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Are You A Helicopter Parent?

It’s perfectly normal to be concerned for your child’s safety.

Parents feel the urge to keep their kids protected from any perceived threat that could harm them. However, our best intentions can trick us into going overboard to make sure our children are safe and lead us onto an emotional slippery slope that could actually harm the child.

One of the biggest parenting challenges is how to support your child in a way that helps them feel secure but also helps them build resilience – the ability to “bounce back” when something goes wrong.

With so many terrifying stories in the media, how can we know that the next risk we take won’t be the one we regret?

Protective Bubble: “I seriously need to wrap my kid in bubble wrap.”

Write down a list of daily concerns you have about your child.
Then, write down the things you do each day to address those concerns.
Now, ask yourself – what would happen if I stopped doing these things?

Our own fears can sometimes overwhelm us. A reaction aimed at helping us cope can easily turn into a habit with time, if it has proven successful. We continue to do things to protect ourselves and people we love, even after the perceived threat has passed. Worst-case scenarios linger in our minds long after the “real” threat is gone.

The protective bubbles we create frequently do indeed protect our children from harm. But when well-meaning protection is carried to extremes, our kids are denied the opportunity to develop their own capacity to deal with difficult situations.

This can mean that, when faced with a challenge, they get trapped by that “fixed mindset” persona inside them that gets scared of a failure they may never have even experienced: “I can’t do it! I’m not ready!” Or they may be experiencing Learned Helplessness that prevents them from even knowing where to start when dealing with a problem.

Clearly, we’re not talking about life-threatening situations where they undoubtedly need your support. We’re talking about those situations where, no matter how much you want to be there for them, you need to let them experience the consequences of their decisions.

Let’s say you’ve invited a couple of families to your home on a Saturday evening. While you’re all talking on the deck, you hear noises in the basement. Turns out, kids were teasing your child and calling them rude names. What do you do?

Your child got a bad grade on a test they’d studied for, because the teacher decided to set different types of problems at the very last minute. They feel really disappointed and think that’s unfair because it’ll affect their grade significantly. Do you go talk to that teacher?

Your son’s or daughter’s soccer coach believes in the “tough love” approach, to which the child doesn’t react well. Do you go talk to the coach?

Before you intervene, we’d like you to give yourself a chance to consider the option of your child being able to deal with these situations on their own.
“What if they fail?” “What if they get hurt?” “What if they get embarrassed?”
You might be having these thoughts. And that’s okay.
You want what’s best for your child and you’re concerned.
Still, does that mean you should run to help every time they stumble?

Removing obstacles, keeping the path of life “clean” and “flat” so that a child can safely walk through childhood is one of those solutions that might seem beneficial in the short-term, but is never a sustainable one. Why? The very world that a parent is trying to protect them from, will reach them eventually. And when it does, it’s important they know how to navigate it.

How can we help?

We want to help our kids develop mechanisms to cope with the world inside them and the world around them.
How can we do this?

Help your child understand the reasons behind your worry and suggest ways they could deal with challenging situations they confront. We know that it’s never easy to put that into words – but try anyway!

Teach them and guide them through these experiences rather than “protecting” them from them. Analyze what happened in situations where they felt they were treated unfairly. Brainstorm on different ways they might handle things next time.

Help them discover their strengths and abilities to deal with different challenges.

If they’re discouraged, try to understand what would encourage them.

Lead by example. Show them that all learning starts by making mistakes from which we grow.

Problems are strength-training for our brains. They toughen our mental muscles. You won’t be able to stop every single obstacle from reaching your child. However, you can be there to support your kids as they learn how to fly on their own. You’ll probably be surprised at how well they do and their sense of pride and confidence will grow the more opportunities they have to handle challenges themselves.

