tag:blogger.com,1999:blog-57422756149911424052017-09-05T18:45:47.116-07:00John Burke's Math BlogA place for dialogue about mathematics, computer-based mathematics and the teaching of mathematics for students and colleagues.John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.comBlogger20125tag:blogger.com,1999:blog-5742275614991142405.post-22270379111760514252013-04-22T16:25:00.000-07:002013-04-22T16:25:01.476-07:00Teaching/Learning Mathematics<!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument></xml><![endif]--><br /><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles></xml><![endif]--><!--[if gte mso 10]><style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;} </style><![endif]--> <br /><div class="MsoNormal">There are two components to learning mathematics: learning skills and learning conceptual thinking.</div><div class="MsoNormal"><br /></div><div class="MsoNormal">Skills are learned through practice and drill. The fact that you understand the concept of parallel parking does not mean you can actually do it. You have to practice and practice and practice some more until you can do it. Once a skill is mastered, you never lose it; you may need some refresher practice after a long time of not using it, but that is all. Think bike riding. Skills are relatively easy to teach.</div><div class="MsoNormal"><br /></div><div class="MsoNormal">Conceptual thinking is a completely different thing.</div><div class="MsoNormal"><br /></div><div class="MsoNormal">The sequence of math classes from primary school through college form a continuum. At the lower levels, it is mostly about learning skills. At the advanced levels, it is mostly about conceptual thinking. In between, it is a mixture of both.</div>John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-83203162114916727132013-04-01T09:36:00.000-07:002013-04-01T09:37:48.285-07:00Resurrecting California’s Public Universities<span style="font-family: Arial,Helvetica,sans-serif;">So, I pick up the Sunday Review section of the New York Times and there on the editorial page is an editorial with the above title.</span><br /><span style="font-family: Arial,Helvetica,sans-serif;"></span><span style="font-family: Arial,Helvetica,sans-serif;"></span><span style="font-family: Arial,Helvetica,sans-serif;">Quoting from the <a href="http://www.nytimes.com/2013/03/31/opinion/sunday/resurrecting-californias-public-universities.html?partner=rss&emc=rss&_r=0" target="_blank">editorial</a>: </span><br /><span style="font-family: Arial,Helvetica,sans-serif;"></span><span style="font-family: Arial,Helvetica,sans-serif;"></span><blockquote dir="ltr" style="margin-right: 0px;"><span style="font-family: Arial,Helvetica,sans-serif;">"The same California State Legislature that cut the higher education budget to ribbons, while spending ever larger sums on prisons, <a href="http://www.nytimes.com/2013/03/13/education/california-bill-would-force-colleges-to-honor-online-classes.html?pagewanted=all" title="NY Times article">now proposes</a> to magically set things right by requiring public colleges and universities to offer more online courses. The problem is that online courses as generally configured are not broadly useful. They work well for highly skilled, highly motivated students but are potentially disastrous for large numbers of struggling students who lack basic competencies and require remedial education. These courses would be a questionable fit for first-time freshmen in the 23-campus California State University system, more than 60 percent of whom<a href="http://www.calstate.edu/eap/"> need remedial instruction</a> in math, English or both.</span></blockquote><blockquote dir="ltr" style="margin-right: 0px;"><span style="font-family: Tahoma;">"The story of how the state’s fabled higher education system got to this point is told in a troubling <a href="http://www.ppic.org/main/publication.asp?i=988" title="PPIC analysis">analysis</a> by the Public Policy Institute of California, a nonpartisan think tank."</span></blockquote><div dir="ltr"><span style="font-family: Arial,Helvetica,sans-serif;">For a variety of reasons, our state legislature is reflecting society at large in trying for the quick fix to every problem that presents itself. This NYTimes editorial and others need to be understood as not antagonistic to online classes in general, but rather against using them in the wrong setting. To the extent MOOCs in mathematics have been successful, they are successful in the more advanced classes where students are already skilled in the basics and are organized, disciplined and motivated. </span></div><span style="font-family: Arial,Helvetica,sans-serif;"></span><div dir="ltr"><br /></div><span style="font-family: Arial,Helvetica,sans-serif;"></span><div dir="ltr"><span style="font-family: Arial,Helvetica,sans-serif;">Online classes at the community college level can be a tremendous aid for the many students with family and job responsibilities who find it difficult to regularly attend on ground classes. However, they are not suited for students missing any of the above mentioned characteristics. The legislature, if it continues to pursue this short-sighted course will only hasten the long slow slide of California's higher education system from the envy of the world to just another state education system fallen on hard times. In my opinion.