Fractals and Art

Mathalogics Blog

FRACTALS and ART 

A cauliflower is a delicious and nutritious vegetable to eat but have you ever studied it up close or

seen a cross section of it. Next time you are in the kitchen make it a fun mathematics lesson for your

children as you discover the patterns inside a cauliflower, notice the bumps and nods on its surface

make a beautiful fractal pattern. Now zoom in and notice one of the florets, does it resemble the

bigger version of the flower head. Zoom in some more what do you see, a pattern repeating at

smaller and smaller scale. Fascinating isn’t it?

Fractals are patterns within a pattern just like the one you saw in a cauliflower . Benoit Mandelbrot a mathematician came up with the idea and the name fractals. You can see fractals in nature like trees, snowflakes and in blood vessels. A famous fractal pattern named after him is called the Mandelbrot set which is made by repeating the iterative equation to create a shape that repeats at smaller and smaller scale just like our Sierpinski pyramid.  

A Fractal Activity

Now let’s get creative, You will need:

• A leaf.
• An A4 size paper.
• Pencil.
• Markers/ oil pastels/ Crayons
• Water colours
• Paint brush.

Step 1:Go on a nature walk and look at the different leaves on trees. Choose a leaf that you liked the most. Study the shape of the leaf, it’s points and edges.

Step 2: Sketch that leaf enlarging it if the size is small or trace it if it is large enough. Look for the largest main vein that divides your leaf in two and draw the same.

Step 3: Now from the main vein, branch out your secondary  veins you can see on your leaf. This is your first fractal from which you will see more veins branching out.

Step 4: Repeat the process branching out further.This is your second level of fractals.Now look for more veins branching of the last veins you drew. What can you see? Are there more fractals that you can see.

Step 5: Now choose three different coloured marker/crayon/oil pastel and mark the main vein with one colour. (I have used red here)

Step 6:The secondary vein with the second coloured marker. (Orange here)

Step 7: Finally fill in the last iteration of more finer veins with another colour. (yellow here)

Step 8: Now for my favourite part.Take out those beautiful water colours and trace the outside of the leaf in one colour and the background in another.

...Nine, Ten, Elenvteen, Twelveteen, Thirteen...

16 February' 2018 

(3 minutes read) 

My son Talha was four when the number fight began.

He was fine till the first 2-digit-number Ten, but he disagreed that there are numbers like 11, 12, and so on.

Number beads with number flashcard

He insisted twelve is merely a one and a two written together. For him, it was not a big deal. Numbers could be friends. He'd always call them "one-two" instead of twelve.

He also thought I am simply exhausting myself by believing there are more numbers than just the ones he has already learned (1-10) and assured me he doesn't need anymore.

He showed me his fingers and his crayons and asked, "Do you see more fingers? They are ten and so is counting".

So it happened that I failed to make him consider counting objects that were more than ten.

Then it struck me he doesn't feel the NEED to count as I haven't created it.

Realizing the mistake, I quickly corrected myself, always having bowls filled with numbers >10; 14 paper clips, 17 raw pasta pieces, 13 counters, 11 cloth pins and so on.

Kids love counters

All my plans came crashing to the ground when he very causally counted only ten of each object and asked me to take away the rest.

I thought harder and harder to try some other ideas. Something that was more than 10 (wwaayyy more than ten and he can't take it away) was right there with him all along, his HAIR!

So I pointed at his head, "you have more than ten hairs on your head, so there is a need to learn more numbers".

He looked at me, nodded, "I only brush my hair, don't count them."

I  have to be smarter than a 4-year-old if I am ever going to teach him math!

A 10 and a four

And that was the end of all my plans to teach him math. 

One day while coming back from school and climbing stairs, he started counting and told me, "Look mama!, I am so strong I'm gonna climb to 10!". 

Light Bulb.

"Oh, Talha! I know you are so brave and strong you'll easily climb 24 stairs!"

And from that day, he counted and counted on!

World Teacher's Day celebrations by Teachers' Lounge

6th October 2018

As they say, 'Teachers Make Other Professions Possible' so on 70th anniversary of World Teachers Day what could have been better than other professions paying back to teachers by making their day so special.

World Teacher's Day was enthusiastically celebrated by Teachers' Lounge at The Nest I/O in appreciation of teachers and honoring them for their contributions in shaping the young minds. The event was organized in collaboration with the OpenMic.

