Published: Feb. 5, 2014

3-D graph of paraboloidSilva Chang projects her lessons from an iPad onto the board in Calculus classes.  She works out problems in different colors, asks students questions to predict next steps, and lets them volunteer answers.  Chang believes that seeing problems unfold live helps students better understand proper solving procedures.

Chang says that now, "Students expect technology," and that attitude earned her a 2013 ASSETT Outstanding Teaching with Technology Award.  She says that she switched from using chalk and dry erase boards to projecting her iPad onto the board about two to three years ago and now has "So much flexibility."  For example, when Chang uses her iPad in class to work out problems, she can actually face her students while teaching (instead of turning her back while she writes on a dry erase board).  Also, using an iPad "certainly saves time," Chang says, as she does not need to erase her work to make room for the next problem.  Instead, Chang can write out the text for word problems on her iPad before class, and then use in class time to read aloud problems and work them out with her students.  Using iPad apps such as Software Garden Note Taker HD, she can quickly bring up an x and y coordinate plane, and use her Stylus pen to drag a straight line to its intersecting point on a parabola.  After each class, Chang posts all of these PDFs of her in class lessons to D2L for her students to review.  This record enables her, too, to recall exactly which problems she had taught her students in class so that she can better write original exam questions for them.  To prevent the chance of any malfunctioning technology, Chang arrives just five minutes early for each class to make sure all technology is ready to go.  

Writing Code to Illustrate Calculus Concepts 

In Mathematica, Chang drags the cursor from left to right to increase the number of rectangles possible under the curve and illustrate Riemann SumChang writes code in Wolfram Mathematica to demonstrate more complicated surface area concepts in Calculus courses, including the use of rectangles to approximate area under a curve (Riemann Sum).  As illustrated in these images above that Chang coded in Mathematica, the user can move the cursor from left to right to increase the number of rectangles that could fit under the curve.  According to the Riemann Sum concept, the more rectangles that fit under the curve, the more accurately one can estimate the area under the curve.  Instantaneously maneuvering illustrations in Mathematica can much more effectively demonstrate a concept than would be taking the time to manually draw and erase images on a dry erase or chalkboard.

In addition to incorporating iPad apps and Mathematica images into lessons, Chang also encourages her students to use technology in their homework.  Specifically, Chang assigns her students Webassign textbooks.  These books have associated online homework problems that are slightly different for each student.  Webassign grades homework problems immediately so that Chang can more quickly see her students' results.  Additionally, Chang teaches students how to write a function in Microsoft Excel so that they can use spreadsheets to plug in different variables to a more complicated formula like Newton's Method.  She also encourages students to use the Desmos free graphing calculator website.

At the end of the week’s lessons, Chang may invite the students to to use their clickers to answer a sample question to assess their understanding of what they have learned.  This way, she can immediately anonymously display the students' results to a question, and everyone in the class can see how many students understood the associated concept.  If a significant number of students answered a question incorrectly, then Chang knows she should spend more time explaining the correct method.

Chang says that she hopes to one day become completely wireless so that she could actually walk around the room while teaching and even sit amongst students as she projects the problems that she is working out on her iPad.  Chang finds inspiration in the Khan Academy's methods of using videos with different colors for different steps to explain math problem solving methods.  Eventually, depending on the results of ongoing trials at other schools, such as at Harvey Mudd College, she may consider using the teaching concept of a flipped classroom, in which students would spend their homework time watching videos that demonstrate new methods.  Then, in class, students would practice working out problems themselves, this time with the professor present.  

Ultimately, Chang strives to teach her students to understand larger mathematical concepts, more than just finding the correct numerical answer for a test question.  

Written by: Moira McCormick