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 – 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. 

Lenses, Not Silos

I am reading an inspiring book about school design and program development with the student at the center. It’s called Building School 2.0: How to Create the Schools We Need by Chris Lehman and Zac Chase. I’m enthralled with the motivational idealism that exists throughout the work; however, this idealism is galvanized by practical experience as the two authors, former school principals, have demonstrated how theory can become common practice. Every so often, a quote pops up which allows me the opportunity to reflect on our School practice. This morning, that quote came from a chapter on “Lenses, Not Silos.”

Good, thoughtful teaching and learning is a process more gerative of questions than of hard and fast answers. – Building School 2.0: How to Create Schools We Need

It’s the Lens

The context for this question stems from the fact that classrooms cannot harbor concepts and skills in exclusivity. In other words, the ideas presented and discussed in a math class must, at their core, facilitate how a student can view the world through a filtered lens. That filter depends on the reference point (or, in the case of school, the material presented); however, a child in the classroom should feel empowered to use this lens as an every day, any moment skill. So when that same student is in history class, there should be an opportunity to utilize a math lens to view the task at hand.

This blending of content areas can happen organically, for instance, in history and English classes. With a little effort, the courses sync to the point where students should not recognize the difference between history or English class…and that is wonderful. But the example I used above (seeing math in history) can be a bit challenging when material is not presented with intention. But this essay is not a challenge to create connections. On the contrary, I’d argue that we should NOT try to create intentional blending between courses that don’t have that organic connection.

On the contrary, I’d argue that we should NOT try to create intentional blending between courses that don’t have that organic connection.

Content as a Vehicle

Instead, I’d offer that educators must focus on building the lens through which a child sees learning. The content used is merely a vehicle for practicing ways to use various lenses. When we can teach students how to think mathematically or process a concept within socio political paradigm, the endgame will present itself tangibly. In our case, the goal must be a capable young learner who can see the comprehensive opportunity to process content as he or she would in the real world.

So I encourage you, in this last month of school, to frame your conversations with the lens of learning in mind. Let’s teach our kids how to see the world as an interconnected classroom, where their ability can bring many thoughts and materials into a useful, practical, and joyful experience.

Making Failure a Priority

This image appeared on my LinkedIn feed yesterday, sparking thoughts and reflection about why the middle school years are so crucial. Tweenagers, children between the ages of 10 and 15, go through a roller coaster of changes. They discover independence and passion for new ideas and interests, particularly during the school day. As they discover opportunities to make decisions sans parent influence, tweenagers find their path more open and free as their capabilities have increased. However, this freedom comes with risk attached. In discovering passions, the inevitability of failure surfaces. For students at my school, a fear of failure predicates all decisions. Quite often, they test the waters only to back off after a mistake or an undesirable result develops. As you can see from the examples below, it’s that “comfort zone” of effort that we need to expunge.

“My parents will kill me if I don’t make an A.”
Students love the easy ‘A.’ The gratification of seeing a good grade on a test or report card starts early and carries forward throughout our adult life. But anyone can take the easy road to make the grade; the more memorable academic work arrives when taking the road less traveled. However, students are hesitant to take risks on a project or paper because the uncharted path, though more interesting and dynamic, may not provide an easy avenue to earning high marks. Pursuing a unique and creative path takes effort and iteration which means patience in academic effort. Teachers are welcoming of this path; looking at a new topic or seeing a student take a new angle with a project is energizing to a classroom. We as educators need to remain vocal in our support of these trailblazers so that they can see the value of the road less traveled.

“We lost the game. We suck.”
When it comes to sports, middle school students are diving into a whole new world. No matter the game, the average tweenager is only developing the concept of being a “cog in the wheel.” After so many years of being in the spotlight, especially in today’s ribbon-happy athletic environment, being a piece to the puzzle versus the solution is humbling at best. Some young athletes reach puberty early, giving them the physical edge; this only adds to the disillusion of the rest of the pack as they watch their classmate get the glory.

Second, so many times in my coaching career I have heard the opinion of “we suck” based on the fact that the team lost the game yesterday. It’s hard for a young person to see the baby steps of progress that it takes to become a strong, successful team. As I speak to students after a game, the response to “how did the game go?” is always black and white. Win or loss. So my second question is always, “How did YOU do?” The response to this question is interesting – after debriefing personal performance, students are very quick to celebrate the success of a teammate. Perhaps the question triggers that “cog and wheel” perspective in the tweenage brain. But coaches and parents alike can help a student overcome that all-or-nothing response by asking about the space between.

Power in Failing
As I return to the image that sparked this post, let’s look at the key pieces to the acronym shown in the picture:


  • F: First – In order to fail, you have to try (and try again). Ramana Maharshi, sage thinker who devoted his life to exploring self-inquiry, is quoted saying, “No one succeeds without effort…Those who succeed owe their success to perseverance.” We must teach young people to take that first leap of faith, and to be comfortable with the outcome, whatever it may be.
  • A: Attempt – These days a young person believes that attempt = successful completion. I host an after school club every other week when students come to play chess and other types of board games. I find it interesting that, even in a gaming situation, students won’t make the attempt against an opponent they know is good (or better than they are) at a game. For instance, Alex is a chess master, and students are afraid to play him. With this decision, there isn’t a way to improve. We must educate tweenagers to re-engineer their understanding of an attempt to one of trial and error.
  • L: Learning – Skill development is the very essence of forming the teenage mind. To me, the definition of learning finds its foundation in skill development. To put it another way, failure is a part of developing skills. Finding out what doesn’t work provides a wealth of understanding for a young person. Failure is a life experience that helps, not only in the current effort, but in all those efforts to come.

