Ed News: Middle Class Squeeze

While not directly IBL related, this affects all of us at the college level.  The rising cost of college education is a growing concern.  UC Berkeley has announced that it will begin subsidizing the cost of education for middle class families.  That is, families with incomes between \$80,000 and \$140,000 per year will receive a reduction in tuition.  The annual cost of attending to a UC school is now up to $32,000 per year for California residents.

The original CA master plan intended to provide free college education for qualified students in CA.  That dream is over for good.  More importantly, the cost of education has risen to the point where even middle class families struggle to afford paying for public colleges.  This is not good if our best and brightest students are not able to attend our best public colleges in our state.  It means we ultimately are squandering chunks of our society's talent pool.  Not good.  More on this later.

Why Students Leave STEM Majors

A recent (11/3) article appeared in The New York Times called "Why Science Majors Change Their Minds"

Quoted from the article:

But as Mr. Moniz sat in his mechanics class in 2009, he realized he had already had enough. “I was trying to memorize equations, and engineering’s all about the application, which they really didn’t teach too well,” he says. “It was just like, ‘Do these practice problems, then you’re on your own.’ ” And as he looked ahead at the curriculum, he did not see much relief on the horizon.

This article is a micro version of the book "Talking About Leaving: Why Undergraduates Leave the Sciences" by Seymour and Hewitt.  It should be on your bookshelf if you are an educator in a STEM field.  The top four reasons why students leave STEM fields in undergraduate education are teaching and learning related.

The Top Four Reasons why undergraduates leave STEM majors:

1. Lack or loss of interest
2. Non STEM majors offer better education/learning experience
3. Poor teaching by STEM faculty
4. Curriculum overload, fast pace overwhelming.

Traditional explanation or "justification" of this is that we are "weeding out" the weak or morally inferior students.  The data presented by Seymour and Hewitt says otherwise.  One cannot predict based on academic measures such as GPA which students will switch out of STEM majors.

In short, we waste talent and turn away many strong, capable students.  In our rush to "get through all the material" our system has to a large degree lost sight of the big prizes.  We can, however, regain this by focusing on the learner and the learning experience.  We can be coaches and mentors rather than gate keepers, and departments across the nation should reconsider the definition of success.

What should success really mean for a Math program?

A Good, But Not Good Enough Idea

In the NYTimes, Sol Garfunkel and David Mumford published a piece titled, How to Fix Our Math Education.  In this column, Garfunkel and Mumford claim that the curriculum should be changed to include more realistic and practical situations that are meaningful to students.  This I agree with 100%.

The problem with their piece is that the curriculum (AKA the specific content in courses) is only one of many issues.  Their analysis is limited, and here's why.

There are numerous examples from the K-12 system, where schools have adopted a research-based, NSF funded curriculum like IMP or CPM.  Many times these programs are shut down by some exogenous force.  For example parents, who have good intentions in their hearts have organized and shut programs down. They say things like, "Well that's not how I learned it...," never mind that the world has changed and students are being prepared for new challenges, not challenges from the 19th century.   Or a new superintendent wipes out the programs, or a new principal comes in and moves teachers to new classes or grade levels, or budget cuts,..., the list could go on and on.  I note that none of these people do this intentionally.  People in education and parents are well-intentioned.  They mean well.  It's just that we don't know better as a society, and look for simple fixes for long-term, multi-layered problems.  Insufficient.

The problems we face now are complex, and my sense is that they are on the order of magnitude to problems related to ecosystem sustainability.  Our educational system is vast and complex, with outdated doctrines interfacing with modern challenges, and a currently fashionable and misguided desire to apply business models to non-business systems.  So when someone says, "Just fix X, and all will be good," I know that it just won't.

