Bringing School Together – Connection Learning in Math and Science (Volume One, Post 3)

“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.

Making Connections

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.

Concluding Thoughts

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.

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

Runco, Mark & Nemiro, Jill. (1994). Problem finding and problem solving: Problem finding, creativity, and giftedness. Roeper Review. 16. 235-241. 10.1080/02783199409553588. 

Bringing School Together – Humanities, Languages, and Identity (Volume One, Post 2)

In my previous (introductory) post, I described the general design and belief system of our middle school program at Presbyterian School. A colleague and faculty member appreciated my use of the word opportunity to talk about learning. I chose this descriptor to emphasize how we encourage students to attain meaningful, joyful learning pathways that fulfill the soul. As educational professionals, we help each young learner see the value of taking a comprehensive approach to learning. Pushing beyond standards and into learning for the joy of discovery is our goal for any child with whom we are blessed to interact.

“An important part of PS is that we coach students and provide them with a decision making framework that enables them to evaluate as-of-yet undefined situations they will face in their lives, the skills to read the lay of the land, and to have the confidence and resiliency to veer from the simple route, and when needed blaze new trails through undiscovered territories in academics and life.”

Gordon Center, Seventh Grade History

During the months of October through January, the majority of our eighth grade students participate in interviews during the high school application process. In these conversations, students describe their successes and missteps with confidence and appreciation for the journey. While our students are incredibly well-prepared to succeed in high school, Presbyterian School prepares the child for the paths presented at every stage of life, a mission moving far beyond grades 9-12. To prepare each child for future challenges, our middle school program instills the essential skill sets and abilities for our students to become Pathfinders. Pathfinders understand the opportunities available to them. They have been given time to reflect on personal strengths when selecting new roads for their learning, competing, and/or performing. Additionally, Pathfinders have developed a unique charisma to carry others into meaningful and fruitful experiences. There are many ways to develop Pathfinding skills through words, thoughts, and actions. Our dream is for each child to gain access to all of them by recognizing and utilizing personal strengths.

One final component in the successful development of students includes the discovery and utilization of empathy as a means to success. Whether it’s built upon a faith-based foundation or moral root, our students learn through our everyday practicum that connecting to the emotions and perspectives of those they lead from, learn from, and walk alongside has immediate and long-term benefits to themselves and the community. 

“Empathy is a crucial theme [in our program]. Stepping outside of oneself and considering others’ perspectives allows us to become more reflective, more forgiving, more considerate, and more productive.”

Kelsey Pedersen, Seventh Grade English

Introducing the Construct

While traditional English classrooms engage in vocabulary, grammar, and writing skill development, our classrooms aim to do this by incorporating learning opportunities that promote one’s ability to use the components as a way to improve a learner’s communication capabilities.  With this goal in mind and in order to develop Pathfinders, we have developed a thematic Identity Pathway in our English, history, and language courses to help the learner understand his or her place in the school community and beyond. The middle grades at Presbyterian School present the following in age-appropriate stages within grade levels. These stages offer students the opportunity to use various lenses to observe, infer, gather, and present.

Sixth Grade - Introduction to and Exploration of One's Identity
Seventh Grade - Navigating Alienation and Pursuing Reconciliation
Eighth Grade - Redefinition and Presentation of Personal Identity

Beginning in sixth grade English class, our students dive deeply into the concept of identity by way of reading, analysis, evidence-based conversation, and research. Our design allows for students to explore parallel experiences in novels, short stories, and poetry in order to develop a basic understanding of identity.

“Throughout the year, students use their growing writing skills to reflect on characters they meet in class readings,  particularly as those characters and their reactions relate to the students’ emerging selves.”

Janice Kemp, Sixth Grade English

History classes in sixth grade provide a similar experience; the observation and research of past civilizations help students to understand the constructs of identity creation. Students explore cultural identities on a global level (and through various time periods) to understand why a civilization decided to follow a certain pathway, and what its success (or failure) teaches us about our own choices as individuals and as a modern culture.

As a culminating, cross-curricular demonstration of their sixth-grade journey, students use their writing and presentation skills at the Genius Hour; this exhibit allows students to share with others a passion for learning they developed during their year-long discovery of self.

Respectful Resolution in the Face of Doubt

During a child’s seventh grade year, we take these constructs of identity and integrate the concept of choice into the conversation. Seventh grade remains the most challenging year of personal growth for our middle school students. Whether it’s a physical or emotional change, or a social disruption among friends or peers because of personal interests or beliefs, our seventh grade learners feel criticism and doubt with increasing impact. They learn to manage feedback, albeit positive or negative,  independent of adult intervention, thus creating the foundations of meaningful and stable interactions. As this struggle ultimately results in a strengthening of personal beliefs, our professional responsibility to serve as positive role models creates wonderfully organic opportunities during the school day, both in and out of the classroom. Our seventh grade Humanities Curriculum therefore emphasizes the appearance of conflict, alienation, and resolution as a part of literature and historical research.

