If a child walked up and asked, “What is an angle?” how would I respond?
Two rays that share an endpoint. A measure of rotation. A fraction of a full turn.
I know those answers. But do I understand what it means to teach that idea to someone?
Geometry has always felt like the “last” unit. When curriculum pacing slips, geometry quietly absorbs the loss. I find myself wondering: what message does that send? If number and operations get months of attention and geometry gets weeks (if we are lucky), are we unintentionally signaling that spatial reasoning is secondary?
And yet, when I look at my classroom, geometry is anything but secondary.
In past years, my students hunted for a “lost angle” in a bucket of Orbeez after solving for missing measures. Each task card showed a set of related angles with one missing value, and once students calculated that missing measure, they searched the Orbeez bin for the matching angle piece to complete their card.
Figure 1. Students searching for the “lost angle.” (Shared with permission.)
They went “fishing” for acute, obtuse, and right angles to rebuild full circles in a game we called Caught Acute Fish. The room was loud. They were moving. They were arguing about 90 degrees.
Video 1. Students playing “Caught Acute Fish.” (Shared with permission.)
It was magnetic.
At the time, I celebrated the engagement. Now, after reading about process standards and participation mathematics (Martínez Hinestroza, 2019), I am asking harder questions.
Were students merely participating in activity, or participating in reasoning?
Did the play invite sense making, or did it simply disguise procedures?
Was I creating space for multiple strategies, or funneling them toward one “correct” approach?
This reflection has sharpened my Knowledge of Content and Students (KCS; Hill & Ball, 2009). I know many of my students are hesitant to speak unless they are certain they are correct. I was that student. Participation, to me, once meant public correctness. Now I interpret participation differently. A student quietly trying a peer’s strategy is participating. A student gesturing agreement is participating. A student revising their thinking mid-game is participating.
Geometry, especially, demands that we broaden our definition of participation. Spatial reasoning is not equally distributed. Some students instantly visualize rotations and symmetry. Other students need physical movement, drawing, and talk. That is not ability, it is experience. The kinds of spatial play historically encouraged for boys often differ from those encouraged for girls. If construction toys and spatial tasks are culturally coded as “for boys,” and relational or doll-based play is undervalued mathematically, then we are not just teaching geometry. We are navigating identity.
That realization has unsettled me in a productive way.
What if expanding participation structures in geometry is also a way to expand who feels like they belong in mathematics?
When I play “Geometry Simon Says” with various lines and angles, I am not just rehearsing vocabulary. I am building embodied understanding.
Video 2. “Geometry Simon Says” in action. Students building embodied understanding of lines and angles through movement and play (shared with permission).
When I label strategies in Number Talks and refer back to them later, I am not just reviewing content. I am preserving student thinking in the room.
Kilpatrick et al. (2001) remind us that mathematical proficiency includes conceptual understanding, strategic competence, adaptive reasoning, and productive disposition. Geometry offers valuable context for all four. But only if we resist the urge to treat it as a checklist at the end of the year.
So now I wonder:
What would it look like if geometry were treated as foundational rather than supplemental?
What would shift if participation were measured by reasoning rather than volume?
How might playful, rigorous geometry experiences disrupt quiet narratives about who is “naturally good” at math?
Perhaps the right angle is not just 90 degrees. Perhaps it is the perspective from which we choose to teach.
References
Hill, H. C., & Ball, D. L. (2009). The curious—and crucial—case of mathematical knowledge for teaching. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 111–155). Information Age Publishing.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. National Academies Press.
Martínez Hinestroza, J. M. (2019). Connecting reflection and practice: Transforming a mathematics classroom culture of participation (Doctoral dissertation, Michigan State University). ProQuest Dissertations & Theses Global. https://www.proquest.com/docview/2281272410
Today I created a forced perspective hallway as part of a quickfire activity, and it ended up being much more engaging than I expected. I initially reached the “no color” stage and could have easily stopped there, but I was enjoying the process and decided to keep going. Once I added color and detail, the illusion of depth really came to life, especially when viewed through the camera.
This activity connects naturally to third-grade geometry standards, particularly 3.G.A.1 and 3.G.A.2. Students must reason about lines, angles, and how shapes fit together on a flat surface while creating the illusion of three-dimensional space. It also strengthens visual reasoning, as students explore how parallel lines can appear to meet and how spacing changes to suggest distance.
