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.
When I first imagined my experience in graduate school, I envisioned reading and regurgitating content and theories alongside systematically following procedural assignments that would teach me educational technology tools to create textbook-like curriculum and lessons. I planned on going through the motions of school and coming out on the other side with a degree that earns me a few more dollars per paycheck and enhances my resume for future education endeavors. Man, I was wrong.
This false sense of reality mirrors my initial expectations of being a teacher in the classroom. I thought I would design and implement lessons that I could continuously recycle year after year, going through the motions of teaching. Professional development might teach me a thing or two that I can bring back to the classroom that would support me changing the lives of my students in the process. Never did I dream that I would be at this point in my life and career, finding myself learning and growing more through experience, trial and error, and collaborative communities that emphasize continuous reflection and adaptation. If you ask me to talk about my journey through life, in and out of school, I likely would not know where to start. It would inevitably be a brain dump of information seemingly disconnected from one idea to the next... but it makes sense in my mind. The only person who loves me enough to tolerate this chaos besides Jesus is my husband Scott. Most of the time, I sense I scare people... Writing and developing my voice to connect the analytical, cognitive side of my perspective to my free-flowing emotional sand spiritual side allows me to take my word vomit ideas and cohesively pain a picture others can view, and hopefully appreciate and be inspired by, to take their own artistry of education and life further. The procedural process of brainstorming ideas, creating an outline, drafting an article, and revising and editing the work based on an abundance of feedback from different perspectives has led me on a voyage to building my courage and bravery to speak louder than my current volume to a larger audience than my collaborative group, my family, and my tight knit community of colleagues at my campus. Promoting my publication through podcasting was definitely a new level of learning too as I relied heavily on my classmates' strengths to create a quality product. Documenting my experience from the burnout (we all need a break) and defeat of student disengagement and lack of student thinking to the renewal of my faith in the future by providing students opportunities to build 21st century skills in a blended learning environment through the lens of mathematics and trying practices from Building Thinking Classrooms by Peter Liljedahl has increased my confidence that my vulnerability will inspire other teachers like me to continue to dream big for our students. I hope to publish at Texas Council of Teachers of Mathematics or National Council of Teachers in Mathematics to expand my community further and speak to other like-minded professionals eager to set sail into the reality of our education future and not the delusion or mirage, figments of our imagination as to what we thought education is. The whole writing process is just what we expect out of our students as we guide them not only to learn our content but also learn to be lifelong learners, continuously evolving, not just going through the mundane motions of life but thrive in adventure and possibility. The work of learning is never done and the journey has more value and fulfillment than any checkpoint or destination. Because of publication consideration requirements, I cannot post my products I created throughout this cycle. However, I do look forward to blogging some day soon with a celebration of formal publication and linking to an official professional website, but in the meantime, keep learning something new every day. I know I am.
References
Conspiracy Charlie Day GIF - conspiracy Charlie Day crazy - discover & share gifs. (n.d.). Tenor.com. https://tenor.com/view/conspiracy-charlie-day-crazy-always-sunny-in-philadelphia-qanon-gif-23738584
Just because I am a mathematics teacher does not mean I dislike reading and writing. In fact, I remember as a young student, one of my dreams was to be an author and illustrator because escaping into stories opened up the universe in the palms of my hands and I wanted to be a part of that creation. As my education progressed, my writing developed from a fictional foundation to analytical in a variety of subjects:
My learning philosophy is rooted in Jean Piaget’s cognitivist theory, identifying and applying patterns and my experience has strengthened my ability to connect the abstract with vivid imagery as I build particular connections between seemingly unrelated ideas. Just the other day, a student was struggling with remembering how to square a binomial. She kept distributing the square to the terms rather than distributing the terms to each other. I tried showing her a numerical example, yet every time I checked in with her progress, she kept making the same mistake. This simple conversation changed everything.
