Archive for the ‘Neuroscience and Learning’ Category

Students and Optimism Bias

In a nutshell, optimism bias is the tendency to make overly positive assumptions.  This serves us well (giving us courage to try new things) but it also leads us astray (viewing the future as rosy despite the bad choices we are about to make).  There’s an excellent article in Time Magazine called The Optimism Bias that I highly recommend reading before you go any further.

Apparently our brains (most of them) are “hardwired for hope.”  When we remember the past, we omit details and our recall contains errors, but when we imagine the future, we tend to construct fiction that is dramatically better than the likely outcome.  This is, for example, why New Year’s resolutions are so intoxicating to us – we construct a “future me” that is thinner, healthier, happier and we can literally see ourselves living that life (even if past experience with resolutions would tell us otherwise).

Consider the optimism bias of our students.  In particular, consider the belief that things will turn out better at the end of the semester.  For example, how many of you have had students who fail exam after exam, but believe that in the end, their grade will come out okay?  There is no indication from the instructor that this will be the case. In fact, the syllabus clearly states the likely outcome by including a grading scale, but the students’ optimistic prognosis keeps them from seeking help when help could still be afforded.  As soon as final grades are published (or sometimes a day or two before the final exam), these students suddenly face reality and are angry that their vision of success is not what actually happened.  Their optimism bias has just met reality and they are usually pissed.

Another classic case of optimism bias is evident in online classes.  Anyone who has taught an online course knows that some students are just not realistic about the commitment to learning.  A recent column in the Chronicle of Higher Ed, called Improving Online Success, by Rob Jenkins tackled the issue from the point-of-view of time-management.  I’ve been teaching online Calculus since 2007, and I don’t think the problem is as easy as time-management.  That’s just what administrators tell themselves so that they can optimistically see themselves fixing the problem.  The real underlying problem is optimism bias.

Students, especially those at 2-year colleges, believe that they are supermen and superwomen, that they will be able to work 40+ hours a week, take care of their families, and go to school full time.  When they sign up for traditional classes, they come face-to-face with the fact that they cannot simultaneously be going to work AND attending a live class.  They cannot be simultaneously taking care of children AND attending a live class (without making childcare arrangements).  With online classes, these students never face this discordance.  They optimistically believe that they will somehow “find the time” to attend the class (even if it is not reasonable).

I used to have students fill out a “study schedule” at the beginning of each semester, where they filled out the blocks of work hours, class hours, family hours, sleeping, eating, etc.  This was to help them see that there was precious little “study time” left.  But this never seemed to have any effect.  The students with the least study time in their schedule still believed that “it all works out in the end.” Lessons in time-management did nothing to bring their imaginings in line with the reality of the need for study time.

For the students who take my online Calculus classes every summer, I meticulously track their participation metrics for the first two weeks.  I call every student, starting with the ones with dismal participation metrics – I walk them through which buttons to press, I ask them if they are sure they have enough time for the class (especially when they’ve logged in only once in 7 days), but they are always optimistic.  ”Well,” they say, “it was just that this week was so busy. Next week will be different.”  Next week is rarely different.

Rather than a course on time management or how to “succeed” in online classes (neither of which would solve the optimism bias issue), I would prefer that we simply offer a 1/2-credit online learning experience as a precursor to the regular semester.  These would be short 2-week “topics” courses, something the professor would like to teach but is not already part of a regular course (e.g. fractals, data visualization, vegetable gardening in cold climates, vampires in literature, etc.).  This course could include advice on time management, but its real purpose would be for the student to prove to themselves that they can (or can’t) learn something (anything) new using an online format.  The topics courses should be rigorous enough to give the students a real taste of online learning (reading assignments, discussion board participation, assignments, and assessments) .  After all, if you can’t cut it in a 2-week online course, you’re not likely to make it in a lengthier and more difficult course.  If a student fails an online topics course, they should not be allowed to take higher-credit online courses.  If, next year, the same student claims they are now ready for online learning, let them take another 2-week topics course to prove it.

