Calculator Literacy

Anyone who has ever taken a math class (especially at a college level) is aware the calculators are a very contentious topic. Should students be allowed to use them? Are they a crutch? Would they be allowed to use them in the “real world”? Some teachers allow only scientific calculators with the most basic operations. Others have an “anything goes” policy, letting powerful TI-Nspires into the classroom. Others still ban them entirely, requiring everything be done by hand. Since I will have to make the same call some day as a teacher of mathematics, the issue of calculators is one close to my heart. 

When I was in high school, I remember being allowed to use calculators and even being required to buy a graphing calculator (I want to say it was the TI-84 that was the most current model at the time). I also distinctly remember resenting these calculators because I had no idea how to use mine. Once I got to college, some of my professors actually took the time to show us how to use calculators and make them do what we needed them to— whether it was manipulating matrices or using Newton’s Method to find zeroes more efficiently and accurately than by hand. I have been attached to my calculator ever since and have ranted tirelessly about how important calculators are.

Consider this: what real world career is going to INSIST their employees do not use calculators? Sure, they will want them to know the math, but certainly calculators will be available to the employees and they would be encouraged and expected to use them. If one of the reasons we teach math is because it is so useful in life, then it seems silly and arbitrary to not allow the most ubiquitous math tool available. I was 100% on this side of the fence for a long time.

The most obvious problem with this train of thought is that it relies on people knowing math before they use a calculator. Too often in my field experience or in my work as a math tutor, I see people relying on calculators for simple operations. “What is 1/3 times 1/3?” or “What is 20 times 1/5?” gets me a blank stare and a hand slowly creeping towards their calculator. Alternatively, and perhaps even more frustrating for the student, people make order of operation mistakes when inputting things into their calculator and don’t realize it is wrong. -3^4 is NOT the same as (-3)^4, but because their mathematical foundation isn’t solid, students don’t realize that the answer they’re getting back doesn’t make sense.

So should all calculators be banned? Should we just make sure that students can do all the mathematics by hand so that they don’t have to turn to a calculator? That seems not only like an extreme overreaction, but frankly not helpful. The further in math you go, the more complicated the calculations get. If I’m trying to find inflection points of a function, I want my mental workbench focused on inflection points— not on arithmetic that I can pass off to my calculator. The question then becomes how do I let students who can appropriately use calculators benefit from them while making sure others don’t use it as a (frequently misleading) crutch?

My current thoughts on the situation would be some form of calculator literacy education. Calculators themselves are here to stay and used so widely that it would be pointless to pretend they don’t exist and ban their presence. Instead of demanding that every student does every problem by hand so that when they get to an instructor who does allow calculators they have no idea how to use one, why not educate students on how to best utilize them? If every math class spent a tiny amount of time showing the right way to use calculators to aid your solution process, we might see fewer mistakes, less resentment towards arithmetic, and better numerical literacy concerning things like PEMDAS and exponents and the like. Learning how to do the math on the calculator would only follow after learning how to do it by hand and the principles the mathematics are founded on. 

My goal as a future instructor is to help prepare my students for the rest of their lives, so it seems only logical that I would help them understand how to make their calculator their friend instead of their enemy. However, I still have a lot of mixed feelings on calculators and hear a lot different takes on the issue. How do others handle the issue of calculators?

Khan Academy in the Classroom

            Khan Academy was implemented by nine study sites (20 schools) and a research brief was done on three of these nine sites. Khan Academy is a website which includes instructional videos on math, economics, history, and art. The teachers at the study sites used Khan Academy to review material and work through the problem sets on the Khan Academy website. Some of the teachers use Khan Academy for a reversed classroom setting, where the students learn the concepts at hoe work through the problems themselves and come to class with questions. The students said that using Khan Academy helped get immediate feedback, filled in gaps of past instruction, the students started holding themselves accountable for their performance, and allowed teachers to spend more time assisting individual students. At one of the sites, during the first year of the study students were spending about 22% of their instructional time on the Khan Academy activities, but during the second year it went down to 10%. The schools at this site changed the setup of their math instruction where it is all self-paced, self-directed approach so the use of Khan Academy was at the discretion of the students. Though, with students using it for their purposes they found it was being used in a more personalized way. The benefits of this style of teaching listed above also come with some negatives. Teachers at these sites noticed there was a lack of alignment between the content to grade-level curriculum which made it difficult to utilize in the classroom. This negative also made it hard to organize the content, because there was no clearly mapped grade-level content. 

            We talked about having a flipped classroom in our Technology for Mathematics class. Overall, our class agreed that using a flipped classroom is extremely beneficial to students, but having personalized videos would be the way to go. Using websites such as Khan Academy to direct the learning of students makes it seem as though the teacher isn’t the one with the knowledge of the content, but the video is. It takes a lot of the respect away from the teacher.

Copyright

As educators and students, we hear all of these warnings about copyright, but how much can it really hurt us? I mean how many times have we actually heard of schools getting in trouble for copyright? Recently in class, we had a discussion about copyright. We went on and on about how it is bad, but with every bad, there was an exception for it to be okay. This is such a vague concept that it is hard to take too seriously. What is considered proper for educational use? What websites can we use in class? How is the proper way to have your students read an article that you, as an educator, think is appropriate? I was left with so many questions that couldn't even be answered, because of all of the exceptions. It is also hard for me to take this to seriously, because throughout my educational career, almost all my teachers would copyright. Most of the time they didn't even realize that they were doing it. I have educators that constantly copyright. Have they heard these long talks about how bad it is? I assume so. Just like any student that has to listen to these conversations about copyright, it is hard to take it seriously when your teacher telling you not to do it, is doing it themselves. Even after they preach the fact that it is bad, they still fail to take it seriously, so why should the students? It is like telling students not to smoke, but the health teacher is outside of school smoking where the students can see. If educators are going to tell students not to do something, they should at least follow the same rules and find ways to avoid copyright.

How safe are we really?

It is no secret that technology is taking over this world, but are we getting too comfortable with what we put on the internet. Last week in our technology for teachers class, out professor asked us to Google our names and see what comes up. It was startling to see what came up when I did that. I ask whoever is reading this to do the same and the results may surprise you as they did me. In this day and age we do not realize what we are putting up on the web for everyone to see. We had an assignment earlier this week to respond to this doxxing article Dr. Vestal sent us. If you are not familiar with doxxing it is when someone puts up personal information about someone else, like their address, phone number and other personal information like that. While I was responding to this article I was doing some research about computer hacking to see how often and easy it was for someone to find this information about someone. I found an article about a 15 year old who hacked the pentagon because he was bored. Obviously this is an extreme case but if this kid could hack the pentagon he could really get any information he wanted from anyone he wanted. More and more of our information is going up on the web and more and more people feel comfortable with putting it on their. I remember watching this TED talk about hacking and the speaker had his laptop out showing the crowd what he could do with it. Credit cards now have these computer chips on them and he could wave this device he created and all the information went straight to his computer within seconds.He could also hack the hotel menu on the TVs and order PPV for free. What was ever crazier was that he could hack other guests in the hotel and mess with there cable and other electronics in their room. I cannot remember the name of the talk but it was very interesting and I would recommend it. I guess it is inevitable that as technology gets more sophisticated there will be people out there trying to exploit it.