“Climb the mountain not to plant your flag, but to embrace the challenge, enjoy the air, and behold the view. Climb it so you can see the world, not so the world can see you.”― Warren Berger, A More Beautiful Question: The Power of Inquiry to Spark Breakthrough Ideas
As you may have read in the previous post highlighting Humanities and Language Acquisition, Presbyterian School has developed a middle school program centered on the construct of Identity, enabling learners to engage with their personal strengths while celebrating and utilizing the capabilities of others through well-developed curriculum based on empathy, determination, and self-worth. The Identity construct remains relevant in all content areas of a child’s middle school career here at PS. While there is a direct exploration of this concept in Humanities, our Connections courses do much to reaffirm the Identity lens within the mathematical and scientific pathways. We place our math and science courses under the umbrella of Connection Learning because these content areas offer the learner an introduction to and practice of trial-and-error (Scientific Method) while building confidence in problem finding.
“The quality of the question you ask — or the way you frame the problem you’re trying to solve — determines the context, meaning and significance of the project.”― Mo Fox, 7 Steps To Better Problem Framing In Design Thinking
The Great Exploration
The science component of our program aims to engage students in opportunities which identify how things work as opposed to simply knowing what things are. In the modern, “Googleable” world, much of the words we find in bold within textbooks provide learners a solid foundation. We take learning a step beyond this foundation, imploring students to consider what they will do with what they know. Our goal rests in the creativity that manifests when students present learning through dynamic construction. Whether it’s a unique presentation, a physical model, or engaging, research-based discussions, our students learn through doing. Further, when considering one’s own personal experience to that of a classmate, learners can broaden their horizons. Students realize that pathways in research may be similar; yet, they are always distinctive and valuable, offering students new methods to use in future efforts.
Our goal rests in the creativity that manifests when students present learning through dynamic construction.
The primary step in this process is choice. Allowing our students to “choose their own adventure” within a framework provided, we can expect engagement in learning to increase and advance to unexplored territory. A child who learns like a Pathfinder will find comfort in taking calculated risks and have confidence when changing direction in the face of failure. As psychologist Jo Moser discovered, the learning that occurs from mistakes is evident in the development of the human brain. In short, when we mess up and learn from past experience, our brain pathways grow and develop, almost like working out a muscle in the gym (Moser et al., 2011). Presbyterian School celebrates these learning opportunities and the strengthening of our neural pathways. We teach students to become engaged individuals who embrace the challenge in learning for the sake of becoming a stronger thinker.
“The general thesis regarding the future of work here is this: the arc is toward problem-solving generalists rather than those with specialized expertise. To be succinct, that means we are going to need more and more people who are quick learners rather than those who are deeply learned. ‘Learning on the job’ will take on a whole new meaning. While “specializations” like doctors and lawyers will still need a deep knowledge base, even they will be expected to learn at an accelerating pace. The most attractive employees will exhibit ‘mental agility,’ the ability to ‘pivot,’ ‘comfort with ambiguity,’ and will be ‘open to new experiences.’”― Will Richardson, Inspecting for Signs of Decay
Will Richardson’s quote accentuates the art of identifying learning pathways while remaining mentally agile. In our hallways, we often talk about “living in the grey” within the development of the adolescent learner. The wonder of discovery is alive and well in years 11-14, and so is the impressionable mind that could choose to shy away from failure. We must embrace both of these characteristics if we hope to enable young minds to develop into Pathfinders who are open to new experiences.
When a child enters the sixth grade science classroom, the world of discovery and how things work begins. For instance, school commences during hurricane season, and Houston is no stranger to inclement weather. Our students begin working on a severe weather unit that has large global maps in front of teams of students analyzing winds, currents, and hurricanes. Students pour over these maps, measuring and plotting the paths of weather systems in an effort to develop research skills which they discuss and display. The intentional pairing of this course with the mathematical discovery taking place in their pre-algebra classroom provides exposure to concepts through an analytical lens. Measurement, observation, inference, scientific sketching/drawing, collecting data, representing and interpreting data using data tables and graphs, and drawing valid conclusions integrate with math skills during scientific investigations.
“When I hear of an event, such as an earthquake or volcanic eruption on the radio, I ask my students about it. They share what they know and then we explore why it happened where it did. I relate the event to Earth processes, such as plate tectonics/subduction or climate change.”-Carmen Druke, Sixth Grade Science
Seventh grade students take that wonder a step forward through hands-on learning experiments in biology. Seventh grade science is all about life and the interconnectivity of one thing to another. We learn to define life, the requirements for it and its interactions within communities over time. Students create, through modeling and experimentation, a bridge of understanding between the concrete and theoretical. Utilizing microscopic observations, dissections, and other interactive activities, students experience how individual parts affect complex systems as a whole. Emphasizing the value of wonder, students begin to view science as a path from mistake to mastery of a skill or idea. Through exploration and discovery, students test theories in order to explain how all sorts of changes will influence projected outcomes.
