tag:blogger.com,1999:blog-2516188730140164076.post4974603223825255381..comments2023-11-04T04:35:23.438-04:00Comments on Devlin's Angle: What is mathematical thinking? Mathematical Association of Americahttp://www.blogger.com/profile/10559021045290192742noreply@blogger.comBlogger18125tag:blogger.com,1999:blog-2516188730140164076.post-85774897657882219632014-09-29T09:50:09.608-04:002014-09-29T09:50:09.608-04:00I have been trying for a very long time to get my ...I have been trying for a very long time to get my students at a pre-service teacher institution not to teach 2X2=4, but let their students acquire mathematical concepts. I am so happy at my old age i can see what professor devlin is after in mathematical thinking.Anonymoushttps://www.blogger.com/profile/08525836599439121688noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-44416504640938097482012-09-22T16:20:41.960-04:002012-09-22T16:20:41.960-04:00Hello Mr Devlin... You wrote "How do you teac...Hello Mr Devlin... You wrote "How do you teach it? Well, you can’t teach it; in fact there is very little anyone can teach anyone. People have to learn things for themselves; the best a “teacher” can do is help them to learn." Which I totally agree with. I just want to add a comment... <br />When my older sister started having children (she has 3) 10 years ago, my father told me "you should play with them and teach them everything you know, because children are like a sponge, they adsorb liquid information which is your example, if you teach them bad thing they will do bad things, and if you teach them good things they will do good things, do the family a favor and don't teach them bad thing..."... (I probably shouldn't add that last part, but even today I find it very funny)... <br />Today, I'm 24 years old, and I believe I can take that comment my father gave 10 years ago and modify it to fit the MOOC learning system:<br />"Mooc students are like a sponge, they will absorb liquid information from the teacher giving the course and use it to enhance their professional, academic, personal, and everyday life." Of course MOOC's are new, so the best thing a MOOC student can have is without doubt the willingness to learn, and that's why 50k-60k people enrolled to your Mathematical Thinking course, because we (yes I am enrolled) think we have the willingness to learn from someone that we don't know, we've never met, we don't have the same native language, we all have different aspects and goals in life. Yet, we all expect to learn as much as possible from you and your TA's in 7 weeks (which would be also amazing). Alfredo Funeshttps://www.blogger.com/profile/18074676536041662800noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-79637790137975660552012-09-17T09:54:22.903-04:002012-09-17T09:54:22.903-04:00Looking forward to your class. Thanks for the effo...Looking forward to your class. Thanks for the effort :)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-71522541389805763212012-09-17T06:45:42.653-04:002012-09-17T06:45:42.653-04:00After reading this..I am excited about taking this...After reading this..I am excited about taking this course.it is what I was hoping for.<br />I will add, I think what a good teacher does is reignite the love of learning..all children start with it..discovery..that is learning.kdAnonymoushttps://www.blogger.com/profile/15582919892111198838noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-40673850170579354172012-09-10T05:18:28.469-04:002012-09-10T05:18:28.469-04:00Yes, the concept seems to be on the line Gestalt t...Yes, the concept seems to be on the line Gestalt theory in Psychology, that the sum of the constituents is less than the total. Here, context is part of the difference. Hope I am close to understanding the concept. Anonymoushttps://www.blogger.com/profile/04536514782089567930noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-9390543259494947742012-09-10T03:12:57.331-04:002012-09-10T03:12:57.331-04:00After reading this article i dont have any doubt a...After reading this article i dont have any doubt abt the course and value its going to offer me.<br /><br />Thanks you professor, See u in the classRakesh Kumarhttps://www.blogger.com/profile/09223873847557695362noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-43454525428147800272012-09-05T09:12:28.529-04:002012-09-05T09:12:28.529-04:00Hector, Here is the definition I gave on my first ...Hector, Here is the definition I gave on my first slide. Just two sentences.<br /><br />A feature F is contextual for an action A if F constrains A and may affect the outcome of A, but is not a constituent of A.