{"id":556,"date":"2014-05-01T19:01:47","date_gmt":"2014-05-01T19:01:47","guid":{"rendered":"http:\/\/onlineteachered.mit.edu\/?page_id=556"},"modified":"2024-12-06T22:48:36","modified_gmt":"2024-12-06T22:48:36","slug":"module-1","status":"publish","type":"page","link":"https:\/\/onlineteachered.mit.edu\/courses\/mathlets\/module-1\/","title":{"rendered":"Mathlets in Lecture, Module 1"},"content":{"rendered":"<p><!--slice begin--><!-- For use on mathlets.org\/training --><\/p>\n<div id=\"tocs\"><\/div>\n<p>This module contains two examples of using MIT Mathlets in lecture. The first illustrates the artistic and dynamic character of the Mathlets. The second and more interactive example shows how formulas can be brought to life using the Mathlets in lecture. Each segment is followed by questions, my remarks about the lecture fragments and the features of the Mathlets, and examples that illuminate their use. At the end there are a couple of exercises.<\/p>\n<hr \/>\n<h2>1. In this module&#8230;<\/h2>\n<p>You will first try out the Mathlets in a separate window. Next, you will watch video segments where you will be instructed to pause and engage in a variety of activities, as well as think about the questions posed.<\/p>\n<ul>\n<li>Download Mathlets in Lecture Slides [ <a href=\"http:\/\/onlineteachered.mit.edu\/files\/2014\/08\/Mathlets-in-Lecture-Slides.pdf\">PDF<\/a>, 2.1 MB ]<\/li>\n<li>Watch <a href=\"https:\/\/vimeo.com\/1036453869\">Mathlets in Lecture, Module 1 Video<\/a><br \/>\n<!-- YouTube\nWatch <a href=\"https:\/\/youtu.be\/WFzygQMe0JY\">Full Module 1 Video<\/a>\n-->\n<\/li>\n<\/ul>\n<hr \/>\n<h2>2. Learning Objectives<\/h2>\n<p>After completing this module, the participant will be able to use Mathlets to:<\/p>\n<ul class=\"mathlet-course-ul\">\n<li>Support lecture-based instruction.<\/li>\n<li>Increase student participation in the lecture.<\/li>\n<li>Use Mathlets to help students correlate visual images with symbols and computations.<\/li>\n<\/ul>\n<hr \/>\n<h2>3. Mathlets in Lecture, Segment 1<\/h2>\n<p>In this video clip, I will introduce the first Segment of this Module, set out its learning objectives, and make some general comments about using Mathlets in lecture. Then you will watch a fragment of a lecture centered on the <em>Linear Phase Portraits: Cursor Entry<\/em> Mathlet. This is followed by some questions for you to consider, and my remarks.<\/p>\n<div class=\"shaded\">\n<h4><em class=\"fa fa-pencil-square-o\"><\/em> Note<\/h4>\n<p>As you watch the\u00a0<em>Mathlets in Lecture,\u00a0Segment 1<\/em>\u00a0video, take notes regarding the following:<\/p>\n<ul class=\"mathlet-course-ul\">\n<li>Your reactions to the Mathlets.<\/li>\n<li>Thoughts about how you would or will incorporate the Mathlets into your own teaching.<\/li>\n<li>Thoughts about the approach you would use to teach the material presented.<\/li>\n<\/ul>\n<h4><em class=\"fa fa-rocket\"><\/em> Launch<\/h4>\n<p>Mathlet:<em>\u00a0<a title=\"Linear Phase Portraits Cursor Entry Mathlet\" href=\"http:\/\/mathlets.org\/mathlets\/linear-phase-portraits-cursor-entry\/\" target=\"_blank\" rel=\"noopener\">Linear Phase Portraits Cursor Entry<\/a><\/em><\/p>\n<\/div>\n<p><!-- ** Vimeo Video Source, hrm@math.mit.edu --><\/p>\n<div style=\"padding:56.25% 0 0 0;position:relative;\"><iframe src=\"https:\/\/player.vimeo.com\/video\/1036462801?title=0&amp;byline=0&amp;portrait=0&amp;badge=0&amp;autopause=0&amp;player_id=0&amp;app_id=58479\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture; clipboard-write\" style=\"position:absolute;top:0;left:0;width:100%;height:100%;\" title=\"MIT Mathlets in Lecture, Module 1, Segment 1.1\"><\/iframe><\/div>\n<p><script src=\"https:\/\/player.vimeo.com\/api\/player.js\"><\/script><br \/>\nTranscript [ <a href=\"http:\/\/onlineteachered.mit.edu\/files\/2014\/08\/Module-1-Mathlets-in-Lecture-Segment-1-Transcript.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a> ]<\/p>\n<p><!-- ** Backup YouTube Video Source\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/xfTYb6U69oY?si=S6Yc38bxLXR_xWBE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n--><\/p>\n<hr \/>\n<h3>3.1 Segment 1 Activity<\/h3>\n<p>The video segment you just completed ended with the presentation of three sets of questions for you to reflect and respond to. The first is regarding your initial thoughts and reactions regarding the Mathlets. Next, reflect on how I introduced the Mathlets versus how you would approach the same task, and finally please take a look to the future and all that you could do with the Mathlets.