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.
Over the weekend, I had the privilege of facilitating a session with IB Primary Years Program (PYP) teachers about inquiry in math class. Because we all work in British Columbia, we share the opportunities (and challenges) of delivering the new BC curriculum within the IB framework. As I prepared the session, the image of a double-headed arrow kept coming to mind.
I have just finished a series of patterns investigations with my math 10 class. In this specific series, students explored the connections between quadratic equations (in both vertex and factored form) in order to connections between the equation and the features of the graph (like the position of the vertex, and intercepts).
These kinds of activities are a regular feature of math in the IB Middle Years Program (MYP) in which students are required to consider a series of specific situations to identify a pattern, describe it as a general rule, verify that their rule works and then justify why it works.
I’ve had a love-hate relationship with this kind of task since I started teaching MYP math almost 10 years ago.
I hate investigations because…
- Students find it difficult to approach novel situations.
- I find it difficult to prepare students for novel situations.
However, I love investigations because…
- Investigating is what mathematicians do. While math students typically spend more time doing tests (i.e. using specific examples to demonstrate that they understand a general rule that someone else discovered), mathematicians are on the frontier of searching for new pattern, generalization and rules. By engaging students in this process (even if they are discovering patterns that are new to them, but well-known to others), they are engaging in the authentic work of mathematics.
- Investigations support inquiry skills. In looking at a variety of specific situations in order to find trends, patterns and generalization, students develop strategies of problem-solving, visualization, hypothesizing and generalizing. These skills support similar processes in other disciplines, like finding trends in a data set, identifying themes in a work of literature or cause-and-effect relationships in history.
- Investigations foster independence. By looking for patterns and general rules, students develop the confidence to use what they know as the basis to discover new things, making them less reliant on the teacher as the source of knowledge.
- Investigations cultivate persistence. Not all problem-solving strategies will work in every situation. The more experience students have investigating patterns, the more comfortable they will be with trying an approach and switching to a different strategy when necessary. Rather than seeing this as a set-back, they will accept it as a normal part of the process.
As you can see, the benefits of investigations outweigh the challenges. Promoting a classroom culture in which students are willing to take a risk on an unfamiliar problem and persist with challenging work requires on-going effort, but I believe the benefits are on-going as well.
Last spring, I had a conversation with a parent that has stuck with me ever since. She initiated a meeting with me because she wanted a textbook (or similar resource) so that she could study the same math content as her child in order to be able to help with homework. At first, the request sounded totally reasonable, and even admirable. I love the idea of a parent modeling life-long learning by learning along with her child; however, I felt uneasy about the request and couldn’t put my finger on why.
Stalling for a bit of time to figure out my own confusing reaction to the request, I asked the parent why she felt responsible for helping with homework (again, a weird question since I’m totally in favour of families supporting learning at home). She explained that both her parents were teachers and were very helpful to her as a student, especially when a teacher had covered content too quickly, or when she didn’t understand the way a teacher had explained something.
That’s when the penny dropped. As a teacher, one of the reasons I assign homework is to gauge whether students understand the content and whether they’re ready to move on. When parents help with homework, the product that I see gives the impression that everything is going well… even when it isn’t. As much as this parent appreciated the help of her parents, her teachers never found out that they weren’t meeting her needs: the homework was complete and correct, indicating (perhaps incorrectly) that the pace and approach were fully effective.
In contexts where there are marks to be earned from homework, there is an incentive in helping children earn as many of those marks as they can; however, if homework is really going to be about learning – the student learning the content and the teacher learning about students’ progress – then that kind of incentive needs to be removed (as I have argued before). Students must be able to present their skills honestly so that teachers can give helpful feedback and adjust their instruction.
So, how can parents help more helpfully? Here are some ideas that come to mind…
- instead of correcting work, prompt your child to check their own work using appropriate resources and strategies (like an answer key, spell-check)
- if your child is unsure whether something is correct, or why something is correct, prompt them to follow-up with their teacher before school or during class (ideally before the assignment is due)
- remind children to use the feedback that they have received… this could mean doing corrections (just for the sake of learning, not for extra credit), or perhaps they can use the feedback to improve subsequent work
If you have additional suggestions, please post them in the comments.
