Consider when you first learned about the concept of numbers and counting. You probably learned one to ten because of your fingers and toes, using a tangible representation. At this developmental stage, this information was the reality, but eventually we learn that there are numbers beyond that.
Counting to 20, or 100, became another milestone. Negative numbers represent the lack or reduction of a quantity, so comprehending we can count forwards and backwards became the new truth. Eventually math extends to fractions and decimals, irrational numbers, and even more abstract concepts like imaginary or complex numbers. When does it stop? Getting metacognitive, what are numbers without objects? Did we discover math or invent it? Jeff Dekofsky addresses this question. This progression through the simple concept of numbers can happen organically in a mathematics classroom. It is not limited to numbers, really any math idea or topic can be expanded upon in this way. Now, consider when we first learn to communicate. We start expressing ourselves through sound and movement, developing oral language starting with simple one-word statements and eventually crawling, walking, and running around to speak through body language. As we age, we acquire new vocabulary in a variety of contexts, such as academically through literature, or socially through friend groups and family dynamics. We develop multiple ways of conveying our thoughts, feelings, and ideas. According to Lingua (2022), there are over 7,000 languages around the world, and new bussin’ words are added to language every year. In her TEDTalk, Lera Bordotisky explores how languages shapes the way we think. Just as math concepts and language can be organically explored, so can 21st century skills. What if this approach is the cheat code to our future? My innovation project,teaching 21st century skills in a blended learning environment through the lens of mathematics has definitely evolved from the past into the present and it will continue to evolve towards the future. As I reflect on my journey, I need to consider how to start at the foundation and root of one idea, building and growing outwards and upwards, expanding to new connections and possibilities.
The Past
When first developing my innovation plan, it really inspired me to start thinking about what education gifted me, which is the skills and characteristics that support my continuous growth and improvement towards success. Being a millennial and growing up in the transition of Y2K, 21st century skills were something society just began articulating and my path through high school in the International Baccalaureate (IB) program and college gave me opportunities to develop these skills real-time. My transition from a student to an educator aligned with my learning philosophy and starting the Applied Digital Learning (ADL) program, I learned about the new digital age and new learning culture. A lot of reading research and literature on blended learning environments and 21st century skills reinforced my experiences and were consolidated in a literature review. I spent the summer producing an implementation outline ambitiously anticipating I could flip my classroom on its head within a year and refine after the follow two. Unfortunately, while I was learning what my mind and spirit felt true all along, putting those ideas into action fell short.
Creating my innovation plan felt natural and sharing my ideas with others was also exciting. A new school year meant this new opportunity to go for it and transitioning from teaching Precalculus (a subject I had taught consistently for the past seven years) to teaching Algebra 2 also provided a chance to use the change for the better. Breaking the cycle of factory model is hard, especially when collaborating with other teachers who have a fixed mindset and are closer to the end of their careers. With the team I am working with this year, I honestly cannot blame them at times for wanting to stick with what is comfortable because everything about education is exhausting. Despite my initial enthusiasm, there were many obstacles hindering me, and the vortex of the whirlwind sucked me right up into the abyss of a fixed mindset, rather than my yet mindset. I found myself ignoring my innovation plan because it seemed like it would have created double work for me on a lonely island under attack from the outside world. My soul has felt crushed one too many times to count for pouring my blood, sweat, and tears into a lesson, unit, activity, student, etc. that feels like no positive results are being produced. I want to be a great teacher, but what makes a great teacher?
Periodically, I would develop a lesson that incorporated some technology components, but it was not done consistently or with intention; I was just using technology for technology's sake or doing a great activity amid all the same old repetitive routine. This barely appeased my guilt of not teaching 21st century skills through the lens of mathematics in a blended learning environment to meet my student needs. Looking at my Implementation Outline – Version 1, it is safe to say I have done nothing since August 2023 as listed in this outline. If I have, it was done by accident or without the focus of the innovation plan. Everything changed though in December to now.
