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So much attention is placed on the \ algorithm that students fixate on the mechanics instead of the underlying \ theme; as such, they can apply the algorithm, but are unable to understand \ how it relates to other concepts or translates to other situations.\n\nA good \ example of this problem is Newton\[CloseCurlyQuote]s Method. 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Students really wanted to visualize the rectangles that are used \ to estimate the area and they felt free to draw them in the textbook. Any one \ graph in the text could have 4 to 8 rectangles (left-hand or right-hand) of \ different colors drawn in. And, of course, the kind students would erase \ their drawing - which would erase the picture of the printed graph as well! \ In the end, they had a mess which still didn\[CloseCurlyQuote]t make any \ sense, and an angry teacher! The amount of time it took to complete a lesson \ was disproportionately long compared to the future time that was spent on \ this material. Mathematica is the tool to visualize these subtleties for lots \ of graphics and do so quickly. Students finally saw the patterns and \ understood the overarching concepts without needing to resort to destroying \ school property. Furthermore, getting to the main point took much less time \ and held my students\[CloseCurlyQuote] interest better.\ \>", "TeacherPerspectiveContent", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.509289784343158*^9, 3.509289796817405*^9}, 3.50930171194786*^9, 3.509323159764473*^9}] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Identify patterns without busywork", "Section", ShowGroupOpener->False, CellChangeTimes->{ 3.485869517171875*^9, 3.485901236125*^9, {3.5060200202484703`*^9, 3.5060200256149054`*^9}, {3.5060201053626165`*^9, 3.5060201056746182`*^9}, {3.506020385222811*^9, 3.506020388046429*^9}, { 3.5060230793971057`*^9, 3.5060230858841057`*^9}, {3.5093231975552516`*^9, 3.509323202417738*^9}}], Cell[TextData[{ StyleBox["In the past, you may have drawn the graph of a function on the \ board, then a series of rectangles for a chosen step size, and then went \ through the process of calculating area for each rectangle, and then adding \ all of the areas up...and then rinsing and repeating for calculating area \ based on the opposite site (or perhaps the middle height of), the rectangle. \ And once that was all finished \[Dash]", FontFamily->"Arial", FontSize->14], StyleBox[" ", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox["usually right before the bell rang! \[Dash]", FontFamily->"Arial", FontSize->14], StyleBox[" ", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox["a student would invariably ask, ", FontFamily->"Arial", FontSize->14], StyleBox["What if that function was ", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "3"}], ")"}], "3"], FontFamily->"Arial"], TraditionalForm]]], " ", StyleBox["instead of ", FontFamily->"Arial", FontSize->14], Cell[BoxData[ FormBox[ SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "3"}], ")"}], "2"], TraditionalForm]], FontFamily->"Arial"], StyleBox["?\n", FontFamily->"Arial"], StyleBox["\nMathematica", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox[" makes teaching this topic much more enjoyable, thanks to the \ ability to quickly run through a variety of situations. The below model lets \ you quickly jump between different functions, change the type of estimation, \ alter the upper limit, and also change the number of quadrilaterals used for \ estimation. This makes it much easier to see that the ", FontFamily->"Arial", FontSize->14], StyleBox["midpoint ", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox["estimation method is more accurate than ", FontFamily->"Arial", FontSize->14], StyleBox["left ", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox["or ", FontFamily->"Arial", FontSize->14], StyleBox["right ", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox["estimation, and that by increasing the number of quadrilaterals, \ we receive a more accurate estimation of area, which helps motivation the \ discussion to the topic of infinite limits.