Mrs. Lee: "You are in wrestling right? How many shoulders do you have to pin to win?" Student, smiling: "Two." Mrs. Lee: "Think of these squared binomials like shoulders, you have to pin both down to win the match, so write both of them to pin them down." That stuck. All I have to do now is walk by and say PIN THEM DOWN, she smiles and builds her confidence in her math abilities. I find myself making analogies, similes, and metaphors constantly to connect the abstract to the concrete for my students and the same is true for my writing. As I have strengthened my voice through my master's program, I am finding myself being bolder with my writing in the sense of sharing my story and journey through life and education with a balance between the creative components of writing and the analytical side. One of my assignments is writing with the intention to submit the work for publication. Some considerations for publications I have found include:
All of these publications have stated that the use of AI is discouraged but if it is used, it needs to be explicitly mentioned. Most require a short biography as well as evidence of other publications. The documents need to be in Word with APA references. Submissions are done via email or directly on the publication website. My writing can go in a variety of directions and with so many options, if rejected, I will adapt writing to meet other publication requirements and needs, but the Texas Council of Teachers of Mathematics Call for Voices from the Classroom fits nicely in my big picture. Thus, I began with an outline and started writing a rough draft about my journey in transforming my mathematics classroom from the past to the future with the practices of Building Thinking Classrooms to build 21st century skills. My Community in Collaboration is diverse, as we serve in a wide range of roles in education, so encouraging each other and providing valuable feedback/feedforward meant establishing a rubric that could easily apply to our various topics and writing approaches. When creating rubrics for students, I have used RubiStar but after exploring ChatGPT, I used AI to generate a rubric for a publication in education. With some adjustments and review from my group, we agreed upon the categories and their breakdown into components and points. These included overall content, organization and structure, writing style and clarity, evidence and support, critical thinking and reflection, and conclusion and implications Not only did we provide comments in each other's rough drafts with all sorts of fixes, adjustments, and considerations, we filled in our rubrics with points and overall feedback/feedforward. Part of the requirements for publication submission is not publishing your work anywhere else, so it would not be appropriate for me to post my rough draft here but you can get a sense of my work from my rough draft peer assessment. Overall, the feedback/feedforward I received validated my perspective but provided meaningful insight on how to enhance it, including fixes to some grammar and punctation, suggestions on how to rephrase ideas to be succinct, and recommendations to bring in more research and literature. The average score I received was a 48.94/50 and honestly, I think my group was generous. Because my imagination and connections are wild and widespread, I tend to be verbose and add unnecessary detail so my clarity can improve. There is also opportunity for me to add more research beyond my classroom setting to demonstrate that my journey is not a fluke but a reality many can experience in their own classroom. Moving forward, I am going to be even bolder and seek feedback from peers at my campus and the district who do not know the context of the graduate school assignment to receive a more comprehensive review of my work. Maybe I will fulfill a childhood dream of being an author in a way I could have neve imagined and be an official published writer! The past few weeks have been challenging. It feels like there's nothing I can do to have a positive impact. Why do this? My masters in education means changing the world, so why does it feel like I am changing the world for the worst and not for the better? These feelings happen in cycles for me and when I am at the bottom, I take a moment to wallow in the misery and validate my feelings. This approach to my mental health comes from my mental health journey, where I learned how to cope with the imbalance between my head and my heart. It usually results in eating French fries and having a stream of consciousness monologue with my husband as my rubber duck. He offers me a safe space to be upset but then encourages me gently to move forward. Moving forward usually takes the form in reading and reflecting. The next term of my master's program starts in January, but I have access to the reading list ahead of time so I decided that's where I would start my journey back up the mountain. The first pitstop is picking a few articles on technology integration at Edutopia and a quick search of math technology resulted in something I had never heard of before, Technological Pedagogical Content Knowledge and this aesthetically pleasing Venn diagram (sometimes it's the simple joys in being a math teacher). Now, breaking this down took a few rereads and a request in ChatGPT to summarize it, but here is my summary:
