The Creativity and Beauty in Mathematics

web_1488873c

Chapter 3 of Mathematical Mindsets

What is mathematics, really? And why do so many students either hate it or fear it – or both?  Mathematics is different from other subjects, not because it is right or wrong, as many people would say, but because it is taught in ways that are not used by other subject teachers, and people hold beliefs about mathematics that they do not hold about other subjects.

Keith Devlin, a top mathematician, has dedicated a book to this idea (mathematics is about patterns). In his book Mathematics: The Science of Patterns he writes:

As the science of abstract patterns, there is scarcely any aspect of our lives that is not affected, to a greater or lesser extent, by mathematics; for abstract patterns are the very essence of thought, of communication, of society, and of life itself. (Devlin, 1997)

An example in life:

The spider web is an amazing feat of engineering that could be constructed using calculations, but the spider intuitively uses mathematics in creating and using its own algorithm.

Mathematics exists throughout nature, art, and the world, yet most school students have not heard of the golden ratio:

https://www.mathsisfun.com/numbers/golden-ratio.html

…and do not see mathematics as the study of patterns.

the questions that drive mathematics. Solve problems and making up new ones is the essence of mathematical life.  If mathematics is conceived apart from mathematical life, of course it seems – dead

Reuben Hersh (1999) What is Mathematics, Really?

Over the years, school mathematics has become more and more disconnected from the mathematics that mathematicians use and the mathematics of life.

Four stages of mathematics:

  1. Posing a question
  2. Going from the real world to a mathematical model
  3. Performing a calculation
  4. Going from the model back to the real world, to see if the original question was answered

 

 

 

The Power of Mistakes and Struggle

mistakes

I recently (well earlier in the year) bought this book –  Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching by Jo Boaler.  I was interested in the mindset work and also the mathematics element.  I know as a student I loved mathematics (sad I know) but as a Teacher it was often the most difficult to instil that same love of learning for mathematics.  I see it in my own children who come home and say “maths is boring”…anyway I thought that I would share this book (chapter by chapter…and only the key points)…Liz borrowed the book off me first and I know she put together some ideas she was going to try in class (maybe she will share…sorry Liz did I just dob you in 🙂 )

Anyway, starting with Chapter 2 on  the power of mistakes…

When I have told teachers that mistakes cause your brain to spark and grow, they have said, “Surely this happens only if students correct their mistake and go on to solve the problem.” But this is no the case.  In fact, Moser’s study shows us that we don’t even have to be aware we have made a mistake for brain sparks to occur…because it is a time of struggle; the brain is challenged, and this is the time when the brain grows the most.

How Can We Change the Ways Students View Mistakes?

When we teach students that mistakes are positive, it has an incredibly liberating effect on them.

The habits of successful people in general:

  • Feel comfortable being wrong
  • Try seemingly wild ideas
  • Are open to different experiences
  • Play with ideas without judging them
  • Are willing to go against traditional ideas

One idea for class

Asking students who have been working on a problem and have knowingly made a mistake to share that mistake on the board.  Allows for discussions around common misconceptions and to solve the problem together.

Other resources:

 

Dealing with Negative Co-Workers

gossip

Negative Nelly
Negative Nelly teaches at my school
She thinks that being negative is cool
She warns of bad students, bad adults, and bad things
Each day, it’s a song of doom that she sings
She’s managed to acquire a very small following
Of other naysayers intent on wallowing
In gossip and pettiness and bitterness and complaints
All who will listen, Nelly gladly taints
So do not listen, and do not follow
In anything negative, do not wallow
Just be the most optimistic teacher you know
And down Nelly’s path, you’ll never go.

Whitaker & Breaux The Ten-Minute Inservice

You may have never yet encountered this type of teacher, but some day you might.

Some questions

  • Have you ever known a negative person? Just get that person in mind.
  • How do you feel around that person?
  • How do others feel around that person?
  • Have you ever known a negative teacher? Maybe you were taught by a negative teacher when you were in school?
  • How was that teacher viewed by you and others?
  • Did you or others try to avoid that teacher?
  • Was that teacher a little intimidating?
  • What kind of influence do you think a Negative Nelly (or Nelson) would have on a school or on students?