What I appreciate most about this task is that it blends creativity with rigorous geometric thinking. It invites students to apply spatial reasoning in a meaningful way while remaining grounded in grade-level standards.
When I started designing my survey for my Wicked Problem Project (WPP), I thought I had my question nailed down. I quickly realized I didn’t. Back to the drawing board.
After refining, I landed on this: Why is elementary curriculum typically structured in isolated, subject-specific programs instead of integrated frameworks that support cross-curricular learning?
Wicked, I know.
This question feels especially important right now. With teacher burnout and staff turnover high, asking educators to juggle multiple disconnected curriculum programs with minimal planning time feels unsustainable. What would it look like if, instead of five separate books, we had one cohesive framework?
Clarifying my problem helped me clarify my audience. While many stakeholders influence curriculum design, elementary teachers made the most sense as they live this structure every day.
Designing the survey was more layered than I expected. I included a filter question to ensure respondents teach multiple core subjects so my data aligns with my question. I also placed demographic questions at the end to avoid unintentionally priming responses, aligning with survey design research on question order and bias (Gehlbach, 2015). I balanced forced-choice and open-ended questions to gather both patterns and lived experiences.
Even small design choices were intentional. I chose a calming green background and a books-themed header to reflect the multiple programs that sparked this inquiry.
Ultimately, this process pushed me to think about alignment. My survey now reflects clarity, not just frustration. I’m curious to see what patterns emerge about the systems shaping elementary curriculum.
If you are an elementary teacher responsible for multiple core subjects, you’re welcome to take my survey here: Understanding Integrated Instruction.
For this week’s assignment, I created a sketchnote video to document and reflect on my Quickfire questioning process. While I have lightly edited videos before, this was my first time producing a short, highly structured video that required visual organization and concise narration. I used iMovie to edit my recording, which allowed me to trim clips, adjust timing, and layer audio and visuals together. One of the biggest challenges was balancing clarity with time. Because I chose to read each question within each category, the video could easily become much longer than desired. I had to be intentional about pacing so that my ideas were not rushed, while still keeping the final product at a reasonable length.
To record, I used my iPhone and a gooseneck tripod to get the correct angle for my lightboard drawings, which added an extra technical step. I then uploaded my finished video to YouTube in order to generate captions, which was a new process for me. However, the captions did not auto-generate as expected, so I ended up typing them manually. In hindsight, I could have completed this step directly in iMovie. While this process took more time than planned, it helped me better understand the importance of accessibility and captioning in digital content.
I also enjoyed experimenting with the lightboard format, which made the process more engaging and helped visually represent my thinking. Creating this video pushed me to think carefully about how to communicate complex ideas efficiently. Moving forward, I could see myself using sketchnote videos with students or colleagues as a way to model reflection, organize thinking, and share learning in a creative and accessible format!
References
Berger, W. (2014). A more beautiful question: The power of inquiry to spark breakthrough ideas. Bloomsbury.
When my students and I work on spiral review of concepts from previous years, they often question why we go back to “easy” math so frequently. This usually leads to a conversation about building a house. “If I wanted to build a house, where would I start?” I ask. “Would I build it on cotton candy? Toothpicks? Q-Tips?” The idea is hilarious to eight-year-olds, and their immediate response is always, “No, of course not!”
Figure 1: Just like this house needs a strong foundation before anything else can work, students need solid number sense before moving forward in math.
That moment opens the door to an important lesson: our ability to be successful mathematicians relies on a solid foundation. We must build and maintain strong mathematical understanding before moving forward. While their excitement fades when they realize there is no actual cotton candy involved, the message stands. Without a strong foundation, our learning is unstable.
Number and Operations are that foundation. Building strong number sense, and learning to question, fail, and grow from mistakes, is essential in early mathematics. When designing an intervention program for struggling third graders, I am reminded of the importance of returning to these foundational ideas.
Video 1: Sometimes doing the same thing over and over doesn’t mean you understand it
Research shows that students can appear successful while relying heavily on rules and procedures without true understanding (Erlwanger, 1972; Skemp, 1978). Reflecting on Benny’s experience and Skemp’s distinction between instrumental and relational understanding has pushed me to reconsider how often students may arrive at correct answers without truly knowing why.
