As members of the IB community, teachers at my school spend a lot of time planning and implementing strategies for cultivating the Learner Profile attributes in our students. This is exactly how it should be. The Learner Profile is central to the mission of IB and, as such, central to the mission of any IB school. Moreover, investing time and energy into proactively developing these attributes is a positive, strengths-oriented approach that is much more inspiring than a deficits-oriented approach. Thus, when it comes to the Learner Profile, our guiding question is “What experiences can we incorporate into our instruction that will help students to develop the Learner Profile attributes?”
From time to time, however, I think there is value in asking the more critical question, “What elements of of our instruction prevent students from developing the Learner Profile attributes?” This sheds light on some of the practices that might (unintentionally) be undermining our efforts in other areas.
In my own practice as a math teacher, I can think of a few habits that, unchecked, get in the way of my primary goal:
- Teaching students tricks or shortcuts undermines their thinking skills if they are not required to first make sense of the algorithm.
- Organizing assignments by topic or skill limits students’ thinking, as they follow the same procedure without having to identify the best skill to use in a given situation.
- Providing all the necessary information for students to solve a word problem undermines their inquiry skills, and passes up a valuable opportunity for students to generate questions rather than answering questions supplied by the teacher.
- Having students consult the answer key (or the teacher) immediately after solving a problem detracts from the value of reflecting on the cues available to determine if the solution is reasonable.
None of these habits is inherently bad, and they are all appropriate in some circumstances; however, if they become the standard operating procedure, students lose valuable opportunities to develop important traits. Imagine the unintended message we would send to students if the habits described above were entrenched in the routines of the class: repeat the process your have been shown (don’t think about what to do, how to do it or why it works), let the teacher ask the questions (don’t generate questions of your own), only the teacher has the answer. Together, these messages reduce students’ independence and self-efficacy.
Parents and teachers alike are constantly making decisions about how to help students develop character and intellect. There are too many decisions to make a pro-con list for every one; however, occasional reflection about the about the extent to which our habits support our goals will help to ensure our efforts yield the best possible result. When teachers and parents establish routines that are consistent with a shared goal, we support each other in developing students’ full potential.
I recently came across this quote from Erica McWilliam’s 2008 article entitled, Unlearning how to teach.
Our highest educational achievers may well be aligned with their teachers in knowing what to do if and when they have the script. But as indicated earlier, this sort of certain and tidy knowing is out of alignment with a scriptless and fluid social world. Our best learners will be those who can make ‘not knowing’ useful, who do not need the blue- print, the template, the map, to make a new kind of sense.
What does it say about our current approach to teaching and assessment if our highest-achieving students are not equipped for the future?
How do we teach our students to thrive in unfamiliar situations?
Some ideas that spring to my mind are…
- making sure that students practice transferring knowledge and skills into new situations (I’ve written about this here and here).
- making sure that assessment is more about monitoring progress than measuring performance (I’ve written about this here and here).
What ideas come to your mind?
I spend a lot of time thinking (and writing) about incorporating inquiry into my math classes. I often classify inquiry in math class into two different categories: math by inquiry and math for inquiry.
Graphing is a great way for students to use their math skills for inquiry. From Kindergarten students using pictographs to visualize trends in the weather to humanities students analyzing government spending, graphing allows students to visualize relationships, make comparisons and formulate hypothesis in a wide range of fields.
This year, I want to make my teaching more about questions than answers. Of course I want students to learn how to find answers independently, but I would also like them to find questions independently. In the spirit of being less helpful, I want to get my students extending problems, generating questions and learning to see math everywhere.
For example, what questions might this picture inspire?
What questions come to mind when you see this?
Given these starting points, what different directions could students take? Post your ideas here…
I’ve been trying to be less helpful to my math students so that they can develop strategies for coping with unfamiliar situations. Last week, I had my final Math 8 class of the year. My students had been preparing for a year-end exam and I wanted to show them some sample problems so that they could focus their studying time on the topics in which they need the most practice. Truth be told, I also wanted to scare them a little bit, so that they would would take their studying seriously. Continue reading
My grade 8 students just spent 40 minutes working on this problem:
A circle with a area = pi is tangent to the x and y axes of a grid. What is the distance from the centre of the circle to the origin?
Other than defining “tangent” for them, I didn’t give them any other hints. They were able to solve the problem using the knowledge that they have just acquired about Pythagorean Theorem, along with their prior knowledge of x-y co-ordinates and the area of circles. The class is a mixed-ability class (as all math classes are at my school), but I had grouped students in similar-ability groups for this activity. As a watched students working on the problem, I was impressed with a few things… Continue reading
I recently wrote about using an electronic graphing tool to speed up the mechanics of graphing so that students could make deeper connections about how the content we were covering. The activities that followed were a totally serendipitous foray into some very rich math discussions. Here’s the story…
One of the requirements of the math framework in the school where I teach is that we assess students’ ability to investigate patterns, describe them a general rules and verify/prove that they are true. So, I had students investigate how the values of m and b affect the shape of linear graphs (y = mx + b). Students used an electronic graphing tool in order to generate a variety of graphs quickly in order to make observations. If you’re interested in that part of the story, you can read about it here. If you’re interested in using electronic graphing tools with your class, you should also check out this one, which I only just discovered and is much better than what I used with my class. Continue reading