<\/p>\n<div class=\"shaded\">\n<h4><em class=\"fa fa-lightbulb-o\"><\/em> Think About<\/h4>\n<p>Introduction to Mathlets: When you first saw the Mathlet, there was a lot of information on the screen.<\/p>\n<ul class=\"mathlet-course-ul\">\n<li>Do you remember how you felt?<\/li>\n<li>Were you confused by it?<\/li>\n<li><em>I ask because your students&#8217; experience will be not too different from your own, unless you have seen an applet like this before.<\/em><\/li>\n<\/ul>\n<h4><em class=\"fa fa-pencil-square-o\"><\/em> Activity<\/h4>\n<p>Presenting Mathlet Functionality<\/p>\n<ul class=\"mathlet-course-ul\">\n<li>I introduced the various windows and functionalities of the Mathlet over a period of several minutes. Make an ordered list of these, in sequence, and think about other ways I might have presented them to this audience.<\/li>\n<\/ul>\n<h4><em class=\"fa fa-eye\"><\/em> Investigate<\/h4>\n<ul class=\"mathlet-course-ul\">\n<li>There are still other aspects of this tool that I did not talk about at all. What are a few additional investigations one can pursue using Mathlets?<\/li>\n<\/ul>\n<\/div>\n<p><\/p>\n<hr \/>\n<h3>3.2 Segment 1 Review<\/h3>\n<p>In a differential equations class, the objectives of a lecture fragment looks something like this:<\/p>\n<p>Mathematical objectives:<\/p>\n<ul class=\"mathlet-course-ul\">\n<li>Demonstrate the variety of phase portraits afforded by homogeneous linear\u00a0two-dimensional systems of differential equations.<\/li>\n<li>Demonstrate the control exercised by the trace and determinant of the\u00a0defining matrix on the phase portrait.<\/li>\n<li>Convince the student that the trajectories deform smoothly as the matrix\u00a0changes.<\/li>\n<\/ul>\n<p>For a more mathematical audience I would have talked about the eigenvalues;\u00a0they are together equivalent to giving the trace and determinant; whether\u00a0they are complex or real determines the region in the trace-determinant\u00a0plane; and the fact that the sign of the real part determines stability.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/onlineteachered.mit.edu\/files\/2014\/05\/mathlets-in-lecture-300x225.png\" alt=\"Photo of Haynes Miller lecturing with Mathlet in background\" width=\"300\" height=\"225\" class=\"alignright size-medium wp-image-1256\" style=\"margin-right: 0;\" srcset=\"https:\/\/onlineteachered.mit.edu\/files\/2014\/05\/mathlets-in-lecture-300x225.png 300w, https:\/\/onlineteachered.mit.edu\/files\/2014\/05\/mathlets-in-lecture-1024x768.png 1024w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>I also would have pointed out what is common among phase portraits of\u00a0matrices with the same trace and determinant, at least in the case that the eigenvalues\u00a0are real (nodes or saddles); this has to do with the relative magnitudes of\u00a0the eigenvalues. For non-real eigenvalues <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=-&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"-\" class=\"latex\" \/> inside the critical parabola <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=-&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"-\" class=\"latex\" \/> the\u00a0phase portrait consists of spirals. It is no longer the case that the space of\u00a0matrices with given trace and determinant is connected. Instead, this space\u00a0has two components, and that is represented by the split window.\u00a0The upper part contains spirals that move in the clockwise direction; the\u00a0lower part contains spirals that move in the counterclockwise direction.<\/p>\n<p>The Mathlet used in this lecture has a cousin, <em>Linear Phase Portraits: Matrix Entry<\/em>. In this Mathlet, you can adjust the entries of the matrix A\u00a0manually (by means of sliders, of course). One can also create the companion matrix, with top row [0, 1], with the given trace and determinant.<\/p>\n<p>In my differential equations course, I use one or the other of these Mathlets\u00a0in several different lectures, focusing on different aspects of it at different\u00a0stages of our study of linear systems of differential equations.<\/p>\n<hr \/>\n<h3>3.3 Segment 1 Conclusion<\/h3>\n<p>To conclude this segment we will discuss the design features of Mathlets. When preparing to teach using technology, it is important for you as the teacher to understand why the tool is designed the way it is. Finally, I will identify some of the advantages to using Mathlet technology during your lectures that were identified during Segment 1.<\/p>\n<p><!