<br /><br />In particular, a situation, environment, or set of circumstances C is said to be a context for an action A if C constrains A or affects the outcome of A but is not a constituent of A.<br /><br />Of course, those sentences contain several terms of art that require elaboration and definition. There is a whole formal apparatus within which the above definition operates: Situation Theory. <br /><br />Situation Theory is a mathematically-based framework for describing and analyzing information flow that was developed at Stanford in the 1980s. (Not to be confused with John McCarthy's AI focused Situation Calculus, also developed at Stanford.) Situation Theory was initiated by Jon Barwise and John Perry, initially as a framework for natural language semantics. I was one of the team that developed it as a more general framework for analyzing information flow. I described the theory in my 2000 book Logic and Information.<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-70649298368811358412012-09-05T05:27:45.346-04:002012-09-05T05:27:45.346-04:00Beautiful and inspired anecdote. A story like this...Beautiful and inspired anecdote. A story like this has a huge impact on students, and we need to use more of these as educators.<br /><br />I am very curious... what appeared on that first slide? (if it is not classified).<br /><br /><br /><br />Hector Floreshttps://www.blogger.com/profile/08609776337145536431noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-49675001937279534762012-09-04T12:17:05.017-04:002012-09-04T12:17:05.017-04:00Prof. Keith,
thank you for introducing your opin...Prof. Keith, <br /><br />thank you for introducing your opinion in such a clever and appealing way.<br />looking forward to taking the course.Taniahttps://www.blogger.com/profile/05149724215231907490noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-83842030833265536442012-09-04T04:35:20.332-04:002012-09-04T04:35:20.332-04:00Hi Prof Devlin,
I appreciate the post you read. I...Hi Prof Devlin,<br /><br />I appreciate the post you read. I signed up for classes in Coursera to fill up some of my free time and this one really attracted me. I cannot claim to be good in math, but I'm really looking forward to learning how to think like a mathematician. Despite my traumatic experience in college, I cannot suppress my love for learning, especially a subject that challenges me. I hope I'll be able to learn as much as I can from this class. Looking forward to September 17.Haeja Francahttps://www.blogger.com/profile/01138698277596440625noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-48234859294892294502012-09-02T14:36:24.958-04:002012-09-02T14:36:24.958-04:00In 1984, Robert B. Davis wrote in LEARNING MATHEMA...In 1984, Robert B. Davis wrote in LEARNING MATHEMATICS of studies that were emerging from several researchers and universities: "They all show that many university students have actually learned far less than everyone had assumed. Students who have completed five or more years of studying mathematics in high school and college may still have very wrong ideas about VARIABLES (or 'unknowns', 'literals', etc., - the ubiquitous x's and y's of algebra). This despite the fact that these same students were thought to have learned about linear equations, systems of linear equations, quadratic equations, graphs of conic sections, and many other things THAT DEPEND UPON A CORRECT UNDERSTANDING OF VARIABLES. At first glance this may seem to be impossible: how can you learn something that depends fundamentally upon various things you don't know? Later in this book we shall see an answer: DIFFERENT TYPES OF 'LEARNING' ARE POSSIBLE. One type does depend upon certain skills, concepts and understandings. Another type does not. This is not entirely mysterious. A singer may sing German lieder without in fact possessing any real command of German as a language; the singing can be a matter of imitation. So in this example we see two different behaviors: the use of German as a language, where the words and phrases have meaning; and, second, the use of German as a set of sounds to be produced imitatively. This is probably a passable parallel to the two different mathematical behaviors, one of which builds on understanding, and the other of which does not. The implications of this unsuspected deficit in students knowledge are extremely far-reaching." (p. 4) Anonymoushttps://www.blogger.com/profile/18420674456589471004noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-49330793020676627972012-09-02T14:17:44.832-04:002012-09-02T14:17:44.832-04:00I added