Take a moment to reflect on how you teach failure in your classroom. It may be the most important lesson you can provide a young person.

Middle School 101: Overtired and Overstressed

A nightmare rears its ugly head all too often from mid August to sometime in early June, aligning very well with the beginning and end of the school year. The scene varies from episode to episode, but one example depicts me in the kitchen preparing dinner. I have chicken on the grill, vegetables on the stove, fries in the oven, and a dining room full of people to serve. However, I can’t get one thing finished without another needing my attention. One thing burns or gets too cold while I focus my attention on the others. The annoyed look on the faces of the diners says it all: I’m working too slow and preparing a sub-par meal. The scene leaves me in a state of panic and stress. I wake up confused, in a sweat, and (worst of all) defeated.

Seems a bit ridiculous, right? Perhaps not. All of these external factors play a major part in our success and sanity. This summer, the teachers in the middle school read a book by Ana Homayoun called The Myth of the Perfect Girl: Helping Our Daughters Find Authentic Success and Happiness in School and Life. The author pegs three major changes in the environment from when we were students to the world our kids live in now:

  1. Our Changing Academic Landscape: Our students seem to know every little bit about another classmate’s academic successes, and find the a valid source of comparison. They know about national averages or GPAs required to get into University of X and how their grades align to these standards (to three or four decimal places). This knowledge can bear the fruit of stressful and unreachable expectations.
  2. Getting Older Younger: Society expects the 11-13 year old kid to be an adult in social scenes, from how tweens dress to how they interact. But the chemistry of puberty is like a class 5 hurricane with multiple eyes in the storm – just when a calm appears, the storm comes roaring back, toying with emotions, physical appearance, and focus. All the while, our middle schoolers think they must be A students without faltering.
  3. Technology: From ridiculous glamorization of the “shock and awe” presented to our students on YouTube to instant social interactions which sometimes lead to destructive decisions, students are behind the 8-ball when it comes to acting with respect and integrity. Pressing “send” is way too easy, and the implications of actions do not keep up with fast-twitch attacks that students wish they could take back. All too often the sharks are yesterday’s best friend; however, the greatest threat is in the mirror.

Although the social and emotional components of academic success are a disillusioning distraction, these are realities of our children’s lives that they must work around. At this point in their lives, middle schoolers do not have the toolset to see past the distractions. The struggles are viewed as “not fair!” or “completely ridiculous.” Students fall prey to the struggles, making statements like “I’m just not smart,” “no one likes me anyway,” or “it’s just not worth the effort.”

Let’s look at this problem from an adult perspective: In order for you and I to complete tasks at work or at home, we have to think ahead and prioritize to ensure that all of the most important concerns are handled. And so we all must make a choice, and often that choice includes sacrifice. Whether we have to miss the first half of the game on television or give up some other form of personal time, we know that sacrifice is necessary because we can work outside of the distractions life throws at us. Our choices are clear because we have erred in the past and have learned how to avoid problems in the future. Further, we are satisfied with doing what is best, even though that road may not take us to results we had previously hope to reach. These are life-long skills you and I have developed via experience. As your child is now in the middle school, it’s time to help them learn these same lessons.

Below I present two concepts I call “Active Learning Tips.” Taken from a concept developed by Jean Piaget (he called it constructivism), active learning occurs when a mind actively questions, explores, and assesses information as it learns, learns more deeply and more meaningfully.  Active learners take in experiences and information, compare them to previous ideas or experiences, add to or alter beliefs, and construct a personal base of knowledge.

Active Learning Tip #1: The first requirement to helping students beat stress and achieve academically falls on us, the adults in the room. We have to realize one central idea: most students don’t get time management in middle school. They honestly think that since they have two tests tomorrow, afternoon soccer practice, and then a piano lesson they just have to figure out how to do it all. They didn’t think about all these things yesterday (or last week as the case ought to be). They are simply under-experienced and without the toolkit necessary to look up and consistently think ahead. We have to be that guide.

  • Have a conversation with your child about what is coming up this week, and have it again throughout the week. Help them to see the layout of the week with the goal of planning to complete each day with success, not simply to wade through the water. Training is a part of mastery.

Active Learning Tip #2Analyzing homework for gaps in learning (highlighting trouble spots, questions written in the margins, etc.) is the key to having success on a test or quiz. Our young men or women can learn from mistakes and focus on the grades that make the most difference (both for a student’s average and for the teacher to analyze academic development). Our middle school has a goal (note that it is a goal, not a law) of assigning on average about 20 minutes of homework per subject per night. That adds up quick. However, analysis of execution should be a component of that homework effort. This analysis will definitely require guidance.

  • Encourage your child to make a priority list daily before starting homework. Make sure there is time to tackle the big things and that the little things, though deserving of respect, wait for your child’s availability. Even then, sometimes a student simply can’t do it all (and violin…and volleyball…). That has to be ok.

While these are just two examples, there are plenty more just like them. It is my hope that this toolset develops for your child while they are in middle school, and that I can coordinate with you to help them become better learners.


Homayoun, Ana. The Myth of the Perfect Girl: Helping Our Daughters Find Authentic Success and Happiness in School and Life. Perigree, 2013.