This post is adapted from a piece I wrote for my school newsletter in the Fall of 2016.
I have borrowed the title of this article from an excellent book by Jo Boaler. A researcher in from Stanford University, Dr. Boaler draws compelling connections between her work in mathematics education and the work of Carol Dweck, another Stanford researcher, who studies the growth mindset. Dweck draws an important distinction between a growth mindset and a fixed mindset. Those with a fixed mindset believe that their intelligence is innate and cannot be expanded, whereas those with a growth mindset believe that they can increase their intelligence through effort.
A growth mindset is essential for learning in mathematics. Research has shown that students with a fixed mindset tend to avoid challenging work. Interestingly, this tendency is particularly pronounced in high-achieving students, likely because an inability solve a challenging problem is a threat to their self-concept as a smart person. Conversely, students with a growth mindset see challenging problems as an opportunity to extend their skills and develop their intelligence. Continue reading
I have recently completed a second graduate program. My first foray into graduate-level studies was just after I completed my teachers’ training, but before I started working full-time as a teacher. I began my second graduate program after six years of teaching full-time. The two programs were different in both content and structure, so I expected the experience to be different; however, I attribute the most significant difference in the experience to how much my experience as a teacher had changed my approach to learning. Specifically, I found myself using many of the strategies that I had taught my grade 6 students. For example:
- K-W-L charts made my reading more purposeful. Rather than doing all the assigned reading and then working on the assignments, I started an outline of each assignment before beginning the readings so that I could identify and organize relevant information as I read. This also helped me to locate gaps in my knowledge and identify areas for further research.
- Breaking a Central Idea into Lines of Inquiry helped me to focus my research. As a teacher in an IB school, I quickly learned the lingo of Central Ideas and Lines of Inquiry. These are used to help students take big ideas, like Body systems play a role in our physical and mental health into smaller subtopics, like The main systems of the human body, The body’s defenses, and Our responsibility to protect our bodies. I used this structure to elaborate on the topic for my major research project. You can see a sample here.
- I used graphic organizers for everything. Whether it was finding information that was relevant to the various lines of inquiry I had developed, or using assignment criteria to make sure that my work was complete, I created charts in which my questions (or the required content for the assignment) were listed on one side and the information that I collected was listed on the other side. I often added a third column for my own thoughts, questions or opinions. By organizing information thematically rather by source (as I used to do), I was able to see key themes, synthesize information, and compare and contrast perspectives efficiently. It was easy to analyze the information, draw conclusion and suggest implications.
- I used the text I had already written. When I used graphic organizers, I would have an outline by the time I finished my research. Rather than staring a blank page, trying to find the words, I would often copy-and-paste my point-form notes (citing and paraphrasing appropriately, of course) and then rework the text into complete sentences and paragraphs. Editing and formatting text was much less daunting than writing from scratch.
All of these are strategies that I have taught my students at various times. As much as I’m tempted to think “why didn’t my teachers teach me how to do this!?”, I prefer to focus on the thought that my students are gaining specific strategies that will support their learning and thinking. If those strategies also help me to be a better student, so much the better!
Inspired by this segment of the BBC’s series, The Code, I recently tried replicating the jelly bean experiment during my school’s science fair.
I filled an old pickle jar with jelly beans and put it on display as students, teachers and parents explored the science fair. All science fair visitors were invited to estimate the number of jelly beans in the jar for a chance to win all the jelly beans. Meanwhile, I collected the estimates to determine whether the average estimate approached the actual number as more and more people participated.
In order to streamline the data collection, I had students enter their estimate in a google form. The estimates were automatically collected in a spreadsheet that I could analyze. It only took a few minutes to graph the results:
The display was a popular exhibit at the science fair and appealed to both elementary and secondary students, as well as parent visitors. As it turned out, the three best estimates all came from elementary students. I just presented the results at the elementary school assembly and it was a big hit. It was great to be able to present scientific evidence that two heads (or many heads) are better than one!
Would you like to give this a try at your school? Here’s a sample Google Form that you can use to get started.