Right now, I feel like I am in the separate entities of the knowledge but no overlap. Even with the decade of experience I have, imposter syndrome feels very real but with the shift in education, it may be appropriate to realize I am beginning all over again in this new digital era. I am also reading Building Thinking Classrooms by Peter Liljedahl as part of a district high school math cohort and within the first few pages, I found myself nodding my head and coming to the sobering conclusion that no thinking is happening in my classroom. I am passively integrating technology by transferring the physical documents to digital but the repetitive, factory-model system of notes, worksheet, notes, worksheet, here's an assessment, next unit has consumed the soul and joy out of my classroom like a dementor. My innovation plan that came out of my first master's program class, teaching 21st century skills in a blended learning environment, is that intersection of technological pedagogical content knowledge. It feels like the whirlwind is taking over and I am finding myself sucked into ineffective familiarity. The struggles students have are not about thinking but about mimicking the steps I have robotically showed them to follow. Purposeful struggle is a phrase I have used before but it seems that there is reason to intentionally incorporate it into my classroom environment and expectations. Cathy L. Seeley's article on Turning Teaching Upside Down through the Association for Supervision and Curriculum Development highlights how we need to shift from teachers showing students how to think first to students showing teachers how they think first. There should be more than just teaching math in my classroom, but right now not even that is happening. I have plans to use the new year, new semester, as an opportunity to transform into the space I have dreamed of, a significant learning environment where students do the thinking and the growing and I just facilitate the surroundings to help it flourish. For now, reading and reflecting, reading and reflecting, so I can move forward a better educator. References Koehler, M. (2012, September 24). TPACK explained. Tpack.org. https://matt-koehler.com/tpack2/tpack-explained/
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. The Parable of the Sower comes from the Bible, Matthew 13. Jesus talks about how a sower scattered seed along a path, amongst rocky places, around thorns, and within good soil. Depending upon the environment depended upon whether or not the seed could develop into a plant, sustain itself through harsh weather, or thrive in the time of harvest. While Jesus was referring to the Gospel, this can also be pertinent to creating significant learning environments for our students and even ourselves as educators. The past few months have really made me step back and reflect, realizing that I scattered the growth mindset ideas onto paths with no depth, rocky places with no nourishment, and thorns with stronger holds. There is beauty in realizing my shortcomings because now I am choosing to walk away towards cultivating the soil that is my classroom and building a space for flourishment. There are some things I have written and creating to get to this place. Through the lens of mathematics, teaching 21st century skills in a blended learning environment demands a fresh approach to the learning culture. The combination of global, uninhibited connections within a structured, safe environment has the power to transform students into who we need to make the future one to blossom in. Amplified by Piaget's cognitive learning theory, my learning philosophy explores how my perspective on education translates into the classroom for my students. We gravitate towards making sense of everything around us through experiences, connections, and patterns so providing students opportunities to start making sense of themselves and others ensures the foundation for future growth. There was compelling evidence that in order to create significant learning environments for students, I needed to create significant learning environments for myself and others to try this together. Through Dee Fink's 3 Column Table, Learning Environment/Situational Factors Outline, and Questions for Formulating Significant Learning Goals and its comparison to McTighe and Wiggins' Understanding by Design Template, I have a metacognitive plan on creating significant learning environments for teachers to learn about how to create significant learning environments. The stage was set by my growth mindset plan but it was really shaped recently when I realized it really takes a village for the rehearsals and performance to take shape and come alive. I am committed to establishing significant learning environments that foster growth mindset through active engagement, not by passive means, by seeking and sowing the soil for our collective growth. With these things working together, the back of the puzzle box is really starting to reveal the big picture. Ideas are meaningless unless acted upon and implemented, and growth only comes out of reflection and adaptation. Creating a significant learning environment focused on authentic learning first will forge a stronger path for my innovation plan to mold students, fellow educators, and myself into the strong, powerful people we are capable of becoming. References Dee Fink, L. (2003a). A self-directed guide to designing courses for significant learning designing courses for significant learning. https://www.bu.edu/sph/files/2014/03/www.deefinkandassociates.com_GuidetoCourseDesignAug05.pdf
Dee Fink, L. (2003b). Creating significant learning experiences : an integrated approach to designing college courses. Jossey-Bass. Dee Fink, L. (2013). Creating significant learning experiences the key to quality in educational programs. https://media.wiley.com/product_data/excerpt/51/11181242/1118124251-7.pdf Matthew 13 NIV - - Bible Gateway. (n.d.). Www.biblegateway.com. https://www.biblegateway.com/passage/?search=Matthew%2013&version=NIV McTighe, J., & Wiggins, G. (2005). Understanding by design (2nd ed.). Association for Supervision and Curriculum Development. McTighe, J., & Wiggins, G. (2009). Essential questions to promote staff inquiry and reflection (examples). https://jaymctighe.com/wp-content/uploads/2013/06/Essential-Questions-for-Educators.pdf McTighe, J., & Wiggins, G. (2012). Understanding by design framework. https://files.ascd.org/staticfiles/ascd/pdf/siteASCD/publications/UbD_WhitePaper0312.pdf
Lately, I have realized that it requires community to build growth mindset. Personally, the last few weeks have been challenging, particularly when it comes to what is going on in my classroom.
