## Thursday, September 1, 2016

### Effort and Circumstances in Educational Achievement

The educational achievement by a student is not only a result of personal effort, but is also dependent on circumstances. Student accomplishments are not acts by a single person, but are also deeply influenced by the circumstances (or environment) in which they live and learn. A factor that often doesn't get the attention it deservers are the circumstances of students as a critical component in student success. This is a multilayered topic, and the goal of this post is to shed some light on the issues.

Before we dive into the details, an obvious sign of the importance of circumstances is the stress parents feel when figuring out what schools to send their children. It's a clear signal that where kids go to school and the people at the school matter. Yet strangely and in near complete contradiction, the notion that education is a solely individual accomplishment exists.

Math Analogy:  There's a difference between functions of one variable and functions of two or more variables.  Symbolically let $x$ be student effort, and let $y$ represent a student's circumstances. Then what is being asserted is that $f$, a student's achievement (whatever that means), is dependent on $x$ and $y$. As math teachers, we may be prone to looking at teaching as $f(x)$ and not $f(x,y)$ perhaps tacitly or perhaps because we don't know what more can be done.

What does $y$ represent? There are of course the usual things. These are factors like location, family income, ethnicity, poverty, school quality, parents' level of education, and so on.  Additionally we can include schools within the broad category of circumstances. Class environment, curricula, daily schedules, the architecture of the buildings, the number of students in the classes, the teachers, ... all these in the aggregate make up $y$.

Claim: $f(x,y)$ is highly sensitive on $y$.

Rationale:  There's evidence that suggests the sensitivity of $f$ on $y$ is rather significant. In a recent article by Ellis, Fosdick, Rasmussen, evidence is presented suggesting calculus apprehensions can steer women out of the STEM pipeline at 1.5 time the rate compared to men. Simultaneously we also know that the use of IBL reduces sizable gender gaps between men and women compared to non-IBL, traditionally taught courses. (See Laursen, Hassi, Kogan and Weston.)  That is, even changing $y$ by only factors limited to classroom pedagogy can change $f$ in ways we can measure statistically.

Researchers in Germany dig partially into circumstances under the label "Error Climate" (Link to a description 1, Link to description 2).  Steuer and Dresel identify factors that support a positive learning environment, such as empowering students to be willing to experiment and try.  In their work they identify factors that are related to how teachers teach and pedagogy.

1.  Error tolerance by the teacher
2.  Irrelevance of errors for assessment
3.  Teacher support following errors
4.  Absence of negative teacher reactions
5.  Absence of negative classmate reactions
6.  Taking the error risk
7.  Analysis of errors
8.  Functionality of errors for learning

In active, student-centered classes these items can be integrated. Mistakes can be de-stigmatized, and students can learn growth mindsets. We can't do much of anything about factors like poverty, at least not directly via classroom instruction. We can, however, do something about our classroom environments that can minimize gender gaps and other inequities.  Small group work, student presentations, portfolios, projects, productive failure are just a handful of IBL strategies that can be used to create a significantly different set of circumstances for your students.

Additive improvement:  Improving teaching often is focused on $x$, or student effort, via things like books, ordering of topics, clearer exposition, better problem sets, getting students to do homework. These are aimed at the experiences of the student and their effort on the subject. Those are of course good places to expend energy, and what I am suggesting is to add.  Add consideration and teacher effort on $y$, without diminished hard won successes in $x$. That is, improving $f$ optimally includes working on $x$ and $y$, and this is not a zero sum game. Instructors do not have to give up proportionally one to gain in the other.

Francis Su eloquently makes the case in his talk, Freedom Through Inquiry. He shares the story of Gloria Watkins, who experienced two starkly different realities in her education during the change from segregated schools to bussing and integration. Su, an MAA President and accomplished mathematician, shares his personal story about perseverance. The environment in which he grows up in and his educational experiences have made a material impact on his career trajectory and life.
"And just like Watkins, I had professors who didn’t believe I was capable of making it through, especially when I failed my qualifying exams the first time...
It’s because I had that inquiry-based Moore-method class with Starbird that I knew that I could do research. I already had the experience of discovering things for myself. I knew that I knew how to ask good questions, because we had the freedom to ask any question in Starbird’s class and figure out which ones were fruitful. And I knew how to use those questions as a springboard to independent investigation.
And because of that, I knew, no matter what anyone said or believed about me, that I could push through. Today’s literature suggests that inquiry-based teaching methods confer significant benefits on underprepared students, and of course I believe it. Because I’ve lived it."
Teachers have opportunities to make transformative changes. Expanding our view to see more variables related to learning helps us see more opportunities to help students succeed. While there are limits, constraints, and societal-level issues that form daunting challenges to improving the circumstances surrounding our students, nevertheless there still exists real and significant opportunities for change, right here in front of us in our classes!