</span></div>John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-13320623905320315372013-03-31T15:16:00.000-07:002013-03-31T15:16:21.357-07:00Stephen Wolfram at SXSW<span style="font-family: Arial,Helvetica,sans-serif;">His complete talk as a streaming video as well as a slightly edited transcript is available on his <a href="http://blog.stephenwolfram.com/2013/03/talking-about-the-computational-future-at-sxsw-2013/" target="_blank">blog</a>.</span><br /><span style="font-family: Arial,Helvetica,sans-serif;"><br /></span><span style="font-family: Arial,Helvetica,sans-serif;">It is impossible to listen to him talk and not come away excited and with many ideas to pursue.</span>John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-9268968024058164872013-03-31T15:11:00.000-07:002013-03-31T15:19:24.330-07:00The 100th Annivsary of Paul Erdos' Birth<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: small;">March 29: There is an amusing article on scientifciamerican.com about <a href="http://www.scientificamerican.com/article.cfm?id=an-arbitrary-number-of-years-since-mathematicians-birth&WT.mc_id=SA_CAT_BS_20130329" target="_blank">Paul Erdos</a> on what would have been his 100th birthday. I actually met him very briefly while a first year graduate student at the University of Colorado. He was treated somewhat like a rock star by the math department; when he took walks around the campus he would be followed by adoring faculty and graduate students.</span></span>John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-62790063222819652802012-08-21T19:45:00.000-07:002012-08-21T19:45:10.944-07:00New GeoGebra Routines<span style="font-family: Arial,Helvetica,sans-serif;">There is a new version of the GeoGebra Arithmetic routines at burke-consulting.com. There are several new routines and all routines have been updated to use the latest version of GeoGebra.</span> John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-45188909851151236702011-10-16T20:21:00.000-07:002011-10-16T20:22:26.279-07:00<div><span style="font-family:Tahoma;font-size:85%;"><span style="font-size:100%;"><span lang="en-us"><span style="font-family:Arial;font-size:130%;">A parabola is the locus of all points equidistant from a given point, the <b><i>focus</i></b>, and a line, the <b><i>directrix</i></b>.</span></span></span></span></div> <div><span style="font-family:Tahoma;font-size:85%;"><span style="font-size:100%;"><span lang="en-us"></span> </span></span><span lang="en-us"><span style="font-family:Tahoma;font-size:85%;"><span style="font-size:100%;"><span style="font-family:Arial;font-size:130%;"><br />The September 2011 issue of The College Mathematics Journal (published by MAA) contains an article by Dan Joseph, Gregory Hartman and Caleb Gibson titled Generalized Parabolas (available online if a member/subscriber or through jstor:</span></span></span></span><span style="font-family:Tahoma;font-size:85%;"><span style="font-size:100%;"><span style="font-family:Arial;font-size:130%;"> <a href="redir.aspx?C=91d18636b48046a087981b16424197e9&URL=http%3a%2f%2fwww.jstor.org%2fpss%2f10.4169%2fcollege.math.j.42.4.275" target="_blank">http://www.jstor.org/pss/10.4169/college.math.j.42.4.275</a></span><span lang="en-us"><span style="font-family:Arial;font-size:130%;"> if you have access to jstor). In their article they investigate what happens if you change the directrix in the definition above to a general curve, for example, a parabola (see example 3 below). The authors took an analytical approach, using Mathematica to find the equation of each generalized parabola.</span></span></span></span></div> <p><span lang="en-us"></span><span style="font-family:Tahoma;font-size:85%;"><span style="font-size:100%;"> <span style="font-family:Arial;"><span lang="en-us"><span style="font-size:130%;">I recognized GeoGebra could be used for a purely geometrical investigation. Go to </span><a href="redir.aspx?C=91d18636b48046a087981b16424197e9&URL=http%3a%2f%2fwww.burke-consulting.com%2fGeneralizedParabolas.html" target="_blank"><span style="font-size:130%;">http://www.burke-consulting.com/GeneralizedParabolas.html</span></a><span style="font-size:130%;"> to see some way cool examples and then try it out for yourself IMNSHO</span></span><span style="font-size:130%;">.</span></span></span></span></p> <p><span style="font-family:Tahoma;font-size:85%;"><span style="font-family:arial;font-size:130%;">John</span></span></p>John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-10843694373375571682011-08-01T12:20:00.000-07:002011-08-01T12:21:25.234-07:00Is mathematics invented or discovered?<!