Teachers from all vicinity of Karachi joined for a thought-provoking discussion. Teachers’ Lounge is the brainchild of Saima Jawaid Khan, she is the founder and chief resource officer at Teachers' Lounge. OpenMic, a platform that encourages students to voice their opinion, led the event as a dialogue partner.

Saima Jawaid Khan

The program was divided into three segments. The first segment was introductory. The second one was about their opinions on the current challenges and inevitable solutions to enhance the quality of education and preparing this generation as changemakers. The last segment was an activity for the audience. A surprise giveaway was also given at the end.

The event started off with a dialogue session led by OpenMic.

In response to the question, ‘what motivated you to become a teacher and what are the aspirations that drove you to join this profession?
 
Huma Jabeen:

“I was a born teacher, from the beginning one skill persisted; I was a listener. If you are passionate to do something for someone then teaching is the profession you chose. I tell my students about everything, be it my embroidery craft or storytelling and I also listen to their stories.

Rehana Saleem

The main challenge for me when I joined the profession was I come from the families of doctors and engineers. When they came to know I want to opt for Teaching as my profession, my father and my friends opposed it.

I opted for Masters of Arts. This decision was not accepted and encouraged by my father at all. As time passed and when I used to tell him stories of Sindh and Baluchistan, the schools, the children, their condition, his mindset changed about this profession and me.

Finally it was when I was leaving for the UK for study, he said," I am proud of you".

He would tell everyone about me and how big the impact a teacher can make.

Asma Kamal Zuberi

In my case, it was my choice!. I choose to be a teacher. Two months long vacation and short hours of working attracted me. It was a decent choice but as time progressed I felt the essence of my work is missing. So I worked harder, took more training and spent hours planning. I sometimes slept with my workbooks besides me.
 
Tahira Khan

I used to play teacher-teacher when I was a child with cousins. Would beat my cousins as that was my experience and observation of the “profession”. After my masters, I had nothing to do so my parents came up with teaching as a profession and that’s the option I took. It’s then I came to know “teaching” is my passion and I am good at it.

In the beginning, I loved it and was always in my class and never left it. I wouldn't stay in the staff room. The idea of being outside when my students were inside the class was alien to me.

From then it’s always exploring myself and learning process.

Mehwish Rehman

My mother was a teacher and a role model for me. I used to copy all my teachers; how they dressed, which side of the board they wrote the date... everything.

Everyone in my family knew I would become a teacher.

After I did my masters of English, I got a call from Happy Home School for managing an event and content writing. I covered that event for them, afterward they asked me to join the school in the capacity of English Teacher, I hesitated but eventually joined.

The day I went to the class, the energy of the students surprised me. I take a senior level, class 5 till university level.

As for the challenges I faced during teaching I would say it has been a smooth sail. I never thought of being Deputy Headmistress and missed teaching so one day I asked my Principal to let me teach a class, she was surprised, "Do you have time?", I responded, "I miss it."
 


The second round of panel discussion was about challenges teachers face, career development, and job satisfaction.

Asra began the second round of discussion by listing the main challenges and asked the panelists about the challenges of today. She began asking:

"Its 21st century, the age of technology and ever-changing dynamic curriculum. No one can be sure of what future student will have, predict which type of job they are going to land on. Besides getting good grades they have to learn the soft skill, social skills, the biggest challenge is the instilling critical thinking, problem-solving, teamwork and collaboration."

"Our generation has to step out and face global interactions more than ever before as in our part of the world we have a fixed mindset."

mindset. There is a lot of hype about us being open to change but our actions tell us we are not yet liberated from the conventional mentality."

"We need to develop a curriculum that is holistic to face the challenges. What our esteemed panelists have to guide us in this regard?"
 
Huma Jabeen

I believe the first challenge is the "workforce" in teaching. They are young, inexperienced and focused only on covering the syllabus. They are focused on only finishing a chapter of the book and the objectives in a way that transfers only the knowledge. It doesn't inspire the student to 'think logically', think out of the box.
 

Member teachers of Teachers’ Lounge

Second challenge is holistic learning; as other panelist mentioned.
Why math can’t be integrated with ethics. I tell my teacher they can make their own problems to teach ethics. Suppose we are teaching arrays; Seven cars in one row, how many are in three rows? You can then discuss how we are so negligent in staying in a row, taking turns in a row and how this related to ethics and civil sense.

