To Wolfram or Not to Wolfram

Madison D. Varnadore

8/27/2018

     Technology, if the students’ usage is regulated and monitored, can provide many opportunities for students to learn and understand the material presented to them. However, if the usage is not regulated and monitored, many students tend to use technology as a crutch and do not learn the necessary problem-solving skills. Technology can be used to further the students’ education by showing different ways of performing tasks. For example, some students learn better when they are lectured to, but others may better understand the material once they have gone through and worked problems at home. The only drawback to working problems at home is the lack of resources available to answer questions that may have come up. This is where a website like Wolfram Alpha comes in. Wolfram Alpha is a computational knowledge engine or answer engine. Possibly the simplest way to describe it would be to compare it to Google, but this is more mathematically condensed.

Now, how can we implement Wolfram Alpha when teaching and learning mathematics? When working with functions, it is helpful for students to see what is going on graphically. Implementing Wolfram Alpha when describing a function allows students to see an accurate representation rather than trying to imagine or draw the graph on their own. A more controversial action of Wolfram Alpha would possibly be the various techniques shown when solving certain mathematical problems. However, some teachers tend to dislike when students work problems differently than what was taught in class.

How do teachers feel about implementing websites like Wolfram Alpha in their classrooms? I spoke with a high school and a middle school teacher to see what they thought about Wolfram Alpha, and I asked what ways they have implemented this answer engine into their own classroom.

I first talked to a practicing 8^th grade honors mathematics teacher who had never been introduced to Wolfram Alpha. He took a few minutes to look through the site and was pleased with its capabilities. He believes that it has potential to be beneficial to the classroom, admitting that first he would need to familiarize himself with the website. I followed up by asking if he has used any similar mathematical tools in his classroom. He discussed ways that he has implemented desmos.com when discussing various functions, but none other than that. However, Wolfram Alpha also has graphing capabilities like desmos, and can be implemented in the classroom as well.

Here is a comparison of the graphing capabilities of desmos and Wolfram Alpha:

Continuing the conversation, he began discussing the opportunities available with technology. However, he believes that the use of technology needs to be monitored. He strongly believes that technology is beneficial, if students do not become reliant on it. It’s interesting that we previously discussed this reliance on technology in class. Each of us agreed that engines like Wolfram Alpha can be beneficial but can also be used as a crutch for students. He ended our discussion by saying something that resonated with me. He said “I sometimes think that good, old-fashioned thinking skills get lost in the overload of technology that our students have at their disposal. The school where I teach is very limited in what technology is available to students, and I still teach classes where there is more focus on students trying to learn fundamental skills and less on applications with technology. I think there must be a balance between teaching students how to effectively use the technology resources that are available while also teaching them to learn to think for themselves” (J. Wilkerson, personal communication, August 23, 2018).

We have often discussed this balance in class, but how can teachers find a balance if the opportunity isn’t there? Many of the readings mentioned a need for change, yet still today there are schools with limited access to technology, and therefore are reliant on lecture style teachings. In Principles to Actions, there is a list titled ‘Guiding Principles for School Mathematics’. In this list it has a section that discusses technology usage. In this section, according to the National Council of Teachers of Mathematics (2014), it states, “An excellent mathematics program integrates the use of mathematical tools and technology as essential resources to help students learn and make sense of mathematical ideas, reason mathematically, and communicate their mathematical thinking” (p. 5). If there is going to be a change from lecture style teachings to more student involved teachings, there might need to be a focus on making more technology available to rural school districts. Conversely, many schools are too reliant on technology and students lose the ability to problem solve. Finding balance is the ultimate end game, but it’s not as easy as it seems.

I wanted to receive opinions from both a middle school mathematics teacher and a high school mathematics teacher. The second teacher I talked to is a 9^th -12^th grade mathematics teacher. She was also unfamiliar with Wolfram Alpha, so she looked through the website to see what all it offered. She saw Wolfram Alpha as a great tool to use for higher level mathematics homework. She acknowledged the possibility of dishonest students using it to simply copy down the correct answer, but for others she believed it could be added instruction. With the step by step solutions, students can see where they might have made a mistake in their computation. I was interested in what she thought about implementing technology in a mathematics classroom, so I asked. She responded by saying “I am starting to use more apps like the ones with graphing calculators, and the protractor app for geometry is cool. However, I believe technology should be supplemental” (J, Harbison, personal communication, August 23, 2018). She too doesn’t want her students to become reliant on technology, but rather use technology to enhance the instruction present.

  Overall, the mathematics teachers I talked to were impressed by Wolfram Alpha. They expressed interest in using it in their classrooms and see it as a possible valuable tool for students. The only concern is the likelihood of students misusing the engine. However, with some monitoring, the tool can help students better understand the material presented in class. It can also show students different ways in which mathematics is used in everyday life. Since I do not have the knowledge an experienced teacher possesses, I enjoyed hearing about different ways these teachers implicated technology in their classrooms. I agree that technology can be extremely useful for students, and I am looking forward to finding new ways to utilize it in my classroom.

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