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:punctuationkerning/> <w:validateagainstschemas/> <w:saveifxmlinvalid>false</w:SaveIfXMLInvalid> <w:ignoremixedcontent>false</w:IgnoreMixedContent> <w:alwaysshowplaceholdertext>false</w:AlwaysShowPlaceholderText> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> <w:dontgrowautofit/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:latentstyles deflockedstate="false" latentstylecount="156"> </w:LatentStyles> </xml><![endif]--><!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;} </style> <![endif]--> <p class="MsoNormal"><span style="font-family:Arial">I often tell students when introducing new (to them) concepts that when mathematicians hit a brick wall in pursuing some investigation, they invent something to knock down the wall. Mathematics is purely an invention of the human mind.</span></p> <p class="MsoNormal"><span style="font-family:Arial">Another way of looking at the same thing is that the tool to knock down the wall was there all along just waiting for someone with the need to discover it. All of mathematics exists as a fundamental part of the universe independent of us.</span></p> <p class="MsoNormal"><span style="font-family:Arial">In thinking about this, I realized that I use the terms “invent” and “discover” interchangeably when talking about mathematics, and yet they are not the same.</span></p> <p class="MsoNormal"><span style="font-family:Arial">Theoretical astrophysicist Mario Livio has an article in the August Scientific American titled “Why Math Works” where he examines both sides of this philosophical argument … and comes down squarely in the middle.</span></p> <p class="MsoNormal"><span style="font-family:Arial">The article is at www.sciam.com; however, I think you need to be a subscriber to read the whole article (unless the college has a site license).</span></p>John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-24741619864410139862010-09-12T08:56:00.000-07:002010-09-12T09:02:04.037-07:00Science News Article About the Status of P not equal to NPJulie Rehmeyer has an article in Science News about the <a href="http://www.sciencenews.org/view/generic/id/63252/title/Math_Trek__Crowdsourcing_peer_review">status of of P vs NP</a>. The explanation is excellent and well worth several reads. Particularly interesting is how the collaborative possibilities of the Internet have come into play.John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-35279220413139745762010-08-10T14:17:00.000-07:002010-08-10T14:26:08.753-07:00HP Labs Mathematician Claims P not equal to NPVinay Deolalikar, who is with Hewlett-Packard Labs, has sent to peers copies of a proof he did stating that P is not equal to NP, one of the Millennium Prize Problems. <a href="http://blogs.discovermagazine.com/80beats/2010/08/10/has-the-devilish-math-problem-p-vs-np-finally-been-solved/">Discover Magazine</a> has a good lay description of the problem. For those interested, the <a href="http://www.scribd.com/doc/35539144/pnp12pt">98 page article</a> containing the proof is online.John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-28401431885094622682010-08-07T14:03:00.000-07:002010-08-07T14:15:16.117-07:00The Online Encyclopedia of Integer SequencesJulie Rehmeyer's August <a href="http://www.sciencenews.org/view/generic/id/61870/title/Math_Trek__The_pattern_collector">Math Trek column in Science News</a> talks about the <a href="http://oeis.org/classic/Seis.html">Online Encyclopedia of Integer Sequences</a> and its creator Neil Sloane. The OEIS currently has almost 200,000 integer number sequences in an online searchable database. This is a passion for Sloane begun in the mid-1960s while in graduate school.<br /><br />From the article, "the OEIS ... provides a sequence’s full 'life story.' Along with listing the numbers that form the beginning of a sequence (sometimes hundreds of thousands of them), it gives all the different known ways to generate the sequence, lists references to the sequence in the scientific literature, links to any sites with information about it, cross-references related sequences, provides a graph of the sequence, and even offers a way to listen to the sequence."<br /><br />It is very easy to lose yourself for hours in the OEIS so be careful ;-).John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-36606494043639386952010-08-06T08:12:00.000-07:002010-08-06T08:24:15.045-07:00Stephen Wolfram on TEDIf you haven't already seen it, spend an enjoyable 20 minutes listening and watching <a href="http://www.ted.com/talks/lang/eng/stephen_wolfram_computing_a_theory_of_everything.html">Stephen Wolfram's TED talk</a> from February of this year. Note that it will probably take a lot longer than 20 minutes since you will find yourself frequently pausing to catch the Wolfram|Alpha search requests and Mathematica code. Well worth multiple viewings.John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-66996278724231003172010-07-28T22:41:00.000-07:002010-07-28T23:06:52.494-07:00New Math Standards?One of the little dramas being played out in California and probably elsewhere has to do with whether the state should adopt