As a math teacher, it’s easy to get frustrated with struggling students. They miss class. They procrastinate. When you take away their calculators, they moan like children who’ve lost their teddy bears. (Admittedly, a trauma.)
Even worse is what they don’t do. Ask questions. Take notes. Correct failing quizzes, even when promised that corrections will raise their scores. Don’t they care that they’re failing? Are they trying not to pass?
There are plenty of ways to diagnose such behavior. Chalk it up to sloth, disinterest, out-of-school distractions—surely those all play a role. But if you ask me, there’s a more powerful and underlying cause.
Math makes people feel stupid. It hurts to feel stupid.
It’s hard to realize this unless you’ve experienced it firsthand. Luckily, I have (although it didn’t feel so lucky at the time). So here is my tale of mathematical failure. See if it sounds familiar.
Thanks to a childhood of absurd privilege, I entered college well-prepared. As a sophomore in the weed-out class for Yale math majors, I earned the high score on the final exam. After that, it seemed plausible to me that I’d never fail at anything mathematical.
But senior spring, I ran into topology. A little like a bicycle running into a tree.
Topology had a seminar format, which meant that the students taught the class to one another. Twice during the semester, each of us would prepare a lecture, then assign and grade a homework assignment. By reputation, a pretty easy gig.
My failure began as most do: gradually, quietly. I took dutiful notes from my classmates’ lectures, but felt only a hazy half-comprehension. While I could parrot back key phrases, I felt a sense of vagueness, a slight disconnect—I knew I was missing things, but didn’t know quite what, and I clung to the idle hope that one good jolt might shake all the pieces into place.
But I didn’t seek out that jolt. In fact, I never asked for help. (Too scared of looking stupid.) Instead, I just let it all slide by, watching without grasping, feeling those flickers of understanding begin to ebb, until I no longer wondered whether I was lost. Now I knew I was lost.
So I did what most students do. I leaned on a friend who understood things better than I did. I bullied my poor girlfriend (also in the class) into explaining the homework problems to me. I never replicated her work outright, but I didn’t really learn it myself, either. I merely absorbed her explanations enough to write them up in my own words, a misty sort of comprehension that soon evaporated in the sun. (It was the Yale equivalent of my high school students’ worst vice, copying homework. If you’re reading this, guys: Don’t do it!)
I blamed others for my ordeal. Why had my girlfriend tricked me into taking this nightmare class? (She hadn’t.) Why did the professor just lurk in the back of the classroom, cackling at our incompetence, instead of teaching us? (He wasn’t cackling. Lurking, maybe, but not cackling.) Why did it need to be stupid topology, instead of something fun? (Topology is beautiful, the mathematics of lava lamps and pottery wheels.) And, when other excuses failed, that final line of defense: I hate this class! I hate topology!
Sing it with me: “I hate math!”
My first turn as lecturer went fine, even though my understanding was paper-thin. But as we delved deeper into the material, I could see my second lecture approaching like a distant freight train. I felt like I was tied to the tracks. (Exactly how Algebra 1 students feel when asked to answer those word problems about trains.)
As I procrastinated, spending more time at dinner complaining about topology than in the library doing topology, I realized that procrastination isn’t just about laziness. It’s about anxiety. To work on something you don’t understand means facing your doubts and confusions head-on. Procrastination pushes back that painful confrontation.
As the day approached, I began to panic. I called my dad, a warm and gentle soul. It didn’t help. I called my sister, a math educator who always lifts my spirits. It didn’t help. Backed into a corner, I scheduled a meeting with the professor to throw myself at his mercy.
I was sweating in the elevator up to his office. The worst thing was that I admired him. Most world-class mathematicians view teaching undergraduates as a burdensome act of charity, like ladling soup for unbathed children. He was different: perceptive, hardworking, sincere. And here I was, knocking on his office door, striding in to tell him that I had come up short. An unbathed child asking for soup.
Teachers have such power. He could have crushed me if he wanted.
He didn’t, of course. Once he recognized my infantile state, he spoon-fed me just enough ideas so that I could survive the lecture. I begged him not to ask me any tough questions during the presentation—in effect, asking him not to do his job—and with a sigh he agreed.
I made it through the lecture, graduated the next month, and buried the memory as quickly as I could.
Looking back, it’s amazing what a perfect specimen I was. I manifested every symptom that I now see in my own students:
- Muddled half-comprehension.
- Fear of asking questions.
- Shyness about getting the teacher’s help.
- Badgering a friend instead.
- Copying homework.
- Excuses; blaming others.
- Anxiety about public failure.
- Terror of the teacher’s judgment.
- Feeling incurably stupid.
- Not wanting to admit any of it.
It’s surprisingly hard to write about this, even now. Mathematical failure—much like romantic failure—leaves us raw and vulnerable. It demands excuses.
I tell my story to illustrate that failure isn’t about a lack of “natural intelligence,” whatever that is. Instead, failure is born from a messy combination of bad circumstances: high anxiety, low motivation, gaps in background knowledge. Most of all, we fail because, when the moment comes to confront our shortcomings and open ourselves up to teachers and peers, we panic and deploy our defenses instead. For the same reason that I pushed away topology, struggling students push me away now.