The Present
As semester exams were just around the corner, an overwhelming sense of regret and frustration brought me to a breaking point. When students were demonstrating that they retained little content but also lacked the skills necessary to take responsibility for their learning, it forced me to reflect and be self-critical. How can I expect students to attain these skills if I have yet to give them the significant learning environment in which to develop and refine them? I had completed practically nothing except the initial stages of my project.
In one of the discussion boards, a classmate recommended Building Thinking Classrooms in Mathematics by Peter Liljedahl, so I added it to my list of books. Coincidently, a few months later, my district launched a cohort to do a book study on that same book. The first meeting in November incorporated the first three practices within Liljedahl’s writing and encouraged implementing some of the 14 practices in our classrooms. I told myself I would wait until the spring semester, or even next school year, pushing what needed to be done now into the future. It hit me like a brick wall. I needed to adapt my innovation plan to utilize these practices that break the norms of a traditional mathematics classroom and through these structures, identify technological components that would enhance the learning through a blended learning environment. I drafted, revised, and finalized an article about my journey from past to present, promoting the publication through podcasting and reflecting on writing through writing. I am learning that I am still a recovering perfectionist and that my life of "balls to the wall or not at all" can really be a detriment to my professional growth and ultimately my students’ learning and engagement. I would not consider my innovation plan a win or a loss, but unavoidable in identifying how to actually follow through with my plans.
The Future
Now that I can reflect on what I have done and am currently doing, seeing the the back of the puzzle box - the big picture, there are some things I intend to address and implement in the future.
Amidst the chaos, I realized the importance of getting more people alongside me earlier on and using my voice to speak up and say that we should try innovative ideas for students. If anyone questions us, we need to stand firm and articulate that what used to work is no longer effective and we cannot be instructing students with the ways of the 20th century, considering where the head and heart meet. This is especially difficult with math because it seems like math never changes. Facts are facts, order of operations will always be true, and there's not really ways to be creative with math when we know the most "efficient" ways to solve problems. This is not true, but the fixed mindset of some of my colleagues believe this in their souls. Fortunately, I have one colleague in my content team, along with the Building Thinking Classrooms cohort, doing similar innovative structures to collaborate with, and I can take my experience from this program and really use it to my advantage (plus there will be so much more time once I graduate!). Another improvement is being slow and steady with my changes within a NOW culture. I initially asked why not now? but it takes time and effort to figure out what works and what does not, along with making the systems and structures that do work more efficient over time. My innovation plan will look remarkably similar to before, but the timeline will be adjusted to refine components at a more appropriate and sensible pace. Focusing on a few 21st century skills, such as communication, collaboration, and reflection, rather than the larger list, will also make things less daunting. This is definitely something I would have done differently if I could go back in time and start again. My ambitious nature can be beneficial in certain situations, but this was a time when the goal’s timeline was too sudden to realistically implement amongst the other obligations as a teacher. Through my roles as a content team member, department lead, and cohort member, I will intentionally share what I am doing in my classroom with my peers through writing, conversation, and even observations. Inviting others into this new world will also hold me more accountable with following through on my plans. My failure to follow through with my plans is actually a win. Often times, educators do dream big, but we have conflicting responsibilities and commitments that hinder our capacity to make these dreams a reality. What I have learned throughout the ADL program is that a lot of work is done behind the scenes before anything can be done in front of the students. This journey of learning and growth highlights the iterative disposition of education, preparing me for the challenges and opportunities that lie ahead.