One of the most famous writers from my country, Duško Radović, says:

“If you solve all of your children’s problems, the only problem they will have is you.“

Do you agree?

by Ana Jovanovic

Coach for Nobel Coaching

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The Growth Mindset – The Power Of Yet

One of the more talked-about topics in psychology and especially in educational psychology is Carol Dweck’s idea of the “growth mindset”, a concept she discusses in her book Mindset: The new psychology of success. Growth mindset isn’t something that Dweck invented and is now teaching us all how to attain. It is a distinctive trait she observed in people who are happier and more successful, which led her to seek ways to help develop and nurture it in people who do not share this predisposition.

So what actually is growth mindset?

While working as a young researcher, Dweck noticed that some children face challenges in a much more “positive” way than others. They would say things like “Oh, I love a challenge” or “I expected this to be informative”, instead of having tragic and catastrophic thoughts when faced with difficulties. Dweck coined the term “fixed mindset” for children who shrink before obstacles, and “growth mindset” for those who seek challenges and become even more engaged when faced with obstacles. Of course, these two mindsets apply to us all, and it is important to note that whereas we can’t have a growth mindset in every area of our lives, we sure can try to develop it.

To show what growth mindset really is, let’s try to contrast it further with the fixed mindset. People with a fixed mindset think that their characteristics are carved in stone and can never be changed. They firmly believe that intelligence, creativity, and personality are things we are born with and can hardly be something we develop. People with a growth mindset believe we can cultivate these characteristics through effort and that the process of cultivating them is more important than the actual outcome. A fixed mindset, on the other hand, wants results right away and doesn’t care as much about the process as it does about the outcome. Of course, Dweck doesn’t deny that people differ from the get-go, but she claims that we can all “change and grow through application and experience” (Dweck, 2006).

Another thing that differentiates these two mindsets is how they perceive and react to failure. People with a fixed mindset are more likely to believe they can fail and that by doing so their abilities will be questioned. Just the act of hitting obstacles would prove to them that they aren’t capable of overcoming them. People with a growth mindset, on the other hand, don’t really see failure as on option – obstacles are just perceived as opportunities to improve and learn, and by being faced with them and, generally something new, we get smarter.

Dweck illustrates this difference further with an interesting remark about language and how we use it to rate success. She mentions how saying “not yet” to students instead of saying they failed a class is a much better way to show them that even if they have difficulties overcoming something now, the time will come when they will succeed if they continue tackling the obstacle from different angles. The use of “yet” shows that there is a learning curve, and points to the process, not the outcome. This also tells children that they aren’t being taught to learn simply for grades, but for their future and it encourages them to dream big and think about what they want to do with their lives, instead of on focusing only on what they are currently achieving in school.

This entire idea of the power of yet and growth mindset isn’t just something Dweck came up with and wrote overnight. She (and many others) actually did research and showed time and time again that if a growth mindset is encouraged, children earn better grades and achieve better results than they did before – even better than some of their peers from much more affluent schools, which shows that growth mindset is a great path to achieving a more equal education system.
This research illustrates two important facts about growth mindset: it does work and it can be developed. It is not something we are born with.

What is a false growth mindset?

Before we dive into the exciting topic of how a growth mindset can be developed, we need to do some myth-busting. As with any other trending topic in education, it is hard nowadays to avoid the words “have to”, “need to”, and “all” when reading about growth mindset. It is often declared that we should all have to develop growth mindsets because they are just so much better, which ignores the principle behind the concept. Firstly, a growth mindset isn’t something you can just achieve overnight. It takes a lot of work and develops over time. Secondly, it isn’t a get-out-of-jail-free card you can use whenever you’re faced with difficulty. Dweck points out that we are a mixture of both growth mindset and fixed mindset, and at different times and in different areas of our lives either one can predominate.

Another point she makes is that people often claim they have a growth mindset when they actually don’t or use the concept of a fixed mindset to excuse why someone is failing when the only failure is actually not providing the context in which a growth mindset can be achieved. It is also easy to think that simply by encouraging children and praising their effort, we are developing their growth mindsets. It’s a bit more complicated than that – it is not just about praising, it is about praising the right way.

