Idealism and Reality in Math Tech? WAKE UP!

Feb 25, 2008 by

I usually don’t use this space to rant about other blog posts, but I really have to do it in this case.
I am a reader of Dangerously Irrelevant (which is geared towards K-12). This week, their guest blogger is writing about mathematics at the high school level. See today’s post entitled “Idealism and Reality in Math Technology

Jason Dyer (guest blogger) says that there are three problems and implies that they are unsolved. I don’t disagree that these are problems, but I do disagree that they are unsolved.

Problem #1: Difficulty in working with Equations on a Computer
Solutions: Download MathType (download the 30-day trial, it becomes MathType Lite after 30 days), use a screenshot to share your equations, use Jing (or a myriad of other image-embedding programs) to embed the image of the equation in HTML, like this:

My calculus students (most of them 19-year-olds, some of them dual-enrolled high school students) are doing just fine with this. It’s not hard. You can also scan or take a picture of handwritten work, take a screenshot, and embed the image using HTML! How many of your students have cameras on their cell phones? Well, here’s a productive use for them. You can share diagrams (from any program or file type) using Jing images.

Problem #2: Students 3.0

I’m not sure how the acceptance or non-acceptance of graphing calculators stops people from using Internet applications. Do you mean that they need to be able to share the results of a calculator online? One easy way is to use emulator software (TI-SmartView, TI-emulators, Casio emulators, etc.).

And … hello …. how many tutorials that TEACH YOU how to use graphing calculators do you find on the Internet? (here’s a bunch of tutorials from my department’s Calculator Help Page) At the college level, we generally pick some “entry-course” in which we teach how to use a graphing calculator and we integrate these new skills throughout the course. After that course … YES, we expect students to know how to use their graphing calculator. We’re NOT going to spend three class hours in every math course teaching basic graphing calculator skills, just as we’re not going to review other material that we consider “prior knowledge.”

Have you guys seen Wolfram Demonstrations? Demos with Positive Impact? Explore Learning Gizmos? NLVM? AMSER? MERLOT? If Wolfram Demos doesn’t convince a math teacher that it’s time to start using the Internet, then you’re right, there’s no hope.

Problem #3: Sometimes there really IS only one right answer

Heard of online homework? (WebAssign, MyMathLab, etc.) Each student gets a different algorithmically generated problem with their own unique right answer. When students go to the message board for help, they have to share what their problem was and what they tried to do so that another student can help them. Other students weigh in with tips for doing the problems. Sure, you aren’t going to have a thread with 100 posts for one problem, but it’s not unusual for 4 or 5 students to comment on a single problem with their strategies. Last week I had a thread with 21 posts on one problem. That’s not too shabby.

Now, I know that you probably can’t assign online homework for high school students, but what’s to stop you from using it and visiting a computer lab twice a week so that students can work on their own individualized problem set? If all you do is collect handwritten homework, it’s likely they are just copying each others work in the hallways (at least that’s what they tell us they’ve done in High School when they get to College). Plus, on message boards, you are less likely to have the “one student dominates the discussion” problem. Students with questions get to ask in a non-threatening environment, and students get to share the multiple ways they get to an answer.

How this week will roll? I doubt you can think of a problem that we (in the online math community) haven’t found a solution too. Maybe we all just need to communicate our needs and solutions better between K-12 and higher ed.

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  1. Jason Dyer

    #1: Let me just save this for tomorrow; it’s not so much the rendering of equations as working with them in the fluid sense you can get with pencil and paper.

    #2: This has to do with buried ideology. The anti-graphing calculator people can also be referred to as the “students should suffer and suffering is good” camp.

    I don’t think colleges should need to teach graphing calculators, no. I was making the point that many high school teachers don’t realize that.

    3: I’m aiming more at the “collaberative wiki” idea here which is supposedly The Future. Online homework is a different thing. (Well, sort of, there’s a limited-collaberative thing that could work, but I’ll wait for my full post to address that.)