I’m sure you can think of dozens more cases of optimism bias in Academe, including cases of professors with optimism bias.  For example, I spend the weeks before classes dreaming of wonderful assignments and projects I can give in my math classes while glossing over the fact that every extra assignment will take time to develop and time to grade.  Only several semesters of past experience grounds me to the reality that I probably can’t change more than one major thing about a course at a time, and at this point, even that one major change is looking kind of optimistically rosy.

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The Rules of the Brain

Do you ever feel like you’re on “auto pilot”?  Or that you’ve lost the ability to learn new things?  John Medina is a developmental molecular biologist and professor at The University of Washington and Seattle Pacific University.  He  has written a book called Brain Rules, which discusses some of the key components in enhancing our brain activity.  Here are some YouTube videos highlighting a few of those rules.

Rule #1 Exercise

Rule #7 Sleep


These might make good “Easter Eggs” to embed in your online course shells to get studnets thinking about how they learn.

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Unraveling the Mysteries of the Emerging Adult Brain

Diana Hestwood has been learning about the emerging adult brain (translation: the brains of our college students) for years. She sent me the latest version of her presentation (which she calls the “condensed” version, which was presented to the Project ACCESS fellows at AMATYC last month.

If you’ve never seen one of Diana’s presentations, it’s worth a look. Actually, even if you have seen the presentations, it’s always good to get a refresher. If nothing else, it might reduce your frustration level with freshmen college students.

Uploaded on authorSTREAM by aSGuest5468

You can download the original PowerPoint and get the Bibliography for Diana’s presentation here.

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Cognitive Assessments for Math

Uploaded on authorSTREAM by wyandersen

If you’re looking for the sample assessments, you can use the chapter on systems of linear equations by downloading the file here or use some selected activities from a variety of sections by downloading the file here. Yes, you can copy these materials and use them in your courses! Enjoy!

If you become interested in these resources, there is a Student Workbook (published by Cengage) of activities for Elementary Algebra, Intermediate Algebra, and the combo of the two.

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Hammer and Nail Problem

Believe it or not, I have been at MathFest for three days and have only managed to attend four sessions (besides the one I presented in). But I talk to a lot of people and talk to a lot of the exhibitors and because MathFest is a lot more research-oriented and focuses more on upper level math, there are actually not a ton of sessions that I am interested in – although, as is always the case, the sessions I did want to go to were all scheduled for the time I was speaking.
I haven’t seen Kien Lim since graduate school – I saw him walking down the street one night in Madison and recognized him. Kien and I used to be involved in some great discussions about how students learn. He invited me to his talk on the “Hammer-and-Nail Problem in Mathematics.” His talk (10 minutes) was briefly about his interest in math education and his experiences with students in Math for Elementary Ed. What he’s seen in teaching future teachers, is the same problem that I think we’ve all seen in different courses.

To a person with a hammer, everything looks like a nail.

Here are some examples that I’ve seen in classes:

    1. After you teach algebra students how to multiply polynomials, some can suddenly no longer add polynomials and will multiply an expression like (x + 3) + (x – 4).


  • In Calc II, I first teach how to use substitution to create new power series for functions. Later, I teach how to find a Taylor series. On the test, I always ask students to demonstrate finding some power series using the known series. But for many students, once they learn the Taylor series, it is the hammer they apply to everything.



  • In Calc I, students learn how to find derivatives using the power rule first. Later on, once they learn the quotient rule, they will try to find the derivative of 4/x using the quotient rule, rather than just rewriting the expression and using the power rule (which was the first, and simpler method).


For algebra, I’ve recorded hundreds of these types of hammer & nail issues in the Instructor Resource Binders I recently authored in the Instructor Tips that are included with each topic. Once you know that the issues exist, you can try to change the hammer-and-nail thinking by continuing to present problems that make students think about alternate methods – or at least show them that using the most recent “hammer” is not the best way to do the problem. After seeing this enough times, the hope is that the students will begin learning to think for themselves.