Most Teachers tend to avoid these negative people.  Worse yet, some even engage in negative conversations with that person.  It’s not necessarily that they enjoy it, but many don’t know what else to do.  Below are some tips on “removing their fuse”…they may know what you are doing when you try these techniques…but that’s a good thing, right?

  • The next time Nelly or Nelson speaks unkindly about a student, simply say, “I love that student.” Even if you’ve never met that student, say, “I love that student.” They will have no comeback for that, and you will have made a very powerful, positive statement about how you feel about students.
  • For teachers new to the school, Nelly is a magnet.  They love warning of the bad students they will be teaching.  When they do, there’s a trick to defusing them.  Simply say, “Thank you so much for telling me about these students.  These kinds of students are the reason I became a teacher.  You obviously must care a lot about them to have taken time out of your busy schedule to come and speak with me about them.  I’m so glad they’ll be in my classroom.  They obviously need caring teachers such as you and me.  I’ll keep you posted on their progress.”
  • If Nelson ever approaches you offering any type of gossip, you can always say, “I’d love to chat, but I’m in a rush.  See you later.”  And then leave.  Gossip is hot.  They’ll quickly feel the need to find another listening ear.  But if you’re all using this technique, their gossip will never travel!
  • When Nelly speaks unkindly about a parent, say, “Whenever I think about the fact that not all parents rear their children as we wish they did, I quickly remind myself of how lucky some students are to spend so many hours with positive people like us at school each day.”

 Implementation

The bottom line is that Nelson or Nelly continue their negativism because someone is enabling them.  There is no place for Negative Nelly or Nelson in a school setting.  Our work is too important!

Happy for your feedback though no names should be mentioned.  The work above comes from the book mentioned under the poem.  I don’t believe we have this person at our school but it is always important to remember and in your career you may be unfortunate to come across this person.  They can be personally damaging and I know from experience that they can make your day unbearable…you can lose your way and why you chose this brilliant profession.  I would not want this to happen to any of you as your job is hard enough.  I would encourage you to be a positive force in your school community and for your students.  Some of them come here just to see your smile and hear your words of encouragement.

Why Understanding These Four Types of Mistakes Can Help Us Learn

Types-of-Mistakes-Chart_v3

We can deepen our own and our students’ understanding of mistakes, which are not all created equal, and are not always desirable. After all, our ability to manage and learn from mistakes is not fixed. We can improve it.

Here are two quotes about mistakes that I like and use, but that can also lead to confusion if we don’t further clarify what we mean:

A life spent making mistakes is not only most honorable but more useful than a life spent doing nothing – George Bernard Shaw

It is well to cultivate a friendly feeling towards error, to treat it as a companion inseparable from our lives, as something having a purpose which it truly has. – Maria Montessori

 

http://ww2.kqed.org/mindshift/2015/11/23/why-understanding-these-four-types-of-mistakes-can-help-us-learn/

 

Growth Mindsets for kids

5 ways to teach children the growth mindset

  • Reward effort, not attainment.
  • Encourage them to take risks with their learning.
  • It’s ok to make mistakes. Use it as an opportunity to learn what could improve the outcome next time.
  • When praising your child,  focus on the strategies and skills they employed to learn about a specific subject, rather than their innate talent or skills.
  • Be mindful of the messages conveyed at home. For example, referring to yourself as ‘bad at maths’ or ‘no good at spelling’ can reinforce the idea that intelligence is fixed.

‘I don’t divide the world into the weak and the strong, or the successes and the failures…I divide the world into the learners and non-learners.’  Benjamin Barber

What ClassDojo Monsters Can Teach Kids About Growth Mindset

Many teachers are excited about the compelling research on the power of a growth mindset to change student perceptions of themselves as learners. Stanford psychology professor Carol Dweck discovered that when kids receive a message that their brains are malleable and their abilities can be developed, they approach learning as a challenge that they are ready to embrace. That message resonates with many teachers who have long wanted that type of classroom environment. But while the research is compelling, many teachers still struggle to weave growth mindset into their daily teaching practice.

To help provide resources for teaching growth mindset the ed-tech company ClassDojo is teaming up with Stanford’s Project for Education Research That Scales (PERTS) center to produce a series of five animated videos on growth mindset featuring the ClassDojo characters many students already know.

http://ww2.kqed.org/mindshift/2016/01/19/what-classdojo-monsters-can-teach-kids-about-growth-mindset/