Running Workshops: Resources

Over the years, we have been dedicated to supporting faculty in their process of bringing more inquiry into the learning and teaching in their classrooms. We are firmly committed to also using inquiry in our work with faculty, since we believe that this is how learning happens best (for faculty just as for students).

On this page, you can access the resources we collected/created to run faculty workshops. These resources are based on ideas that we found in journal articles and books and on tasks that we invented. We used the tasks in many workshops to refine them and make sure that they work (for us, that is). We would love to get feedback on how they work for others to see what’s missing or could be changed.

Invitation: Explore The Bigger Picture

We recommend you read the following blog, which is written in an interactive style, to explore the bigger picture of concepts and procedures of teaching with inquiry. These ideas guide our perspective on designing these faculty workshop modules. The blog invites you, the reader, to make connections yourself and discover new ideas as you read and think along.

In this blog we invite the reader to think deeply about professional development opportunities for faculty. The focus of this professional development is to improve teaching by including more inquiry in the mathematics classroom. Our hope is that faculty developing professional development will use some of our ideas to create new opportunities that lead to transformational change and deep conceptual learning about teaching.

Accessing the Materials

For each of the workshop modules we describe below (labeled A-H), we provide a Powerpoint presentation that includes hidden pages with recommendations for the workshop facilitator; the Powerpoint also contains audience prompts that can be used to visually structure the workshop. Where needed, we also provide handouts and work sheets. As a guide, we decided to include the minimum that we would need to actually run each workshop. (Warning: this may not necessarily be sufficient for everyone.)
If you have experience in teaching and learning with inquiry, as well as some experience working with a faculty audience, these may be helpful starting points to design and run your own IBL workshops.

For simplicity, you can download the whole package of modules and resources through Google Drive . A description of the modules is provided on this page below.
You can use our materials for your own workshops and adapt them as needed.
Disclaimer: Use at your own risk. If you have questions, feel free to check in with us. We also would love to hear from you if you would like to collaborate on a joint workshop.

Quick Overview of the Modules

  • Module A: Immersion in Inquiry (with options for a variety of audiences),
  • Module B: Identifying Meta-Goals for our students (ie. non-content goals like persistence, creativity, etc.)
  • Module C: Analyzing IBL Classroom Videos
  • Module D: Creating IBL Materials (incl. modifying materials)
  • Module E: Staging Whole Class Discussions: choosing and ordering student work for productive discussions
  • Module F: Practicing Whole Class Discussions
  • Module G: Practicing Asking Good Questions
  • Module H: Assessment
  • Module I: “Why IBL Works” (Research)

To get a clearer sense of these workshop modules, please read on. We provide a short description of each module below, as well as brief context for their design.

Transformative Learning

Context: Loucks-Horsley et al. in [18, p. 70] point to features of a workshop experience that are likely to lead to transformative learning--a term they contrast with additive learning. (You can find the references we make on this page by consulting the references of the blog.)

  • Create a high level of dissonance.
  • Provide sufficient time, structure, and support for teachers to think
    through the dissonance experienced.
  • Embed the dissonance-creating and -resolving activities in teachers
    situations and practices.
  • Enable teachers to develop a new repertoire of practice that fits
    with their new understanding.
  • Engage teachers in a continuous process of improvement.
Module A: Immersion in Inquiry

Immersion in Inquiry is an approach to doing mathematics together with the participants so they can "experience the power of learning in this mode at their emotional level" and then to reflect together on the experience. It is important that participants can be their honest, authentic, mathematical selves in this immersion. In addition, the debriefing about the experience can help make visible participants' beliefs and assumptions at an emotional, experiential level.

The area of mathematical inquiry must be chosen carefully to be challenging enough, but still within reach, for the particular group of workshop participants. We have assembled a broad collection of mathematical activities so you have choices for a good fit.

We included options we have used with a variety of audiences:

  • Straight-cut origami (e.g. for math research faculty),
  • 3a+5b (e.g. for community college faculty concerned about algebra),
  • Bottle Activity (e.g. related to Calculus Sequence, Functions, …),
  • Dance Symmetry (e.g. for a very mixed audience, or one where art can serve as a shared entry point),
  • Number Game,
  • Chain Letter Activity (K-12 level),
  • Hex (intro to proof, general audience),
  • Nim (intro to proof, general audience),
  • Pennies & Paperclips (intro to proof, general audience),
  • RK Puzzles (intro to proof, general audience, w/ cool application),
  • Rubik’s Cube (general audience).

Embed activities in faculty's situations and practices

In their paper “The 5E Instructional Model: A Learning Cycle Approach for Inquiry-Based Science Teaching“, Duran and Duran [2] describe a (not necessarily ordered) sequence for learning with inquiry: engage, explore, explain, elaborate, and evaluate.