  2. RolandOD

    I’m following this conversation from Dangerously Irrelevent and am enjoying the fact that others are pointing a finger at math department. I know they, I’m one of them, are difficult to move. I think there are more basic issues with a willingness to look at pedagogy than a willingness to adopt technology. Most math teachers who are unwilling to look at technology are unwilling to look at any mode other than present examples through lecture, practice, answer questions on the board. A way out mode might be to let the students work in groups and then repeat the previous process. Have you ever tracked the level of thinking in most math classrooms, it is almost exclusively lower level recall quesions. How do we get math teachers to understand that they must change their approach to such a basic issue?

    I know that this issue is off track to a certain extent, but i think they are incredibly entwined with each other. Once a teacher is willing to look at their own instructional approach and make refelctive changes then they will more easily adapt new technologies or old ones that are effective for that matter.

    I work with teachers in KY and have sat in classes where one or two questions out of thirty were of DOK level 2 or higher. When the teachers were presented this information, they respond, “Oh I think I asked more than that,” or “well I couldn’t get the students to respond to anything.”
    So it doesn’t surprise me that there are teachers unwilling to use a graphing calculator or wiki to get students thinking, creating, sharing, observing when they aren’t doing it with pencil or paper either.

  3. David

    I can’t accept the notion of web-based math homework. Math homework should be corrected by human beings. A computer can check whether an answer is correct, most of the time, if the student can master the arcane syntax. It cannot explain why an answer is incorrect. It cannot distinguish between an error in calculation and a conceptual mistake. It cannot tell if a correct answer was found by an incorrect or incomplete procedure. It cannot assess a student’s ability to write a clear mathematical argument using correct notation.

    I have observed that more and more colleges are using web homework instead of hiring paper graders. In my opinion they are stealing money from students. They are charging a fortune for tuition and they ought to offer an education, not outsource it to an electronic idiot-savant.

  4. Maria H. Andersen

    David: Thanks for your comments. In an ideal world, all teaching would be one-on-one. But in our world, it is not feasable, so we teach in groups of anything up to 200 students (not that anyone thinks that is ideal.

    I don’t know any community college instructors that have ever had “hired paper graders.” Many instructors start their careers grading homework by hand, and then quickly realize that it is a waste of time – many homework assignments are just copied off of someone else’s paper, out of a solution manual, out of an instructor’s edition of the book, or out of the back of the book – there’s little you can do to stop it. Plus, most of the students just cram their papers back into their bags (or throw them away on the way out the door). So all that time and energy is usually just put towards a lost cause for all but the best students. So, after a few semesters of that, you just stop collecting homework.

    It’s not so much that we’re replacing hand-graded homework, as that we are actually holding students accountable to DOING homework again. If the colleges would like to hire graders, and can do it without a significant hike in tuition, I don’t think there’s a soul among us who wouldn’t jump at that.

    Many of the homework systems we use now have WYSIWYG editors (what you see is what you get) where you simply click on a fraction button and you see a fraction – there is no arcane syntax and no complicated LaTeX involved.

    Granted, the programs cannot tell a student why an answer is incorrect (… yet…), but the other students and the instructor can help that student if there are message boards set up for the class. This “having to think about why an answer is wrong” vs. the “ask the instructor to tell me why it is wrong in class” fosters metacognitive skills – a skill that our students sorely need improvement on.

    Many of the programs also ask for students to submit their answers in steps … and these are improving with every iteration. Newest versions of software now contain the ability to grade graphs.

    What I see as the most significant change, is that our students now continue to work on a problem until they figure out how to do it correctly. With graded homework, this was never the case. A student would make an attempt, and then stop trying – figuring the instructor would do it for them in class. I wholeheartedly believe that the students are learning valuable skills from having to correct their own work and think about their own mistakes – they are NOT without help. Help is just a click and a sentence away on the message board – I sometimes see a string of messages posted at 1am – when I can’t be avaialable to help them. These students are learning in that critical time period right when they realize that there is a gap in their knowledge.

  5. Maria H. Andersen

    P.S. Tuition at my college is currently $67 for one credit if you are an in-county student. $145 per credit for out-of-state.

    16 credits each for 2 semesters would run the student $2144 + fees and books.

    Not everyone is charging an arm and a leg for tuition.

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