Setting an Objective for a Math Activity

Most lesson planning begins with defining some kind of lesson objective, often in the form of "Students will be able to [insert skill here.]" In Massachusetts, this lesson objective should be mapped onto a specific standard from the Curriculum Frameworks, standards that were never defined for individual grade levels in Massachusetts until 2000 to adhere to newly-administered MCAS standardized testing. Whether or not a teacher believes they are teaching to a test, the act of writing a lesson objective is a product of standardized testing.

Constructing a lesson objective is an act of instrumentalizing understanding. Instrumentalism is the construction of knowledge for external purposes; its product, instrumental understanding, is necessarily opposed to relational understanding which connects to deeper internal structures. For example, a seventh grade student with instrumental understanding of  𝜋  may utilize 𝜋  to find the circumference of a circle without ever appreciating the relational understanding of a ratio that must be irrational. After all, content standards require students to learn to use 𝜋 in seventh grade and wait till eighth grade to introduce irrationality.  This distinction between instrumental and relational rationales for learning has direct implications for how students experience school mathematics.

The Game

An article by researcher Michael Ford from the Journal of Learning Sciences outlines a particularly useful framework for lesson planning where he compares the context of a lesson to a game, where the resources are pieces and the community are players. I find this particularly useful in thinking about what "game" we expect students to win upon engaging in a lesson. The game to win, or the purpose of learning activities in math class, should be to foster deep thinking and problem-solving specific to the values of both individual learners and communities of learners.

Relational objectives are messier than instrumental objectives. Lev Vygotsky, the grandfather of relational learning, proposed that “children grow into the intellectual life of those around them.” In other words, learning will depend on who's around, which requires tasks to be rooted in cultural and disciplinary contexts unique to each learning community. Teachers must be attuned to learners and ready to react to their worlds so that learners can express ideas with precision and expertise from their own lives.

Relational objectives depend on the living soul of a classroom. Ultimately, learning activities should shape and be shaped by values like intellect and compassion that learners will bring into their adult lives. These are relational objectives.

The Players

It is naïve to believe I can saunter through a teaching career by writing "it depends what we all get excited about" as my lesson objective. This is all well and good for me, my teaching collaborators, and my students. We all play the same game: we want to engage in authentic learning and building strong connections.

There is a more sinister game being played when we include testing administrators, college admissions counselors, and future employers as players. Whether I like it or not, school is not just about learning, but is equally a game about accountability through scored performance. I try my best to keep the players who are concerned with accountability on as separate a board as possible, and to be transparent with students when we are engaging with this other game. Students must be adept at playing both boards.

The Pieces

The pieces of the game of school include the lesson plan, which brings me back to the original subject of this post: setting an objective. There has been a trend in progressive spaces to design spaces of uncertainty for students to participate in discovery. This discovery is not the objective, but rather a means towards a standardized objective. From my understanding, unpredictability can be threatening to many students, especially those most marginalized in our communities. When discovery is a means to an end, students are anxious about whether they will get to that end.

I have increasingly found success in both relationships and testing scores when I am transparent about separating the learning game from the performance game. A good place to provide that separation is in my lesson objective. Letting students know ahead of time if my goal is to get excited about math with them or to train a performable math skill goes a long way in providing security and strengthening trust.

Assessing success in meeting an objective depends on which game we are playing too. If my objective is instrumental, presentations, tests, portfolios, and informal assessments work perfectly fine. If my goal is relational, I can assess success through connecting with my students. We engage in spirited debates, we celebrate aha moments, and most importantly, we all have a great deal of fun.