Mate Wierdl is a professor of mathematical sciences at the University of Memphis and a frequent commenter on the blog.
He writes:
“In math education, there’s not a single thing computers do that is necessary for a great math class. Not one. Occasional calculations? A $5 calculator does everything needed, and even at the university, a $30 Casio can even do symbolic calculations so it does more than needed. But of course, all calculations can be done by hand.
“There’s a free software called Sagemath. It does all possible math and statistics (and chemistry, etc) related calculations, visualizations. It can be used online or can be installed on any computer. At the university, I show it to the kids where it can be accessed. That’s all they need. It’s simple to use, and it has a freely available user guide. At home or library or computer lab, kids can use it as much as they want to. They can use it to check the solutions to all their home work, or they can do experiments with it.
“But whatever Sagemath can do has nothing to do with great math teaching. Great teaching is done by great teachers, so there is no choice between tablets and teachers when it comes to students’ need.
“If teachers’ pay doesn’t keep up with inflation, the quality of teaching will decline. If you don’t use computers in classes, quality of teaching doesn’t decline.
“So that’s where my priorities are: in great teaching. I believe, that’s very much in the interest of students, isn’t it?
“Before making yet more assumptions about my motives or state of mind, also consider the fact that I maintain computers, email and web servers, various free software, and each year I evaluate the newest software offerings that are supposed to help teachers in their work.
“Without exception, they are designed to take over a teachers’ job by distorting what math education is supposed to be. Kids, and that includes my daughter in 10th grade and my college freshman son, learn to press buttons, do calculations, enter solutions online with cumbersome interfaces instead of learning real math—math that would be useful and interesting for them.
“My daughter comes home every day and demands me to explain what she really learned in math because in class she just “learned which buttons to push to get the answers.”
“This pragmatic push to perceive math as a subject to get correct answers via calculations truly destroys math education.”
Diane Ravitch's blog 
SENSATIONALLY BEAUTIFUL!!!
Are we to be a nation of robots or a nation of thinkers?
Anthropologists have stated that when a species becomes too specialized they disappear. We are well on the way to that.
Romans became slaves to their slaves and they started their slide into history.
Technology has become the slave to which we are becoming slaves. We can use it for our benefit or become a slave to it. The choice is ours – perhaps. Unless the makers of technology hoodwink the public as is being done by so much of our corporations.
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Robots.
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It’s going on in the social sciences as well. Not only can my students look up answers on the Internet, they share answers with each other. So classwork and homework become meaningless.
Discussion in class, meaningful dialogue, thoughtful research. All out the window.
Thank you technology.
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“Discussion in class, meaningful dialogue, thoughtful research. All out the window.”
All things a computer cannot do. All things that actually require students to think rather than regurgitate!
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Isn’t it possible, though, to leverage technology to make the classroom environment more welcoming of robust discussions? For example, to design an activity where students get answers and collect data as a prep activity for a more active debate or discussion in class? Why does technology necessarily preclude the things you are mentioning?
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Amen!!!!
As a science teacher I concur; there is nothing that software and the web offer that really teaches kids any of the necessary skills in physics and chemistry. Technology can make things easier, more accessible, in greater volume/magnitude or frequency, but IT CANNOT substitute for a knowledgeable human explaining things to students and modifying instruction to each students needs.
My son in our public school uses Khan Academy for Algebra 1, for homework. While the lessons are well-designed the software only explains things in one-way, one-method, one-mode, and is NOT adaptable to the different ways by which problems can be solved. If my son makes one mistake the program makes him go back to the beginning and redo questions he’s already mastered. The program treats him like a machine and forgets he’s human and does not need to be retaught to the n-th time whenever a mistake is made. Nor, will it let him jump ahead when he already knows the next topic.
No, Khan Academy is step-by-step…..ad-nauseum, teaching our students as if they are clones.
But hey, run a charter school, place lots of kids in a computer lab and “teach” them Algebra with Khan Academy, and then wonder why they never mastered skills and later on hate math. Yup, that makes a lot of sense (to some people’s profit margins).
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Math professor here with a few extra thoughts on this. There is a false dichotomy lurking here that bothers me.