Within my third-grade class, I have a small group of students—my intervention group—whose knowledge ranges from deep misconceptions to unfamiliarity with basic concepts. When I work with them, our shared goal is to address misunderstandings, strengthen number sense, and move beyond counting by ones. While this may seem simple in third grade, it can be overwhelming for some students.
Mathematical proficiency includes conceptual understanding, strategic competence, adaptive reasoning, productive disposition, and procedural skill working together (Kilpatrick et al., 2001). Many of the students in my intervention group show gaps in conceptual understanding, which limits their ability to reason flexibly and persevere when challenged. This reinforces the importance of returning to foundational number and operations concepts as part of our work together.
I often wonder how many of these students were previously rewarded for speed and accuracy rather than depth of understanding. What if their struggles stem not from lack of ability, but from years of learning mathematics as rule-following rather than sense-making? Perhaps this work is not only about rebuilding skills, but also about rebuilding students’ confidence as mathematical thinkers.
This work has also deepened my Mathematical Knowledge for Teaching, particularly my Knowledge of Content and Students (KCS). Through working with this intervention group, I have become more aware of how easily students rely on counting strategies and rule-following when they lack strong place value understanding. I now anticipate common misconceptions, such as assuming that every addition problem requires counting by ones, or believing that speed matters more than reasoning. This awareness helps me design instruction that directly addresses these tendencies and supports students in developing more flexible and meaningful strategies.
Exploring different pedagogical strategies has strengthened my instructional decision-making. Practices such as thinking aloud with justification and number talks align with the NCTM Process Standards for communication, reasoning, and representation (NCTM, 2000), as well as the Standards for Mathematical Practice, particularly making sense of problems and persevering (CCSSO, 2010).
Ultimately, this work has reinforced my belief that strong number and operations instruction is not about remediation, but about restoration. Restoring confidence, curiosity, and conceptual understanding is central to my teaching. As I continue to develop my mathematical knowledge for teaching, I am increasingly aware that my instructional choices shape not only what students learn, but how they see themselves as learners.
References
Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics. National Governors Association Center for Best Practices and Council of Chief State School Officers. https://www.corestandards.org/Math/
Erlwanger, S. H. (1972). Benny’s conception of rules and answers in IPI mathematics. Journal of Children’s Mathematical Behavior, 1(1), 7–26.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academies Press. https://doi.org/10.17226/5109
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM.
Skemp, R. R. (1978). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
In a world where we seem to have all the answers at our fingertips, are we unintentionally failing to understand? Technology has brought about numerous opportunities and pathways to obtain answers to our questions. However, should simply getting an answer be the end goal or should there be an end goal at all? Through the introduction, and first two chapters of W. Berger’s “A More Beautiful Question,” he discusses our innate nature to question and problem solve, and how it seems to almost fade as we age. He questions how we can teach questioning and inspire this need for change. Essentially, can we rekindle our questioning spark (Berger, 2014)?
Video 1: How many questions do children ask in a day? This video demonstrates Berger’s claim that young children are naturally curious and highly inquisitive, reinforcing the idea that questioning declines as students grow older.
Children spend a significant amount of time questioning things to simply gain understanding. In fact, four years old is our questioning peak (Berger, 2014). So why do we become more complacent over time? Are we fulfilled with the answers we have? Are we losing the ability to ponder deeply? Or perhaps we are underestimating our own ability to answer our own questions. Questioning enables innovation, problem solving, and brings about change (Berger, 2014). We are capable of bringing about such change if we know how to question.
Berger covers three major steps to simplify questioning: Why → What if → How (Berger, 2014). Stopping at why is stunting our growth in its tracks. “If you never do anything about a problem you’re not questioning, you’re complaining” (Berger, 2014). For some this could be because there are experts around whom seem to have (or think they have) all the answers. Berger argues that “what ifs” are not always welcomed in “what is” spaces. This calls into question our education system – are teachers the experts that have all the answers so students are failing to ask? If so, how can we ensure we are teaching students to ask beautiful questions? Beautiful questions are ambitious, actionable questions that can begin to shift the way we think and perceive something and can be used as a catalyst to bring about change (Berger, 2014). He states that questioning + action = innovation, and inversely questioning – action = philosophy. As an educator, my goal is to push my students towards innovation, in turn teaching them to question is the first step. This connects closely to my favorite third-grade lesson: “It is okay to make mistakes, but it is not okay to not try.” This lesson encourages students to take academic risks and view mistakes as learning opportunities, which reflects what Berger describes as the importance of “failing forward” in the questioning process.