the K-12 Common Core standards for mathematics and English developed by a consortium of 48 states, including representatives from California. The Sacramento Bee <a href="http://www.sacbee.com/2010/07/24/2911470/state-should-adopt-us-math-standards.html">editorialized</a> that the state should adopt the US math standards, agreeing with 19 of the 21 members of the California Academic Content Standards Commission, the Governor's Office and most of the academic community. The editorial referred to California's "mile-wide, inch-deep" math curriculum as a problem the Common Core addresses. In an <a href="http://www.sacbee.com/2010/07/24/2911462/proposed-math-standards-unteachable.html">Op-Ed piece</a> by the two dissenting members in which they claim the new standards "would gut the state's successful program", they also refer several times to "high-performing foreign countries" teaching to something like California's current "mile-wide" curriculum. Several days later in a <a href="http://www.sacbee.com/2010/07/28/2919033/head-to-head-should-state-join.html">point-counterpoint debate</a>, the same arguments were raised.<br /><br />In a <a href="http://www.sacbee.com/2010/07/28/2919025/letters-to-the-editor.html">letter to the editor</a> published on July 28, I pointed out the real problem and the real difference between the US and "high-performing foreign countries" is the length of both the school day and school year:<br /><br /><span style="font-size:130%;"><span style="font-weight: bold;">Fix class time, not standards</span></span><p>Re: <a href="http://www.sacbee.com/2010/07/24/2911470/state-should-adopt-us-math-standards.html" target="_blank">"State should adopt U.S. math standards"</a> (Editorials, July 24) and "Proposed math standards unteachable" (Viewpoints, July 24): Both the editorial and op-ed column miss the point.</p><p>California's current curriculum is indeed "mile wide, inch deep." The reason it is an "inch deep" is because the school day and school year are too short and because students are not required to take mathematics through 12th grade.</p><p>"High-performing foreign countries" teach the same breadth of material, but they can teach it better because the school day and school year are longer and students have more years of mathematics instruction.</p><p>The state's current system is not a "successful" program, it is just broken differently.</p><p>No amount of changed standards or national commission reports will catch us up with the many countries ahead of us in math education; only the realization that, like learning to play well some musical instrument, learning mathematics requires many hours and years of study and practice.</p><p>- John Burke, Sacramento</p>John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-85056490105879985692010-07-27T23:31:00.000-07:002010-07-27T23:33:50.841-07:00Can playing chess improve kid's concentration?Interesting article in the <a href="http://www.hindustantimes.com/Can-chess-improve-kids-concentration/Article1-578820.aspx">Hindustan Times</a> suggests the answer is yes. I wonder if the same can be said for video games?John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-69912218363484141482010-07-26T08:18:00.000-07:002010-07-26T08:21:23.761-07:00GeoGebra 4.0 Beta ReleaseThe <a href="http://geogebra.org/">GeoGebra 4.0 Beta Release</a> is well worth a look. Among the new features I've found useful are numerous additional statistics functions.John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-86989345555623899192010-07-25T14:55:00.000-07:002010-07-25T14:58:54.544-07:00Math TrekScience News has a (mostly) online column called <a href="http://www.sciencenews.org/view/dispatches/type/column/collection_id/2/title/Math_Trek">Math Trek</a> that appears roughly monthly and is a great source for interesting math stories, many of which can be shared with your math class.John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-81044176892253536082009-08-18T12:16:00.000-07:002009-08-18T12:21:21.080-07:00<span style="font-family: arial;">MAA Online has just published an article on Wolfram|Alpha by David Bressoud that has references to much of what has been published so far. He takes a somewhat more even view of W|A when he says towards the end <span style="font-family: arial;">"</span>[it] is not a trivial change, but it need not be revolutionary." The link is to the right.<br /></span>John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-72690006819546341272009-08-17T06:33:00.000-07:002009-08-17T06:43:13.445-07:00More on Wolfram Alpha<span style="font-family: arial;">I finally found the link to an interesting article by Jeffrey Young from the Chronicle of Higher Education that explores what Wolfram Alpha may mean to the way we teach: http://chronicle.com/article/A-Calculating-Web-Site-Coul/47316/. I love the quote: "It makes graphing calculators look like slide rules." </span><br /><br /><span style="font-family: arial;">Seriously though, W/A will change the way we teach mathematics.