Accordingly certain ingredients are important for a teacher to create and provide for an inquiry classroom:

  • engage: establish a classroom atmosphere where students will engage in inquiry (big topic!),
  • explore: prepare a sequence of questions the students will inquire into (e.g. course materials),
  • explore: support students in engaging productively with the inquiry (big topic! e.g. teacher asking good questions),
  • explore: help make student thinking visible to the whole classroom community (e.g. presentations or whole class discussions),
  • explore and explain: help the whole community make sense of the evolving mathematical ideas themselves (e.g. whole class discussions),
  • elaborate: get students to apply their new understanding, and
  • evaluate: assess student reasoning (e.g. homework, reflections, assessment).

The following workshop modules engage workshop participants in building their skills and confidence with these faculty actions (or identify areas where more work is needed). We include a brief description of each workshop activity. Download the materials to take a closer look.

Module B: Identifying Meta-Goals for our students

In addition to content goals, we often also have non-content goals for our students, such as to develop persistence, creativity, etc. We call these meta-goals. In this activity participants brainstorm and collect meta-goals they have for their students, and then reflect on classroom practices that can help students further develop these practices.

Module C: Analyzing IBL Classroom Videos

This module allows a different introduction to IBL than the immersion mentioned above. Participants watch video clips of IBL in action and then reflect on the ingredients of IBL. While this experience is not as powerful as immersion in inquiry, some participants may be more open to this representation of practice. It also shows that students "can really do IBL."

Module D: Creating Materials

This activity starts with participants brainstorming features of a "good" inquiry activity. Depending on the level of participants' prior experience with IBL, this activity provides three different pathways to creating inquiry materials: (1) taking existing closed tasks (e.g. from a textbook) and opening them up, (2) analyzing the level of guidance, openness, and breadth of representations in three activities from a Calculus class, and (3) offering a pathway for creating inquiry materials from scratch, by starting with a concept map, identifying the big ideas, and then reverse-engineering activities to help students grapple with common misconceptions to develop and clarify the big ideas.

Module E: Staging Whole Class Discussions: choosing and ordering student work for productive discussions

One powerful aspect of whole class discussions is to decide what to discuss and in which order. In this module, participants first practice predicting student work. This is an crucial task because participants need to find several ways (correct and incorrect) of working on a mathematical task. They then choose which student artifacts are productive for a particular whole class discussion. This requires to really gain some clarity about which goals they are pursuing for their discussion - and the goals should be much more than just "getting the answer right."

Module F: Practicing Whole Class Discussions

In our experience, facilitating a productive whole class discussion is perhaps one of the most important skills to become fluent with. Often, facilitators are tempted to just explain the mathematical ideas, instead of eliciting student ideas, helping students listen to and disagree with each other, and helping the class to come to a common understanding.

To this effort, we developed an activity to practice some whole class discussion moves we learned from the elementary school classroom, see our blog on Whole Class Discussions and Suzanne Chapin's books [20, 3]. Two participants lead a mini inquiry lesson (15-20 minutes) with all other participants being students (but also being their true mathematician selves). The leaders are supposed to just ask questions and not add their own mathematical thinking or sense making. The facilitators of the professional development are helping the leading participants if they fall back into old patterns or feel stuck in the process of facilitation.

Module G: Practicing Asking Good Questions

Inspired by Suzanne Chapin’s talk moves for whole class discussions, we decided to identify and organize talk moves for a conversation with just one student (or a small group). Our categories are chosen so that a teacher can easily decide which groups of questions to select from in a given situation. They include questions related to different stages of problem solving, moves to clarify thinking and provide emotional support, as well as graceful ways of ending the conversation. In this activity, participants practice supporting another participant's authentic mathematical inquiry by asking only good questions that are not too leading (Do not explain anything.) Participants reflect on their experience in the student and teacher roles.

Module H: Assessment

In this module, participants think about different kinds of assessment, as well as differences between skills, methods, procedures, meta skills, and conceptual understanding. After engaging in a mathematical task together (ideas from algebra/pre-calculus), they create and analyze assessments using the idea of the prior activity. In our experience it is very rich to think about what exactly we would like to assess and then find or create appropriate tasks. It is easiest to assess skills, facts and methods - but how do we assess meta skills or conceptual understanding?

Module I: “Why IBL Works”

These resources summarize some of the findings and graphs from a seminal study by Laursen et al that shed some light on who benefits in what ways from learning with inquiry.

Ready to take a closer look? Access to modules and resources through Google Drive.

Desmos Activities to Support Faculty PD

Thanks to Dr. Mairead Greene for sharing the following Desmos activities that model how Desmos can be used in an IBL classroom while working on developing IBL teaching skills:
Activity 1
Activity 2.