Tuesday, March 10, 2015

Call for Abstracts, RLM and IBL Conference

College math faculty -- please consider submitting an abstract to present at the 18th Annual Legacy of R. L. Moore and IBL Conference, June 25-27, Austin, TX.  We hope to see you in Austin!


  • My favorite IBL activity
  • Teaching Inquiry and promoting questioning
  • Student success outside of academe: IBL fostering success in business and industry
  • Flipped course environments and IBL: Blending ideas and methods effectively.
  • IBL Innovations: new happenings
  • Poster Session 

Link to Conference Web Page

Tuesday, March 3, 2015

Math Anxiety Realities: Student Voices

In the interest of trying to ensure things are interpreted appropriately, I need to mention some very important caveats.  I deeply respect the people who work in education at all levels.  No one I know, who works in education, intentionally creates or supports building anxiety.   This post isn't about pointing fingers at specific groups of people.  This is why we do scientific research.  We seek to find out whether what we are doing is working or not.  This post is intended to be a call to action, and an invitation to open, intellectual dialogue about a critically important issue.

Math anxiety is real.  In our discussions about education reform, an overlooked piece is what students think and feel about Mathematics.  Learning skills, concepts, and habits of mind are part of the core of education.  Associated to this is the enjoyment of learning or lack thereof, in the case of math anxiety.  If a student learns how to do math and hates it, it's clearly not the outcome we desire.  Standardized testing does not measure attitudes about math, and because of this our debates are skewed in that we are ignoring very real problems.

My motivation for sharing student quotes comes from a couple different places.  One is that instructors rarely ask students to write about their own personal experiences with Math.  Getting to know your students and what they think and feel about math is valuable, so I encourage math instructors at all levels to include an assignment that asks students to write a math autobiography (or something equivalent) to get a sense of what your students are coming into class with.  The more you understand your students, the easier it is to find a place to meet them and build something positive.

Another source comes interestingly enough from talking to parents about CCSS.   As a mathematician I get asked about my opinion about CCSS Math.  (My short answer is that science is there, and that we need to work out the significant implementation challenges.)  The discussions often end up in a category I call the "back in the day" category.  It goes something like this.  We talk about some of the evidence I have seen in my work in IBL, how it's important to learn skills on a foundation of understanding, and so on.   But then the conversations ends up with, "Well, when I was a kid..."  The usual thing I learn about that person is the assumption that what we did as kids, back in the day, was good, effective math education.  I mean, look at us.  We turned out okay, right?

One common misunderstanding is that Math is equated with doing basic calculations.  It's about getting answers fast to computations and doing algorithms.  Math is not viewed as the subject mathematicians know it as.  This topic has made the rounds again and again, and it's likely to be here so long as we continue traditional teaching practices.

Another more subtle misunderstanding is that the reform efforts have to prove themselves better than the tried and true traditional form of math instruction.  There was never any base of high quality.  See John Dewey's writing at the turn of the 20th century or Warren Colburn (1830) The reality is that education systems need to evolve like healthcare systems.  New knowledge leads to new practices.  Teaching is not a fixed, static entity, and education systems that adapt and incorporate scientifically-validated methods are the ones that are going to set their societies up for success.  Further, decades of education research studies show that we (in the U.S.) need to make significant changes to curricula, methodology, assessment, teacher professional development, and more.   Traditional, memorize-and-regurgitate curricula and instruction has some unintentional and catastrophic consequences.  Many students hate math.  These students think it's only for geniuses to understand.  Problem solving, independent thinking, creativity, and curiosity are not associated with Mathematics.

The tacit assumption, however, is that we don't need to move forward and evolve.  It's understandable for people, who are not in education, to feel this way. They don't have access to data (at least easily), and can only base their opinions on the information they get from mass media, word of mouth, and school report cards.

Consequently, I'd like to bring to life math anxiety through the words of real college students.  Math anxieties are carried into adulthood, by highly intelligent people, and I believe it affects how they learn, interact with new ideas, and perceive themselves.  The quotes were collected from just two sections of a course for future elementary teachers and two sections of a G.E. math course at Cal Poly.  I could share similar quotes from my previous job (Cal State Dominguez Hills), despite being from a demographically different group of students, suggesting this is a widespread phenomenon.  In courses for future elementary school teachers, it is typical for 50-75% of students to have negative or somewhat negative associations with Math.

