00a0 We told students:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">There\u2019s no cap on the number of students who can get an A in this class.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">This was technically true.\u00a0 We didn\u2019t stick to a strict curve.\u00a0 But, with many years of experience, we wrote exams for which we could predict the distribution of scores with remarkable accuracy and then set the grades around the median.\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">You get the idea.\u00a0 The structure of the course was undermining pretty much all of my pedagogical ideals.\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">What did we do about it?\u00a0 We instituted Outcomes-Based Assessment (also known as Mastery Grading, Standards-Based Grading, or Specifications-Based Grading).\u00a0 There are many different versions of this, but the basic idea is that you have a list of the ideas, skills, techniques, etc., that you want your students to learn over the course of the semester (\u201ccontent outcomes\u201d, or \u201coutcomes\u201d for short, in our terminology).\u00a0 You have some way for them to demonstrate mastery of those skills.\u00a0 The grading is credit\/no-credit (either they have demonstrated mastery or not).\u00a0 And the students can try multiple times to demonstrate mastery of each outcome.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-weight: 400\">Our Version of Outcomes-Based Assessment<\/span><\/h3>\n<p><span style=\"font-weight: 400\">Our initial version of this was copied pretty much wholesale from Jeff Ford of Gustavus Adolphus College.\u00a0 We\u2019ve tweaked it a bit around the edges since then, but it still has the same basic format.\u00a0 I\u2019d also like to give an official shout-out to Eric Hanson, currently at the Norwegian University of Science and Technology, who, as a graduate student at Brandeis, was instrumental in converting our first class (Precalculus).<\/span><\/p>\n<p><span style=\"font-weight: 400\">Here are the components.<\/span><\/p>\n<p><b>Content Outcomes:<\/b><\/p>\n<p><span style=\"font-weight: 400\">Our outcomes are fairly fine-grained.\u00a0 Here are a few sample outcomes for our Differential Calculus class:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Determine information about a function from the graph of its derivative (or vice versa).<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Find and classify the extrema of a function.<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Solve an optimization word problem using the methods of Calculus<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">It was important to us that our students also be able to apply their knowledge on problems they haven\u2019t seen before, so we include a few outcomes like:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Solve a challenging problem that combines different skills and\/or presents material from Chapters 2-3 + Pre-Reqs in a different way.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">We also decided that there were some things that were so fundamental that a student shouldn\u2019t be able to pass the class without mastering them, so we split these out into a category of \u201cFundamental Outcomes\u201d.\u00a0 Some of these are prerequisites, like factoring polynomials or evaluating trig functions, and some are key elements of the class, like finding the equation of a tangent line or calculating derivatives.\u00a0\u00a0<\/span><\/p>\n<p><b>Assessments:<\/b><\/p>\n<p><span style=\"font-weight: 400\">We test our students every Friday.\u00a0 On each test, we have a problem corresponding to every outcome we\u2019ve covered so far in the course.\u00a0 Students have to earn credit on two different Fridays to master a particular outcome.\u00a0 After this, they no longer have to do those problems.\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">Our bar for earning credit is B+\/A- level work.\u00a0 If it\u2019s on the border, we ask ourselves questions like, \u201cdo they really understand the idea and have they communicated that?\u201d and \u201cdo I think they need to spend some more time on this?\u201d.\u00a0 These are the questions that really determine the cutoff<\/span><\/p>\n<p><a href=\"https:\/\/i0.wp.com\/blogs.ams.org\/matheducation\/files\/2021\/05\/Picture1.png\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-3636\" src=\"https:\/\/i0.wp.com\/blogs.ams.org\/matheducation\/files\/2021\/05\/Picture1.png?resize=300%2C225\" alt=\"\" width=\"300\" height=\"225\" srcset=\"https:\/\/i0.wp.com\/blogs.ams.org\/matheducation\/files\/2021\/05\/Picture1.png?resize=300%2C225&amp;ssl=1 300w, https:\/\/i0.wp.com\/blogs.ams.org\/matheducation\/files\/2021\/05\/Picture1.png?w=468&amp;ssl=1 468w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p><i><span style=\"font-weight: 400\">Illustration by Simon Huynh<\/span><\/i><\/p>\n<p><span style=\"font-weight: 400\">Students\u2019 grades are then determined by how many of the outcomes they master.