### Introduction

The idea of Intelligent Fast Failure resonated with me instantly, that giving students the opportunity to not only try but to fail allowed them to fully engage in the learning process. “Students who tried lots of ideas in a short period of time were going through a process of fast failure wherein each failed idea constituted knowledge acquisition,” (Tahirsyla, 2012) this reminded me of something I heard a lot growing up that “a fail is a First Attempt In Learning” (Miller, 2015). For me this is something I often find challenging to accept, feeling like I need to get it right and do it perfectly right away, that there is no room for error, but without error there is no room for growth. Accepting failure is something that I grapple with both in my personal and professional lives, the idea that it must be perfect, or it is no good. For me part of my stretching, innovating and taking a risk is being okay with things not being perfect, not getting it right the first time. I’m the student who rewrites assignments 5 or 6 times before handing them in. When I lesson plan I typically over plan and have plans A, B and C ready with a mental plan if none of those work. While this planning accepts some elements of Intelligent Fast Failure, being able to notice when a plan isn’t working and adapting accordingly quickly it also limits my ability to fully follow where my students’ wonders. For me sharing my plan felt like a risk, it felt vulnerable, to discuss how I want to change and update how I am teaching math. It also opened me up to failure, that those reading it would completely disagree with my ideas, think I am foolish or that my ideas would never work. For both my students and I, it is going to be necessary to create opportunities to fail in a way that is safe, “when we fail in safe ways, we want to learn more. Our frustration in the face of failure helps us to develop the grit we need to succeed,” (Miller, 2015). Miller gives the example of sports teams that may lose back-to-back games but still go out and try again. I am also reminded of my past as a competitive dancer, the dance studio was one of the few places that mistakes at least in class didn’t feel embarrassing.

Why Mathematics?

“Without numbers, we cannot send rockets roaming the solar system, nor could we build bridges, exchange goods, or pay our bills. In some sense, then, numbers are cultural inventions only comparable in importance to agriculture or the wheel. But they might have even deeper roots,” (Dehaene, 1997). Math is an area I’m deeply passionate about teaching and having my students engage with in a positive light. My own experience with math as a student was not always pleasant and included a lot of anxiety inducing math drills. In post-secondary I initially struggled with math, and it wasn’t until I had a passion project involving Geographic Information Systems and I suddenly had to do math and be good at it. That project meant that for the first time I had a reason to embrace math and mathematical thinking as well as a professor that pushed me to see the power of my own thinking and encouraged me to try new things and innovate shaping my outlook on learning and on myself. I also find that math is often something that makes my students and their parents anxious. Applying my efforts to innovate in math and building a positive math culture is my priority for the upcoming school year. I need to focus my time and attention on opportunities for students to apply Sternberg’s 3 Rs and provide them with opportunities for choice in their learning.

### My Plan and the Risks

In developing my plan, I created a unit plan of what I would like students to learn in the number sense unit and how students will have the opportunity to be given choices as well as to practice the New Three Rs. I started with my number sense unit when planning for innovating math in my classroom for two reasons, the first is that number sense is the unit I begin the year with, second, we need strong number sense to support learning in other areas of mathematics. Number sense is the set of skills that allows people to work with numbers. Number sense skills include: understanding quantities, the concept of more and less, the concept of larger and smaller, understanding of the order of numbers, understanding that numbers are symbols represent quantitates, making number comparisons and understanding the relationship between a single item and groups of items (Cunningham, n.d.). Number and number sense are essential to navigating our world, communication, navigation, banking, shopping, and cooking rely on numbers in a variety of forms. Australian educator Eddie Woo states in his 2018 Ted Talk, “mathematics is a sense, just like sight and touch, it’s a sense that allows us to perceive realities that would otherwise be intangible to us. ” (Woo, 2018) he continues to assert that, “surprisingly deep down we are all born to be mathematicians,” (Woo, 2018). Seeing number sense as something that is innate in all people, it makes sense that our focus in math education should be on number sense. If we develop number sense first, we will help all students develop the essential skills needed to solve increasingly complex problems. Math is our ability to organize information and find patterns, to make connections. Building the skills for connection and logical reasoning in math we are also strengthening the same skills across the curriculum. Building number sense gives students the foundations to reason through mathematical problems.