-- ** Vimeo Video Source, hrm@math.mit.edu --><\/p>\n<div style=\"padding:56.25% 0 0 0;position:relative;\"><iframe src=\"https:\/\/player.vimeo.com\/video\/1036465527?title=0&amp;byline=0&amp;portrait=0&amp;badge=0&amp;autopause=0&amp;player_id=0&amp;app_id=58479\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture; clipboard-write\" style=\"position:absolute;top:0;left:0;width:100%;height:100%;\" title=\"MIT Mathlets in Lecture, Module 1, Segment 1.2\"><\/iframe><\/div>\n<p><script src=\"https:\/\/player.vimeo.com\/api\/player.js\"><\/script><br \/>\nTranscript [ <a href=\"http:\/\/onlineteachered.mit.edu\/files\/2014\/08\/Module-1-Mathlets-in-Lecture-Segment-2-Transcript.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a> ]<\/p>\n<p><!-- ** Backup YouTube Video Source\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/-UmClxvP5Yk?si=tclJuiolLehmh_f_\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n--><\/p>\n<hr \/>\n<h2>4. Mathlets in Lecture, Segment 2<\/h2>\n<p>Segment 2 provides an introduction to a more interactive approach to teaching with Mathlets which is supported with research regarding active learning. During this segment of the video pay particular attention to and take notes regarding my interactions with the students in the workshop.<\/p>\n<div class=\"shaded\">\n<h4><em class=\"fa fa-rocket\"><\/em> Launch<\/h4>\n<p>Mathlet: <a title=\"Graph Features Mathlet\" href=\"http:\/\/mathlets.org\/mathlets\/graph-features\/\" target=\"_blank\" rel=\"noopener\"><em>Graph Features<\/em><\/a>\n<\/div>\n<p><!-- ** Vimeo Video Source, hrm@math.mit.edu --><\/p>\n<div style=\"padding:56.25% 0 0 0;position:relative;\"><iframe src=\"https:\/\/player.vimeo.com\/video\/1036466030?title=0&amp;byline=0&amp;portrait=0&amp;badge=0&amp;autopause=0&amp;player_id=0&amp;app_id=58479\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture; clipboard-write\" style=\"position:absolute;top:0;left:0;width:100%;height:100%;\" title=\"MIT Mathlets in Lecture, Module 1, Segment 2.1\"><\/iframe><\/div>\n<p><script src=\"https:\/\/player.vimeo.com\/api\/player.js\"><\/script><br \/>\nTranscript [ <a href=\"http:\/\/onlineteachered.mit.edu\/files\/2014\/08\/Module-1-Mathlets-in-Lecture-Segment-2-Transcript.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a> ]<\/p>\n<p><!-- ** Backup YouTube Video Source\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/YTui8OWFhGE?si=QMREtHOzojHzlhQZ\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n--><\/p>\n<div class=\"shaded\">\n<h4><em class=\"fa fa-lightbulb-o\"><\/em> Think About<\/h4>\n<ol class=\"mathlet-course-ol\">\n<li>This was an interactive lecture, with quite a few suggestions and answers from the audience. How many students do you think provided feedback? Do you think I had any information about how much the others were understanding?<\/li>\n<li>What further lessons could you draw from this Mathlet in a lecture setting?<\/li>\n<\/ol>\n<\/div>\n<p><\/p>\n<hr \/>\n<h3>4.1 Segment 2 Review<\/h3>\n<p>It is a good exercise to analyze what the different objectives of a lecture are,\u00a0at a pretty fine level. For example, here is a listing of the components of the\u00a0lecture fragment about the\u00a0<em>Graph Features <\/em>Mathlet.<\/p>\n<ol class=\"mathlet-course-ol\">\n<li>Talking through what you see on the screen<\/li>\n<li>Discussion of evaluation, set <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=x%3D0&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"x=0\" class=\"latex\" \/><\/li>\n<li>Graph features: rising, falling, concave, convex<\/li>\n<li>Question: Control of behavior for large <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=z&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"z\" class=\"latex\" \/>?<\/li>\n<li>More features: minima, maxima<\/li>\n<li>First degree case<\/li>\n<li>Second degree case<\/li>\n<li>Question: What makes the graph go through the origin?<\/li>\n<li>Question: What is the effect of increasing <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=b&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"b\" class=\"latex\" \/>?<\/li>\n<li>Commentary on flash cards<\/li>\n<li>Question: What is the role of linear term?<\/li>\n<li>Completing the square<\/li>\n<li>Checking the result<\/li>\n<li>Getting more from the formula: effect of <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=b&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"b\" class=\"latex\" \/><\/li>\n<li>&#8230;And verifying it on the Mathlet<\/li>\n<\/ol>\n<h4>Comments<\/h4>\n<p>One of the things Mathlets let you do is break down the lecture into\u00a0small fragments. This keeps the students interested, and lets them pick up\u00a0the thread after attention lapses.