References
Boroditsky, L. (2018). How language shapes the way we think | Lera Boroditsky [Ted Talk]. In YouTube. https://www.youtube.com/watch?v=RKK7wGAYP6k
Dekofsky, J. (2014). Is math discovered or invented? - Jeff Dekofsky [YouTube Video]. In YouTube. https://www.youtube.com/watch?v=X_xR5Kes4Rs Fractions explained - a guide for parents. (n.d.). Komodo Learning. https://komodomath.com/us/blog/fractions-explained-parents-guide Lamb, R., & Shields, J. (2008, June 24). How are Fibonacci numbers expressed in nature? HowStuffWorks. https://science.howstuffworks.com/math-concepts/fibonacci-nature.htm Liljedahl, P. (n.d.-a). 14 practices. 14 Practices. https://buildingthinkingclassrooms.com/14-practices/ Liljedahl, P. (n.d.-b). Https://buildingthinkingclassrooms.com/. Building Thinking Classrooms. https://buildingthinkingclassrooms.com/ Liljedahl, P. (2021). Building thinking classrooms in mathematics, grades K-12 : 14 teaching practices for enhancing learning. Sage Publications Inc. Lingua. (2022, June 29). How many languages are there in the world? | lingua.edu. Lingua.edu. https://lingua.edu/how-many-languages-are-there-in-the-world/ Newmarket. (2019, November 30). How to get past counting on fingers & toes. https://www.mathnasium.com/ca/math-centres/newmarket/news/how-to-get-past-counting-on-fingers-toes TEDx Talks. (2017). What makes a good teacher great? | Azul Terronez | TEDxSantoDomingo. In YouTube. https://www.youtube.com/watch?v=vrU6YJle6Q4
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When I first applied to the Applied Digital Learning (ADL) program, I genuinely thought this would be a walk in the park, breezing through the content in a few weekends, taking any assessments, and having the rest of the time to relax. I would follow what seemed to be the easiest path to learning some information, regurgitating it in assignments and tests, and walking across the graduation stage with a master’s degree, ready to change the world. I now know how naive that perspective was but how grateful I am to be wrong. It was apparent from my first course in ePortfolios that choice, ownership, and voice through authentic learning environments (COVA) would be something I would experience firsthand (Harapnuik et al., 2018). It did not take me long to be VOCAL and embrace the COVA approach despite the discomfort. Looking through all of the examples and suggestions on how to build an ePortfolio, I was overwhelmed with the abundance of options within a number of blogging websites for layouts, fonts, and colors that I would have to choose from to represent my brand, my spirit, and my passion for education. I quickly realized my use of language, pictures, and videos would help me be vibrant and share my love of teaching. I even wrote about my path in building my ePortfolio a few times early on... ePortfolios - GenuineLee Me, ePortfolios - GenuineLee Me Pt. 2, and Exploring Worlds through ePortfolios. Getting feedback that did not address my lack of color but really about the content supported my understanding that I genuinely had choice, ownership, and voice over my products and even the process to building them. The initial shock of the program being the exact opposite of what I had anticipated wore off pretty quickly, but that also is likely due in large part to being a life-long learner (see my post on the Living Museum of Me, Math, and More). I figured out quickly that this program is the antithesis of my previous experience as a student, which initially was overwhelming. Freedom and responsibility for my learning means making more decisions on top of the numerous other decision I make daily as a teacher, leader, wife, dog mom, and friend. Embracing the challenges and discomfort of freedom has nurtured substantial personal growth than a factory model program I expected. One decision I am beyond thankful I made was taking ownership and tackling everything head on, including forming a collaborative group. Finding others as eager as me meant looking at discussion boards, actively engaging in breakout rooms during class meetings, and being bold to initiate the awkward conversation of “hey, do you want to be in my collaborative group?”. This actually reinforced my confidence in my own voice. I have always had a strong opinionated voice and being more confident and comfortable in my own skin came out of my mental health journey (one which I am still very firmly on...). What this program is helping me to do is to speak more boldly at school. My innovation plan, Teaching 21st Century Skills in a Blended Learning Environment, is very authentic but has evolved into one that utilizes Building Thinking Classrooms by Peter Liljedahl to provide opportunities for students to use 21st century skills. First semester, I did little to nothing regarding my innovation plan with the exception to telling colleagues about it in the first week back to school. The challenge has really been about how to articulate my plans effectively in my organization and acquire the support I feel I need to bring people alongside me in my innovation plan to help me be intentional and consistent in my work. As we learned about how to influence people by identifying vital behaviors in my big picture growth and catering to the six sources of influence, motivation, and ability in the personal, social, and structural categories (Grenny, 2013), as well as Covey’s four disciplines of execution in my big picture goals, (Covey et al., 2018), realized why I was ineffective in gaining traction from the beginning of the school year, essentially