I was asked to complete a quickfire exercise that encapsulates this idea. Having us question starting with just the “why.” Set a timer for five minutes, and write all the questions (related to your practice) that come to mind. Being asked to question in that way was a bit intimidating and difficult to not over think, however, below are the questions I was able to generate.
Figure 1: Development of quickfire questions from initial responses (top left) to final reflection (bottom right).
Some questions related to others while some came out of left field. I also found it difficult to sustain the questioning process mentally over time. As soon as I had a question written I wanted to start thinking about the next step, searching for answers, the what if.
After the why comes the what if. Moving from asking to action. This is where imagination takes over – where the seeds of innovation are planted (Berger, 2014). What if is finding the space to connect interesting ideas in unusual ways involving both connections and questions. Berger coined this as “connective inquiry.” He then states that a questioner’s ability to conform to their ideas and make them real is what sets them apart and leads into the final critical stage of questioning: the how. This final stage is where we work to figure out “how do I actually get this done?” It is driven by practical questions to lead to an answer. However, each answer brings a fresh wave of questions, which lead to mine: should there be an end goal? If we want to impart on our students the ability to ask beautiful questions I believe the first step is to be a questioner ourselves. As we continue to read, I look forward to learning how Berger suggests we do that. This reinforces my belief that cultivating a culture of questioning in the classroom must be intentional, modeled, and continuously supported.
References
Berger, W. (2014). A more beautiful question: The power of inquiry to spark breakthrough ideas. Bloomsbury.
Dyslexia impacts much more than reading time for many students. Students with dyslexia can understand grade-level ideas but struggle to access written materials because decoding is so demanding and stressful. This becomes an ill-structured classroom problem because there is no single fix. Students encounter text in every subject in various ways, and success depends on factors like classroom routines, available tools, and whether students feel comfortable using support in front of peers.
Research supports the use of assistive technology to reduce barriers to text-based learning. In a five-year follow-up study of dyslexic students’ experiences with assistive technology, Almgren Bäck and colleagues (2024) found that tools like audiobooks and text-to-speech were consistently beneficial for accessing content over time. The study also highlighted that continued success depends on contextual factors in school (such as consistent support and expectations) and students’ emotional comfort using the technology in real classroom settings. Making this technology available to the whole class can help it feel less like a crutch and more like a tool.
One technology that can address this need is Speechify, a text-to-speech platform that allows students to scan printed text and listen to it read aloud. This is particularly valuable in non-reading-centered contexts, such as math assessments, where students may understand the math but struggle to read directions or word problems. A unique affordance of Speechify is its flexible navigation: students can pause, replay, and jump to specific parts of the text, supporting independence. A constraint is that scanned text can sometimes be misread or read out of order when layouts are crowded, which may confuse students who have difficulty identifying errors.
For Speechify to be successful, classrooms need clear routines for scanning and a shared understanding that listening counts as learning.
Screencast demonstration
References
Almgren Bäck, G., Lindeblad, E., Elmqvist, C., & Svensson, I. (2024). Dyslexic students’ experiences in using assistive technology to support written language skills: A five-year follow-up. Disability and Rehabilitation: Assistive Technology, 19(4), 1217–1227.https://doi.org/10.1080/17483107.2022.2161647
Learning is a living process that grows through connection and purpose. It begins in community, is sparked by curiosity, strengthened through exploration, deepened through reflection, and sustained by the people, tools, and world in which we live. Learning takes hold in what we already know and who we are, then stretches beyond those roots as we engage with others and move toward meaningful goals. It is not passive. Learning is active, living, and continuously growing.
Figure 1. Learning as a Living Tree: A visual representation of my Theory of Learning. Created by Alexis Flanders using ChatGPT.