What great teachers in any subject do is set up what Ken Bain called a “natural critical learning environment” where students work on challenging, authentic, interesting tasks and, by working on these with the support of a teacher and peers, construct knowledge of the subject at hand. Great teachers set up and maintain this environment, pay attention to the needs of their students and the demands of the subject, and give support to students as they work to provide evidence that they have mastered the ideas of the subject. This is what great teaching and a great class look like, in any discipline.
It should be obvious to those of us who teach, just by looking around at what goes on sometimes in our schools, that technology does not by its mere presence push classes or an instructor’s teaching closer to greatness. Very frequently technology drags it away from greatness with alarming speed and strength. Very frequently great teaching has to struggle past technology to create the natural critical learning environment we want. Technology can absolutely ruin education sometimes and it’s wrong to think that tech improves teaching just on the face of it.
But what a great teacher does is look at technology in terms of how it can be leveraged to make learning great. And I would argue that in mathematics at least, quite often technology is really an essential ingredient in creating an environment where students explore, try, fail, and ultimately learn mathematics in a way that lasts.
Example: Students are learning about parabolas in an algebra class and the meaning of the parameters in the general form y = a(x-b)^2 + c. A class on this topic can be done entirely without technology except for pencil and paper and chalkboard. Or, you can use Desmos to have student experiment with this and then discuss their results: https://www.desmos.com/calculator/ejh9xa67f1 Which method makes the math class closer to greatness? If a teacher is committed to great teaching and great learning, would she eschew the use of technology in this case?
Example: My discrete structures students right now are learning about graph theory. I can teach this class without technology whatsoever, and I am confident I could make it at least very good if not great. On the other hand, Sagemath (mentioned in the article) allows me to create actual graph models using real data, and then visualize and probe the model for information and insight. Again, what makes the class “greater” — using technology or not using it?
So I don’t think it’s right to say that technology has nothing to do with great teaching. Great teaching strives to create a certain kind of learning environment and sometimes the use of technology — carefully thought through, of course, and skillfully used — makes the learning environment so much better that great teaching and great technology use are inseparable.
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These are all salient points. I think you would also agree that any technology used to teach should mean that the student came away with a richer experience. Unfortunately, many are so enamoured of some programs that they are blind to their effectiveness or lack thereof. It’s hard to admit when you work hard at something and it flops.
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Great god we’ve got grating greatness in this great crowd except for this ungrateful common tater. A grating post on greatness, ay ay ay!
(just half way funnin ya, Robert)
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Robert: “So I don’t think it’s right to say that technology has nothing to do with great teaching.”
Robert, the question is what makes a great math class: the teacher or technology? Despite what we are lately told about personalized learning, technology only enhances a math class, but we cannot rely on technology to make a class great.
The context of my remarks was to emphasize the priority of the teacher. If, in a school, teaching needs to be improved, take care of the teachers first, and then, if there’s left over money, think about obtaining some hardware. (I doubt there’s any need to spend money on software, since great ones are available for free.)
Here’s a perfect (imo) “applied” math class with proper use of technology (in this case, calculator). Clearly, the main actors are the kids and the teacher.
Here is a similar class without any apparent use of technology—I don’t think the experience is lacking.
Here’s a video of a TED talk by the teacher from the videos. It’s clear that to accomplish the three goals he sets for the general population, technology is secondary (but can be helpful).
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“And I would argue that in mathematics at least, quite often technology is really an essential ingredient in creating an environment where students explore, try, fail, and ultimately learn mathematics in a way that lasts.”
This is where we differ. Technology in math in K-12 and in most college courses is not essential. Convenient, but not essential. The explorations you are talking about can be done by hand, if nothing else is available.
It’s great to be able to use some programs exactly as you describe it, and many of us do experiments in our own research using software. But essential? The inventors of calculus (Newton, Leibniz, Gauss, etc) clearly didn’t need any technology and Paul Erdős, one of greatest graph theorists, didn’t make any use of computers either.
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The NCTM Technology Principle got this right, to me. Technology needs to influence how we teach as well as what we teach. Log and trig tables are not needed now. Computation support for doing real world modeling with messy numbers is necessary. Online and free software like Sage, Desmos, GeoGebra and more can allow students to become mathematical makers. Learning to program (Logo, Scratch, Processing, Python…) is a powerful context for and application of mathematics. Using dynamic geometry and algebra software to discover your own conjectures is now possible. Furthermore, the software can support students who can’t do in their head what successful students could do before. Computers also offer opportunities to share, give peer feedback, publish student writing and remix in ways that promote creativity in the classroom.