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/onlineteachered.mit.edu\/files\/2014\/05\/haynes-miller-235x300.png\" alt=\"Photo of Haynes R. Miller\" width=\"235\" height=\"300\" class=\"alignleft size-medium wp-image-1254\" style=\"margin-left: 0;\" srcset=\"https:\/\/onlineteachered.mit.edu\/files\/2014\/05\/haynes-miller-235x300.png 235w, https:\/\/onlineteachered.mit.edu\/files\/2014\/05\/haynes-miller-803x1024.png 803w, https:\/\/onlineteachered.mit.edu\/files\/2014\/05\/haynes-miller.png 1041w\" sizes=\"(max-width: 235px) 100vw, 235px\" \/>I decided to begin by accepting the rather interesting graph of the cubic, but\u00a0to ask a question which reverses the usual sequence: instead of starting with\u00a0the formula for our function and asking what can be said about the graph,\u00a0I started with the graph and asked how you had to adjust the coefficients to\u00a0achieve particular effects: behavior for large <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=x&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"x\" class=\"latex\" \/>, and behavior for <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=x%3D0&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"x=0\" class=\"latex\" \/>.<\/p>\n<p>While I was lecturing, I was inviting students to help me perform the demonstration. So, for\u00a0example, as soon as a student proposed reversing the sign of <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=a&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"a\" class=\"latex\" \/> to make the\u00a0function decrease for large <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=x&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"x\" class=\"latex\" \/>, I accepted it and tried it out on the Mathlet.\u00a0This is a good example of how you can perform experiments in class with Mathlets.<\/p>\n<p>I decided to pose this question before talking about other graph features,\u00a0critical points and point of inflection, to break up the descriptive part of the\u00a0talk a little bit.<\/p>\n<p>I invited a vote about the effect of increasing <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=b&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"b\" class=\"latex\" \/>. This is a <em>concept quiz<\/em>. By chance, the camera picked up one of the virtual votes I was referring to in my lecture. You can see the hand go up and then quickly down again, in the back of the room.\u00a0A number of participants thought\u00a0that increasing <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=b&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"b\" class=\"latex\" \/> would make the parabola fatter. They put up their hands\u00a0in support of fatter, but when the saw they were in a minority they quickly\u00a0put their hands down again. I think the sense of shame (surely undeserved!)\u00a0probably negated any learning they might have experienced.<\/p>\n<p>I said that asking about the role of the linear term was unfair. Well, whether\u00a0it is unfair or not depends upon the context. If I want students to exercise\u00a0their skill at completing the square and interpreting the result, or taking the\u00a0derivative and setting it equal to zero, this would be a perfectly appropriate\u00a0question. But these were not skills I wanted to challenge this audience with in this particular lecture fragment.<\/p>\n<hr \/>\n<h3>4.2 Segment 2 Conclusion<\/h3>\n<p>To conclude\u00a0<em>Mathlets in Lecture, Segment 2,\u00a0<\/em>I will provide a few useful hints on using Mathlets in your lectures, and discuss the use of concept questions.\u00a0Finally, I will once again identify some of the advantages to using Mathlet technology that were identified during this segment.<\/p>\n<p><!-- ** Vimeo Video Source, hrm@math.mit.edu --><\/p>\n<div style=\"padding:56.25% 0 0 0;position:relative;\"><iframe src=\"https:\/\/player.vimeo.com\/video\/1036470627?title=0&amp;byline=0&amp;portrait=0&amp;badge=0&amp;autopause=0&amp;player_id=0&amp;app_id=58479\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture; clipboard-write\" style=\"position:absolute;top:0;left:0;width:100%;height:100%;\" title=\"MIT Mathlets in Lecture, Module 1, Segment 2.2\"><\/iframe><\/div>\n<p><script src=\"https:\/\/player.vimeo.com\/api\/player.js\"><\/script><br \/>\nTranscript [ <a href=\"http:\/\/onlineteachered.mit.edu\/files\/2014\/08\/Module-1-Mathlets-in-Lecture-Segment-2-Conclusion-Transcript.pdf\" target=\"_blank\" rel=\"noopener\">PDF<\/a> ]<\/p>\n<p><!