In English, we reflect on counter-cultural figures who appear in such works as The Outsiders and The Lion, the Witch, and the Wardrobe. Writing and revision sustains an ongoing process through which students research with intention to express ideas in relation to others while becoming more articulate in speaking, writing, and sharing their convictions. In history we analyze choices made by opposing nations as students explore the tolerance needed for peaceful resolutions as opposed to the devastating cost of war. From treaties to respectful “agree to disagree” tactics, seventh grade learners consider how decisions can burn bridges and/or build them. Some structured practice of this brain development appears in the form of Harkness discussions — a consistent conversation framed within mutual respect even as disagreement arises. As a part of their final trimester, students present a self-assessment of particular skill sets developed over the course of the school year in an all-school presentation for younger learners and families to witness.

“All human societies contain inventive people. It’s just that some environments provide more starting materials, and more favorable conditions for utilizing inventions, than do other environments.” 

― Jared Diamond, Guns, Germs, and Steel

As Jared Diamond begins, our students explore the conditions which give rise to the decisions of others, and thus learn to interact with better understanding and perspective. Most importantly, students consider the value of patient, deliberate decision making based on a multitude of facts rather than split second decisions. This translates directly into their everyday lives as they navigate the messiness of adolescence and the empathetic development of self while learning from choices, histories, events, struggles, and emotions.

Empathy Built on Wise Use of Perspective

“You either walk inside your story and own it or you stand outside your story and hustle for your worthiness.”

― Brené Brown, The Power of Vulnerability

Brené Brown offers endless support to our Identity Pathway. Each step is built on a similar foundation to the platform she has so successfully created – vulnerability, trial-and-error, and authentic self-definition. The child in a middle school program is very much a work-in-progress, with years to go on his or her journey. For this reason, we extend the concepts initiated in seventh grade into the heart of our eighth grade year. Additionally, the eighth grade program focuses on individuals who reaffirm their position and beliefs to stand up for what is right.

Vulnerability exists throughout our eighth grade Humanities Program, specifically called The American Experience, which gives respectful attention to perspective – that of classmates, characters, and historical figures. As students dive into social conversations via Harkness discussions and Socratic Seminars, they gain a deepening of perspective which leads to comprehensive respect of others. Further exploration towards understanding exists in extensive, thematic literary/historical research by choosing their own texts based on interest and need. Additionally, our Pathfinders engage in a reflective, iterative writing process to demonstrate their learning in various capacities such as expository essay and prose.

“Our lessons from the past allow students to directly connect to the present world events. And the study of language arts/English helps them to communicate clearly and concisely their understanding and perspectives.”

Danielle Filas, Eighth Grade English

As a vehicle for learning, students explore the Holocaust and Civil Rights Movement, navigating the various perspectives that created these uniquely polarizing events. By learning from others and reflecting on their own perspective amidst a diverse community of interests, each student develops a Manifesto, or a statement of intentions, opinions, and vision. Students present this Manifesto as a part of their final action as a Presbyterian School learner.  In the spirit of vulnerability and personal growth, their projects are displayed for all to see.

Communication in Any Environment

Our Language Program at Presbyterian School focuses on Spanish as its principal pathway.  While we spend intentional time in grades 6-8 developing a vocabulary and grammatical foundation in Spanish, our efforts focus primarily on the development of skills that enable students to communicate in the target language. This skill set includes listening, reading, writing, and speaking.  Our program affords each student the means to demonstrate proficiency on their high school course placement test at destination schools for ninth grade Spanish courses; however, our methodology moves far beyond the standard of “test prep.”  Students at Presbyterian School learn that defining their identity and considering the opinions of others should exist in any media and in different languages. Houston is home to a wonderful Latino community which strongly contributes to our city’s unique identity. According to the Institute of Hispanic Culture of Houston, the Latino population in the city sits close to 37%, less than one percentage point below the Anglo population. For this reason, speaking Spanish has become an essential part of growing up in Houston (and in Texas). Our Spanish program, recently expanded to include the sixth grade, takes this need into account. Spanish language and various Latino cultures are an essential part of our community identity. We must celebrate this component as an enriching benefit to being in Houston. 

Every year, a culminating, student-led event takes place at Presbyterian School as we participate in “Día de Immersión” – Spanish Immersion Day. This day focuses on the gifts given to us by the Latin American cultures of Houston, including dance, song, movies, art, food, and games. The day exists for the benefit of our students, who oftentimes find themselves in a unique bubble living in parallel to this wonderful culture.

“Día de Immersión exists so our students can authentically interact with each other and community in the Spanish language, and we hope this positive experience can encourage students to become more comfortable interacting with Spanish-speaking people in our area.”

