This blog post is the 2nd part of the Learning Design series blog that started last week. This week, we will cover Math. After that, there are snippets of ActonKL happenings!
Look at the equation above. Math! This very word might trigger anxiety. Or you might be a Math nerd and love to teeth into these symbols of human ingenuity. If you are, does the piece of Math give you a sense of what does the equation means, intuitively? Or you just happened to teeth into Hindi symbol manipulation, regardless of its meaning?
Math is the Study of Patterns. The reality is that every child (and hopefully adults who have not sold their soul) has some love to that. Pause and imagine—the fractals of the seashore, the prime number patterns of a flower, the way the sunset changes color through time, and the patterns of the night sky. Nature has inspired human to create Mathematics since the dawn of time. Not exactly in the forms of Hindi symbols and Greek alphabets, but certainly in the recordings of language, poetry, and culture. But most of us have, as a famous Mathematician, Paul Lockhart puts it in the controversial piece A Mathematician’s Lament—a nightmare.
The Nightmare
LOWER SCHOOL MATH. The indoctrination begins. Students learn that mathematics is not something you do, but something that is done to you. Emphasis is placed on sitting still, filling out worksheets, and following directions. Children are expected to master a complex set of algorithms for manipulating Hindi symbols, unrelated to any real desire or curiosity on their part, and regarded only a few centuries ago as too difficult for the average adult. Multiplication tables are stressed, as are parents, teachers, and the kids themselves.
The Math prescription seems eerily exact as to how Lockhart wrote it in 2002. That is how Mathematics education has become—dry with little resemblance of the original pursuit of the human curiosity. And these format of Mathematics education probably had been the standard recipe for the last century. I urge you to read it; at least go through the first two pages and last page in detail, and browse through the rest for his alternative proposal.
At Acton Academy, we too face similar challenges. As an American accredited school, we do want to meet the US Common Core standards. Fortunately, we have the flexibility of a Learning Design that incorporates a large amount of hands-on learning through real-world projects. But we have generations going through Math in the nightmare fashion and believe that it’s the only way to learn. So, besides knowing how Acton Academy does it, I will share parenting tips on how to support your Eagle. So, let’s get on with it.
In short, ActonKL start by developing an interest in Math first using Montessori materials, then via a combination of online software programs, and we mix it with projects. The Mathematics in the Quests are complementary and delivered on an as-need basis. We admit it: It is not perfect. You might want Eagles to learn Geometry through Art, fractals through nature observation, or balancing equations in the Newtonian mechanics. The reality is that Eagles will only learn if they need it to solve a problem that is natural rather than artificial. For example, calculating the time required to cook a perfectly soft-boiled egg is natural, but it would be artificial to have a challenge in estimating the curvature of the eggshells (why do I need that anyway?). But we hope it provides the foundation for our Eagles to develop an interest to patterns around them, certainly much more than traditional education Lament’s nightmare. Our goal is not having a Math curriculum, but developing Eagle’s character to have the patience and perseverance in learning logic and thinking, or as Angela Duckworth’s put it—grit. 99.9% of the time, Eagles learn how to figure each problem mostly by themselves, and help each other. Teaching others is one of the best ways to learn :)) OK, let’s break down studio-by-studio:
Early Years (Preschool)
Our young Eagles start with Montessori materials. Maria Montessori designed each Montessori element to be self-correcting and scaffolded to develop a young child’s interest and ability in Mathematics. Eagles learn through an intuitive sensorial experience. Each step of the way, they discover patterns and sequence of thought that resembles what we call “Mathematics.”
Take Counting for example. Does counting means looking at a series of Hindi words and call out words of “one, two, three,…”? Or does counting means relating the words and expression to the abstract concept of scale? The later has far more context. A Montessori learner applies the scaling concepts to length, the number of units, cubic sizes, and so on. The Montessori materials distinguish this in their well-designed tools. Maria Montessori genius is building tools and methodologies that work for children, and meet them at their level. We draw the inspiration from her work. Our only additional contribution is the Hero’s Journey: we use the Hero story narrative for encouragement or when coaching an Eagle through a struggle.
If you take this idea further, humans have extended scaling and numeracy to other tangible characteristics of the world: colors, shape characteristics, and even communication of love.
The ultimate goal is developing an Eagle’s curiosity to the world, appreciate beauty and patterns intuitively. There is some manipulation of Hindi symbols, but just good enough to enter Elementary School!
What can I do as a Parent? Nothing much except for following their curiosity when you spot any language of pattern recognition. Even your car ride home can spark plenty of conversation:
“Between A car & B car, which car is bigger? How much bigger?”
