The Art of Balancing Inquiry and Content (in Collaboration!)


Do you teach a subject that is heavily driven by syllabus content? Any chance your students take major exams at the end of the course, and that those exam marks help decide their future opportunities? Yeah, me too. It’s a balancing act teaching in the IB Diploma Programme: on the one hand, Mathematics is about big concepts encompassing Truth, Beauty and Usefulness*; on the other hand, the better my students’ exam scores are, the more choices they potentially have for university studies. The temptation to teach completely to the test is understandable, isn’t it.

While the IB DP recognizes the importance of, and encourages, teaching the big concepts and linking them to other subjects, it can often feel impossible to do those concepts justice in the face of the exam pressure. Mastering the optimal combination of conceptual understanding, skill development, inquiry-based learning and content-focused instruction is one of my professional goals. The collaborative revamp of the grade 12 unit on Vectors is one of the best units I have worked on this year, and it may come closest to that optimal balance. We’ll see how the results are after the unit assessment, and whether students retain their knowledge and skills when they take their external exams in May.

The team approach to unit planning is exciting, as we have pooled our talents and resources into a first attempt at a unit overhaul that moves away from chalk-n-talk and shifts into the territory of hands-on, collaborative learning for students. In the few years we have experimented with various methods for “flipping” instruction, my colleagues and I have found that the standard flipped model has a few drawbacks:

  1. All your time and energy are poured into creating videos, at least in the first run of a flipped unit. Class time is spent doing homework, and that is ho-hum.
  2. Class time could be spent doing better, more meaningful things. Like what? We have struggled to find relevant ideas here for Mathematics.
  3. It is still just direct instruction + independent practice.

In our current unit, therefore, we decided to do flipped learning for all of #3 above. It looks a bit like this:

  1. Students work on course modules. Per module, they have a minimum of one week to watch 3 lesson videos (15-20 min each), take textbook notes, and do the independent practice problems.
  2. Each module has a due date, and there is a formative assessment on that date.
  3. Class time is mixed-use. So far, we have: run a scavenger hunt in teams formed from all three classes (54 students!), built 3-d coordinate systems to model vectors in space, taken all 54 students on a field trip to a pool hall to “do vectors” in reality, and had students work collaboratively to solve problems then present their solutions to the class. Other activities to come include creating mathematical models of the vectors produced at the pool hall, and collaborative work on “proofs” of dot-product properties. The farther we move into the unit, the more class time is oriented toward theory and problem-solving.
Student-built 3-d coordinate system. See the vector toothpicks attached with play-doh?!

Student-built 3-d coordinate system. See the vector toothpicks attached with play-doh?!

Running the modules has allowed students more freedom in planning their time. We are attempting to get them to focus on the skill of note-taking to increase their own independence in learning, and are checking these notes at each module due-date. In terms of the activities during class time, we are finding that we aren’t perfect on this first run, and can improve on clarifying our expectations, but the students are largely engaged and enjoying the learning. As we move toward more problem-solving classes, we teachers are free to spend our time as observers and facilitators, rather than as instructors. Watching students discuss and argue over solution methods, and listening to them present solutions and answer questions from their audience, allows us plenty of opportunities to guide their thinking and help clarify understanding.

Happily, all the videos were created in past iterations of flipping this unit, so we are benefiting from one colleague’s enormous investment of time. It is my hope that my colleagues and I have split up the workload so that we are each doing our fair share, and also playing to each individual’s strengths. One person has the videos, another is an expert organizer, another builds the tasks. Together, this team effort is producing a Vectors unit unlike any before!

It is exciting to produce a series of learning opportunities for students that actually breaks the mold of the standard math classroom. If you’re wondering how their summative assessment will look, it will look very much like unit tests as we all know them. With their final 2-year exam in just a few months, we can’t throw out everything. However, hopefully the increased focus on conceptual and connected learning will positively affect student understanding – meaning that they don’t have to cram as much for the exams, as they already get the big picture.

* This is my humble opinion, having teased out the answers to “why do I need to learn this” for over a decade. 

Another student busy building a 3-d coordinate system, this time with the amazing Zometool kit.

Another student busy building a 3-d coordinate system, this time with the amazing Zometool kit.

5 Replies to “The Art of Balancing Inquiry and Content (in Collaboration!)”

  1. This is truly inspiring Ruth! What a great example of the power of team and risk taking. The pressures of IB are real, and it’s so great to see that you and the rest of the crew at The York School are innovative in your approach to student learning.

    Will you be taking advantage of Edpuzzle at all to check for understanding when students complete the module? I’m dying to see how the modules work out and I’ve been thinking about how this looks in French.

    Looking forward to reading more about your journey!

    • Thanks Derek! We aren’t using Edpuzzle this round, although we talked about it. The formatives are on paper, as math is a written subject and often requires diagrams or special notation.
      So far I think the modules are an effective learning option for some students. We used the first formative as a way to direct our further teaching – the second formative will give us more information on their progress. The activities we are doing in class are giving me huge insight into their thinking, which is what I am really gaining from the entire process!

  2. This is inspiring work, Ruth! I think that everyone on the sidelines will be cheering on your students as they head into the final assessments; it is our hope that engaged, meaningful learning really does contribute to better test results. What you have done is a prime example of how successful projects in education require collaboration, effective use of technologies, and the foundation of professional development, not to mention enhanced skills with a pool cue!
    Great work!

  3. Ruth, so lovely to read your post. You are exemplary in best practices; observing and gathering evidence to your planning, asking yourself questions, seeking out collaborative opportunities, finding engaging opportunities for students to connect and see relevance in their learning and putting a plan into place. Very inspirational. Bravo!

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