03/22/14

Math, Choice, and Sharing With Peers

This is an conversation that Lara and I had with each other regarding both of our inquiry topics. Her focus is the math classroom. What a lovely way to spend a sunny Friday afternoon!

 

What we chat about:

Motivation in Math: How do we keep students motivated when they’re working on drilling? This ties to the important notion of relevance of learning. Check out this tweet. It’s in response to an interview on The Current about how math is taught, specifically in regards to drilling.

#TheCurrentCBC The only reason to memorize the times tables is to add speed…no magic here. Concepts before facts.

— Kirsty Gourlay (@Stampgame) March 27, 2014

 

“Concepts before facts.” Relevance before concepts?

Self-Efficacy: How do students’ perceptions of their abilities in math affect their motivation? How is this different in math than it is in other subjects, for example with reading?

Differentiation in math: Should we do this? Can we? Montessori classrooms do this really well through the organization of time in the day, and through the set up of the classroom and materials.

Teamwork in the classroom: how organic/forced should it be?

How do we grade in the math classroom? Pre-Tests, Post-Tests, and Re-tests.

What does it mean to be “fair”?

03/19/14

Grades and Choice

Grades are a big part of how we as teachers, and we as a culture do school. There is a lot of debate, particularly right now, about the merits of grades. It is something that I am wrestling with quite a bit, but I believe that grades are well worth mentioning when we want to talk about motivation and choices in the classroom.

I believe that grades are so entrenched in our system that it is now very difficult to change them or remove them, even at the early grades. Grades are a symptom of a much larger factory system of schools that ignores individual difference, apart from the “good student/bad student” dichotomy. Someone once pointed out to me in a very interesting argument against single grade classrooms that the only other place in life where you would ever see that kind of age stratification is in a conscription army. In many ways, our schools model a militaristic form. Grades act as a sort of ranking system. They are the classism of the education system, and are equally meaningless and powerful. This being said, I believe grades can be transformed. When we start measuring progress on an individual level rather than insisting that students all meet the exact same outcomes, we make grades more meaningful. When grades are allowed to evaluate and reward learning rather than simply product, we make grades more meaningful.

Alfie Kohn lays out an excellent, though not exactly new, series of arguments against grades in the article ‘A Case Against Grades’. One of the most compelling among them is that “grades tend to diminish students’ interest in whatever they are learning” (Kohn, 2012: 9) This point is very much connected, I believe to the next, which is that students are less likely to take risks in their learning or to challenge themselves when they know that marks are on the line (Kohn, 2012). This has important implications for my question of choice. How do grades affect the choices students make? If there is a grade associated with a task and I provide my students with choices then perhaps the fact that I’m grading them will dissuade them from self-regulating and making the level-appropriate choices I’m hoping for. Are grades a hindrance to self-regulated learning?

Can we even measure the types of learning we dream of for our students? Kohn quotes McNeil in this article as saying that “measurable outcomes may be the least significant results of learning” (McNeil in Kohn, 2012: 11). Kohn mentions that “the imperatives of data collection seem to upstage the children themselves and the goal of helping them become more enthusiastic about learning” (Kohn, 2012: 11). While we are told time and again in our curriculum classes that we are never to compare students when assessing, in the assessment course we take as teacher candidates we are sent a truly mixed message. The focus is on “acurate” data collection. While assessment of whatever kind should be meaningful, I do not see the value in making it one-fits-all. For example, a teacher assigns a project on WW2. Emma went into the course knowing all of the battles and tactics and key figures in the war. Charlie knew almost nothing about it. How it meaningful to create a one-fits-all rubric that assesses the knowledge of the students at the end of this project? While Charlie may have worked hard to obtain this knowledge and could get an A, Emma is able to get an A without actually learning anything. This is a problem with testing, but it is also a problem with rubrics. Though we like to think that comparing students to a set standard is different and better than comparing them to each other, we are lying to ourselves if we think that the rubric model is necessarily fair, or is socially just.

Furthermore, let us extend the example of Emma and Charlie to question the very validity of many types of assessment for actually measuring the learning and understanding that we care about. Imagine now that Emma got an A for this term because of her great score on the test about WW2. Charlie worked hard, learned a lot, and while he came to understand many of the factors and consequences of the war, failed to memorize all of the names of the battles. He got a B. As they are both leaving class, Emma turns to Charlie and asks, “So, in WW2… who won?”. This is a real example. I won’t say of who. Granted, this situation could have been avoided by more careful consideration of the assessment methods, but it does illustrate one common and damaging problem with grades. We often assess what is easy to count, rather than what really matters. Many students are motivate by grades, and learn the material directionally to score well rather than due to a desire to really understand. I have come to realise that a combination of these two situations is extremely common. As long as grades are something that teachers are required to produce, we must do everything in our power to avoid this situation, as it makes grades not only meaningless, but dangerous. Fortunately, the PLO’s are changing in ways that will (hopefully) force our hands in this direction, putting the focus on skills and processes rather than facts and fragments of information. I wonder what this will mean for the provincial exam in SS11.

Kohn argues vehemently against the use of grades in their entirety. While I find this notion theoretically compelling, I am aware that as a new teacher going forth into the pre-fabricated school system I will have to operate to some extent within its confines. With this in mind, I wonder what I can do to minimize the detrimental effects of grades in my classroom on students’ psyches, on their peer relationships, and on their motivation to learn.

Drawing on some of the methods and ideas that I’ve gathered from other educators, I propose a growth attitude towards grades, rather than a set of standard outcomes. Instead of making our assessment tools express specific knowledge or understanding outcomes, we can use them to help us measure growth. For instance, in a classroom where students work independently on math plans, they may understand that completing 5 sections of the program within a term means that they get a B. In this way, a student who moved from multiplication to factorials in this time may get a B, while the student who shows progress from addition to skip-counting may also be eligible for a B. When we create rubrics or use grades to measure growth, we devalue them as competitive capital, and we make them mean something that better reflects what we actually care about as educators. This can also make grades less damaging to the motivation of students. While fixed-outcome rubrics and other assessments make risk-taking or attempts at more difficult material less enticing to students who fear a lower grade, if grades represent growth, students may be encouraged to try something new. Of course, this does not solve all of the problems of using extrinsic rather than intrinsic motivation, but again, when working within the system, how can we best meet the needs of our students?