“Do all big cars have more exhaust pipes? Is there a relationship between the size of a car and the number of exhaust pipes?”
The goal of these conversations is not “instilling mathematical concepts,” but clear thinking and cultivating curiosity. Ideally, let your child lead the discussion. They might speak odd things, like imagining a dinosaur walking across the road. Even that trigger a question: “How tall is the dinosaur, measured in the number of humans?”
Elementary
Numbers, multiplication tables, divisions, fractions, decimal places, algebra—are those the natural progression of a Math curriculum? Yes and No. They are the natural progression in the forms of complexity and required scaffolding, but they might not be how children experience the world. We try to cover both aspects of Acton Academy. Thankfully, the “scaffolded standard curriculum” comes in the form of game-based adaptive programs. Here are a few features which make it a no-brainer:
- Eagles can move to one problem after another, at their own pace.
- Eagles receive immediate feedback about their work. And if they struggle, there are multiple pointers, such as videos and tips. And the “teacher” won’t fret any sign of frustration if you replay ten times.
- The whole process is gamified, such that the Eagle feel motivated enough to move on. It’s not the case all the time, but it sure beats most of the passive worksheets.
- Data has been captured throughout the whole process so that Eagles and his support (peers, Guides, and even parents) can provide necessary feedback further.
- The completeness of Data, particularly a feature of Khan Academy, solves the Swiss-cheese foundation issue by focusing on Mastery.
At Acton Academy, we used the following Software programs: Dreambox at the lower Elementary level (eight years old and below) and Khan Academy at the Upper Elementary level (usually nine years old and above). Often, Eagles use both software, but they eventually end up using Khan Academy, which is far superior regarding data completeness and tracking (though not necessarily the most engaging).
The solution is not static. We continuously explore other Math tools with Acton Academies around the world. Whenever we discover a new software worth trying, we let Eagles test it out and ask for feedback. They know what works for them far better than we (the adults) do. Here’s one quick test: try doing Fractions via Oppia and Khan Academy. Which one worked for you?
During Quest time, the Eagles will use Math as they see fit. Often, this is in the context of counting, measuring, and applying basic formulas. For example, in the current Growing Curiosity Quest, the Eagles learn to color based on pixel boxes last week and build stick structures this week. For both cases, they manipulate abstract numerical concepts into concrete situations. Every year the Eagles measure profit and loss, unit costs, and breakeven points during the Children’s Business Fair. In addition to Quests, the Eagles studios work with data from weekly points, Eagle Bucks, and ratings. Math is a universal language among the Eagles, as they use it as part of their daily tribe lives.
At the end of the Elementary School, Eagles will have a Grade 5 mastery in Math. Also, they have an appreciation in Math, with experience of applying it in at least 15 projects throughout five years. We estimate half of our projects have some Mathematics component into it.
What can I do as a Parent? Similar to Preschool, have conversations!
There is one additional thing that your Eagle might need your help. It is not teaching Math. It is merely there to support them when they are struggling. It is as simple as being next to them, while you are doing your work (and they do theirs). When they make that 1% progress in Khan Academy, celebrate with a drink. They might negotiate a McDonald’s Big Mac for 10%, but that’s life—some negotiation, some give and take, and some American consumerism 😛
Middle School and Beyond
Mathematics at Middle School has the same structure as the Elementary School. However, there are some caveats. The critical difference is that we only use Khan Academy for measuring progress & feedback, although Eagles can learn in any platform. Khan Academy has the advantages of superior data analytics, and also a full alignment to the US Common Core. And the data can be viewed through a studio level, such that they can help each other.
For the Quests, the Eagles dig deeper into tools and methods that mimic real-world experiences. Elements of Data Science, Psychology experiment statistics, Personal Finance compounding equations, balancing Chemical equations were the few things worth mention. Often, they used Google Sheets to compute.
Clark Aldrich said this in his book Unschooling Rules:
One computer + one spreadsheet software program = math curricula.
Spreadsheets are under-rated. You can build a Heat Diffusion model, a Financial Derivatives pricer, a tax calculator, and all forms of real-life Mathematics application on it. These skills are fundamental when the Eagles take on specific apprenticeships. That’s when they fully connect Math to real-world scenarios. There’s a world out there in Maths: Data Science, Origami folding, Computational Math, and even more in the world of automated cars and the technology-powered world.
Also, the Eagles can also take on Math-related Deep Books, ranging from ancient classics like Euclid’s Elements to modern contemporary, like Fermat’s Last Theorem. The sky is the limit in what an Eagle want to pursue!