Sternberg listed the new three Rs as reasoning, responsibility, and resilience, (Sternberg, 2008) these connect with the strategies discussed in *Building Thinking Classrooms*. In *Building Thinking Classrooms*, Peter Liljedahl advocates for the use of check your understanding problems, a set of questions that the teacher neither collects or assesses, this philosophy ties well with Sternberg’s assumption that students need to develop responsibility and that responsibility needs to be taught and practiced. Much of Liiljedahl’s work focusing on mathematics and building student ability to think and reason mathematically ties well with Sternberg‘s idea of reasoning. In *Building Thinking Classrooms *Liljedahl asserts that all students are capable of thinking and reasoning mathematically and it is our approach to teaching mathematics that needs to shift to encourage students to think more deeply about the math (Liljedahl, 2021). Also when considering the work of Dan Mayer we look at the idea of students making choices and taking responsibility for their learning in math by working through a good problem that provokes thinking and is directly linked to the real world (Meyer, 2010). This type of problem may include three act math tasks, open middle and open ended problems, these provide an opportunity for students to practice many of the skills that we are working on related to Sternberg‘s new 3Rs. These types of tasks require students to be critical thinkers and their reasoning skills, they also require resilience in problem solving because our first attempt at a problem may not be correct and we need to back up, reset and try again often repeating the cycle many times in order to solve the problem.

Solving open ended and open middle problems it gives students an increased level of choice. In giving students increasing choice and working more with open ended and open middle problems it is also necessary for the teacher to step back and give up control. We want students to think, collaborate, discuss, and discover sometimes this can feel chaotic in a classroom. While “CHAOS stands for Creating

Havoc Accelerates Outrageous Success and it means that the product needs to be refined, improved and redesigned,” (Tahirsyla, 2012), embracing chaos as a teacher is a challenge and a risk. Flipping chaos to be an acronym changed my thinking, however it is going to be a risk. Allowing for CHAOS allows students to have choice in their learning, however it also creates opportunities for loss of classroom management. This also creates opportunities for students to choose to disengage or to sit back and let their teammates solve the problem off-loading the responsibility for thinking and learning onto others.

Choice also builds responsibility, students will be able to select the problems and approaches that work for them. Open ended work that allows students to make choices also helps avoid the trap of looking only at the middle when planning and teaching. It provides opportunities for differentiation within the same problem or problem set by choosing low threshold high ceiling tasks. While this sounds great, I think in practice I will need to balance it with some opportunities for more traditional learning. The risk with choice and chaos is that instead of incredible deep learning happening the exact opposite happens and limited progress or no progress is made. Giving open ended problems you run the risk that the student who is reluctant to think and relies on algorithms and formulas shuts down and disengages. I also wonder how it will be received by the parents in my school community as previous attempts at change and innovation have needed time to be accepted by our parent community.

When reading about positive failure and Intelligent Fast Failure both are intricately linked with resilience. The idea of having students fail then learn from the failure also connects with the applied design skills and technology curriculum in BC. The design project and making a product testing it and refining it is part of one of the curricular competency’s for ADST. We need to create a classroom culture that fosters resilience, this is backed up in Angela Duckworth’s work on grit and is highlighted in

Sternberg’s work on The New Three Rs as well as being supported in Miller’s work on the *Freedom To Fail*. As teachers we need to create an environment that students feel that they have the freedom to fail and a failure is not an end point but beginning, in math this could look like trying a problem again using a new strategy to solve the problem. Miller states, “if we want students to truly value and learn from failure, we must be intentional about creating a culture that gives them the freedom to do so. By establishing classroom norms and routines that support a safe environment, we can provide students with the scaffolding they need as they fail forward,” (Miller, 2015). Creating an environment where students feel safe to take risks and to fail also relies on connection, students must feel connected, supported, and cared for before they will be confident taking risks. This is also an opportunity for us to take a risk as teachers, giving up control to allow students to take more control. For me it is also a risk with my parent community, who often struggle when their student is not the absolute best or instantly successful, parents need to understand that learning and resilience comes from the chance to struggle. Many of my students have previously struggled with resilience

### Feedback

When sharing my plan, I received some positive feedback but also areas to enhanced or better explained. One of the areas that I received a lot of feedback on was the assessment and aligning my assessment with the goals I laid out in my framework for planning and my unit plan. While I had innovated in my framework and in my unit plan, trying new things in some areas and adapting others to improve them I had done little to update my assessment. By updating my assessment based on the feedback from colleagues I am able to more accurately assess my students based on my teaching style and give my students a chance to truly show their thinking and not just rote memory of algorithms.

