Monday, April 27, 2015

Triangulation: I Understand the “Why,” Now Please Tell Me the “When”


In the last four weeks and across several provinces, there is one question that is being asked over and over again – “I know that it is a good idea to gather evidence of student learning from more than product, but when does it make sense to gather evidence from observations and conversations?”  Maybe this question is surfacing as a result of impending mid-semester report cards or perhaps it is because curricular redesign is resulting in a renewed focus on triangulated evidence.  Whether it is because of these reasons or something else, it is a question worth asking and one worth thinking more about.

Triangulation – gathering evidence from multiple sources over time – is based on research in the areas of social sciences.  Look to Lincoln and Guba (1984) for an early reference and to current provincial policy statements from most jurisdictions in Canada for more contemporary citations.  Growing Success by the Ontario Ministry of Education (2010) and the WNCP document, Rethinking Classroom Assessment with Purpose in Mind, (2006) offer two such examples.  Most times, triangulation is explained by suggesting that evidence of student learning can come from three sources specifically – products, observation of process by the teacher, and conversation between student and teacher, between student and student, and between the student and him- or herself.

Even though this sounds logical and understandable, the question remains – “When?”  In recent work in Northern Ontario with le Conseil scolaire public de nord est d’Ontario, we spoke of triangulation in the following four ways:

The term ‘triangulation’ is often accompanied by a drawing of an equilateral triangle, like this.




 For the mathematicians in the group, this offers a sense of equality; that is, if in a unit of study or over a cluster of lessons we gather 9 products, then we should also gather a commensurate 9 observations and 9 conversations.  Tell this to a physical education teacher or a technical vocational teacher and they might chuckle.  For them, equality in triangulation is an absurd concept.  And the same is true for all other subject areas.  For me, this is an inaccurate representation of the deeper purposes of triangulation.  Rather, we need to look to other cues to help us respond to the question of “When?”

Thinking about triangulation in relation to the notion of validity is helpful.  Validity can be described as “…extent to which the evidence from multiple sources matches the quality levels expected in light of the standards or learning outcomes” (Making Classroom Assessment Work by A. Davies, 2011).  Each subject area and its curricular documents or program of studies have outcomes, standards, learning expectations, or learning intentions that are best demonstrated through observations or conversations.  A simple example from Language Arts might be oral communication.  We don’t ask students to write something on paper in order to determine whether they can orally communicate.  Another example might be the safe use of materials and equipment during a Chemistry lab.  The most valid method to decide whether a student is engaging safely in a scientific investigation is to observe them engaging in a scientific investigation.

We identify outcomes that can be tightly coupled with either conversation or observation by referring again to our curricular documents.  For example, just a few days ago, I worked alongside a secondary science teacher in Ontario as we examined the Grade 11 Biology document to determine where it would best make sense to gather evidence from conversation.  Here are a few opportunities we found which require students to communicate their understanding orally and, therefore, in a valid manner:
·      One aspect of scientific literacy is the ability to represent scientific information in oral reports.  Areas for an oral report in Biology might be to consider critically the role of Biology in students’ daily lives and the impact of scientific developments on society and the environment from the field of Biology.
·      Communicate ideas, procedures, and results in a variety of forms (e.g., orally, in writing, using electronic presentations).
·      Through purposeful talk, students not only learn to communicate information but also explore and come to understand ideas and concepts; identify and solve problems; organize their experience and knowledge; and express and clarify their thoughts, feelings, and opinions.

And yet, validity cannot be the complete response to the question of “When?”  For another perspective, let us look to the term ‘differentiation,’ which can be defined as the means of adapting instructional strategies to meet the needs of all students.  Triangulation as a method of differentiation makes good sense.  For example, in a Grade 11 Pre-Calculus classroom of 29 students, most students are able to write down how they arrived at an answer to a trigonometry problem.  In other words, they could represent their thinking and prove the steps that they had taken to accurately answer the problem.  As we know, our curricular documents require that students not only ‘get to an answer,’ but are able to communicate the means by which they arrived at that answer.  As stated earlier, most students are probably able to put that into the written word and symbol.  However, there may be a student or two who, though he/she arrived at the correct answer, has only a sketchy outline of the steps that were taken.  Nevertheless, you are certain that his thinking is much more comprehensive than those few words on the paper.  For that student, having him/her talk to you about the steps that he/she took allows you to be certain of your earlier hunch.  Leveraging technology and applications may make that even more efficient.  Instead of meeting you in a face-to-face conference, the student might submit an audio file or use Explain Everything to record his/her writing and explanation or create an aura in Aurasma.  The possibilities, though seemingly endless, still have, at their core, the notion that triangulation provide us with permission to collect evidence in a way that might better suit a student’s strengths and competencies.

And finally, as I reflect on the question of “When?”, I also think about taking a step back.  From time to time, our policy documents might lead us to believe that triangulation needs to occur at each moment in each lesson.  A more measured stance is one of surveying a unit or a cluster of lessons and, from that perspective, looking for triangulation.  To expect that triangulation needs to occur in a 30 or 70 minute class might be to set ourselves up for failure.  A phrase that I used earlier makes more sense to me – ‘over time.’  Can you, as you look at the evidence that you have collected over time, confidently say that it includes evidence from multiple sources?  This longer-term view serves us well.

These four points can be further illuminated by your experiences and understanding and yet, they serve to respond to a question that seems important to so many with whom I have worked recently.  As Peter Elbow stated, “Certainty stunts growth and learning.”  Posing questions is evidence of uncertainty and it is in that stance that we can inquire and learn together.  Thank you to the teachers and leaders of Edmonton Public Schools in Alberta, CSPNE in Ontario, and Mountain View School Division in Manitoba for asking questions that mean we can all learn more!

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