I understand learning as a developmental process rooted in meaningful experience and nurtured through relationships with others. Our learning is like a tree, grounded in prior knowledge and identity, shaped by the environment and those around us, and strengthened through purposeful engagement. A tree grows from a seed, not in isolation. Its growth depends on the soil that surrounds it, the climate, the supports or challenges it faces, and the network of life that interacts with it. In the same way, learning develops through active participation in the social, cultural, and intellectual worlds that surround us (Vygotsky, 1979; Lave & Wenger, 1991). Knowledge is not something that can simply be spoken into a learner. It is constructed, tested, revised, and extended with others through lived experience (Ackerman, 2001).
Roots
The roots of a tree firmly ground it and supply the nutrients that allow it to grow. In learning, roots represent prior knowledge, our own personal identities, and the motivations that give learning meaning. New understanding takes hold by connecting to what a learner already knows and values. Without our roots, information may be memorized temporarily, but it rarely becomes true, valuable understanding.
Learning deepens when it has purpose. Purpose fuels the will to persist and improve. The things I have learned most fully in my life have been those tied to meaningful goals. When I trained for a half marathon, the learning involved far more than accumulating miles. It required coordinating nutrition, pacing, strength work, and reflecting on what was and was not working for my body. That process drew from what I already knew about persistence in athletic training, but it also required new knowledge, trial and error, and constant reflection about how to adjust and be better. The learning was anchored in who I was, the goals I was working towards, and my desire to grow. Like roots taking hold in soil, purpose gave that learning a reason to deepen.
A tree cannot grow without the right environment. The soil quality, climate conditions, and surrounding organisms influence how well the roots absorb nutrients and whether growth is supported or restricted. Similarly, learning is inseparable from the social and cultural environments in which it takes place (Vygotsky, 1979). The community, language, tools, values, and social norms of a learning space shape what is available to learn, how learning is expressed, and what forms of knowledge are recognized.
The sociocultural perspective views learning as a process of becoming through participation in cultural practices (Lave & Wenger, 1991). People learn by engaging with those around them, using the tools and symbols of their community, and gradually moving from peripheral observation to more active participation. Within these shared practices, learners actively construct understanding by connecting new experiences to what they already know, reflecting a constructivist view of learning as developing meaning rather than passive absorption (Ackerman, 2001). What a person knows and who they are becoming cannot be separated from the environments in which they learn. Constructionism further emphasizes that this process is strengthened when learners create and explore ideas through hands-on activity, using the tools and practices of their community to make thinking visible (Harel & Papert, 1991). Identity and learning develop together.
This anchoring of new understanding to what someone already knows further reflects constructivist and constructionist perspectives. Together, these theories emphasize that learning grows through active meaning making and purposeful creation rather than passive reception (Ackerman, 2001; Harel & Papert, 1991).
Not all learners experience alignment between their identities and the environments where they learn. When the soil does not reflect or value a learner’s cultural background, language, or ways of knowing, the learner is not nourished in the same way. Recognizing the role of culture in learning does not prescribe a particular teaching action, but it acknowledges that the environment deeply matters. The soil that surrounds a learner supports or limits the root’s ability to take hold and grow.
A young tree growing on the edge of a clearing leans toward the sunlight. It adapts to the conditions it was given. The trees deeper in the forest grow straighter, supported by shade, shelter, and rich soil. Each is learning how to grow, but not under the same conditions.
Trunk
The trunk of a tree represents the development of structure, strength, and overall coherence. In learning, this development occurs through doing something with knowledge. Constructionism emphasizes that learning becomes most powerful when people actively create, experiment, and make meaning with real tools and materials (Ackerman, 2001). Through making, ideas take form, becoming testable and adaptable. Understanding moves from abstract to tangible.
Harel and Papert (1991) expand on this by recognizing that learning grows through the interplay of constructing ideas in the mind and constructing something in the world, allowing each to strengthen the other.
Constructionist learning is evident when learners are able to design, build, write, perform, or create something that expresses and tests their thinking. The process of making becomes the process of understanding.
Video 1. Video illustration of constructivist and constructionist perspectives, supporting the idea that learners build understanding through active creation.
This perspective reflects my own experiences. Whether learning to use my bow with my family or preparing for a race, learning developed through practice with feedback, making adjustments, and applying what I was discovering. It was not a lecture or a list of steps that built my understanding. It was the act of doing.
