puzzle project

I was never what you wanted
But you faked a smile well
And maybe that was enough
For both of us for a while
But now that the dust has settled
And I’m trying to climb out of the rubble
I’m slowly realizing
That this foundation was full of lies
False bricks and crumbling wood
That I was stupid and naive enough
To use as the building blocks
For my walls and support beams
And maybe the most disappointing part
Is that I’m still not sure
If you were lying to me
Or lying to yourself
I used to fight for this
Because I had faith that you belonged here
But now I’m realizing
That if you have to cut a shape
For the puzzle piece to fit
It doesn’t count as a solution
—  “Jigsaw” by Jessy Hudson

At the end of every unit we do these formal assessment projects called “puzzle pieces.” Each piece has to have 7 components to it, the most important one is the connection.
The connection explains how this current puzzle piece (unit) was caused by the puzzle piece (unit) that came before it.
It shows me that the students have a true understanding of not just the current unit but the pervious one as well.
At the end of the year we put all of our puzzle pieces together to make one big historical analyzation: that history is in fact NOT a straight line. One event breaks off to cause another event which causes two more.

I LOVE when I get puzzle pieces that look like this!!!

Flowers for Kasumi Blog!

As of today, Flowers for Kasumi has now opened a blog so you can follow the development of the RPG puzzle mystery game! We have a functioning about page, team page, character page, and questions are open as well.

If we receive any questions we will sign the posts by the devs’ names so you can tell who replied. We hope you show Flowers for Kasumi lots of love!

Here’s an article I wrote ages ago on learning/MBTI stuff.

We all know that children have individual personalities of their own and that everyone learns differently. Some of us are more hands on than others, some prefer the abstract world, and some would like tangible puzzles to solve. Let’s take a look at some different personality combinations in children based off of the Myers-Briggs Type Indicator (MBTI). Knowing your child’s personality type will help you figure out the teaching philosophy that suits her best. After an overview of different personality traits, you’ll see a list of teaching philosophy options and how they best match your child’s traits.

Essentially, there are four letters that go into making up an MBTI personality type and each of these letters corresponds to one of four categories.

One can either be:
       -  extroverted or introverted
       -  sensing or intuitive
       -  thinking or feeling
       -  judging or perceiving

Extroversion, iNtuition, Thinking, and Perceiving give me my type as ENTP. But what do all of these letters mean?

Below is a list of personality traits (identified by letters), try to recognize which letter in each set describes your child best. Keep in mind that it can be very difficult to assign all four letters, so even if you can only pick one, it’s a good start!

Personality Traits

  • Is your child introverted or extroverted?
    (E) Extroversion: Extroverts tend to have a marked tendency towards interacting with and being very expressive about their thoughts and feelings; may be dramatic or over-reactive.
    (I) Introversion: Introverts tend to focus on an inner world; process and internalize information, will likely prefer to work alone rather than in a group; slow to approach people.
  • Is your child intuitive or sensing?
    (N) Perceive world through patterns, connections, may not always be aware; aloof.
    (S) Perceive world through five senses, like facts, uses common sense.
  • Is your child more of thinking or feeling type?
    (T) Things must make sense to them, may be preoccupied with winning or being right.
    (F) Will have a tendency to be less composed and enjoy harmony over disruption.
  • Is your child perceiving or judging?
    (J) Take information in, process it and draw conclusions, typically neater, prefer structure and regulations. Do not like fast change or unexpected routine changes. Planners.
    (P) Take information in and likely create with it, typically messier, and like to take their time; likes a flexible schedule.

Now that we’ve put at least a few letters together, let’s go through the different personality types.