It would be realistic to say that we all have students who simply do not care about our course or about school... or at least they give on this perception. This looks like heads down on desks, hands glued to cell phones, mouths talking about anything but the subject or talking poorly about the subject. What this really comes down to is attribution theory. Are students acting the way they do because of who they are or because of the situation they are in? It is easy to say that a student is just lazy or does not care... and it is very hard to realize that we are putting students in situations that produce the behaviors we get frustrated by the most. As the semester comes to a close, there are days where I just want to throw my hands up and stop investing my heart in caring about what other people are doing because it is exhausting having to face that they will not always (or seemingly ever) do what we want or believe they are capable of. This reflection really is a fixed mindset, something I claim to almost never have. I feel powerless, helpless, like there is no point in trying anything else because nothing will come of it. Naturally, by what I consider divine intervention, I find this infographic. Right now, I am definitely at the beginning of the road, the fixed mindset place. It feels like I am moving the opposite direction on a moving walkway, not getting anywhere. Since writing about my growth mindset plan, The Yet Mindset, I have learned that it takes more than just talking about a growth mindset to get there. It requires action to move forward into it and what I really need is to turn people around and walk against the grain with me. Developed in September this year, my growth mindset plan had an outline of steps but not how to implement the steps, picture frames but with no pictures. I also did not really have any walls to hang these pictures on. What has shifted is I am not waiting anymore for someone to build the walls while I twiddle my thumbs. I have to be the carpenter of the setting or I have to look for others who have walls built to learn from. This analogy translates directly to my professional learning, which transfers to the learning environment in my classroom. Being a part of the community built within my master's program has been the start, but since August I have joined a Building Thinking Classrooms cohort amongst high school math teachers in my district, as well as delivered professional learning opportunities for Algebra 2 teachers to move from the outdated factory model of education into innovative significant learning environments, which has began the cultivation of another professional learning network. With these groups, I have found some resources to start implementing in my classroom:
This is just a handful of resources I have available, but what does implementing them look like? It starts with my own mindset and reflection on what my classroom actually embodies versus what I think it should (but then blame the students for it not being a sparkly ray of sunshine). To really have an impact on growth mindset with my students, it starts with me creating the significant learning environment for it to grow and be reinforced. I periodically model growth mindset to my students; not a day goes by that I do not mess up an answer on the answer key or a plus or minus symbol in an example. When these mistakes do happen, I will be the first to confess that I made a mistake but show immediately how I will fix it and try to keep that experience in mind for the future. How do I give students this opportunity? The first place I see the biggest area of improvement is feedback. Using blended learning and the station rotations model, students would have access to content but also be required to go through feedback/feedforward cycles. These cycles can be teacher to student, student to student, student to teacher, or student to self. The feedback can be on explicit math content but more importantly, on the process of growing to have a better understanding of the world, strategically within the mathematics lens. Consistently investing the time for students to be a part of the conversation is necessary. I should not be doing all of the work because the ones doing the work are doing the learning. Does this exempt me from learning alongside my students? Absolutely not, but it does empower me to model for them what learning looks like, especially as they are young adults about to go out into the real world and get big jobs (like being a teacher). This has potential to shift away from grades being the key to the future but rather learning being the open door. Does this mean throwing them into the fire and just hoping they do not get burned? Does this mean throwing them into the deep end and just hoping they can swim or survive by floating? No. Supports are needed to wade into the water, get familiar with the foundations, and work towards the deep. Within my class on creating significant learning environments, I developed resources to expand my capacity to actually implement the concepts I have been reading about.