\n\nThe fact that we can do this \ type of exploration with ", FontFamily->"Arial", FontSize->14], StyleBox["Mathematica", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox[" so quickly not only saves us time, but also affords us the \ opportunity to investigate the topic in more detail.", FontFamily->"Arial", FontSize->14] }], 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if the graph is wrong, there is no way to \ tell\\n where the student went wrong with the problem\"", StripOnInput -> False, FontFamily -> "Arial", FontSize -> 18]}}, GridBoxAlignment -> {"Columns" -> {{Left}}}, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"]}, "Row", DisplayFunction->( RowBox[{#, "\[InvisibleSpace]", #2, "\[InvisibleSpace]", #3}]& ), InterpretationFunction->(RowBox[{"Row", "[", RowBox[{"{", RowBox[{#, ",", #2, ",", #3}], "}"}], "]"}]& )]], "Output", CellChangeTimes->{{3.5093018390745716`*^9, 3.5093018734790115`*^9}, { 3.5093019072983932`*^9, 3.509301954196082*^9}, 3.5093156654478774`*^9, { 3.50931576477981*^9, 3.509315797641095*^9}, {3.50932327774427*^9, 3.5093233100525007`*^9}, 3.509323552405733*^9, {3.5093235982433167`*^9, 3.5093236446089525`*^9}, 3.5100735174047623`*^9}] }, {2}]], Cell[CellGroupData[{ Cell["Teacher perspective", "TeacherPerspectiveTitle", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.509289777495473*^9, 3.509289796817405*^9}}], Cell["\<\ No matter the class, I knew that the ability levels of my students would vary \ greatly. Even in Calculus, I found it a challenge to meet all my students at \ the level at which they were. With Mathematica\[CloseCurlyQuote]s ease-of-use \ and point-and-click menus, learners who struggle to stay on pace can excel. \ Furthermore, more accelerated learners are also encouraged by how easy it is \ to use Mathematica and can begin changing parameters, options, and \ calculations to explore new mathematical functions and ideas.\ \>", "TeacherPerspectiveContent", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.509289784343158*^9, 3.509289796817405*^9}, 3.50930171194786*^9, 3.509323159764473*^9, 3.5093235087483683`*^9}] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Help students of different abilities", "Section", ShowGroupOpener->False, CellChangeTimes->{ 3.485869517171875*^9, 3.485901236125*^9, {3.5060200202484703`*^9, 3.5060200256149054`*^9}, {3.5060201053626165`*^9, 3.5060201056746182`*^9}, {3.506020385222811*^9, 3.506020388046429*^9}, { 3.5060232764501057`*^9, 3.506023282713106*^9}, {3.509323486903184*^9, 3.5093234912216153`*^9}}], Cell[CellGroupData[{ Cell[TextData[{ "Solids of revolution with ", StyleBox["Mathematica ", FontSlant->"Italic"] }], "Subsection", CellChangeTimes->{ 3.48586975321875*^9, 3.485901236125*^9, {3.5092898903787603`*^9, 3.5092898971004324`*^9}, {3.509301975940257*^9, 3.509301977515414*^9}, { 3.5093232064441404`*^9, 3.509323208225319*^9}, {3.5093235375062437`*^9, 3.5093235413446274`*^9}, {3.509323669527444*^9, 3.509323671438635*^9}}], Cell[TextData[{ StyleBox["The below Demonstration is a great example of how ", FontFamily->"Arial", FontSize->14], StyleBox["Mathematica", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox[" can address the problem of meeting a particular student\ \[CloseCurlyQuote]s needs. This type of model could be invaluable during \ lecture presentations \[Dash] I mean, have you ", FontFamily->"Arial", FontSize->14], StyleBox["ever ", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox["been successful at drawing this type of stuff on the board?! \ \[Dash] but the interface provided is simple enough to maneuver that students \ could also explore this concept on their own without special instruction.\n\n\ This is one example of how ", FontFamily->"Arial", FontSize->14], StyleBox["Mathematica", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox[" can address a particular learning style, but there are other \ capabilities to help support other types of learners as well. 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Rarely did I find the time to use data from the \ real-world and incorporate it into a lesson. I never considered having my \ students to in-class research for data because of all the time it would take \ \[Dash] and I already was (most likely) behind schedule! However, Mathematica\ \[CloseCurlyQuote]s built-in curated data offers me real-world data instantly \ in a variety of areas (money, chemistry, weather, isotopes, etc.). My \ students get the benefit of finding large amounts of real data and instantly \ incorporating that data into a Mathematica notebook. In addition, the \ information that I pull in from Mathematica\[CloseCurlyQuote]s Computable \ data sets is the most current information. Here, we can do all sorts of \ Calculus work and keep the student on-task. And, keeping Calculus, not data \ retrieval or compilation, at the front of what we are doing.\ \>", "TeacherPerspectiveContent", CellGroupingRules->{GroupTogetherGrouping, 10000.