One of the reasons that I love using the methods I outlined in “Back to the Board” is that I can instantly see which students that are trying to rotely apply the latest learned technique, and throw out new problems that use other techniques or tweaks until I see that they are no longer “thinking with a hammer.”

SIDE NOTE: These little 10-minute talks at conferences drive me crazy. Ten minutes is barely enough time to introduce a topic. If conferences are really going to use this format, then they should be sophisticated enough to have a website where presenters can link to a longer-format presentation that is hosted online. For some presenters, that might mean a set of slides from a longer presentation, and for others, it might be a recording (with slides) of the actual longer presentation. I just get annoyed with getting a 10-minute teaser and then not having instant access to the rest… which is why I always post my presentation prior to presenting. Just like our students, the best time to gain the attention of the audience is when they are interested in the topic – like when they go back to their room after the presentation.

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Mysteries of the Emerging Adult Brain

Here are a few selected handouts from Diana Hestwood’s workshop “Unraveling the Mysteries of the Emerging Adult Brain Ages 18-20 (Often until Age 25)”

If you are looking for the PowerPoint presentation to use with students in the classroom, it is in an earlier blog entry here.

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How your Brain Learns and Remembers

This is a wonderful presentation designed by Diana Hestwood and Linda Russell (of Minneapolis Community & Technical College). After last year’s presentation about “the emerging adult brain” I asked Diana if there was an existing presentation that we could use to explain the brain science to students when we go back to our classrooms. This year, Diana held a workshop to help us implement the teaching of brain science in the classroom, and part of that was this PowerPoint presentation.

Because Diana wants this presentation to be used in classrooms, I am posting three versions of this file:

If you have any questions about the presentation, email Diana Hestwood and I’m sure she will be happy to answer them.

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Lots of talks on brain science

There seem to be quite a few talks this year on brain science and how it relates to teaching… specifically math. The one I could attend in my schedule was Ed Laughbaum’s talk “Teaching Developmental Algebra Isn’t Brain Science. Wait… Yes it is.” Here is a link to Ed’s website, where I assume he will post the presentation.

Ed had a fantastic list of references (some of which I have read and some that I have not… so it will be time to abuse my account again):

  • On Intelligence by J. Hawkins (2004)
  • Wider than the sky: The phenomenal gift of consciousness by G. Edelman (2004)
  • The first idea: How symbols, language and intelligence evolved from our primate ancestors to modern humans by Greenspan & Shanker (2004)
  • How the Mind Works by S. Pinker (1997)
  • The seven sins of memory: How the mind forgets and remembers by D. Schacter (2001)
  • Minds, brains, and learning: Understanding the psychological and educational relevance of neuroscientific research by J. Byrnes (2001)
  • Memory by Thompson & Madigan (2005)
  • The power of mindful learning by E. Langer (1997)
  • The mind and the brain: Neuroplasticity and the power of mental force by Schwartz & Begley (2003)
  • The new brain: How the modern age is rewiring your mind by R. Restak (2003)

This last one looks like one I will definitely have to pick up SOON because I’m being rewired faster than I can adjust! If someone who is not at this conference will send me an email or comment with all the links to these books on Amazon or B&N, I will happily add them, but right now I am too tired! : )

At the end of Ed’s talk, there was a “Call for Action” which I will republish here:

  • Use contextual situations with the introduction of a mathematical concept
  • Use visualizations at the beginning of a lesson
  • Use teaching/learning/priming activities as homework
  • Use questioning as a tool for teaching
  • Use handheld technology
  • Develop conceptual understanding first
  • Vary the delivery/methods
  • Re-visit concepts
  • Use a variety of homework activities
  • Use functions as the underlying theme to facilitate all research implications

(from Ed Laughbaum’s 2007 AMATYC presentation slides)

I will also be posting Diana Hestwood’s material on her two presentations about brain science, so if you’re looking for that… it’s coming… as soon as I get it from Diana!

And I have a few reading suggestions of my own… but I don’t have my library with me… if you have a suggestion, please add a comment and share!

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