a paragraph and an endnote after it became...I added a paragraph and an endnote after it became clear that not all readers recognized the parody of mathematical precision in my opening paragraph. What my DoD experience conformed for me was how anyone who has spent time thinking hard about something has something of value to offer. Just because something fails according to one metric, does not mean it is without value, and indeed could be of immense value. A person who derides someone else for "failing" should be cautious. One day they may find themselves working for that other person! :-)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-6173703715703350222012-09-01T15:07:41.582-04:002012-09-01T15:07:41.582-04:00Hi Prof. Keith,
I`ve enrolled to your MOOC course...Hi Prof. Keith,<br /><br />I`ve enrolled to your MOOC course with big expectations, but they are already satisfied :) so, I feel like a Maths thinker already, and a doer in the sense that you say thinking "is" doing.<br /><br />I find your ideas and examples -particularly gestures and enthusiasm, very different in flavor and sharp indeed.<br /><br />Looking forward to having the course. <br />Thanks for all the brilliance you share. Anonymoushttps://www.blogger.com/profile/12525084834226703779noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-54012650048176252782012-09-01T00:15:24.816-04:002012-09-01T00:15:24.816-04:00Mathematics inspires me, through mathematical thin...Mathematics inspires me, through mathematical thinking, through this post, and through you... :)Arun.Jhttps://www.blogger.com/profile/09669319721662896089noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-68846544638540840352012-08-31T23:47:53.197-04:002012-08-31T23:47:53.197-04:00Loved this particular blog. Read it twice already....Loved this particular blog. Read it twice already. I can still read it again :-). Can't wait for it to be 17th September.Alakshendra Tripathihttps://www.blogger.com/profile/00038324986627146674noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-34331797206211601152012-08-31T20:53:35.866-04:002012-08-31T20:53:35.866-04:00This is exactly the reason why I'm taking this...This is exactly the reason why I'm taking this course. I have no way to affirm or validate if I am already practicing "Mathematical Thinking". I've been trained heavily on qualitative analysis but I feel that, in order to "organize" my thoughts and contemplations, I would need to represent the "mess" in a way that goes beyond ordinary language. At least, this is one of my major concerns.<br /><br />I am looking forward to a lot of insights and learnings from this course, Professor Devlin. As a fellow academic, I think that offering this through MOOC is a wonderful opportunity for university academics/researchers like me, who are unable to afford Stanford education, but very interested in learning further about mathematics and its applications in other disciplines.<br /><br />Cheers!<br /><br />~ Jalton jalskihttps://www.blogger.com/profile/11632596291643796051noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-13537357819558082062012-08-31T18:34:05.301-04:002012-08-31T18:34:05.301-04:00I am very excited for your course. I'm a biolo...I am very excited for your course. I'm a biology/chemistry student currently and and am immersed in math but wanted to learn more about how I should/could be viewing math. That there is an actual way to frame the information more mathematically. There was no transition class at the start of my college career and have been sharing my excitement over your MOOC class with my husband after reading your wordpress blog. Thank you for the time and effort you are putting into this endeavor! Mariahttps://www.blogger.com/profile/02069708527859290259noreply@blogger.comtag:blogger.com,1999:blog-2516188730140164076.post-30613362247851443242012-08-31T13:29:25.946-04:002012-08-31T13:29:25.946-04:00After posting the article, I came across this grea...After posting the article, I came across this great quotation regarding what good teachers do:<br /><br />"[Good teachers] demonstrate by example what it is to think through a problem. Because the way experts think through a problem differs by field, so what professors are doing when they teach this way is communicating content knowledge but also initiating students into an intellectual discipline."<br /><br />It's by Prof. Robert Art of Brandeis University, and is quoted in<br /><a href="http://anniemurphypaul.com/2012/08/what-the-best-teachers-do/" rel="nofollow">Annie Murphy Paul's excellent "Brilliant Blog"</a>Anonymousnoreply@blogger.com