\u00a0 Here\u2019s the grade breakdown from our Differential Calculus class:\u00a0\u00a0<\/span><\/p>\n<p><a href=\"https:\/\/i0.wp.com\/blogs.ams.org\/matheducation\/files\/2021\/07\/missing-image-for-torrey.jpg\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-3687\" src=\"https:\/\/i0.wp.com\/blogs.ams.org\/matheducation\/files\/2021\/07\/missing-image-for-torrey.jpg?resize=300%2C200\" alt=\"\" width=\"300\" height=\"200\" srcset=\"https:\/\/i0.wp.com\/blogs.ams.org\/matheducation\/files\/2021\/07\/missing-image-for-torrey.jpg?resize=300%2C200&amp;ssl=1 300w, https:\/\/i0.wp.com\/blogs.ams.org\/matheducation\/files\/2021\/07\/missing-image-for-torrey.jpg?resize=1024%2C681&amp;ssl=1 1024w, https:\/\/i0.wp.com\/blogs.ams.org\/matheducation\/files\/2021\/07\/missing-image-for-torrey.jpg?resize=768%2C511&amp;ssl=1 768w, https:\/\/i0.wp.com\/blogs.ams.org\/matheducation\/files\/2021\/07\/missing-image-for-torrey.jpg?w=1064&amp;ssl=1 1064w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p><span style=\"font-weight: 400\">Students need to earn the minimum points for all categories across a given row to earn the letter grade in the left column.\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">In practice, the grades are pretty much entirely determined by the General Outcomes column.\u00a0 (The homework and participation scores are quite lenient, so that students who are doing their homework and coming to class can easily meet the A-level for those requirements.)\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">The key idea here is that the outcomes the students have mastered are ones they <\/span><i><span style=\"font-weight: 400\">really<\/span><\/i><span style=\"font-weight: 400\"> know.\u00a0 They have demonstrated that they can do these at a B+\/A- level.\u00a0 The grades are determined by how <\/span><i><span style=\"font-weight: 400\">many<\/span><\/i><span style=\"font-weight: 400\"> of the outcomes they have mastered.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-weight: 400\">Outcomes-Based Assessment Sends the Right Message<\/span><\/h3>\n<p><span style=\"font-weight: 400\">Let\u2019s go back to the beginning and reconsider all those pedagogical ideals.\u00a0 What does our Outcomes-Based Assessment (OBA) structure tell students about them?<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Regular practice is important.<\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><i><span style=\"font-weight: 400\">OBA: You have to be ready for our test every week.<\/span><\/i> <span style=\"font-weight: 400\"><br \/>\n<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Carefully review exams and the solutions.<\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><i><span style=\"font-weight: 400\">OBA: If you didn\u2019t get it right this week, it will be on the test again next week, so you\u2019d better review your work and our feedback.<\/span><\/i><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">It\u2019s ok to get things wrong and learn from mistakes.<\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><i><span style=\"font-weight: 400\">OBA: It doesn\u2019t count against you when you get it wrong, but it does count *for* you when you get it right, even if it takes a while to get there.<\/span><\/i><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">The idea that we can improve through practice applies in math just as it would in anything else they want to learn.<\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><i><span style=\"font-weight: 400\">OBA: You are rewarded just as much if you try a few times and then get it right as if you get it right on the first try.<\/span><\/i><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">\u201cThis test has not shown any gender or racial differences in performance or mathematical ability.\u201d <\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><i><span style=\"font-weight: 400\">I wish I could say with authority that OBA helps this.\u00a0 I don\u2019t know yet.\u00a0 It seems like it should, since the whole point is that students can get feedback, learn what the expectations are, and then implement them.\u00a0 We\u2019ll be setting up a multi-year study starting this year to learn more about the impacts (short and long term) of OBA on all of our Calculus students, but particularly on our students of underrepresented backgrounds.<\/span><\/i><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">We care primarily about your understanding of the math and communication of it.<\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><i><span style=\"font-weight: 400\">OBA: This is precisely where we draw the line between when a student gets credit on a particular outcome and when they don\u2019t.\u00a0 Students learn that the only way to succeed in our class is to review, revise, and to seek help when they don\u2019t understand something.\u00a0 With OBA, students are much more likely than ever before to come in asking us to help them *understand* something, because they know that\u2019s the only way they\u2019re going to perform well enough to earn credit.