The Rationals: Let’s keep calm and carry on

  • The Puzzle-Solver (INTJ) “I want to figure this problem out, no matter what.”
    Young INTJs are perfectionists who always wonder “why.” INTJs are independent, focused, serious and intense. When given a problem to solve, INTJ will attack it relentlessly until they understand it. They want to be intellectually stimulated and may find themselves debating with others on ideas.
  • The Leader (ENTJ) “I’ll show you how to do this efficiently.”
    Young ENTJs are systemic and concerned with being right and tend to find themselves in positions of leadership, whether they choose to be in that role or not. ENTJs are careful, orderly, and methodical. They dislike arbitrary rules and regulations.
  • The Scientist (INTP) “I looked to the stars and wondered how they were formed.”
    Young INTPs tend to keep to themselves and are typically focused on the abstract world, be it writing and literature, science, or art. They like to discover new facts and think about possibilities.
  • The Inventor (ENTP) “I just discovered a new mushroom!”
    Young ENTPs dislike following or being ordered around. They enjoy getting reactions out of people (even out of teachers) and may talk loud or fast. If a rule doesn’t make sense to them, they will likely break it and wonder why they got in trouble.

The Artisans: Let’s discover the physical world

  • The Tinkerer (ISTP)  “I took apart a watch today and almost got it back together.”
    Young ISTPs are curious problem solvers and tend to focus much on logic. They are independent, unstructured and shy, and may be easily pushed around. They tend to enjoy working with physical puzzles like Legos.
  • The Go-Getter (ESTP) “Look at how fast I can run!”
    Young ESTPs are very gregarious and frequently athletic. Although they can be extremely competitive, they also want everyone to get along even when they want an established “winner” and “loser.” They value teamwork immensely and like making an impact with their accomplishments.
  • The Artist (ISFP) “Sometimes, I prefer to be alone and express myself through art.”
    Young ISFPs tend to keep to themselves and focus on concrete forms of expression; they typically greatly enjoy finger painting, talking with one or two friends, and going on calm walks. Disharmony upsets them greatly, although they might not express their discomfort immediately.
  • The Impact-Seeker (ESFP) “I bet you I can squirt milk out my nose!”
    ESFPs are spontaneous, unstructured and flamboyant. They love to get reactions out of people and will typically be the “class clown.” They are good natured, naturally love people and focus on in-the-moment sensations. They typically prefer hands-on, creative and collaborative group activities.

The Guardians: Let’s keep order

  • The Dutiful (ISTJ) “But the rules say…”
    Young ISTJs are quiet, dutiful, and don’t like treading on toes (unless someone is doing the wrong thing). They enjoy concrete facts and specific feedback. They can be very sensitive and closed to experimenting as they tend to prefer using established methods.
  • The Manager (ESTJ) “This worked before, why won’t it work now?”
    Young ESTJs tend to adopt positions of managing others willfully. They tend to think they have the best system for doing things “right” and have a natural ability for seeing what has worked in the past and what hasn’t.
  • The Nurse (ISFJ) “I’ll take care of anyone, because everyone deserves to feel good.”
    Young ISFJs are typically very concerned with how other people feel. If another child gets hurt, an ISFJ will likely be the first to be quietly on the scene, attending to the wounds (physical or emotional). They tend to do their duty to their peers and be on their way.
  • The Cheerleader (ESFJ) “You can do it! I believe in you!”
    Young ESFJs thrive on everyone getting along harmoniously. They tend to like gossiping and can accidentally hurt other people’s feelings, although they don’t try to. When they discuss others, they view their information as factual. They like to cheer others on and see them to success.

The Idealists: Let’s keep the peace

  • The Protector (INFJ) “Sometimes, my fantasies seem more real than real-life.”
    Young INFJs are very quiet, dreamy individuals. They may not always be aware of what is going on around them because they are so focused on their individual perception of the world. They will likely develop a very strong emotional attachment to a few things and people, and protect them no matter the cost.
  • The People-Pleaser (ENFJ) “Let’s not fight, please.”
    Young ENFJs are inherent people-pleasers who do not like criticism that can be construed as offensive. They are very sensitive to others’ wants, are warm and caring, and will typically have a large circle of friends with whom they make sure to always feel comfortable and secure.
  • The Dreamer (INFP) “I wrote a poem for you today about my feelings.”
    Young INFPs are a shy, dreamy and sensitive group. They tend to be very peaceful, and prefer one-on-one contact and discussion. They like activities and communication to be consistent with their value and prefer cooperation over competition.
  • The Creator (ENFP) “I stapled a giraffe to some stars because maybe animals can go to space one day.”
    Young ENFPs tend to have a diverse, large group of friends and like to fantasize about all kinds of things. They like harmony and exploring new people. It’s been said that an ENFP has never met a stranger. They will typically use their large imaginations to create wonderful works of art.