Branches
Branches stretch a tree upward and outward, reaching for the light and for new possibilities. In learning, branches represent the ways we grow through observation, imitation, and social interaction. Much of what we come to know is influenced by the people we watch, observe, and interact with.
Video 2. Animation of social learning theory illustrating how learning develops through observing and interacting with others.
Social learning highlights that understanding often begins by noticing how others think or act, holding on to those ideas, trying them out for ourselves, and refining them over time (Bandura, 1971; Cherry, 2025).
Throughout my life, I have learned a great deal by observing the practices of others in both my personal and professional worlds. When I became a teacher, I watched colleagues greet students, the ways they structured their days, and how they communicated with families. I noticed what felt authentic to me and what did not. Listening to professors talk through their thinking and share their own classroom experiences allowed me to picture new possibilities for my own development. Even social media has become a space for that, influencing my learning. Observing different creators, educators, coaches, and all of these digital experts who provide ideas and strategies gives me things I can try, reflect on, and reshape into something that fits who I am.
Growing through observation is not always positive, though. The same visibility that inspires growth can also influence habits, beliefs, or behaviors that limit us. I have learned ineffective practices simply because they were common or praised. There have been moments when I caught myself speaking in a way that did not feel like my own voice, only to realize I had absorbed the language of others without questioning its impact. I see students experience the same thing. You become a product of your environment, and that’s not always positive. Observation is powerful, but not always beneficial. It takes awareness to notice what we are internalizing and whether it supports the kind of learner or person we are becoming.
A moment that stands out is when I first began sharing classroom ideas with coworkers. Early in my career, I often mirrored different management styles because that was what I had seen modeled as successful. Over time, I realized the classroom environment I wanted relied on warmth, relationships, and shared ownership. I could not simply imitate what I had observed. I had to notice, evaluate, adapt, and then integrate the ideas that aligned with who I was and who I hoped to become. That is where learning expanded. Not just a copy and paste, but reflection and application.
Observation creates opportunities, but reflection transforms them. Branches grow toward the sun that feels most sustaining. In the same way, learners expand in directions they find meaningful through support and inspiration.
Rings
The rings within a tree tell the story of its life. Each ring marks a season of growth shaped by the conditions of that time. Some years produce wide rings, full of nourishment and expansion. Others are thinner and harder earned. Reflection works in a similar way. It helps us notice what we’ve learned and how it’s shaped us, revealing how our learning has grown over time.
Some of the most important learning in my life has come from looking back. Reflection gives meaning to experience and reveals how one season of learning prepares us for the next. The process of training for my half marathon and learning to hunt did not feel profound in single moments. The understanding came later through looking back at the choices I had made, the successes I experienced, the discomfort I pushed through, and the growth that followed. Reflection helped turn isolated experiences into a connected story of who I was becoming.
In the classroom, I often observed this same process. A student who struggled early in the year would look back months later and suddenly recognize the progress they had made. They could see how their thinking expanded and how they were able to handle challenges differently. Their practice shaped confidence. The moment of noticing became another ring of growth, marking not only what they had learned, but how learning had changed them.
These moments of realization also reflect sociocultural and constructivist perspectives. reflection allows learners to internalize shared experiences and recognize their understanding, turning social participation into personal meaning (Vygotsky, 1979). Constructivist views similarly recognize reflection as the process through which new experiences reshape existing knowledge frameworks (Ackerman, 2001). In this way, reflection does not sit outside the learning process. It is one of the ways new rings form.
Reflection is what helps learning settle into the trunk of who we are. Without it, experiences remain scattered like fallen leaves. With it, they become the rings, strengthening our sense of self and expanding our understanding of the world.
The Living Network
A single tree is never truly alone. Even trees that appear separate above ground are often connected through shared soil and nutrients in underground networks. Learning also exists within systems that extend beyond human interactions. The natural world, animals, technology, and environments all influence how we learn and who we become.
Some of my most memorable learning has come from interacting with the natural world. Practicing archery outdoors, observing animal behavior, and learning how to track movements in the woods required attention to the environment, the wind, and the sounds. The learning came from direct interaction, not from another person explaining it. Instead, learning developed through repeated observation paired with feedback from the environment and adjustment over time. The woods themselves taught me to be still, patient, and aware. This process embodies social learning theory, which emphasizes learning through observation and interaction with your environment rather than solely through direct instruction (Bandura, 1977). Learning in this sense was relational, but the relationship extended beyond human interaction.