What can I do as a Parent? Similar to the Elementary School support of conversations and “being there during struggles,” there’s one more thing needed. It is a realization of how much little of higher Math we need in our lives! For most of us, our daily lives require Math similar to basic Algebra and a good understanding of Statistics. Statistics are needed to prevent fooling—people abuse numbers to “influence” you. Your perspective is necessary to maintain the right composure in influencing your Eagle in the Personal Learning Plan, and avoid the pitfall of “you need Higher Mathematics because of…”. The best way to see if your Eagle needs or wants Higher Mathematics in their Learning Plans: encourage them to do apprenticeships that exposes them to advanced Mathematics.
Finally, do have faith in Khan Academy (KA). As per this post from Middle School studio in Austin:
The bottom line? KA Math works. If your Eagle is struggling, we hope you’ll follow our lead in the studios, and use Growth Mindset encouragement and focus on incentives and consequences designed to address Resistance; Distraction and Victimhood, until KA math becomes a deeply embedded habit.
Thank you for reading thus far. This piece was written deliberately to cover all bases because of the doubts about learning Maths from Khan Academy and online resources, the continuous wanting for a Math tutor, and a deeply embedded misunderstanding of Math Education. Anyways, here’s to the lighter part of the blog: Studio Updates!
Studio Updates
The second week of the Sprint marks further progress in all the studios. The Preschool start diving deeper into the Montessori materials, the Elementary had a blast doing projects led by Naomi and Arjun, and the Middle School had their mini-exhibition!
Preschool (PS)
The Eagles spent most of last week forming bonds through challenges. This week, it’s about building the habits of Core Skills. In Preschool studio case, this is mainly Montessori materials. There were many moments where Eagles were in experiencing flow, figuring out the sequence and learning the concepts.
How do we organize ourselves so that we take turns? Not all Preschoolers know how to read. But fear not, there are other ways to organize! History has provided proofs: there are civilizations like the Incas who built Machu Picchu and coordinated a population of 10 million with no system of writing.
And we celebrate Aarav’s 4th birthday with a watermelon cake! Happy Birthday Aarav!
The Eagles continued to bond further, both within the studios and with the other studios. It’s fantastic to see how the Eagles mixed in a dynamic group of 4 to 16 years old.
One thing’s for sure, many of them love tag.
Elementary School (ES)
Arjun and Naomi lead this week’s Curiosity Quest. Their topic: the weather. The Eagles learned about thunderstorms, rain, and the water cycle. The exciting parts are the hands-on simulations. They brought different simulations with a common element—water!
The first project was building an ark using sticks, one that weathers through a storm. There was a productive buzz of building both inside and outside the studios.
Then, the water action began! Flashfloods!
https://youtu.be/aXmbR3JSEdY
Next, is the simulation of clouds and storms using colored water. The goal is to observe color diffuse at different speeds under varying conditions. There were lots of oohs and aahs.
The Eagles also kick start three new things: Grammar game, the Pomodoro Method during Core Skills and football. Ms. Caryn led the grammar game as part of the Writer’s Workshop; it was a chase of catching various conventions and honing writing skills.
The Pomodoro Method was a hit among the Eagles. The idea is to breakdown the Core Skills time in a series of 25-minute Pomodoros. Some Eagles took more time, and had a guided process; while most Eagles managed themselves and worked with substantial freedom. It’s the governance model at Acton Academy—freedom and responsibility come together.
We had our first session of football this Thursday. Unfortunately, the coach did not show up! The Eagles decided to take the first training on their own. They are getting a good hang of an Eagle-led studio :))
Middle School (MS)
It was an intense week for the Middle School. Their goal: a mini-exhibition involving their Hero Essay and a Film Festival. The pressure was high. The Film Festival challenge was to make music videos with a narrative. It must have three surprise elements: a banana prop, a mime character, and a fishing action. One team wanted to create a cutting-edge production. But there were no professional materials in the studio. The solution? Improvise!
There was plenty of teamwork in creating these videos: detailed planning, syncing it down to their chosen song’s timeline, the number of scenes, and the number of shots for each scene. Having everything planned out eased the burden of the final editing. The Eagles experience of doing animation three months back was useful, they knew what to look out for and avoided the same mistakes. They delivered their work on-time!
During the tribe-building Quest, the Eagles reflected on Dave Logan’s Five Levels of Tribal Leadership:
Many of the Eagles stepped up from Level 3 to Level 4 during this period. Here are two examples:
And then on Friday, the Exhibition! It started with a warm welcome and showing the two short films:
The crowd loved it. Then, Eagles read the two best essays: Haidan’s and Dhanya’s. You just might have a further appreciation of the potential of the new generation: Heroes who can change the world.
Finally, it was Hero Boards viewing, where each Eagle had a booth with their own story.
Phew. That’s it for this long post!