}, CellChangeTimes->{{3.509289784343158*^9, 3.509289796817405*^9}, 3.50930171194786*^9, 3.509323159764473*^9, 3.5093235087483683`*^9, 3.509363849800517*^9, 3.509365662118745*^9, {3.509468306399032*^9, 3.50946830667906*^9}}] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Connect calculus to the real world", "Section", ShowGroupOpener->False, CellChangeTimes->{ 3.485869517171875*^9, 3.485901236125*^9, {3.5060200202484703`*^9, 3.5060200256149054`*^9}, {3.5060201053626165`*^9, 3.5060201056746182`*^9}, {3.506020385222811*^9, 3.506020388046429*^9}, { 3.5060243116986885`*^9, 3.506024316522171*^9}, {3.5093655437139053`*^9, 3.5093655470972443`*^9}, {3.509449931685669*^9, 3.5094499351684246`*^9}}], Cell[TextData[{ StyleBox["Mathematica", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox[" has access to a vast, expertly-curated database (around 10 \ trillion pieces of data, at last count) \[Dash] that you can easily access \ and integrate into a lesson. There\[CloseCurlyQuote]s no need to search for \ data; you can simply query for it directly within ", FontFamily->"Arial", FontSize->14], StyleBox["Mathematica", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox[" and start computing. The fact that this data is readily available \ is a huge bonus \[Dash] especially if you have ever tried to keep students on \ task while searching the web for data and know what a difficult task ", FontFamily->"Arial", FontSize->14], StyleBox["that", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox[" can be...\n\nLet\[CloseCurlyQuote]s walk through a lab activity \ that uses this curated data to examine population trends and their \ correlation to calculus concepts...", FontFamily->"Arial", FontSize->14] }], "ScriptCell", CellFrame->None, ShowCellBracket->False, CellOpen->False, CellChangeTimes->{{3.5003739300256195`*^9, 3.5003739716306195`*^9}, { 3.5094492604916945`*^9, 3.5094493876149426`*^9}, {3.509449435557685*^9, 3.5094496238282313`*^9}, {3.5094496980786643`*^9, 3.5094497041157866`*^9}, { 3.509449761070657*^9, 3.509449903091236*^9}, {3.5094499425093307`*^9, 3.509449968013804*^9}, {3.509450016755765*^9, 3.509450239474165*^9}, { 3.5094680496673613`*^9, 3.5094680604034348`*^9}, {3.509468215898983*^9, 3.509468216810074*^9}, {3.509468397729164*^9, 3.5094685157259626`*^9}, { 3.5094685926096497`*^9, 3.509468755232911*^9}, {3.5094687864260297`*^9, 3.5094688867100573`*^9}, {3.5094689571300983`*^9, 3.5094689934587307`*^9}, { 3.5094690612215066`*^9, 3.5094691308164654`*^9}, {3.5094692038867717`*^9, 3.5094692168540688`*^9}, {3.509543244666912*^9, 3.5095432834643607`*^9}}, Background->GrayLevel[1], CellTags->"script"], Cell[CellGroupData[{ Cell[TextData[{ "Analyzing world populations with ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Subsection", CellChangeTimes->{ 3.48586975321875*^9, 3.485901236125*^9, {3.5092898903787603`*^9, 3.5092898971004324`*^9}, {3.509301975940257*^9, 3.509301977515414*^9}, { 3.5093232064441404`*^9, 3.509323208225319*^9}, {3.5093235375062437`*^9, 3.5093235413446274`*^9}, {3.509363877252262*^9, 3.509363878804417*^9}, { 3.5093656922967625`*^9, 3.5093656956400967`*^9}, {3.5093659498435144`*^9, 3.5093659517627068`*^9}}], Cell[TextData[{ "Let\[CloseCurlyQuote]s take a closer look at how this can be done in ", StyleBox["Mathematica", FontSlant->"Italic"], ": ", StyleBox[ButtonBox["World Population Lab Activity", BaseStyle->"Hyperlink", ButtonData->{ FrontEnd`FileName[{ "S03MathematicaForCalculus", "S03MathematicaForCalculus", "Courseware"}, "WorldPopulationLabActivity.nb", CharacterEncoding -> "WindowsANSI"], None}], FontFamily->"Arial", FontWeight->"Bold", FontColor->RGBColor[1., 0., 0.]] }], "Text", CellChangeTimes->{ 3.485869857578125*^9, 3.485901236125*^9, 3.506023037322106*^9, { 3.50936595909944*^9, 3.509365998456375*^9}, {3.5095449194753613`*^9, 3.5095449202709627`*^9}, {3.5280406320204897`*^9, 3.528040663820669*^9}, { 3.5280423812934*^9, 3.5280423967489448`*^9}, {3.5280616696140203`*^9, 3.5280616956316214`*^9}}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["What\[CloseCurlyQuote]s next?", "Section", ShowGroupOpener->False, CellChangeTimes->{ 3.485869517171875*^9, 3.485901236125*^9, {3.5060200202484703`*^9, 3.5060200256149054`*^9}, {3.5060201053626165`*^9, 3.5060201056746182`*^9}, {3.506020385222811*^9, 3.506020388046429*^9}, { 3.506024642999815*^9, 3.506024645880103*^9}}], Cell[TextData[{ StyleBox["That concludes our seminar today. I hope you\[CloseCurlyQuote]ve \ learned why teaching calculus with ", FontFamily->"Arial", FontSize->14], StyleBox["Mathematica", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox[" can provide a more enriching experience for your students when \ compared to traditional methods of instruction, and that you have some new \ ideas for things you\[CloseCurlyQuote]d like to try out in your own \ classroom.\n\nDepending on your interest, the below links provide additional \ resources to help you get ", FontFamily->"Arial", FontSize->14], StyleBox["Mathematica", FontFamily->"Arial", FontSize->14, FontSlant->"Italic"], StyleBox[", find materials, or connect with other users around the world, so \ please check those out. 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