abandoning my notion of change in the fall semester. Even if I had gotten others invested in my ideas and dreams, the whirlwind got in the way, and I did not focus on my big audacious goals. My goal, like most teachers lately, became to survive. Lately though, it has become overwhelmingly clear that the work is hard, but necessary and I should not let obstacles or fixed mindsets hold me back. My innovation plan was not just created to get through the course work; I really hope to change my organization from inside out, starting in my classroom and working out in waves across my content team, department, campus, and district. One major change that I desire to bring is actually utilizing COVA and creating significant learning environments in the math classroom. The analytical logical person I am finds comfort in the cognitivist mindset within my learning philosophy, building connections between what I know and what I am learning to weave everything into the existing web of information, but the ADL program has evolved my perspective into a blend of cognitivism and constructivism. If I cannot find a connection, I ask questions and search for my own answers, making and creating new connections. Another way I fuse these viewpoints together is through my writing and the use of analogies. They help me to create a picture of what my brain visualizes and understands to be true, attempting to articulate that viewpoint to others also have their own unique perspective and internal philosophies. With this new viewpoint of the importance and necessity of COVA and CSLE, I am empowered to make decisions that disrupt the comfort of students, parents, colleagues , and administration with purpose, to engage students in deeper learning than they have probably ever experienced inside the walls of a classroom. My campus has a legacy of high achievement in the state and nation, so changing the pedagogy that produced those results seems ridiculous. Why fix what does not seem broken? If it worked before, it should work now, right? Realistically, because our society has evolved exponentially over the past decade, we cannot continue implementing past practices in a future world. Disturbing the sense of order is daunting because it directly impacts others and their sense of comfort and safety in what they feel should be normal. Going through this program though has immersed me in the environment I know I need to build for my students. Having lived the life of a learner breaking out of my comfort zone of regurgitating information on an assessment and into a world of connections and creation, it is inspiring me to really consider the possibility of what might come out of doing this in a mathematics classroom. Conflict will inevitably arise from developing an expectation that what was once the norm is now in the past is scary, because it will be, at times, exhausting to manage the combatting side. It will definitely require me to be even stronger in my conviction that COVA and CSLE need to happen now and not later, breaking the chains my current setting has me in. If we want to maintain the legacy of high achievement, we must evolve with society to reach these new heights. I will start by bringing in other members of my content team to come beside me and learn by implementing innovative plans together. I will use the knowledge and resources I have built within the structures I have learned about in the ADL program to develop professional learning that models the blended learning environments we should be creating, providing those attending a glimpse into what our students’ realities could be. I need to be intentional about what I am doing and why. Explicitly sharing the reasoning behind my actions can obtain buy-in and continuously reiterating this rationale throughout the year will only emphasize its importance to me. It is challenging still for me to consider what choice, ownership, and voice looks like in a math classroom bounded by state objectives, grading guidelines, and standardized tests. In a subject where the question usually leads to one correct answer, being intentional about questioning that requires open-ended responses and can lead to multiple answers and even more questions will take work, time, and energy. Current available resources like this are few and far between. Also, the control aspect of the classroom is why teachers, specifically math teachers, tend to stick with the factory model. Math logic is “always” true but when computers can run calculations, we are essentially training our students to also be computers cranking through calculations rather than making connections. Students have been subconsciously conditioned to expect this from a math classroom, which is why my innovation plan and Building Thinking Classrooms principles are so troublesome for a lot of people. I can already hear the complains in questions:
Nobody will argue that 21st century skills are vital to one’s future and society’s survival, but the learning environment needed to facilitate acquiring and refining these skills does not meet the norm. Again, I need to be intentional about what I am doing and why. Explicitly sharing the reasoning behind my actions can obtain buy-in and continuously reiterating this rationale throughout the year will only emphasize its importance to me. Being transparent in my purpose will begin building a culture of trust and collaboration, encouraging students to take risks and explore in their learning. To incorporate COVA, I must provide opportunities for students to have choice, ownership and voice.