Digital tools also expand learning. Technology allows us to join communities beyond our physical spaces, explore interests, and gain access to knowledge that would otherwise be out of reach. Learners can develop understanding through interaction with tools that extend what they can see and do. Through digital spaces, learners also engage in vicarious learning by observing others and modeling strategies while adapting behaviors based on shared experiences.
Research on out-of-school learning illustrates the same idea. Learning happens in museums, community centers, outdoors, in homes, and in digital environments where people get to explore interests, engage in cultural practices, and make meaning with others (Vadeboncoeur, 2006). These spaces broaden the network that supports growth by offering experiential learning that is flexible and self-directed while being connected to the real world. This supports social learning by allowing learners to observe, experiment, and reflect within authentic environments.
These influences also echo social learning theory, where learning develops through observing, interacting with, and responding to both human and non-human elements within the environment through reciprocal relationships between behavior, personal factors, and environmental conditions (Bandura, 1977; 1986). Whether watching the behavior of animals, responding to environmental cues, or engaging with digital communities, learners draw from the networks around them to construct understanding. Learning remains relational even when the relationship extends beyond direct human contact.
Closing
Learning is a living process, like a tree. It is rooted in who we are and where we come from. It grows through experiences, connections, and our ability to reflect and reach outward into new possibilities while drawing strength from what has come before. Over time, learning becomes part of our identity, shaping how we see the world and how we move through it.
Taken together, these ideas show learning as an interconnected system rather than a single process. The Roots reflect constructivist and constructionist perspectives, grounding learning and prior knowledge, identity, and purposeful engagement (Ackerman, 2001; Harel and Papert, 1991). The trunk represents the growth that develops through active making and doing. The branches reflect social learning, expanding understanding through observation and modeling while participating with others (Bandura, 1971). The Rings highlight reflection as the force that deepens meaning and connects experiences over time (Vygotsky, 1979). Even the living network surrounding the tree illustrates how environments and communities continually influence growth. Together, these perspectives form a theory of learning that is dynamic and grounded in experience.
These ideas align with research on out of school learning which captures the idea that a learner’s growth spans across settings, cultures, relationships, skill levels, and life experiences rather than being confined to formal environments (Resnick, 1987).
The most meaningful learning is not quick nor passive. It is lived, appreciated, shared, and carried forward. It leaves rings within us, marking who we were, who we are, and who we are becoming.
References
Ackerman, E. (2001). Piaget’s constructivism, Papert’s constructionism: What’s the difference. Future of Learning Group Publication, 5(3), 1–11.
Bandura, A. (1971). Social learning theory (Vol. 1). General Learning Press.
Cherry, K. (2025, March). Albert Bandura’s biography (1925–2021). Verywell Mind.
Harel, I. E., & Papert, S. E. (1991). Situating constructionism. In I. E. Harel & S. E. Papert (Eds.), Constructionism (pp. 1–11). Ablex Publishing.
Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge University Press.
Resnick, L. B. (1987). Learning in school and out. Educational Researcher, 16(9), 13–20.
Vadeboncoeur, J. A. (2006). Engaging young people: Learning in informal contexts. Research in Education, 30(1), 239–278.Vygotsky, L. S. (1979). Consciousness as a problem in the psychology of behavior. Russian Social Science Review, 20(4), 47–79.
For my final project, I designed a third-grade social studies unit that weaves computational thinking into map skills and navigation. What began as a simple idea about teaching directions became something much bigger. It turned into a five-lesson sequence integrating decomposition, abstraction, algorithms, debugging, and digital creation.
At first glance, it looks like a social studies unit about maps. But underneath, it is computational thinking in action!
Students begin by identifying where they live in nested geographic layers: Earth → North America → Michigan → City → School (see supplemental materials, p. 1 Final Supplemental Materials). That layering alone introduces abstraction. We zoom in and zoom out, deciding what matters at each scale.
Figure 1. Students examine geographic layers to understand how abstraction works when we zoom in and out
From there, students analyze and create school maps (p. 9 Final Supplemental Materials), write step-by-step navigation instructions using landmarks and cardinal directions (p. 13 Final Supplemental Materials), revise those directions after partner feedback (p. 23 Final Supplemental Materials), and eventually build digital mazes in MakeCode Arcade.
