I am working to write learning objectives for multivariable calculus this Fall. This article helped distinguish between overarching goals (that students are able to fit the math in the course into a greater understanding of math and of the world) and the learning objectives, of what I hope students will be able to do mathematically after taking the course.<\/p>\n
Thinking about goals reminded me that, as in all classes, learning to learn within a disciplinary setting is a goal I think is important. In addition, specifically for multivariable, there is a real potential to start seeing the world through the lens of the course. Thinking about wind as a vector field, about falling leaves via flux, and about everyday shapes via the functions and parameterizations of the course is a possibility. The article also brought up history as a possible goal. I have not actively worked to situate the math we learn within the history of mathematical problem solving, but it is something I would like to\u00a0learn more about\u00a0in the longer term.<\/p>\n","protected":false},"excerpt":{"rendered":"
I am working to write learning objectives for multivariable calculus this Fall. This article helped distinguish between overarching goals (that students are able to fit the math in the course into a greater understanding of math and of the world) and the learning objectives, of what I hope students will be able to do mathematically […]<\/p>\n","protected":false},"author":8032,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_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":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[157887,1010],"tags":[],"class_list":["post-32","post","type-post","status-publish","format-standard","hentry","category-learning-and-teaching","category-math"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7E5LF-w","jetpack-related-posts":[{"id":36,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2017\/08\/25\/reading-mental-maps-and-learning-objectives-the-fast-slo-algorithm-for-creating-student-learning-objectives\/","url_meta":{"origin":32,"position":0},"title":"Reading “Mental Maps and Learning Objectives: The FAST-SLO Algorithm For Creating Student Learning Objectives”","author":"siams","date":"25 August 2017","format":false,"excerpt":"This article is focused on a method for writing student learning objectives for a course (SLOs).\u00a0 I find writing learning objectives challenging when working alone.\u00a0 They can be written at so many different levels of detail.\u00a0 Almost every example or question in a textbook has an implicit objective associated with\u2026","rel":"","context":"In "Learning and teaching"","block_context":{"text":"Learning and teaching","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/learning-and-teaching\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":65,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2017\/10\/04\/other-versions-of-multivariable\/","url_meta":{"origin":32,"position":1},"title":"Other versions of multivariable","author":"siams","date":"4 October 2017","format":false,"excerpt":"Resources for multivariable calculus: Some challenge problems (not multivariable): https:\/\/www.math.unl.edu\/~mrammaha1\/Challenging%20problems\/Challenge-Problems.pdf Cornell is using workshops activities for their engineering students this year (2017): http:\/\/www.math.cornell.edu\/~web1920\/workshop.html Materials from Math 53 at Berkeley (2016): https:\/\/math.berkeley.edu\/~auroux\/53s16\/ Lots of past multivariable exams for Math 215 at Michigan: http:\/\/www.math.lsa.umich.edu\/courses\/215\/17exampractice\/index.html","rel":"","context":"In "Math"","block_context":{"text":"Math","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/math\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":58,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2017\/08\/25\/vector-calculus-earlier-in-the-semester\/","url_meta":{"origin":32,"position":2},"title":"Vector calculus earlier in the semester?","author":"siams","date":"25 August 2017","format":false,"excerpt":"Flux is a particularly central scientific and mathematically idea that appears in the context of a multivariable calculus course. \u00a0Given a velocity vector field and a surface, the flux of the vector field through the surface tells us the rate at which fluid is flowing through the surface. \u00a0This leads\u2026","rel":"","context":"In "Math"","block_context":{"text":"Math","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/math\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":74,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2017\/10\/04\/webtools-for-math-teaching\/","url_meta":{"origin":32,"position":3},"title":"Webtools for math teaching","author":"siams","date":"4 October 2017","format":false,"excerpt":"This semester I'm using Gradescope for homework and exam grading.\u00a0 It is working relatively well, although not perfectly.\u00a0 This enables us to reuse feedback, makes it easy for me to review regrade requests, and gives us access to all student work in the course. For our discussion board, we're using\u2026","rel":"","context":"In "Learning and teaching"","block_context":{"text":"Learning and teaching","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/learning-and-teaching\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":108,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/06\/10\/dynamical-systems-math-1b-differential-equations-background\/","url_meta":{"origin":32,"position":4},"title":"Dynamical systems: Math 1b differential equations background.","author":"siams","date":"10 June 2019","format":false,"excerpt":"I have been using the Strogatz textbook for teaching dynamical systems. \u00a0The course has multivariable calculus and linear algebra prerequisites. \u00a0Students might take the prerequisite courses different places. \u00a0For students who have taken Math 1b, AM\/Math 21a, Math 21b, there was 6-7 week of differential equations background (11 classes in\u2026","rel":"","context":"In "Dynamical Systems"","block_context":{"text":"Dynamical Systems","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/dynamical-systems\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":186,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/07\/22\/notes-on-calculus-blue-volume-1-chapter-1\/","url_meta":{"origin":32,"position":5},"title":"Notes on “Calculus Blue” Volume 1, Chapter 1","author":"siams","date":"22 July 2019","format":false,"excerpt":"These notes are on the Calculus Blue videos by Ghrist on YouTube. \u00a0He emphasizes that the math will involve substantial (and worthwhile) work, which I really appreciate. 01 (0:51) \"Vectors & matrices: Intro\" \u00a0\"Your journey is not a short one\". \u00a0To learn \"calculus, the mathematics of the nonlinear\", prepare with\u2026","rel":"","context":"In "Math"","block_context":{"text":"Math","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/math\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/posts\/32","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/users\/8032"}],"replies":[{"embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/comments?post=32"}],"version-history":[{"count":2,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/posts\/32\/revisions"}],"predecessor-version":[{"id":57,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/posts\/32\/revisions\/57"}],"wp:attachment":[{"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/media?parent=32"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/categories?post=32"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/tags?post=32"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}