Not understanding topology doesn’t make me stupid. It makes me bad at topology. That’s a difference worth remembering, whether you’re a math prodigy, a struggling student, or a teacher holding your students’ sense of self-worth in the palm of your hand. Failing at math ought to be like any failure, frustrating but ultimately instructive. In the end, I’m grateful for the experience. Just as therapists must undergo therapy as part of their training, no math teacher ought to set foot near human students until they’ve felt the sting of mathematical failure.
This article originally appeared in Math with Bad Drawings.
Using technology in the classroom is one of those issues that makes it easy to be a fence sitter. It’s difficult to be 100% for the use of educational technology all of the time, when there are so many convincing arguments against it. Most teachers find a happy medium with technology—it’s useful in some situations, but a distraction in others.
This great article on Huffington post offers an example of a kindergarten classroom where young learners use technology naturally and in authentic ways. The article also goes on to discuss the problems many pediatricians have with technology use by young children, such as excessive screen time, which can lead to poor sleep habits. In addition, doctors worry that children who use devices at a very young age become more focused on learning to select and swipe than on developmental processes, like handwriting and shoe-tying.
Technology gives children the ability to learn in ways their parents and grandparents never had. Today’s learners have immediate access to answers and research. Yet, that immediate access is changing the way students think about work and how they feel emotionally. We’ve put together a list of some the pros and cons that surround the technology in the classroom debate.
Pros of Technology in the Classroom
- Data and analytic reporting: Apps and platforms offer teachers ways to combine all the information they might need to know about a student—title I status, attendance history, performance on quizzes, English language proficiency, participation in special education. With this information, teachers can easily see how their students are preforming as a whole class, as a subgroup, and as individuals, and can provide intervention as needed. Most edtech apps include easy to use reporting features, so that assessment data can also be shared with administrators and parents.
- Just in time information: This article from Computerworld explains how just in time learning is helping cooperate workers learn what they need to in order to solve immediate problems, rather than siting through entire classes full of information they may not ever use. The same goes for classroom learning. Edtech is allowing teachers to see where students may be missing particular pieces of understanding and to then target lessons just for that knowledge. Instead of sitting through hour-long lectures of material they’ve mostly mastered, technology is allowing students to learn what they need, when then need it.
- Differentiated instruction: Educational apps allow for students to progress at their own pace. Many are adaptive, meaning that questions and problems will get easier or more difficulty, depending on student performance. Programs can adjust to meet students at their precise learning levels. In addition, the multitude of apps and software available means that students in the same classroom might be using different systems to learn similar material, depending on their interests and learning.
- Different learning modalities: Incorporating technology into the classroom means that students have exposure and access to different ways of learning. Maybe some students do thrive in a lecture environment; others might be great independent learners, who can gather information from educational software. Giving students the choice of different ways to learn means they’ll likely explore and try different techniques, and in the end, learn the best strategies for themselves as individual learners.
- Assistive tech for special needs: We’ve covered apps specially designed for special education teachers and students in the past. Educational technology makes it possible for students with special needs to thrive in academic settings. From adaptive word processor apps to programs that speak for children who struggle with language, technology allows students to communicate and be involved with their teachers and classmates.
Cons of Technology in the Classroom
- Replacing teachers: Many tech enthusiasts roll their eyes when people voice their concerns that educational technology is a way to replace teachers in the future. But do their concerns lack validity? You don’t have to look too far in the past to find instances of technology replacing workers: the auto industry, agriculture, and manufacturing industries have all mechanized many parts of their process, laying off workers in the process. While few people think that teachers will become obsolete, the newest advances in edtech are powerful enough to deliver content, assesses, and set students on a new course of learning, all without teacher intervention. What does that mean for the future of teaching?
- Distracting: This is probably the number one worry of teachers who consider implementing classroom technology: the concern that students will be too busy tweeting and Snapchatting to pay attention to the lesson. Students’ innate curiosity, coupled with their tech savvy could lead to more online socializing in environments where devices are easily accessible.
- Easier to access others’ work: Plagiarism has been plaguing teachers forever. Students today can easily access essays, reports, class notes, tests, etc. online, making it that much more difficult for teachers to know if the work their students hand in is original. Though there are tech tools to help teachers discover if the work is plagiarized, no system is perfect.
- Disparity of access outside of class: Not all of our students have access to technology tools outside of the classroom. Yes, the library is an option, but there is often a wait for computers connected to the Internet, and even then, you can’t download apps and software onto public computers. Assigning technology use in the classroom is fine if all students have access to the device. But when edtech programs are considered for homework, at home intervention, or even flipped learning, student access to the Internet must be considered.
- Privacy: Privacy of student information and data is enough of an issue to keep many teachers and schools away from implementing any sort of broad reaching tech initiatives. Apps and platforms have come a long way in improving their privacy measures, especially where students are involved, but is it enough to convince schools that it’s worth the potential risk? Student data is invaluable within the classroom walls, but can teachers feel safe that that is where the information will stay when they use edtech apps?
There’s no right or wrong side of this debate. Educational technology has its plusses and minuses. It’s up to teachers, administrators, and district personnel to decide whether the good outweighs the bad. We’d love to hear where you stand on these issues.
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