I like that the author is against technology as lecture replacement, but they are missing out on the opportunities that technology allows.
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“Computation support for doing real world modeling with messy numbers is necessary. ”
I don’t see how this is needed to make students understand math concepts or even applications of math. Let’s not equate math with calculations—especially with messy calculations.
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I attended University of Memphis several years back and earned a second undergraduate degree in mathematical sciences after having been an elementary school teacher before I moved to Tennessee. When I started teaching I was terrible at math, and it was a goal of mine to fix that.
Mate came in and taught for my Calculus II professor once and he was so awesome that I went to him many times with questions. I know he wouldn’t remember me…. but Mate: I’m so glad you are a reader of this blog and that you were part of my education and one of the people who shaped my understanding of mathematics… which in turn shapes my students. I learned to love math and to even feel creative while doing it when I was a student at the U of M. I ditched elementary ed. and went to high school so I could teach math all day long!
And I agree wholeheartedly!
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🙂 I actually do like to hear back from students about how they ended up doing in life.
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Where do we find “great math teaching”? How will we know it when we find it?
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That will depend on whether the teacher and the student reach the same point at the same time. I guarantee no rubric of evaluation can delving such a phenomenon.
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“Spoiled Dinner”
Math is like the entrée
But tech is like a snack
Which sometimes holds you over
But sometimes sets you back
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I’ve hit the limit on nested replies, so I’ll start at the top here with a reply to Mate’s response to my comment. (Make sense?)
“Robert, the question is what makes a great math class: the teacher or technology?”
And I am saying that this is a false dichotomy. The teacher alone does not make a class great. Nor does the technology alone. What makes a class great is the _learning environment_ of the class, which is a function of both the teacher and the tools that he or she selects for the class, and the ways in which he or she puts them to use. A “great teacher” can create a classroom environment that is good enough, but which would be much better if certain technologies were involved in the right ways.
Why would I, as an instructor, choose not to incorporate technology into my class if I know that — when properly used — that technology will result in a better learning environment for my students?
Also:
“Technology in math in K-12 and in most college courses is not essential. Convenient, but not essential. The explorations you are talking about can be done by hand, if nothing else is available.”
This is like saying, the technology that we see in modern operating rooms is not essential because everything in a surgical procedure can be done using pre-1980 technology, if nothing else is available.
My discrete structures students could hand-draw graphs for an hour and try to guess at the relationship between the maximum degree of a vertex and the graph’s chromatic number. Or they could go to Sage and enter in four lines of code that will produce a large data set within milliseconds and then spend their time reasoning instead. Do they _have_ to code this up? Of course not. Does it create a better learning environment for them if they do? I would argue absolutely yes, to the point where withholding technology form them is tantamount to making them write with their opposite hand.
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“Why would I, as an instructor, choose not to incorporate technology into my class if I know that — when properly used — that technology will result in a better learning environment for my students?”
Because the technology may not be available.
The dichotomy between teacher and technology arises exactly because many K-12 schools are forced to make a choice whether to support technology or teachers. Nowadays, even poor schools are made to opt for technology, and are willing to spend money on computers, software while citing budget constraints when it comes to teachers’ raises.
At my university, I’d have a hard time teaching your kind of graph theory course since many kids don’t have laptops—they simply cannot afford them. Still, good teachers can and do work around this problem.
Note that the main issue was around technologies that are supposed to take over teachers’ roles: variants of MOOCS (so online courses with grading capabilities) and personalized environments.
I agree with you, that I’d be a fool not to tell my students about Sage—I just can’t have them use Sage in the classroom regularly unless I am assigned one of the 3 classrooms equipped with computers. Despite this shortcoming, I doubt our students have any disadvantages in generic courses like calculus or algebra—and the same applies to K-12 math courses.
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Good stuff, btw: http://chronicle.com/blognetwork/castingoutnines/2012/12/21/we-need-to-produce-learners-not-just-students/
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