Student Voices
"The first time I remember doing anything with numbers was in kindergarten... I wrote all the numbers from 1 to over 500.  I remember feeling very proud of myself.  And that is the last time I felt brilliant at math.  I do well in the classes but I don’t feel as though I understand it." 
"There is a very popular American phrase, 'love at first sight,' which describes an intense overwhelming sensation felt by a person who has experienced something or someone that they can not stop thinking about for the first time.  This phrase would be completely inappropriate to describe my relationship with Lady Math.  In fact, quite the opposite.  My first memory of math dates back to 2nd grade.  I remember taking the 'Times Table Test' every friday, and wondering to myself, 'why on earth is this relevant to anything I will ever need to do for the rest of my entire life...' As I made my way through elementary school, I would find myself wondering the same thing more and more each year." 
"My math experience overall has not been a positive one... I remember always feeling extremely embarrassed because I didn’t know the answer as fast as the other students.  Since then I had a fear of math."
"I always dread math classes because of the many negative experiences I have had with them."
"Math has become one of my personal enemies..."
"I believe there are two types of people in the world: math people or people who despise math.  I fall into the latter category."  
"My first memory of math is the times tables in third grade.  I liked the competition, and the racing to the end, but I wasn't so hot on the accuracy.  And then when we got to fractions... my struggles really began.  In fifth grade, I effectually stopped doing all math homework and doodled my way through class.  This lasted until my first parent teacher conference, at which point, my parents became aware of my math maladies."
"Math and I are old adversaries.  It all began in first grade, when we were learning simple math.  We used to get these little math worksheets for practice... I was one of the slowest kids to move through my worksheets and advance on to the more complicated puzzles the entire year... I would plod along miserably through my homework and worksheets and pray every class period that I had somehow suddenly developed the ability to become invisible.  Sadly, that was never to be the case. Every time I was called upon to give an answer became an embarrassing spectacle of epic proportions complete with cherry-tomato-red faced stuttering and incorrect answers." 
"In this math tutoring program [in elementary school] I was drilled over and over again on simple mathematical concepts.  Doing pages of multiplication and division on a time limit, and doing pages of simple problems for prolonged amounts of time.  Naturally, I grew to despise math even more than I had before, and it hardly improved my bad habit of solving problems too quickly and making small mistakes... I was placed into a Trig class that renewed my dislike for math.  Once again my ability to correctly answer was impeded by rushing too much through the problems, and I struggled once again to solve problems correctly." 
"I attended math tutoring at the tender age of six, where I was rewarded with graham cracker and stickers for the correct answers, and I felt that this was something to be ashamed of.  In seventh grade I began pre-algebra, and I had a teacher who was just entering her second year in the field... I repeated the course in eighth grade, with better success.  I felt a lack of self efficacy at that point, highlighted by the notion that I was not meant to excel in math, and that I should accept that and work towards other goals." 
"From a very young age I always had several words I would attach to my response to anything math related.  These lovely describing words included anguish, struggle, frustration, and confusion.  Needless to say, I do not have a good relationship with math... In high school my math grades began to reflect an amount of incompetence in my math classes, which irked me to no end, as I was doing quite well in my other courses.  Earning high grades was something that was expected of me, and I felt like I was floundering...  I had to hire a tutor to pull me through trigonometry and calculous and I still have many foggy areas in both subjects (as well as a deep seeded hatred of the courses)... A key reason I decided upon my major and career path was to avoid math at all costs..." 
"To say the least I was scared of math.  It has always been the subject that no matter how hard I worked, or how many problems I did, the test always was a struggle... I think I became ingrained and almost have an irrational feat of it.  I became so used to saying 'I'm not good at math' 'I don't like math' that I became used to not being successful at it." 
"My experiences in math through my much of my life have been horrendously painful; I would begin every summer in middle school and high school crossing my fingers that my final would raise my math grade to a C-... It really wasn't always like that, some of my earliest memories involving math were those speed tests where you got a sheet filled with simple addition and you had to see how fast you could solve them.  I always remember being one of the fastest in my class.  But I guess that was more memorization then problem solving at that point, because when algebra began my grades declined drastically." 
"Throughout my education, I have earned A's and B's in average level math classes, but those grades were not earned easily.  As an underclassman in high school, I worked my way through Geometry and Algebra II without too much strenuous work, but as I got to Pre-Calc/Trig in my junior year the difficulty level rose while my success slowly declined.  That year I needed all the extra tutoring hours I could get, and I still felt unconnected, uninterested and as confused as ever with all of the equations and formulas that were drilled into my brain.  My problem with math is not that it is hard -- I realize that most things in life will be difficult and I always enjoyed the work that goes into achieving greatness.  My problem with math is that I often feel like I just don't get it no matter how hard I study, which only adds to my stress levels." 
"... I can remember that third grade was the year where we were forced to learn and memorize by heart our times tables, up to the twelves... I didn't realize it at the time, but looking back on that year it is obvious that my anxiety and doubts about my own math skills started then." 
"Tenth grade was a horrible year for my appreciation in math... I took the final and passed with a C- after that year I never wanted to do math again."
"Math and I have not always been the best of friends.  Since the beginning, it's never been my best subject.  I struggle with remembering all the different formulas required for getting problems done correctly;  I even struggle with the fact that everything has to have one certain answer and no free thinking is allowed.  Your own thoughts and ideas are not involved whatsoever in math, and I have always had annoyed feelings toward that." 
"I honestly cannot remember my first negative emotion towards the subject of math, but I can say that it developed early on.  Math is the only subject that I try to avoid at all cost.... Thinking back now, I can recall the first time I realize that I would struggle to achieve a high understanding of math.  In the second grade, I remember the timed tests we would be given weekly to test our addition and subtraction skills... I hardly ever finished the entire sheet before time was up.  Every week, I felt defeated.  If anything, these weekly quizzes degraded my spirit.  I wasn't learning how to practice my math skills or challenge my intelligence;  I learned to despise the subject that had me seemingly beat." 
"Math became painfully difficult for me around the fourth grade.  I could not for the life of me learn my times tables beyond 6.  Week after week I took the test for 7 and week after week I was unable to pass it.  Everyone in the class had a magnet that moved along the wall from number to number as we passed each test. One by one my classmates moved along the wall all the way to 12 until I was one of just a few children left.  Of course, I was humiliated... High school was much of the same.  I worked long nights with a tutor for C's."   
"My experience in math has been very negative, long, and discouraging." 
"Saying I do not like math is an understatement."