-- ** Backup YouTube Video Source\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/Rv9yzWHPBMA?si=tDk_b4NjNL599MYk\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n--><\/p>\n<hr \/>\n<h2>5. Post-Module Activity<\/h2>\n<div class=\"shaded\">\n<h4><em class=\"fa fa-pencil-square-o\"><\/em> Exercise<\/h4>\n<p>For two of the four projects below, design an appropriate use of a Mathlet in\u00a0lecture. Write notes describing the precise learning objective, what motions\u00a0you will make with the Mathlet, what you will write on the blackboard, and\u00a0what you will ask your students.<\/p>\n<ol class=\"mathlet-course-ol\">\n<li>The simplest use of a Mathlet is to verify calculations. So design a lecture\u00a0fragment in which you compute the location of critical points and the point\u00a0of inflection of a cubic polynomial and then verify your answer using\u00a0<em>Graph\u00a0Features<\/em>. You might want to make use of the crosshairs.<\/li>\n<li>A converse usage is to make measurements on the Mathlet and verify them\u00a0by calculation. This has the virtue of giving visual significance to symbols\u00a0in advance. Devise a lecture fragment using\u00a0<em>Graph Features<\/em>\u00a0which focuses\u00a0on the question of whether there is a point of inflection or not. I suggest fixing <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=a%3D1&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"a=1\" class=\"latex\" \/>.<\/li>\n<li>You are teaching calculus and you are at the point of discussing the\u00a0meaning of the tangent line to a graph, and its slope. Develop a lecture\u00a0fragment using\u00a0<em>Secant Approximation<\/em>\u00a0to help students get intuition about\u00a0this.<\/li>\n<li>Pick a target audience and match a learning objective with one of the\u00a0Mathlets. Then sketch a lecture fragment using this Mathlet to help students\u00a0meet the chosen learning objective.<\/li>\n<\/ol>\n<\/div>\n<p><\/p>\n<hr \/>\n<p>These materials are Copyright &copy; 2013, Massachusetts Institute of Technology and unless otherwise specified are licensed under a <a href=\"http:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported<\/a> license.<\/p>\n<hr \/>\n<p><!-- For use on mathlets.org\/training --><!--slice end--><\/p>\n<div class=\"prev-page-container\"><a href=\"http:\/\/onlineteachered.mit.edu\/courses\/mathlets\/introduction\/\"><em class=\"fa fa-hand-o-left\"><\/em> Introduction<\/a><\/div>\n<div class=\"next-page-container\"><a href=\"http:\/\/onlineteachered.mit.edu\/courses\/mathlets\/module-2\/\">Module 2 &#8211; Mathlets in Group Work <em class=\"fa fa-hand-o-right\"><\/em><\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>This module contains two examples of using MIT Mathlets in lecture. The first illustrates the artistic and dynamic character of the Mathlets. The second and more interactive example shows how formulas can be brought to life using the Mathlets in lecture. Each segment is followed by questions, my remarks about the lecture fragments and the &hellip; <a href=\"https:\/\/onlineteachered.mit.edu\/courses\/mathlets\/module-1\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Mathlets in Lecture, Module 1<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":32,"featured_media":0,"parent":552,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"jetpack_post_was_ever_published":false,"footnotes":""},"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P4sx5t-8Y","_links":{"self":[{"href":"https:\/\/onlineteachered.mit.edu\/wp-json\/wp\/v2\/pages\/556"}],"collection":[{"href":"https:\/\/onlineteachered.mit.edu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/onlineteachered.mit.edu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/onlineteachered.mit.edu\/wp-json\/wp\/v2\/users\/32"}],"replies":[{"embeddable":true,"href":"https:\/\/onlineteachered.mit.edu\/wp-json\/wp\/v2\/comments?post=556"}],"version-history":[{"count":143,"href":"https:\/\/onlineteachered.mit.edu\/wp-json\/wp\/v2\/pages\/556\/revisions"}],"predecessor-version":[{"id":2222,"href":"https:\/\/onlineteachered.mit.edu\/wp-json\/wp\/v2\/pages\/556\/revisions\/2222"}],"up":[{"embeddable":true,"href":"https:\/\/onlineteachered.mit.edu\/wp-json\/wp\/v2\/pages\/552"}],"wp:attachment":[{"href":"https:\/\/onlineteachered.mit.edu\/wp-json\/wp\/v2\/media?parent=556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}