“Science isn’t about seeing what the ‘right’ answer is. Science is being able to recognize a reasonable answer and explain what could have caused an unreasonable result via testing and data collection.”-Anna Head, Seventh Grade Science
As we move towards eighth grade, the education of each child develops into a self-driven, inquiry-based approach to discovery and opportunity. Whether they are creating prototypes, informing others on scientific issues, or simply exploring something new, students embrace learning because they must own their pathways. Digesting scientific journals has been a part of a middle school student’s entire experience, and an emphasis on scientific literature becomes vital to the Pathfinder’s mission in eighth grade in order to analyze expert knowledge with greater awareness and correlate this information when presenting research.
Additionally, our eighth grade classrooms enjoy greater emphasis on cross curricular activities as a way to solidify student understanding and recollection of knowledge. In fact, much of what an eighth grade student experiences in math class can be practiced in the science classroom, essentially creating a block of time during the day when a learner can explore through a very focused lens. For example, eighth grade students design their own catapult during math and science classes. Math class time allows for measuring parabolas made by their catapult projectiles, while science class focuses on the engineering and structural design of a student’s machine.
Laying Foundations for Creative Problem Solving
Presbyterian School highlights the “why” in mathematics where hypotheses can be tested, facts can be proven, and results can be shared. Our goals for mathematical learning at Presbyterian School include:
Seeing math as a language used to communicate logical arguments which will solve problems
Developing a lens capable of critical reasoning and astute investigation
Communicating mathematical thinking clearly to classmates and community
Creating and using models to organize, record, and communicate mathematical ideas in ways that speak to personal learning styles
Our math program in both sixth and seventh grade utilizes the curriculum designed for thinkers by Open up Resources in coordination with Illustrative Mathematics. This curriculum focuses on mathematical literacy (similar to the lens of learning) by targeting the ability to verbalize, demonstrate, and write about mathematical processes in very specific ways. Fundamental skill sets incorporate concepts where making sense of problems means estimating and trying different approaches. Students select and use appropriate tools while evaluating the integrity and significance of answers. They practice pattern recognition and are able to make generalizations while listening to the reasoning of others. A child continuously builds on previous knowledge to advance conceptual understanding of a topic and moves towards procedural fluency. The use of intentional mathematical language and instructional routines provides a structure for the classroom which students can enjoy with consistency. Our sixth and seventh grade classrooms accentuate the 5 Practices for Mathematical Discussion which allow students to have rich discussions about their understanding, ask better questions, compare and contrast various techniques, and note misconceptions about a concept.
“I love when a student discovers that they really understand a concept. Their eyes light up, they get a huge grin on their face, and they are loud and excited. The student feels successful, and feels like a real mathematician, maybe for the first time in their lives. They feel like they belong in a class that is intellectually challenging, even if math has been hard for them in the past.”-Beth Robertson, Seventh Grade Math
By the end of eighth grade, our students complete a curriculum equivalent to a high school Algebra I course; the concepts presented in eighth grade become increasingly abstract as students work to define a mathematical model for each problem they discover. Our students find consistent success in their high school math placement, primarily based on the mathematical reasoning capabilities they build in their classrooms. The Formula we enjoy, pun intended, is one that centers on the most engaging pathways that offer challenging real world problems in order to make the material relevant. We aim to drive the “what is this for / when we will ever use this” question to obsolescence as the application of concepts presented directs our mathematical conversation. Gamifying practice sets and assessments in digital learning centers like Kahoot, Quiziizz and home-grown healthy competitions inspire engagement and childlike joy into the classroom.
“From the moment students walk in the door, my goal is to both engage their critical thinking and problem solving skills as well as make the method by which we learn and practice fun.”-Brandon Walker, Eighth Grade Math
Math at Presbyterian School often presents itself as a puzzle with multiple ways to find a solution. Learning from challenges and mathematical misconception serves as amplification of our Growth Mindset, or the capacity to learn from mistakes and improve one’s approach to problem solving. This is true for both students that struggle and students deemed “strong” in math.
We believe that the world of learning is beautiful, and Presbyterian School encourages students to discover this beauty with an open mind and full heart. Connection Learning advances this effort through a unique set of skills and lenses. Pathfinders in our math and science classrooms create pivotal and expansive platforms on which they can discover new and dynamic things. Each child has a voice that is heard and celebrated as a phenomenal contribution within our own learning environment and beyond, bringing meaningful and joyful opportunities to share.
Boaler, Jo, and Carol S. Dweck. (2016). Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching. First edition. San Francisco, CA: Jossey-Bass; a Wiley Brand. Print.
Fox, Mo (2018). 7 Steps to Better Problem Framing in Design Thinking. LinkedIn.com
Moser, J. S., Schroder, H. S., Heeter, C., Moran, T. P., & Lee, Y. H. (2011). Mind Your Errors Evidence for a Neural Mechanism Linking Growth Mind-Set to Adaptive Posterror Adjustments. Psychological Science, 0956797611419520.
Nabb, K., Hofacker, E. B., and Ernie, K. T. (2018). 5 Practices in Mathematics Teaching. Mathematics Teacher, vol 3, no. 5. 366-373.
Richardson, Will (2019). Inspecting for Signs of Decay. Modern Learners via Soundcloud.com.
Runco, Mark & Nemiro, Jill. (1994). Problem finding and problem solving: Problem finding, creativity, and giftedness. Roeper Review. 16. 235-241. 10.1080/02783199409553588.