Sharing my plan was a great moment for refining my ideas even if it felt very vulnerable and was an opportunity for me to try failing forward and intelligent fast failure. I had to acknowledge that some of my ideas were too much content for a single unit or would fit better in other math units, “even among the selected ideas, not all will prove worthy of further development but instead will just become one-shot contributions that soon lead to dead ends,” (Simonton, 2015). I had many of these moments when sharing my plan and the accompanying assessment. I would work on something, share it with someone else get their feedback and edit it before sharing it again. Regarding my actual unit plan a lot of the feedback I had was about time and how would it be possible to do in a short amount of time each day as well as it not taking an entire term. This led me to think about how I structure my day and consider moving math to the longer afternoon block. Traditionally we have done math first thing in the morning which also happens to be my shortest block of the day, however before I can make the scheduling decisions for next year I need to see where my prep blocks, PE times and DPA times fall and when collaboration time is. There was a lot of positive feedback about the New 3Rs and incorporating those into daily practice. In discussing the New 3 Rs with my colleagues it became clear that these are things that really could be a school wide focus and brought forward as whole school character goals. The focus on student choice and student reasoning was also something that my colleagues appreciated when discussing and looking at this unit. We had an ongoing discussion of how choice and the challenge by choice philosophy allowed for differentiation within the unit. Using rich tasks and open-ended tasks my colleagues also pointed out how they would be very easily adaptable to doing small group focused instruction at the rainbow table, which meets the needs of all learners. We would be able to focus on specific strategies with our group that’s not quite at grade level to decode the problem and understand what it is asking as well as beginning to solve it, we would be able to work on extending the problem looking at multiple strategies to stretch student understanding with our on level group, or to give our group at extending problem that is very similar but yet adds of another layer of knowledge another layer of thinking and reasoning to the problem. We also discussed that adding digits to a math problem is not adding significant learning, instead to challenge our extending learners by stretching their reasoning skills. By focusing on the New 3 Rs; reasoning, resilience, and responsibility we are giving students the opportunity to use their voices and make choices and to help tailor their own learning. This is something I am looking forward to implementing in the new school year and seeing what happens. Us this my opportunity to fail forward and practice intelligent fast failure or do I have some elements here that are going to be successful?

### Bibliography

Cunningham, B. (n.d.). *What is number sense?* Retrieved from Understood.org:

https://www.understood.org/en/articles/number-sense-what-you-need-to-know

Dehaene, S. (1997). *The Number Sense: How the Mind Creates Matematics.* Oxford: Oxford University Press.

Liljedahl, P. (2021). *Building Thinking Classrooms in Mathematics.* Thousand Oaks: Corwin.

Meyer, D. (2010, May 13). *Math Class Needs a Make-Over.* (D. Meyer, Performer) TEDxNYED, New York, New York.

Miller, A. K. (2015). *Freedom to Fail : How Do I Foster Risk-taking and Innovation in My Classroom?* ASCD.

Simonton, D. K. (2015). Thomas Edison’s Creative Career: The Multilayered Trajectory of Trials, Errors, Failures, and Triumphs . *Psychology of aesthetics, creativity, and the arts*.

Sternberg, R. J. (2008). Excellence for All. *Educational Leadership*, 14-19.

Tahirsyla, A. S. (2012). Stimulating creativity and innovation through Intelligent Fast Failure. *Thinking Skills and Creativity*.

Woo, E. (2018, July 24). *Mathematics is the sense you never knew you had .* (E. Woo, Performer) TEDxSydney, Sydney, Australia.