<\/span><\/i><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">There\u2019s no cap on the number of students who can get an A in this class.<\/span><span style=\"font-weight: 400\"><br \/>\n<\/span><i><span style=\"font-weight: 400\">OBA: This is just straight-up true.\u00a0 Any student who meets our threshold gets an A.\u00a0 End of story.<\/span><\/i><\/li>\n<\/ul>\n<h3><span style=\"font-weight: 400\">What\u2019s the Catch?<\/span><\/h3>\n<p><span style=\"font-weight: 400\">For all my enthusiasm for this new system, I must admit there are some challenges.\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">The two biggest obstacles are:<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">It takes a lot of work to set it up.\u00a0\u00a0<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">There\u2019s a lot of proctoring and grading time.<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400\">It took a fair amount of work to set up, especially for the first class we converted.\u00a0 (We started with Precalculus, which has a much smaller enrollment and fewer sections than our Calculus classes.)\u00a0 There are many decisions to make and details to iron out.\u00a0 You won\u2019t get it perfect on the first try, so just go for it and adjust as you learn.\u00a0 We also spent a lot of time writing and proofreading problems for tests.\u00a0 Over time, we\u2019re building a large problem bank, but the first semester really requires a lot of work on this.<\/span><\/p>\n<p><span style=\"font-weight: 400\">Since there is a large start-up cost, it makes the most sense to convert classes that you teach regularly so you can reuse your work.\u00a0 But once you get the hang of it, it really seems like a better way to teach so it\u2019s hard to go back to the traditional method.\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">We decided to test our students every week, and to have no restrictions on how many attempts they get at each outcome.\u00a0 This means that we\u2019re proctoring and grading every week.\u00a0 It also means that if we have even one straggler who is struggling to get credit, we\u2019re writing new problems for them every week.\u00a0 I know other people (including Jeff Ford) who do not test so often and\/or restrict the number of times a particular outcome shows up on the tests.\u00a0 I think some restriction is better, both for the sanity of the faculty and because a little more pressure on the students means they have to follow up sooner and can\u2019t just choose to put it off.\u00a0 We\u2019re currently considering the pros and cons of different options for next fall.<\/span><\/p>\n<p><span style=\"font-weight: 400\">Some other ongoing challenges include:<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Introducing the system to students<\/span><\/li>\n<li style=\"font-weight: 400\"><span style=\"font-weight: 400\">Conveying students\u2019 grades during the semester, particularly around drop decisions.<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400\">For most students, this structure is completely foreign.\u00a0 It\u2019s absolutely necessary to spend some extra time introducing it and selling it to students.\u00a0 We hammer home the idea of \u201chigh frequency\/low stakes\u201d testing.\u00a0 I made a few videos to introduce the pedagogy to our students:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/echo360.org\/media\/2c8487db-e233-440e-a405-d2c785321299\/public\"><span style=\"font-weight: 400\">What is Mastery Grading?<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/echo360.org\/media\/1747e7bc-a696-493b-93fe-540debbbda43\/public\"><span style=\"font-weight: 400\">How is my Letter Grade Determined?<\/span><\/a><\/li>\n<li style=\"font-weight: 400\"><a href=\"https:\/\/echo360.org\/media\/c21da614-6491-499a-8e6b-7aab6b3fa4fa\/public\"><span style=\"font-weight: 400\">Pace &amp; Flow of the Semester<\/span><\/a><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400\">Some students are really anxious about it and have a hard time understanding at first.\u00a0 Most pick up on it after the first week or two, when they have seen all the components work in class.\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">It helps a LOT to have used the structure before.\u00a0 Our students who have experienced it typically love it, and are happy to endorse and explain it to students who are new to the system.\u00a0 We introduced Outcomes Based Assessment in our Single Variable Calculus sequence for the first time this fall (yes, along with moving online for Covid AND switching to a team-based learning format AND switching to a new textbook &#8212; can you say, \u201cgluttons for punishment\u201d?).\u00a0 Several students who took Differential Calculus this fall reached out to me to ask whether we would be using this system for Integral Calculus in the spring.\u00a0 They made it clear that they were only going to take Integral Calculus if we used Outcomes Based Assessment.<\/span><\/p>\n<p><span style=\"font-weight: 400\">I still struggle with communicating to students what their grade is likely to be when we\u2019re midway through the semester.