And the good ones leave Math too...
"Math became my favorite subject from then on, I just never admitted that to anyone because I didn't want to be a nerd.  The simplicity of math is what I continued to love:  there was almost always one correct answer.  No more and no less.  I received A's in every semester...  Moving along the math train pretty quickly, I found myself in algebra 2 my freshman year.  This was advanced for my high school, at least.  After A's in both semesters, I moved onto trigonometry/pre-calc.  Again, I received A's as the norm.  This was the point that I realized it.  Math bored me.  I knew I would be one of the most unhappy people in the world if I was doing nothing but math problems for the rest of my life..."  
"The reason I was not a fan of math was the lack of discussion involved.  I loved learning about the stories involved in history, and reading about experiences in English as well, but when it came to math it was just cut and dry; formulas and data compilations.  I also associate with math the feeling of frustration and disappointment."   
"Since elementary school I have always done pretty well in my math courses, but I never seemed to enjoy the subject quite as much as other subjects... it was never as appealing or enjoyable to me because it seemed to be more rote based and did not capture my attention because it did not allow for creativity...  there was always one right answer..."

Links and Further Reading

  • Jo Boaler on Math Anxiety
  • Post on Students' Attitudes and Beliefs in Mathematics
  • "Talking About Leaving: Why Undergraduates Leave the Sciences" by Seymour and Hewitt is a careful study about why students leave the Sciences, which is a related topic. While math anxiety isn't a identified to have a role with undergraduates leading the sciences, the broader issue that is connected is that education systems can unintentionally push away students from subjects.

Friday, January 30, 2015

Creating Time for More Engagement

Sometimes we teach in situations where we cannot use a full IBL approach.  Perhaps the class is too large or there are "coverage constraints" that are outside of your control.  Despite such restrictions due to environmental factors outside of the instructor's control, there exists strategies that be used to create time to engage students.

Think-Pair-Share (TPS) is a core piece.  What's nice about TPS is that one can expand or contract the size of the TPS task so that it fits into your existing system and/or the specific need at the moment.  Simple, quick concept questions to longer problem-solving tasks span the typical range of TPS uses in Math.  So the goal is to get time to insert TPS, and engage students through specific tasks where they get to think for themselves.