It is not enough to just say have a growth mindset and make students say "I don't know yet". I am setting the expectation for myself to create a significant learning environment where my students can thrive and embody a growth mindset through action and I am setting myself up for success by creating, finding, and joining significant learning environments for myself as a learner. It really takes a village to learn and grow.
References
Gerstein, J. (2014, July 27). The educator and the growth mindset. User Generated Education. https://usergeneratededucation.wordpress.com/2014/07/27/the-educator-and-the-growth-mindset/
Gerstein, J. (2014b, September 28). How educators can assist learners in developing a growth mindset. User Generated Education. https://usergeneratededucation.wordpress.com/2014/09/28/how-educators-can-assist-learners-in-developing-a-growth-mindset/ Practical Psychology. (2021, April 9). Attribution theory (examples and what it is). Www.youtube.com. https://www.youtube.com/watch?v=WoTBPwMeAyo
I resonate with Piaget’s cognitivist theory, so I constantly incorporated and applied the patterns I recognize in my life and other topics by using analogies (like riding a bike in my discussion post turned blog post New Digital Age, New Learning Culture) and personal stories (like in my post on Effective Professional Learning for Math Teachers) to foster relationships and connections with my peers. Frequently, there were remarks that these perspectives enhanced others’ learning and broadened perspectives. I would also gravitate towards other analogies, but I intentionally found discussion posts or replies that held a different viewpoint than my own. Doing so allowed me to link the new perspective to my working schema. Even when I met the minimum expectations of one initial post and at least two replies, I revisited the discussion boards and replied to ideas every time a new post was submitted. These discussion posts became the foundation for some blog posts, and I intentionally incorporated my peer’s comments (with their permission) into my writing, such as in my post Being Comfortable with Being Uncomfortable. Some of the discussion board replies turned into conversations and collaboration outside of them. I have spoken with Katie Beauchene periodically since the beginning of our journey in our master's program but recently, we engaged in class individual chat conversations, text message threads, and email exchanges to elicit feedback/feedforward on resubmitted assignments, flexible seating structures, and even components of our jobs that do not directly correspond to our class assignments. Contributions have also been made between individuals through Blackboard messaging and breakout rooms. Usually, I gauge the audience of my peers by sharing my work and perspective and then leaving the door open to receive feedback and give the same for others. Something I could try to do better is take a step back and not being so eager to be the first to speak up, but rather encourage others behind the scenes to be bold. This could enrich others' learning and teach me how to have impact in the silence, connecting dots in a new way. Every term we are encouraged to use the student/faculty lounge discussion board and I find myself trying to engage with others to do the same. When they did not get answered, I reached out to the professors, instructional assistants, and my collaborative group. I also never hesitated to ask questions during class meetings and when I got answers, I posted my own reply with that information for others to reference. Usually, if I have a question, others also have a similar question or concern, but I take the initiative to speak up and be bold, ignoring the subconscious concerns of looking incompetent or oblivious. My core collaborative group has been steady since the summer with Amanda, Hillary, and Lindsey. These relationships I have built with these beautiful women are something I will cherish for the rest of my life. We have really struggled for various reasons, such as personal illness and home ownership woes, along with balancing everything else that comes with life and being in education. Our contribution to each other’s learning and ourselves has really come in the form of encouragement. We also continue to divide and conquer readings and when someone has to miss a class, our text message thread recaps the class conversations real-time. We would connect when working on assignments and discuss our different perspectives on how to meet the rubric criteria. In the in-between, we would talk about our Halloween or Thanksgiving plans, sending pictures of our kids (or in my case, my dog Bruce). This really gets to the caring component of collaboration and learning. For this term, even though my group divided readings, I still read and annotated every reading assigned, including supplemental readings, and looked to connect them more concretely to the work I am doing for individual courses