Sara Broussard, Sixth Grade Spanish

In Conclusion

Our students experience a wonderfully made journey of self-discovery with each class and every year. Like Harry Potter’s exploration and discovery of his own Patronus incantation, one’s power unfurls when recognition of and appreciation for personal identity takes center stage.   Though sensational in design, Harry recognizes that, in the face of danger that questions his very being, a person’s most powerful counter lives in his or her personally-defined system of beliefs. This belief system remains in constant development; however, at the moment of need, its core values must be ready for presentation.

We are confident that students find themselves at our Commencement Ceremony upon completing eighth grade with a sense of preparedness for the pathway that lies ahead.  Success shines in the steps our young learners have taken to consider personal identity and responsibility in their greater community. The impact that their beliefs can make as Pathfinders will lead us to a better tomorrow.

Bringing School Together – Volume One, Part One

Launch Initiated in 10…9…8…

For those of you diving into Educationomics for the first time: my name is Charlie Gramatges, and I am the Head of Middle School (principal) at Presbyterian School in Houston, TX. I have blogged for a number of years, building a catalog of experiences I have enjoyed during various stages of my career in education. I have learned much, and now have an opportunity to do something I have never done before.

This post marks the start of a new series I hope to share over the summer months and through the upcoming school year. The series is filled with the inner workings of our Presbyterian School educational system, specifically in the middle school. In addition to defining our middle school identity, I hope to document the coming months of our institutional future. I’ll reflect on the physical, pedagogical, and programmatic design of our institution and the educators who serve as guides and thrive as co-learners to the young people who explore within our current (and future) learning spaces.

More than any other time in the history of our good school, we are leaning into our counter-cultural mission to deliver meaningful, joyful, soulful learning to every child, every day.

Dr. Mark Carleton, Headmaster

Volume One of this journal will include a number of additional entries, all focusing on the ethos and belief structure that makes Presbyterian School truly unique. Not because we have something that other schools do not; I believe that the culture of Presbyterian School provides the opportunity for each child to build an experience that energizes and celebrates learning pathways, enabling children to move past our program and into high schools with advanced capabilities to research, perform, discover, and extend interests to fit every challenge they will face.

For further detail, here is the topical index of both Volumes. An entry from Volume One will be released each week through the middle of July. Volume Two will begin in mid to late August.

  • Volume One
    • 21 June: Introduction and Main Beliefs
    • 28 June: Humanities and Language Acquisition
    • 26 July: STEM Connections in Math and Science
    • Student Voice and Choice
    • Faith and Fine Arts
  • Volume Two
    • Location and Partnerships
    • Classroom Spaces in Renovation
    • Common Spaces in Renovation
    • General Conclusions

This We Believe

Our middle school students develop a resiliency they emulate when contributing to future institutions of learning. Through encouraged voice and choice, our young people become community leaders, team captains, and ambitious contributors to the world around them. Typically, students and Presbyterian School go on to 12-15 different high school programs, impacting the entire city of Houston with their dynamic expectations in learning. These successes stem from an intentional focus on giving one’s personal best and seeing how to push these limits through age-appropriate risk. We have worked hard to develop this culture as a faculty, reflecting how we present discovery opportunities to our students and encourage them to become the best versions of themselves.

In short, what a child learns should be up to him or her. How that child discovers knowledge through trials, successes, and happenstance must be cultivated and harnessed as a part of skill acquisition.

Our smaller class sizes provide students the opportunity to learn about themselves, to appreciate differences of opinion, and to celebrate the different perspectives that exist around them. We encourage students to consider unique ways to demonstrate their learning, and expect the various pathways to be bumpy. That is why we encourage our students to embrace the learning process by modeling grit and determination in the face of missed opportunities. We design the various pieces of our curricula as challenging to master, yet engaging to experience.

Teachers have the opportunity to connect to each child during any class period. Students receive direction as a means to find their next step on the path. While we are bound by a traditional grading structure in core courses (STEM, humanities, or foreign language curricula), all faculty consider the overarching skill sets that a middle school student develops to remain essential and a priority over content. In short, what a child learns should be up to him or her. How that child discovers knowledge through trials, successes, and happenstance must be cultivated and harnessed as a part of skill acquisition. Faculty work as grade level teams to ensure that skills being developed are complimentary and useful no matter the scenario. Similarly, our content areas meet and develop a vertical alignment within to ensure the skills a child develops are scalable and dive deep into learning pathways, preparing them for more challenges in the years to come. We are in the business of developing capability, not databases, in the minds of each child.

tune in next week…

Next week I’ll dive deeper into the first of our two thematic pathways – Humanities and Language Acquisition.  We will walk through the progress our students make in preparing themselves as capable representatives through a deep dive into the concept of identity.