An Inquiry-Based Approach to Math

I am thrilled to present this guest post. Reflective in nature and representing a strong synergy across two books, Ryan and I connected on twitter and brought this collaboration together over the past few weeks. Enjoy the read and as always, find and follow the amazing educators sharing their work here. Thank you Ryan!

I’m the kind of person who gets fired up by big ideas. And, for me, the scaffolded approach to inquiry-based learning described by Trevor Mackenzie in Dive into Inquiry is a really big idea. For a couple of days in July, I read Dive into Inquiry on my couch, verbalizing my excitement since my roommates were all at work. When I finished, I felt strongly that this approach to inquiry would foster deeper learning for my students, but I needed to adapt it to my specific class environment.


I teach 7th grade math at a public charter school in Washington D.C. We’re an “IB for All” school which means that all of our 1000+ students are a part of the International Baccalaureate program which places a heavy emphasis on inquiry-based learning. In the hope of furthering inquiry-based learning at our school, our leadership team assigned Dive into Inquiry as summer reading for every faculty member.

Last year was my first full year as a middle school teacher and I started the summer eager to improve my practice with books like Dive into Inquiry. I really appreciate how Mackenzie uses his own Senior level English course as an exemplar throughout the book. I loved how students could choose a text that they’re curious about and investigate its theme or research a passion and write an essay on it. 

But, who has a passion for supplementary angles? How curious are any of us about what happens when we multiply two negative numbers? I needed to figure out the middle school math equivalent to how Mackenzie tapped into his students’ passions, curiosities, and goals. Fortunately, the next book I decided to pick up was Mathematical Mindsets by Jo Boaler. Together, these two books showed me how I could unlock the power of inquiry-based learning in a math class. 

Real Math vs. School Math

Boaler’s book completely reframed how I think about math. She explains that, in school, math is often framed as a set of procedures we follow to find specific answers (i.e. any question that asks you to “Find x”). But, this is completely different from the work of real mathematicians. Real mathematicians, as described by Boaler and others cited in her book, start by asking a really good question. 

“How many years do we have before the global temperature rises 2 degrees celsius?” 

Then real mathematicians use their understanding of mathematical concepts to create a model that represents the situation. 

“Let’s account for all of the factors that contribute to global temperature rise and create a model that calculates their cumulative effect.” 

Then, they calculate what the answer should be. 

“Run the model on the computer.” 

Finally, we go back to the real world and see if our answer makes sense. Sometimes it’s easy to see if our answer makes sense. But sometimes it’s not. And that’s where math has so much value. It’s the quantitative reasoning we need to make a decision when we can’t run an experiment to see what happens (which is Science, by the way.) 

The work of real mathematicians sounds a whole lot like inquiry-based learning to me. When I start thinking about math class as a space to investigate interesting questions using quantitative reasoning, the scaffolded approach to inquiry-based learning proposed in Dive into Inquiry fits perfectly. Not only do we need to enable students to investigate interesting questions using math, but we need to show them what real math is through guided and controlled inquiry. 

Math as a Toolkit

What became immediately apparent to me is that this approach is going to dramatically change how I teach math concepts. Instead of the objective of a unit being for students to learn specific math concepts, these math concepts become a set of tools that enable students to investigate interesting questions. It’s my job as a math educator to help students learn certain math concepts by posing interesting questions that highlight these concepts, but my job in a true inquiry environment is also to let students find and use their own tools. 

For example, this year I want students to investigate how the Nazca people created the Nazca Lines without modern (or alien!) technology by using proportional relationships to scale up drawings. The unit leading up to this project is on proportional relationships, but a true inquiry process might also involve finding the area of different shapes (geometry) and understanding the relationship between lines and angles (trigonometry). We might even get into the historical and social context of the Nazca Lines, the tools and methods used to create them, and their meaning as a form of expression (world history, design, art, anthropology...). I’m realizing that in order for math class to be truly inquiry-based, math needs to the toolkit, not the goal.


Learning from Mistakes

In Mathematical Mindsets, Boaler points out that when we allow math to be a toolkit for answering interesting questions rather than a procedure for getting the right answer, we open ourselves up to something really scary for students in a math class - a lot of wrong answers. Boaler explains that’s exactly what we want (she has a whole chapter on it!). Research shows that people learn best from making mistakes. 

In the context of inquiry-based learning, I see an additional benefit. Not only do we learn the most math by making mistakes, we learn the most from math by making mistakes. 

Imagine I want to make a cake, but the recipe I have is for 12 servings and I only want a cake with 2 servings. Well, I could simply use ⅙ of all the ingredients. If the cake turns out fine, great. But, imagine instead that my smaller cake explodes in the oven! What did I fail to account for when I found ⅙ of all the ingredients (my mathematical model)? 

Did I leave the smaller cake in the oven for too long? Was my new cake pan too small? Did I just divide everything incorrectly? All of these questions could be factored into a stronger mathematical model for making smaller cakes, but I never would have known to check if my cake hadn’t exploded in the first place. Math that leads to incorrect answers enables us to learn more about math and the world. As I bring more inquiry-based learning into my classroom, I want to think about how I show students that mistakes are the most exciting part of math. 

An Inquiry-Based Approach to Math 

What I’ve taken away from Dive into Inquiry and Mathematical Mindsets is that inquiry-based learning is a deeper, more authentic way of learning math than traditional approaches. This year, I want to reframe my units to start with interesting questions and let key math concepts serve as important, but not exclusive, tools in answering those questions. I also want to orient students toward a growth-mindset that turns mistakes into rich learning experiences.

That’s a lot of changes for one year. Implementing these changes will require a lot of work, experimentation, and student input before they lead to the big ideas that I’ve shared here. But, I also believe that making these changes is going to help me better understand and deliver the true value of math for my students. And, like I said, big ideas fire me up! 

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Ryan Steinbach is an educator and facilitator. Currently, Ryan is a math teacher at DC International School, an International Baccalaureate (IB) for All public charter school in Washington D.C. Ryan is also passionate about social entrepreneurship and is an after-school program leader and abroad trip leader for LearnServe International, a DC-based nonprofit that equips high school students from diverse backgrounds with the entrepreneurial vision and leadership skills needed to tackle social challenges at home and abroad. Prior to his work as an educator, Ryan helped young professionals build careers in the social enterprise and nonprofit sectors in India, Kenya, and Washington DC. Ryan earned a Bachelor's of Science degree in Marketing and Management at the University of Maryland, College Park. He duel certified in middle school mathematics and special education.