Content (i.e. textbooks or materials) is just one small slice of the education pie.   In addition to content is

• Instruction (and all this huge category entails)
• Student attitudes, beliefs, habits of mind, experience with math, and their natural cognitive development mathematically.  (Example: the developmentally appropriate order of topics is sometimes different than the logical order in a subject.)
• External issues to the classroom like tenure and promotion for research (but not teaching), pacing plans, poverty, etc.
• Systemic issues like standardized testing (K-12) or standardized courses (calculus)
• The factory model mindset held by most people regarding education.  We value certain kinds of intelligence.  Math and reading are at the top....Art, Dance, Music, craft, and manual skills are at the bottom, which leaves some students feeling marginalized for being born with the "wrong" abilities.    
• We educate students in disciplines in ways such that they are not connected to each other, even though they often are connected and of more value when studied as a whole.
• Community and culture.  Most people think math is "2+2 = 4."  That there is only one answer.  That there is only one way to get to that singleton answer.  That math is immutable and the same across all time.  Learning math means you know how to calculate.  Additionally, Parents, even well educated ones, can destroy a positive change, thinking that they are doing a good thing.  I do not doubt parents' love of their children or desire for good education. It's just that we as a society are generally naive about what math is.  What we assume to be true about math is actually false.  So based on false assumptions we act unwittingly against our own interests. Mathematicians bear some of this responsibility, as we are not good ambassadors of our wonderful subject. 

Viewed even from this slightly broader perspective, changing the content without thinking about the education ecosystem is limited.

So how does IBL come into play?  At the college-level, a math instructor, who uses IBL, can control enough of the ecosystem within the classroom to construct a little, temporary greenhouse.  This little greenhouse has enough of the conditions necessary to foster intellectual growth and provide opportunities for students to undertake the effort required for transformative changes.  Considering how to scale these little greenhouses up is one way to realize the enormity of the challenge in education reform, and emphasizes that changing a textbook or the curriculum is like upgrading the rake or the shovel to a new, more effective one.  While it's a necessary step in the right direction, it is insufficient.

The Colorado Study: The Vectors Are All Pointing in the Same Direction

Sandra Laursen, Marja-Liisa Hassi, Marina Kogan, Anne-Barrie Hunter, at the University of Colorado Ethnography & Evaluation Research and Tim Weston, ATLAS Assessment and Research Center University of Colorado Boulder have conducted a large, mixed-method study of IBL at 4 research universities in the U.S.  This is the largest study of its kind, and the results are striking.  (Link to the study)

What did they learn?

• LESS instructor talk time, results in BETTER outcomes.
• Women in IBL classes reported as high or higher gains than their male classmates across all cognitive, affective and social gains areas (3.2.3). But women in non-IBL classes reported statistically much lower gains than their male classmates in several important domains: understanding concepts, thinking and problem-solving, confidence, and positive attitude toward mathematics.
• Among students who entered with low math GPAs (<2.5), IBL students generally earned better grades in later classes than did their non-IBL peers (6.4.1).
• Attitudinal changes were modestly positive in IBL groups, and mixed and somewhat negative in non-IBL groups.  Overall, IBL math courses tended to promote slightly more sophisticated and expert-like views of mathematics and more interactive approaches to learning. In contrast, traditional mathematics courses appeared to weaken students’ confidence and enjoyment, and did not help them to develop expert-like views or skillful practices for studying college mathematics.

The overall results of the Colorado study points in the same direction as the bulk of the results from the Math Education literature.  When students are (a) deeply engaged in high quality mathematical tasks requiring critical thinking and reasoning, and (b) have some form of collaboration, then student outcome are statistically significantly better compared to students in a non-IBL setting.  (Collaboration is broadly defined here.  Collaboration is not only group work, but includes activities such as class discussion and student presentations to the whole class.  In this last instance, the class is peer-reviewing the presenter's work.  This is collaboration.)

When the Colorado study is combined with the literature from Math Education, then we start to put together a rather clear picture.  We have known already that students have historically had poor attitudes and beliefs about Math from K-college.  Students have beliefs such as "all problems can be solved in 5-minutes or less" and "it's the form of the answer that important, not the quality of the process or content of the proof."

We also know that students, even college students, have limited ability in problem solving and proof.  Students are rarely exposed to the kinds of experiences necessary to develop problem solving, the critical thinking and reasoning for proof, and other higher-level thinking strategies.  High stakes testing and the drive for further standardization has made it more difficult for students to develop the kinds of attitudes and thinking skills needed to learn math beyond rote skill.  

In light of this, the Colorado study shows that IBL methods (broadly defined) is a glimmer of hope.  When students are given a chance to think for themselves and are properly supported by the instructor and their peers, that students are capable of rising up and fulfill their potential.

The data speaks -- all the vectors are pointing in towards IBL.