</span>John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-38378801092001998492009-08-16T16:53:00.000-07:002009-08-16T17:08:51.023-07:00GeoGebra<span style="font-family: arial;">From the web site's About: "GeoGebra is dynamic mathematics software for all levels of education that joins arithmetic, geometry, algebra and calculus. On the one hand, GeoGebra is an interactive geometry system. You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterward. On the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum. These two views are characteristic of GeoGebra: an expression in the algebra view corresponds to an object in the graphics view and vice versa"<br /><br />Truth is, GeoGebra is impossible to describe. You need to see it in action. The web site has many examples, as does www.john-burke.net. Note that GeoGebra is free and is actively being enhanced. You can install GeoGebra on any PC or Mac (it is completely written in java), run it through a browser, or even run it off a thumb drive.<br /><br />The best way to learn to use GeoGebra on your own is to download the examples and then run the the Construction Protocol step by step (not the algebra window, but View -->Construction Protocol).<br /><br />For my colleagues at ARC, I will be giving a short presentation on GeoGebra Thursday, 8/20 and Friday, 8/21 at the Math Department meetings.<br /><br />For my colleagues at Sierra College, I will be giving a four hour hands on tutorial Tuesday, 8/25 from 1 - 5PM where you can (will) learn to use GeoGebra and leave with several constructions you can use in your classroom.<br /></span>John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-31974214723920746432009-08-16T16:35:00.000-07:002009-08-16T16:47:43.350-07:00Wolfram Alpha<span style="font-family: arial;">Speaking of the MathForum at Drexel, the MathEdCC (Math Education Community College) forum has had quite a discussion lately about math anxiety, what it is and isn't and what, if anything, we can do to ameliorate it.<br /><br />There have also been a few posts so far about <span style="font-weight: bold; font-style: italic;">Wolfram Alpha</span> (http://www.wolframalpha.com) and how to incorporate it into our teaching ("if" to incorporate is not an option since students will use it whether we want them to or not). If you have not seen what <span style="font-weight: bold; font-style: italic;">Wolfram Alpha</span> can do, just check out some of the math examples at http://www.wolframalpha.com/examples/Math.html.<br /></span>John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0tag:blogger.com,1999:blog-5742275614991142405.post-26632297042008601762009-08-13T12:15:00.000-07:002009-08-13T12:33:52.161-07:00Two New URLs<span style="font-family: arial;">I've added two new links to the right.<br /><br />The first is for the <span style="font-weight: bold;">MathForum @ Drexel University</span>. It is hard to describe in a few words everything this site offers to both instructors and students. </span><span style="font-family: arial;">You can easily spend several hours just looking into everything available, some free, some for a fee. </span><span style="font-family: arial;">From the "about" page: </span><br /><p>"<span style="font-family: arial;">The Math Forum is a leading center for mathematics and mathematics education on the Internet. Operating under Drexel's </span><a style="font-family: arial;" href="http://www.drexel.edu/academics/soe/homepage.html">School of Education</a><span style="font-family: arial;">, our mission is to provide resources, materials, activities, person-to-person interactions, and educational products and services that enrich and support teaching and learning in an increasingly technological world.</span><span style="font-family: arial;"> Our online community includes teachers, students, researchers, parents, educators, and citizens at all levels who have an interest in math and math education."</span></p><p><span style="font-family: arial;">The second URL is for the <span style="font-weight: bold;">National Library of Virtual Manipulatives</span>. These are java applets that illustrate interactively many basic arithmetic and mathematics concepts. While nominally aimed at K-12, many of the virtual manipulatives are suitable for the skills development course taught in community colleges (College Arithmetic through Intermediate Algebra)</span>.<span style="font-family: arial;"> Since statistics is commonly taught now in high school, the library also contains several virtual manipulatives (I am particularly enamored of the Monty Hall Problem manipulative) suitable for a college Elementary Statistics course. The Library can be used freely through any Internet connection or can be downloaded for a nominal fee. If you teach any skills development courses or Elementary Statistics, you should be able to find something here to use in the classroom.</span><br /><span style="font-family: arial;"></span></p><p><span style="font-family: arial;"><br /></span></p>John Burkehttps://plus.google.com/100035162645904279739noreply@blogger.com0