They do not understand shallowness, because they do not experience depth.

How often do you catch yourself being frustrated with your students because they seem to focus more on the points of an assignment or the grade rather than the learning?  In most cases, it is not their fault as throughout their schooling they are often not put in situations to counter the strong message we give them about grades.  Jacqueline and Martin Brooks, in their book “The Case for Constructivist Classrooms”, point out “they do not understand shallowness, because they do not experience depth” when referring to why students struggle to construct an essential understanding of a subject.  Our students don’t experience depth because we have a tendency to come to their rescue once they begin to struggle, we over scaffold a lesson so they gain a clear understanding, we show them rather than allow them to discover a point just in case they don’t find it, and we lead them down the path we want them to travel to make sure they get to where we want them to go.  We send a message that it is the product, not the process that is important to us and then we wonder why they worry about the grade.  

The importance of the  “process” is exactly what Robert Kaplinsky addresses in his hilarious but thought provoking video on Productive Struggle.  In only six minutes, Kaplinsky shares a key ingredient to why our students need to experience depth.  Productive struggle is basically a more user friendly version of Vygotzky’s  Zone of Proximal Development, but Kaplinsky uses a powerful analogy to make his point.  He also mentions that when we put our students in situations that cause them to struggle there will be push back from students, other adults such as parents or our colleagues, and even ourselves (when we ask, why are we doing this to ourselves).  However, the keys are that the struggle the students experience  is productive rather than unproductive struggle and that we send the message that we are there to support the students in their learning.  It is a “teach a man to fish” sort of thing.  We can help our students to experience depth through productive struggle by promoting a student centered classroom through strategies such as problem based learning, competency based education, and other constructivist related activities that allow students to build upon their own understanding.  Up until a few days ago, I knew this was a good idea, but couldn’t say I was completely convinced.  

Recently, Jo Boaler and Sarah Kate Selling shared their research titled “Psychological Imprisonment or Intellectual Freedom?  A Longitudinal Study of Contrasting School Mathematics Approaches and Their Impact on Adult’s Lives”.  In short, they first describe research in which a traditional method of teaching mathematics was compared to a project based approach to teaching mathematics and how the students developed profoundly different relationships with mathematics knowledge that contributed towards the shaping of different identities as learners and users of mathematics.  Boaler and Selling then revisited the students from the study eight years later to look at the long term impacts of the traditional method of teaching vs. the one that promoted more productive struggle and what they found was very interesting.  In my mind they provided evidence of the power of productive struggle.  

This research is applied to math, but productive struggle can work across the curriculum. I would encourage you to try a group worthy task, create a problem based learning unit, or even develop a competency based education course.  Because I strongly believe, the more we put our students in situations which cause them to experience productive struggle, the more they will experience depth, and then the more they will come to realize shallowness.  

Here is a graphic summary of Boaler and Selling's research article:

Scenario	Traditional Pedagogy	Productive Struggle
Math Teacher Focus	Mastery of the content	Understanding of content along with to develop inquiring, problem solving, and responsible young adults
Pedagogy Taught while in school	Follow rules: rehearse content from the textbook , practice methods shown by the teacher, and use cues from the questions to know what to do	Freedom to Explore:  learned to ask questions, choose from different methods, adapt and apply methods, draw conclusions using mathematical evidence
Perception of Math in School	Uninteresting and unrelated	Positive including descriptions such as brilliant, ideal, and brave
Authority resides with...	the teacher and textbook	the students who demonstrated a strong sense of responsibility, agency, and authority along with an adaptive form of knowledge
Expertise developed	Routine Expertise	Adaptive Expertise
Mathematical Identity	submission to outside authorities with cannons of knowledge and list of content	Actively use, adapt, and apply knowledge to solve problems
Perceived usefulness of math learned in school after 8 years	None thought their school math helped them in life, although 75% reported liking math as adults	All those interviewed found the math learned was useful in their job and 100% reported enjoying math as adults
Use of school math in their jobs	Did not use school math and deferred to authorities to know if the math that was done was correct	Worked flexibly with math  with responsibility and agency