\u00a0 In many ways, our grading is more transparent than the traditional system.\u00a0 Students know exactly where they stand at all times.\u00a0 They know what they already have learned and what they still need to work on.\u00a0 They can see clearly what they still need to do to get a particular letter grade.\u00a0 I built out individual spreadsheets for them to follow along with their progress.\u00a0 But, on the other hand, no one in the class is even passing until quite late in the semester.\u00a0 (I think this is right &#8212; after all, they haven\u2019t even learned most of the material yet.)\u00a0 They have a hard time seeing if they\u2019re on track to succeed, especially if they\u2019re not getting everything right on the first try.\u00a0 And I have a hard time predicting what will happen.\u00a0 Will they get those outcomes they\u2019ve been stuck on?\u00a0 Most will, but I can\u2019t guarantee it.\u00a0\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">Overall, our grades are higher.\u00a0 It seems that a lot of students who would probably have gotten B\u2019s in the traditional system are able to get to A\u2019s in this system.\u00a0 The system rewards good study habits and guides students on what they need to do so they can do it.\u00a0 And most students feel really comfortable in the last couple of weeks of classes, when they can see things slowing down and they don\u2019t have much left to finish.\u00a0 But it\u2019s hard in the middle to say which way things will break for students who are getting behind.\u00a0 I haven\u2019t solved this problem yet.<\/span><\/p>\n<p><span style=\"font-weight: 400\">This year probably would have been exhausting even without all this extra work we took on by introducing Outcomes Based Assessment.\u00a0 We\u2019re definitely tired and ready to be done with proctoring and grading for the year.\u00a0 But even with all the challenges of online education, I think this structure has helped my students learn more and better than they did under our old, traditional structure.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-weight: 400\">Is it worth the hassle?<\/span><\/h3>\n<p><span style=\"font-weight: 400\">Yes.\u00a0<\/span><\/p>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-weight: 400\">Acknowledgements<\/span><\/h3>\n<p><span style=\"font-weight: 400\">If you got the idea in this article that I did all or most of this on my own, I apologize.\u00a0 It\u2019s not true.\u00a0 This has been a multi-year team effort.\u00a0 Eric Hanson (mentioned above) was the one who wanted to try this out in the first place, and introduced us to Jeff Ford, who generously shared everything with us to help us get started.<\/span><\/p>\n<p><span style=\"font-weight: 400\">My colleague, Keith Merrill, has been vital in making this work, along with many amazing graduate students (some former): Te Cao, Shujian Chen, Tarakaram Gollamudi, Abhishek Gupta, Simon Huynh, Shizhe Liang, Wei Lu, Ray Maresca, Ian Montague, Rose Morris-Wright, Rebecca Rohrlich, Alex Semendinger, Jill Stifano, and Jiajie Zheng.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">Our initial implementation in our Precalculus course was supported by a Teaching Innovation Grant from the Provost\u2019s Office and the Center for Teaching and Learning at Brandeis University.\u00a0\u00a0<\/span><\/p>\n<p>&nbsp;<\/p>\n<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" ><\/div>","protected":false},"excerpt":{"rendered":"<p>by Rebecca Torrey Associate Professor of Math Brandeis University Traditional Grading Sends the Wrong Message For many years I taught Calculus with a traditional structure, in which the students\u2019 grades were mostly determined by a few high-stakes exams (a final &hellip; <a href=\"https:\/\/blogs.ams.org\/matheducation\/2021\/07\/31\/outcomes-based-assessment-structural-change-in-calculus\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" data-url=https:\/\/blogs.ams.org\/matheducation\/2021\/07\/31\/outcomes-based-assessment-structural-change-in-calculus\/><\/div>\n","protected":false},"author":4849,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3632","post","type-post","status-publish","format-standard","hentry","category-testing"],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p6C2AC-WA","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/posts\/3632","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/users\/4849"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/comments?post=3632"}],"version-history":[{"count":7,"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/posts\/3632\/revisions"}],"predecessor-version":[{"id":3686,"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/posts\/3632\/revisions\/3686"}],"wp:attachment":[{"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/media?parent=3632"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/categories?post=3632"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ams.org\/matheducation\/wp-json\/wp\/v2\/tags?post=3632"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}