As I include these opportunities in the classroom, I can use strategies I have learned about action research to determine the impact of specific structures and share my findings with colleagues to further enrich the work they are doing in their classrooms. Applying effective structures and strategies within professional learning and reinforcing their effectiveness by including my findings will further develop the same culture of taking risks and exploring ideas I hope for in my classroom. If you had told me a year ago that this is where I would be, after ten years of experience in the classroom, ready to start again like a first-year teacher by finding my groove and establishing what my classroom looks, sounds, and acts like with the COVA approach to create a significant learning environment, I would likely say you are nuts. But let’s go crazy and change the world. References Covey, S., McChesney, C., & Huling, J. (2018). 4 Disciplines Of Execution. Simon & Schuster Ltd.
Grenny, J. (2013). Influencer : The new science of leading change. Mcgraw-Hill Education. Harapnuik, D., Thibodeaux, T., & Cummings, C. (2018). Choice, Ownership, and Voice through Authentic Learning. Creative Commons License. Liljedahl, P. (n.d.). Building thinking classrooms. Building Thinking Classrooms. https://buildingthinkingclassrooms.com/ Liljedahl, P. (2021). Building thinking classrooms in mathematics, grades K-12: 14 teaching practices for... enhancing learning. Sage Publications Inc. This term has been rough on a number of fronts. The figurative rollercoaster has me going all over the place. Most of the time, I just ride the ups and downs with a growth mindset, knowing the chaos will periodically subside and I can rest before the tide rushes back in. These current eight-week terms of graduate schools have felt like eight days and eight months simultaneously. I am going to use one of m favorite picture of myself, my husband Scott, and my sister-in-law Stephanie to describe this most recent chapter in my life. Let’s start with Stephanie. The first big drop hit, and I went all in screaming my lungs out. It was also in the beginning that Katie joined our “core four” collaborative group. Her and I had worked together individually, authentically connecting and contributing to the dots, and circumstances led her to looking for others to work with in addition to her core group. I got ahead in a lot of assignments, posted enthusiastically in discussion boards, and even read most resources before the term officially started (thank you Dr. Harapnuik for blogging about the resources once upon a time). My collaborative group probably thought I had a new kind of chaotic energy with all my gifs and texts in our group chat. Being labeled an overzealous overachiever can be exhausting, especially when I hit the lows. Scott’s entire body position and face embodies the middle of this term. I felt paralyzed with all of the work I had for school, teaching, and life as a wife and daughter. Crippled by overstimulation and anxiety, I froze and went missing in action for a while. Assignments were getting done last minute and I did not always get to class on time, if at all. I’ve talked about my mental health journey and these few pages of the story could have been ripped out of that book and glued straight into this one. I went from "balls to the wall" to not at all but not at all was not an option. Fortunately, those around me continued to support and love me, being a sounding board to hear my frustrations and sorrows and allow me time and space to come out of the darkness into the light. In this last week, I am getting back to being more me, smiling almost in a psychotic way while the whirlwind swirls around me. I have revisited discussion boards, revised my assignments, provided feedback and encouragement to my peers, and started to coast into Spring Break. My publication about Building Thinking Classrooms by Peter Liljedahl, blended learning, and 21st century skills goes hand in hand with my action research plan, which will hopefully answer the question “in what ways do Desmos activities (a technological tool) impact student growth in 21st century skills of communication and collaboration (two key components of Building Thinking Classrooms) so my contributions to learning are interconnected and tightly intertwined. Seeing connections in my learning and investing myself more in the authentic learning experiences my master’s program has strengthened my resolve to keep fighting the food fight and give my best of right now. For both of my classes, Resources in Digital Environments and Assessing Digital Learning Instruction, I would give myself a 97/100. While I definitely did not do my best this term compared to other terms, I did my best given the circumstances and stresses I was facing. |
My husband lovingly teases me when I reflect on my day with him and say "I learned something new today!" because he would be surprised if I didn't learn something new.
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