The main topic of this post is creating time.  Below are some strategies to buy a little time.
  1. Instead of coping the statement of problems, exercises, definitions on the board only for students to copy them into their notes, a handout can be used where all of this is printed or available on electronically.  The time used for all this writing can now be used to process, think, and discuss.  Handouts potentially save quite a bit of time.  In traditional courses, a chunk of each class period is spent on writing on the board and writing in notes, often of things that are already printed in the textbook.  Further, the time it takes to write your lecture notes, can be used to type up a handout.  It really doesn't take that much more prep time.
  2. An example of the above is the typical "working an example" for the class.  Normally a teacher works through each step and shows what to do to the students in class.  If this example was printed on a handout, then those 5-6 minutes of instructor show-and-tell could be made much more active.  It can be from a quick, "Think of how you'd start this example... then check in with a neighbor" to a more involved "Try it, and we'll have someone share it on the board in a few minutes."
  3. On a related note, having students read or work on basic material outside of class can create time to do something deeper in class.  This is based on the "flipped class" idea.  Flipped classes of course can create much more time, but not all faculty can invest this much time for every class to do this.  An intermediate step between zero and fully flipped classes is to use reading assignments or similarly constructed tasks done outside of class to get students up to speed.
  4. If you're going to use group work for part of the time, ask students to move into groups at the beginning of the class.  Then they are ready to go, and discussions ramp up faster.  Less time is spent on the students getting up to the point where they are talking.   It's noted that when students are in rows and have been passive for long stretches, there's more inertia.  This inertia can be a time sink.  Setting up the class "Feng Shui" can move things along faster.
  5. Use more efficient prompts and questions. Several times during a lecture instructors often ask "Do you understand?" or "Are there any questions?"  And wait a minute... and no one has anything to say... You might as well swap out those few empty minutes in class for a more useful bit.
  6. Cull optional material from the course.  Some topics are more valuable than others.  Learning how to minimize some topics, gives you extra time to spend on more important material in a more engaged way.  The uniform distribution of time across topics isn't likely to be optimal, since some topics are more important than others.  
One or two of these strategies gets you a fair amount of time to get things going.  In aggregate, you actually get a significant chunk of time.  It's similar to Moneyball in major league baseball.  Small advantages are pushed in aggregate over large sample sizes.  An extra 15-20 minutes of quality time, every day over a term or year can lead to significant learning results.

Friday, January 23, 2015

IBL Workshop 2015, July 7-10, Cal Poly San Luis Obispo

Attending a four-day IBL workshop is one of the best ways to get started with IBL or take the next big step in your teaching.  Long workshops are like retreats.  Away from the daily routine, faculty can focus on how to implement IBL methods, build up a target course, collaborate with colleagues, and build IBL-specific teaching skills.  

Full details are available at www.iblworkshop.org

The 2015 IBL Workshop is part of the Mathematical Association of America's PREP program.  More information about MAA PREP and registration for the IBL workshop can be found via this LINK.

*The IBL Workshop is funded by NSF DUE 1225833 (SPIGOT), and space is limited to faculty who teach at colleges and universities.  Early-career faculty (assistant professors, postdocs, and grad students) are especially encouraged to register!  A limited number of travel scholarships are available for early-career faculty.  

Saturday, January 3, 2015

Looking Back at the Previous Term: Reflective Practice with Efficiency

Just a quick post here as we start another year that applies to all teaching, not just math and IBL...

At the end of the term (or recently after a term ends), I like to look back at the courses I have taught and reflect on the successes and productive failures.  What I like to do is set aside 30 minutes or 1 hour, and write down my thoughts, go over my notes, look for patterns, and try to identify areas I can work on.  I look at the problems that were successful and the ones that were not so successful.

Then I put them into my to-do list manager (Omni Focus).  A variety of programs and workflows are out there related to to-do list managers, and the choice of software is not important.  It is important to use some system, however.   The upshot is that I like to put my ideas and thoughts into my to-do list app, and then set a date for to add more things in.  Repeat every week or so for just a few minutes.   Then when it's time to get moving with the next course prep, I have my thoughts about what I can improve ready for action, which leads to me adding in something new that is good or improving something much more frequently. 

Small bits of time used efficiently and computer-aided organization can help us learn faster and grow faster as teachers.  These small bits of time are like prepping the prep time.  This idea can be adapted to suit your needs, and I can see it as part of regular, ongoing reflective practice.

I don't think I'll ever be done learning about teaching, and truthfully that's a good thing.  It's akin to craftsmanship or being an artisan, where the work spans the arc of a career.  It's an enjoyable, fulfilling way to look at the profession, and it's a component of what makes teaching fun, positive, and optimistic (at least to me).

Warm wishes for a successful 2015!

Friday, November 14, 2014

Instructor Voices Part 4: "What Makes a Good IBL Instructor?" (Video)

Here's the fourth episode in the Instructor Voices series on the AIBL channel.   This time just a quick take on what a handful of IBL instructors think about important attributes or skills of an effective teacher.

I'll add on to their good comments by saying that these aren't a complete list.  What goes into becoming a solid IBL teacher isn't the size of a sound bite.  If you're interested in taking the next steps, please consider attending the IBL Workshop in July 2015. Registration opens in January.

Careful listening, providing appropriate structure for exchanging ideas, restraint, patience, understanding the learning process, and compassionate joy.

Friday, November 7, 2014

Instructor Voices Part 3: Importance of Failure (Video)

In an earlier posts, I wrote about de-stigmatizing mistake.  Some of us are now  doing things (when appropriate) in our classes now to raise mistakes to their proper place in the learning (Productive Failure).  This post is a continuation of this theme.

Here's another short video of IBL instructors sharing their thoughts on the value of mistakes or getting stuck.  Thanks again to the interviewees for sharing their beautiful insights!