Using discrete examples in the beginning of integration - Mathematics Educators Stack Exchange most recent 30 from matheducators.stackexchange.com 2022-01-27T02:12:31Z https://matheducators.stackexchange.com/feeds/question/14669 https://creativecommons.org/licenses/by-sa/4.0/rdf https://matheducators.stackexchange.com/q/14669 4 Using discrete examples in the beginning of integration Jasper https://matheducators.stackexchange.com/users/667 2018-10-15T18:01:38Z 2018-10-15T18:59:38Z <p>In Germany, one usual example to start teaching about integrals is to look at a simple (piecewise constant or with constant slope) functions that make up a water flow vs. time diagram and ask about the total flow during a given time span. This leads to the idea that the area under the curve is of interest and represents exactly the desired quantity. </p> <p>I was thinking about a discretisation of this example because my dog requires pain medication and I plotted a daily dose vs. day graph. This is basically the same as the water flow diagram, but already with discrete steps, probably leading to the "rectangular stripes" method. </p> <p>Is there any research or experience about this approach? </p> https://matheducators.stackexchange.com/questions/14669/-/14671#14671 2 Answer by Nick C for Using discrete examples in the beginning of integration Nick C https://matheducators.stackexchange.com/users/470 2018-10-15T18:59:38Z 2018-10-15T18:59:38Z <p>Some of my students have a real a-ha moment when they first graph the integral of a constant function (using the area-so-far concept), seeing a new line of non-zero slope emerge. Then having them graph piecewise constant functions reinforces the <em>height</em> <span class="math-container">$\rightarrow$</span> <em>slope</em> connection they will depend on when they learn the short-cut rules for antiderivatives.</p> <p>No research to speak of here, but I think beginning with something simple and concrete like this is an excellent idea.</p>