It is important to also identify other values such as the child’s need to:

  • Get along with others in harmony (especially “feelers”)
  • Have healthy competition (commonly seen in extroverted thinkers or ExTx’s)
  • Have a project or puzzle-based learning environment (common in Rationals, Idealists, and Artisans)
  • Have a structured environment (Guardians)
  • Have concrete information relayed to them and sensory activities to participate in (common in Artisans and Guardians)

So now that you have (hopefully) established your child’s personality type, what method  works the best for them?

Montessori and Play-Based Methods: iNtuitives and Creative Artisans

If your child is an intuitive (INTJ, ENTP, etc.), or a creative Artisan (ISTP, ESTP, ISFP, ESFP), it is important to place them in an environment where they can solve problems at their own pace. Testing child’s capabilities through solving problems will also make them feel more accomplished.

Extroverts and introverts alike thrive in play-based environments, although introverts in particular do well as they have a high need for one-on-one contact. There is just enough interaction in a Montessori school that the young introverts will be socialized, and extroverts will be satisfied and still able to focus on work.

Academic and Traditional Methods: Guardians and Practical Artisans

Most children learn better through play and hands-on activities than through rigid learning; however, there are benefits to the more traditional styles of learning for SJs (ESTJs, ISFJs, etc.), who like order, structure, and predictability. Some SPs (ISTPs, ESFPs, etc.), who are concrete, factual learners may also benefit from traditional academic methods.

This particular method has a lot of stability (which is necessary for the young Guardian to feel secure) and has enough practical application that all sensors (ESFPs, ISTJs, ISTPs, etc.), will feel a degree of satisfaction. It is important to remember that Artisans can fall into either category of method, and it is important to establish whether they are more creative and hands-on or practical and factual.

Remember that every child is an individual, and that it is important to take the time to assess their individual needs and wants. As a parent, it can be hard to understand a child who is very different from you, but hopefully the information provided in this post will help you better assess your child and put them into a learning environment that will allow them to learn the best while still enjoying themselves.


“One of my favorite things that I got, it was actually a lot of you that helped put this together, but there was the puzzle piece project. Where there were these puzzle pieces that this group of fans organized and each one of them made one. And they were all over the world, and they put so much effort into it. There were all these glittery beautiful artistic puzzle pieces, and every time it seemed like every time I turned around at a show someone would show up at a meet and greet and give me these puzzle pieces, and I kept them! And when it got to the end of the puzzle after the 15 month tour was over, I had all these puzzle pieces and I put them together and it made the shape of this giant heart. And so I decided to, the other day I did this actually, I went and I got this giant canvas and I painted the canvas and then glued the puzzle onto the canvas, and I’m getting it framed and it’s gonna be very prominently placed on my wall. So thanks you guys!”

О потерянных пазлах

Собирая жизнь по кусочкам, словно большой пазл, я не вижу ни итоговую картинку, ни даже получающийся результат, но оглядываясь назад я замечаю среди отдельных вроде бы завершенных участков недостающие кусочки и стараюсь их восполнять, подбором случайных - что обычно затягивается или точно зная, где спрятавшийся кусочек. Эти участки как завершенные этапы жизни, что-то пройденное, оставшееся за спиной и лучше этому быть целым, чтобы не отвлекало зияющими пустотами от продолжения сборки. Этим и хочется заняться: завершить то, что вроде бы осталось в прошлом, что осталось такими вот незаконченными островами и все еще напоминает о себе бликами тусклого света, играя в пустующих ячейках. Это странный процесс - ты вроде бы продолжаешь пазл, но среди новых кусочков ищешь те, которые смогут завершить недостающие участки, а не продолжить общую картину. Будто не двигаешься вперед, хотя совершаешь ровно такие же действия - топчешься на месте. Впереди еще целая гора кусочков и огромный простор, требующий осмысления и завершения общей картины - это ждет впереди, а пока что несколько дней можно посвятить попыткам завершить то, что вроде бы было уже завершено, но не полностью - попробовать найти недостающие кусочки пазла и не возвращаться к этому, не беспокоясь и не оглядываясь больше назад. А может, просто кто-то случайно унес с собой пару кусочков или я сам незаметно смахнул их на пол или под диван, вдруг эти прогалы так и останутся пустыми, потому что просто нечем их закрыть, каждый раз вновь и вновь приковывая взгляд обратно. Посмотрим, но пока я попробую поискать, поискать недостающие части, чтобы прошлое не висело грузом, не заставляло оглядываться каждый раз. А потом вновь возьмусь за привычное продолжение картины, и, может быть, совсем скоро общее изображение начнет складываться во что-то более внятное, чем есть сейчас.