Figure 2. Students create precise step-by-step directions, practicing algorithmic thinking
What looks like map practice is actually:
Decomposition: Breaking navigation into manageable steps
Algorithms: Writing clear, ordered directions
Debugging: Testing directions with a partner and revising when they fail
Abstraction: Designing maps with only essential details
Automation: Turning clear instructions into repeatable digital behavior
The final “Design Your Own Navigation Challenge” pushes students to synthesize everything (p. 19–21 Final Supplemental Materials). They create a challenge, design a simplified map, write precise directions, test with a partner, revise, and then imagine a digital upgrade.
It’s playful, structured, real thinking!
About the MakeCode Component
I intentionally kept the MakeCode portion simple. Click the map to test my example!
Figure 4. Students translate their written algorithms into a simple MakeCode maze, where precision becomes essential
It was actually harder to make it simple than to make it complex. I wanted this to feel realistic for third graders encountering block coding for the first time. The goal was not a flashy arcade game. The goal was clarity.
Students apply their written algorithms to a digital maze, where mistakes immediately surface. The computer does not “interpret.” It follows instructions exactly. That tension is where learning happens.
A New Tool I Tried
For this project, I experimented with something new: uploading my slides into Google Vids and using the AI voiceover feature. It generates narration that aligns with slide content, adds transitions, and even infers context (how cool)! The voiceover for this unit was entirely AI-generated from my slides.
Figure 5. Google Vids AI voiceover feature used to generate narration for the lesson slides
It was surprisingly natural.
This tool is currently blocked on my MSU account, so I tested it using my personal account. I wanted to include it because I think it’s a powerful option for teachers who need accessible, flexible presentation tools.
What This Project Changed for Me
Designing this unit made something obvious: computational thinking already lives in my classroom. I just did not always name it.
When students revise directions, they are debugging. When they simplify maps, they are abstracting. When they break a route into steps, they are decomposing.
My professor challenged me to make the computational thinking vocabulary more explicit with students. I agree. Third graders are capable of those words. Naming the thinking gives it weight.
This unit does not add computational thinking to social studies.
I used AI as a support tool while creating this unit. AI helped me check grammar, generate a few images, and create slides. All decisions about the content, structure, and final materials were made by me.
Automation felt straightforward at first. Systems follow rules. They remove repetitive work. They free up time and mental energy. Simple enough…or so I thought.
For my automation creation, I created an unplugged classroom activity where students act as robots. Partners give step-by-step instructions to complete a task. If the directions are unclear, the “robot” fails. If the steps are precise, the task works.
Figure 1. Unplugged “Be the Robot” activity designed to introduce automation through step-by-step programming
It connected beautifully to sequencing and debugging. Students would:
Break a task into small pieces.
Test their “program.”
Revise when something went wrong.
It felt natural. It mirrors how I already teach clear routines and procedures in my classroom.
And then I received feedback…
My professor pointed out that while the activity clearly connected to algorithms, it did not yet make the need for automation obvious enough. It showed how to follow instructions, but not necessarily why we automate in the first place.
That distinction mattered. Algorithms are about steps, while automation is about reducing repeated thinking. That subtle difference pushed my thinking further.
When I revisited my brainstormed examples of automation in my students’ lives, it became clearer:
Logging in with QR codes instead of typing credentials
Math programs adjusting difficulty automatically
Google Classroom surfacing commonly used links
Spell check correcting without teacher intervention
Classroom timers running routines
All of these systems remove the need to re-decide something over and over again. My unplugged activity captured the structure of instructions. What it almost captured was the relief automation brings when something becomes repeatable.
That feedback didn’t invalidate my lesson. It helped refine my understanding. Automation is not just following steps. It is designing systems so the steps no longer require new effort each time.
As an elementary teacher, I see this constantly. Routines become automatic. Transitions become automatic (hopefully). Classroom systems become automatic. And when they do, students have more energy to think deeply about content instead of logistics.
That realization felt bigger than the activity itself.
Automation is not flashy. It is the sneaky invisible efficiency.
And understanding that difference sharpened my thinking far more than simply completing the assignment ever could.