We have somehow assumed a (course) book is a Holy Literature; we need to read from start till finish without reflecting on its contents.
She asked the audience;

"Don’t you agree a dedicated teacher is the biggest challenge?"
 
Tahira Khan

Yes, we are short of dedicated professional teachers. 2nd challenge is “fussy parents”. When we were students some two decades ago, our parents never took our side stating,”Tum ny hi kuch keya hoga" (you must have done something wrong). Now parents enter straight to the administration office and argue about teacher’s complaint about a child.

This is a common perception we can’t find a (trained) teacher, I believe the teachers are available but they don’t have passion, sincerity, and dedication. On the other hand, no matter how much training is provided, sometimes there is no change; the reason is passion.
 
Rehana Saleem

Our teachers belonged to Boomers. We are their students, Generation X, our junior teachers are from Millenniums. So we are the "midstream" of teachers. We have worked with both the Boomers and the Millenniums and it's our responsibility to put forward the best of both.

I believe the intrinsic motivation is what produces good teachers. No external reward can bring that out.

Reward based parenting is responsible for the culture of dissatisfied generation X. So I would say let's pat them on the back and talk to them about their issues.

My teachers were upset the management didn't arrange for the teacher's day celebration, I tell them the cards, flowers, and cakes from their students is the real acknowledgment!.
 
Asma Kamal Zuberi
 
Young teachers are different from the generation before them; senior teachers, headmistresses, principals, and administration. They were old school.

Change should come from that generation. We, at the senior level of school administration, should put ourselves in junior teacher’s shoes. Intrinsic motivation, flexible timings, open communication, and growth opportunity will make a change not nagging about deadlines and "micromanagement".

One more thing I will add here is this generation is diversified and multitasking. They get bored easily and want change contrast to us who have to spend 20 years teaching the same subject. 

 

Mehwesh Rehman

Student is a customer in the eye of the school. The customer is always right. Parents as customers force management as to why their child doesn’t take a position. An "under pressured management" channels this pressure towards teachers. It's very common that management takes more admissions in a class that affect teacher’s quality of delivering the knowledge.
 
Huma Jabeen

This also seems like a challenge; mentors and teachers need to give "time" to students. To "connect" with them on an individual level. This might seems a daunting task provided we have only 45 minutes, but if you keep aside 5 minutes connecting with the children, it's possible.

Only a paradigm shift in terms to course completion and following syllabus can change that. Taking up both the roles as a counselor and a coach that enables A* grades for students within classroom limitation is what we call a dedicated teacher.

Asma Kamal Zuberi:

When teachers apply for the job s/he might have a preconceived notion of an 8-hour job, with two seasonal vacations. Your reach home and the job is done.

The true nature of the job keeps you occupied even when you are at home, of course, it makes you stressed but this is "passion".

Our school acknowledges stress factor and have allowed us a Yoga class weekly. It has helped teachers to give themselves time and de-stress. The Human factor should not be ignored if we want to enhance the quality of education.

Rehana Saleem
 
We have major seasonal workload weeks, where teachers are preparing for exams, checking papers and compiling results. Once that cycle is over, I tell my boss my teacher will relax for the next week; watch a movie, read a novel or sketch. They gave their best to us, this is what I can do for them.

Tahira Khan

A good team leader has good team members. A leader knows each and every one; people tell me they worked for a set up for 5 years and don’t know the names of their teachers!.

When I quote the problems of my teachers and how they can to solve them, they get surprised how come I know each and every one! Not just their name but their (life) stories too.

I currently have a team of 100 teachers and I know each and everyone personally. They come to me to discuss, I have given them space to discuss their problems while maintaining professionalism.




This drew us closer to a brainstorming session.

Saima came on stage to elaborate on the brainstorming session. This session was an engaging activity that involved teachers to come up with a lesson plan.

The event concluded by Saima Jawaid Khan, with a thank you note followed by a giveaway.

SURPRISE GIVEAWAY
A whole year of the free digital subscription of

The Reformer magazine!!

I am Saima Faisal, passionate math teacher and blogger. Share and comment below and let me know how you celebrated Teachers' Day!