my most unruly puzzle/project - there are hundreds of images hidden within the double-sided drawing - to teach you how things change with perspective 

works best on a flat surface rather than midair…can be used for divination, meditation, or as a brain game (there are some folds even I’m not sure how I got to them…challenging!)

(song is Holdly by Florist)

Happy birthday, John Conway!

Today marks the 77th birthday of one of the world’s most eminent mathematicians: John Horton Conway, currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University. Conway earns my admiration for countless cool contributions in many branches of mathematics.

Conway became interested in mathematics at a very early age: as a four year old kid, he could already recite the powers of two, and at the age of eleven his ambition was to become a mathematician.

A selection of the topics Conway has touched:

  • Conway invented a number system called the surreal numbers, which form the largest possible ordered field (in some sense). Study of this system was motivated by mathematical games, which could be solved using the surreal numbers. Conway wrote the delightful book On Numbers and Games about it.
  • During his research into mathematical games, he invented a whole bunch of new ones: Sprouts, Hackenbush, Phutball, Conway’s Soldiers, the Angel problem
  • One of the early and still celebrated examples of a cellular automaton, the Game of Life, is a creation of Conway, whose early experiments were done with pen and paper, long before personal computers existed.

  • Conway’s 15 theorem states that if a positive definite quadratic form with integer matrix represents all positive integers up to 15, then it represents all positive integers.
  • Together with Michael Guy he established the classification of convex uniform polychora (4-dimensional analogues of polyhedra), discovering the grand antiprism in the process.
  • Conway extensively investigated lattices in higher dimensions, and determined the symmetry group of the Leech lattice.

  • In knot theory, there is a variant of the classical Alexander polynomial named the Alexander–Conway polynomial which is an invariant for knots. He also developed the beautiful tangle theory, which built a bridge between knot-like structures and fraction arithmetic.
  • Conway played a major role in the classification of finite simple groups. He discovered the three sporadic Conway groups, based on the symmetry of the Leech lattice, and was the primary author of the ATLAS of Finite Groups.
  • Without hesitation, the most famous finite group is the Monster group. Together with Simon Norton, Conway formulated a conjecture relating this gargantuan group with modular forms, and labeled it “monstrous moonshine”.

  • He extended the Mathieu group to the Mathieu groupoid and presented it as a sliding tile puzzle played on a projective plane.
  • Conway proposed the Turing-complete esoteric programming language FRACTRAN, in which a program is an ordered list of positive fractions together with an initial integer input value.
  • Ever heard of Conway’s icosian numbers? They’re a specific set of quaternions and exhibit lots of symmetry.
  • Conway’s doomsday algorithm can be used to calculate days of the week. The story goes Conway’s computer isn’t protected by passwords, but by a quiz of random dates, in order to improve his mental arithmetic speed.
  • Together with Simon Kochen he proved the free will theorem. In Conway’s own wording, the theorem states that “if experimenters have free will, then so do elementary particles”.

  • The LUX method is an algorithm to generating magic squares.
  • Conway introduced and analyzed the look-and-say sequence and proved the Cosmological Theorem: every sequence eventually splits into a sequence of “atomic elements”, finite subsequences that never again interact with their neighbors.
  • As a spectacular counterexample to the converse of the intermediate value theorem, Conway defined the monstrous discontinuous base 13 function, which takes on every real value in each interval on the real line.

  • Conway’s criterion gives a simple but powerful sufficient criterion for a prototile to tile the plane.
  • Pinwheel tilings are the first known non-periodic tilings to each have the property that their tiles appear in infinitely many orientations, and were based on a construction due to Conway.
  • The thrackle conjecture is an open problem in graph theory.