but also between current courses and past courses. One specific example is my inquiry on the difference between big hairy audacious goal (BHAG) and wildly important goal (WIG). I also found direct correlations to developing effective professional learning and creating significant learning environments. This led to a major adjustment in the implementation of my innovation plan, shifting from piloting blended learning environments using the station rotations model in my classroom to inviting others to join me through professional learning cycles so we can implement blended learning environments together. As assignments were turned in, I would take the feedback and adjust my work, as well as revisit and revise components as bigger connections emerged or more details were discovered and analyzed. Something new this term I did to authentically start connecting the dots was when certain experts would show up in videos or reading, such as Angela Duckworth, L. Dee Fink, and Grant Lichtman, I would always research further what they are currently up to. Through this, I found some incredible resources that support my learning for my masters’ program but also resources that I could integrate in the classroom immediately. Just accepting what was provided in our modules has not become enough for me; the blended learning environment I have come to love has shown me to embrace the opportunities to do my work extension of thinking, even if no one requires or encourages me to. The line between the courses has been blurred because they have become so closely related. I cannot develop effective professional learning without creating a significant learning environment for those in the professional learning sessions. There is always room to grow, so I would grade myself 99/100 for both courses. This feels arrogant but definitely justified with the work I have done up to this point to continue pushing myself to learn and grow as I work towards earning my masters’ in the spring of 2024.
Something that has been coming up as another component of a teacher's role that feels more catered towards checking off an administrative box than serving students is writing "I Can" statements on the board. Take a quick look at social media teacher groups and you will find the dark humor that comes with coping with the millions of expectations and decisions we face daily.
If I am being honest, "I Can" statements are really to support me along the path of the curriculum to maintain focus in moving forward with students. I use them to determine if students are on track or not. There are also attempts to bring students into the conversation about I can statements. You can find them on every set of notes, every Canvas page, every review. These "I Can" statements come from just taking the Texas Essential Knowledge and Skills (TEKS) and adding "I Can" to the beginning, with an occasional break down in the TEKS (i.e. Algebra 2 TEKS 2A.4 says solve quadratic and square root equations, which is typically broken into I can solve quadratic equations and I can solve square root equations). There are also "I Can" statements with English Language Proficiency Standards (ELPS). For example, ELPS c4D could be written as "I can monitor understanding and seek clarification through listening." Let's be realistic, do these mean anything to students? My guess would be no. We do not intentionally bring students into the "I Can" statement creation because they are out of their control. It comes from state curriculum requirements to earn credits for specific subjects. What if instead we had "I Will" statements? All of my students can add, subtract, and multiply polynomials to some degree, but which ones will choose one method over another to demonstrate their understanding? All students can put their phones away but will they choose to do so? I bring this up because there is a distinction between something we can do and something we choose to do and will do accordingly. I can go to the gym every day for at least thirty minutes but will I? I can clean the dishes in the sink but will I? I can stop working during a holiday break but will I... depends on how much I can shut off the balls to the wall mindset I have going on. If we want students to be VOCAL and have ownership of their learning, we need to give them choice in what they will choose to do. We can tell them all we want on what they can do, but it comes down to will they do it and what learning environments are we creating to foster a sense of self-worth to decide they can and they will. More on teacher "I Can" statements for another day... but just something you can think about now, but will you think about it later and take action?
References
Bored Teachers. (2023, September). Instagram. Www.instagram.com. https://www.instagram.com/p/Cw2seuWvgXR/
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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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