http://www.mapleprimes.com/maplesoftblog/134197-Teaching-Concepts-With-Maple en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Tue, 09 Jun 2026 18:24:32 GMT Tue, 09 Jun 2026 18:24:32 GMT The latest comments added to the Blog Entry, Teaching Concepts with Maple http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/maplesoftblog/134197-Teaching-Concepts-With-Maple http://www.mapleprimes.com/maplesoftblog/134197-Teaching-Concepts-With-Maple?ref=Feed:MaplePrimes:Teaching Concepts with Maple:Comments#comment134304 <p>The use of Maple for learning and teaching is one of its advantages. Unfortunately, I don't see Probability with Mathematical Statistics, Logic, and Graph Theory in Teaching Concepts with Maple. Using the opportunity, I would like to refer to <a href="http://mathoverflow.net/questions/60255/information-about-publishing-and-citations">http://mathoverflow.net/questions/60255/information-about-publishing-and-citations</a> .</p> The latest comments added to the Blog Entry, Teaching Concepts with Maple 134304 Thu, 17 May 2012 08:17:10 Z Markiyan Hirnyk Markiyan Hirnyk http://www.mapleprimes.com/maplesoftblog/134197-Teaching-Concepts-With-Maple?ref=Feed:MaplePrimes:Teaching Concepts with Maple:Comments#comment134317 <p>I appreciate the value of re-sequencing concepts and skills. But my take on the value of Maple in undergraduate education diverges from the "clickable math" paradigm. The real value of Maple in education comes from a feedback between syntax, content, and cognition.</p> <p>For example, a student in Calculus I is asked to display the graph of y=x^2 and its tangent line at x=2. Student erroneously ends up with y=4+2*x*(x-2) as the equation of the tangent line. The graph of the curve and "line" looks wrong and causes cognitive conflict. In resolving the conflict, the student learns. In clickable math, it seems too easy to circumvent cognitive conflict.&nbsp;</p> The latest comments added to the Blog Entry, Teaching Concepts with Maple 134317 Thu, 17 May 2012 18:19:54 Z Alex Smith Alex Smith http://www.mapleprimes.com/maplesoftblog/134197-Teaching-Concepts-With-Maple?ref=Feed:MaplePrimes:Teaching Concepts with Maple:Comments#comment134318 <p><a href="http://www.mapleprimes.com/maplesoftblog/134197-Teaching-Concepts-With-Maple#comment134304">@Markiyan Hirnyk</a>&nbsp;</p> <p>The subject areas touched by the 44 problems posted so far are those that the "typical" college student in math and science programs meet in their first two years of study. The point of the work is to show both a pedagogical approach and to demonstrate how to implement this pedagogy in a syntax-free manner.</p> <p>There are more than 100 additional problems in the pipeline, and as of this moment, more than half that have now been recorded and are being readied for posting. But initially,&nbsp;the six subject areas themselves&nbsp;will&nbsp;be augmented&nbsp;with problems only&nbsp;from precalculus math&nbsp;(algebra and trig).</p> <p>Beyond that, where the "clickable" paradigm works, problems from additional areas can be considered. But it would be useful to understand that the primary goal of this collection of activities is to demonstrate an approach to the use of technology in teaching and learning college-level mathematics, and to show that the ease-of-use techniques in Maple that flatten itslearning curve make it possible for this pedagogy to be implemented in a syntax-free manner.</p> <p>Maple is certainly a useful tool in many other subject areas of mathematics. The pedagogy advocated in the problems so far posted is certainly applicable, and has already been demonstrated in&nbsp;my <a href="http://www.maplesoft.com/products/ebooks/aem/index.aspx">Advanced Engineering Mathematics </a>ebook. However, not all of what's in that volume is easily rendered in a syntax-free form. Perhaps there is need for a separate web area reserved for problems in which the "clickable" paradigm is less well-developed.</p> <p>By the way, a number of improvements in the syntax-free environment of Maple have come from pushing the boundaries of what could and could not be captured in this format. So, perhaps one outcome of extending this project to other subject areas will be the augmentation of the syntax-free tools in Maple. Is this something our user-community can contribute to?</p> The latest comments added to the Blog Entry, Teaching Concepts with Maple 134318 Thu, 17 May 2012 18:27:31 Z rlopez rlopez http://www.mapleprimes.com/maplesoftblog/134197-Teaching-Concepts-With-Maple?ref=Feed:MaplePrimes:Teaching Concepts with Maple:Comments#comment134319 <p><a href="http://www.mapleprimes.com/maplesoftblog/134197-Teaching-Concepts-With-Maple#comment134317">@Alex Smith</a>&nbsp;</p> <p>Let's see if I correctly understand this comment.&nbsp;Does it suggest&nbsp;that the chance for cognitive conflict is diminished with a tool that makes it easier to make the exact same mistake described in the example?</p> <p>Suppose the student wrote the same wrong expression for the tangent line, and then added it to a graph of the function via drag-and-drop instead of via some more complex syntax. The same cognitive conflict would arise, only it would happen faster&nbsp;and more easily with "syntax-free" computing. And with syntax-free computing, the student&nbsp;wouldn't have to check out the detour "Is my syntax correct, or is the error in my math?"</p> <p>Bottom line: I don't see that ease-of-use in any way reduces the pedagogical opportunities afforded by cognitive conflict. Am I missing something?</p> The latest comments added to the Blog Entry, Teaching Concepts with Maple 134319 Thu, 17 May 2012 18:38:38 Z rlopez rlopez http://www.mapleprimes.com/maplesoftblog/134197-Teaching-Concepts-With-Maple?ref=Feed:MaplePrimes:Teaching Concepts with Maple:Comments#comment134331 <p><a href="http://www.mapleprimes.com/maplesoftblog/134197-Teaching-Concepts-With-Maple#comment134319">@rlopez</a>&nbsp;</p> <pre>I watched the "Tangent and Normal Lines-Solution by Task Template" video.</pre> <pre> There is a box in the template where one is prompted to enter a value for x0,</pre> <pre> where the default is x0=0.</pre> <pre>My comment was meant to suggest that the tool makes it too easy to &gt;not&lt; make</pre> <pre> the exact same mistake described in my example. Making the mistake is good,&nbsp;</pre> <pre>because it causes cognitive conflict. An environment where the learner is insulated&nbsp;</pre> <pre>from this is not "bad." It just supports a different philosophy of learning. </pre> <pre>&nbsp;</pre> The latest comments added to the Blog Entry, Teaching Concepts with Maple 134331 Fri, 18 May 2012 00:16:28 Z Alex Smith Alex Smith http://www.mapleprimes.com/maplesoftblog/134197-Teaching-Concepts-With-Maple?ref=Feed:MaplePrimes:Teaching Concepts with Maple:Comments#comment134332 <p><a href="http://www.mapleprimes.com/maplesoftblog/134197-Teaching-Concepts-With-Maple#comment134331">@Alex Smith</a>&nbsp;</p> <p>Yes, its just a different philosophy of learning. My experience in the classroom (35 years) convinced me that I best served my students if I helped them to avoid mistakes. I always found that I had the hardest time learning something I had previously gotten a wrong impression of. Unlearning is hard, so I always tried to get my students to "get it right" right from the beginning.</p> <p>Just a different perspective on what works best for both student and instructor. But it's good to be reminded that others have different views, and that these differences for the most part need to be respected.</p> The latest comments added to the Blog Entry, Teaching Concepts with Maple 134332 Fri, 18 May 2012 01:12:13 Z rlopez rlopez