So how is a growth mindset developed?

Developing a growth mindset is a complex process, but it is not unattainable and can actually serve as a great first obstacle on which to practice our mindsets.

The main point that Dweck makes is that a growth mindset is developed through praise, but not the usual after-the-fact praise which focuses on outcomes, but the praise that focuses on the process of learning. This isn’t about blanketing children in praise for any of their efforts, but about praising the strategies they used and the entire process that leads to outcomes. A simple example of this would be saying “I love how you tried all these different strategies while solving this problem until you got it” instead of saying “Great job. I knew you’d get it, you are smart!”

That example showcases another point that Dweck makes; we should praise the process, not the abilities. Praising abilities encourages the fixed mindset that these things are set in stone, which definitely doesn’t promote change or development. Rather, it makes children think that what they can do is what they can do and the same applies for what they can’t do.

Another reason why Dweck insists “it is not the outcome, it is the effort that counts” is ineffective is because it lets students believe that if they try hard enough, they will succeed no matter their strategies. In effect, it can bring them to repeat the same futile strategies over and over again. On the other hand, insisting on the process or the use of multiple strategies until the obstacle is overcome, and praising that effort, teaches them that they need to change their strategies in order solve the problem. It also shows them they can use all the resources available and ask for help when they need it.

And finally, Dweck points out that even failure should be addressed as something that enhances learning. We can ask children “What is this teaching us? What should we do next?” instead of either praising the effort or protecting them by saying things like “Don’t worry, not everyone can be good in everything. You are not the only one that failed.” In both cases, we are developing a fixed mindset and letting children know that we believe they can’t do better, while a switch in mindsets would help them achieve so much more and help them in their future lives.

If you are already thinking of implementing these ideas while raising your child, there is more encouraging news. The growth mindset isn’t something we can start developing only in early childhood, Dweck says it is never too late for change, so why not try it on yourself, too, and see how it goes.

Resources:

  1. Dweck, C. S. (2006). Mindset: The new psychology of success. New York: Random House.
  2. Dweck, C. S. (2012). Mindset: How you can fulfill your potential. Constable & Robinson Limited.
  3. Dweck, C. S. (2014). Developing a Growth Mindset.
  4. Dweck, C. S. (2016). What Having a “Growth Mindset” Actually Means.
  5. Gross-Loh, C. (2016). How Praise Became a Consolation Prize.
  6. Romero, C. (2015). What We Know About Growth Mindset from Scientific Research.
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6 Tips to Support Self-Awareness Development in Teens

by Milena Ćuk,

Life Coach and Integrative Art Therapist-in-training

“He who knows others is wise; he who knows himself is enlightened.”
― Lao Tzu

Research has shown that a high self-awareness score is a crucial predictor of overall success. Acclaimed psychologist Daniel Goleman points out that self-awareness is the foundation of emotional intelligence and that mastery of emotional self-awareness is a key attribute of successful leaders

Why is self-awareness important for teens?

Who am I? What makes me special, a unique human being, different from others? What do I want from my life? Why do I feel like this? What made me react like this? These are just some of the questions adolescents ask themselves.

Answers to such questions build the foundation of a teen’s self-awareness. Practically speaking, being self-aware means we are able to understand our thoughts, emotions, beliefs, traits, and motivations and perceive how they affect our performance.

This skill develops naturally over time through experience and maturity. However, since  it is crucial in taking ownership of our lives and the direction we choose, we all need to foster it in ourselves and in our children.

There are a variety of practices and exercises to help you enhance self-awareness as you guide your child’s development, and we describe these below. Your teen doesn’t have to choose only one as they begin to discover which of these practices resonates the most with his/her unique being. Each can become a habit of daily routine, which is the best-case scenario.  And remember, it’s  good for all of us to be open to applying them in our own lives. Let’s not forget that we thrive together with our kids!

Time and space for self-reflection

We live in a busy world where speed and multitasking have become the norm. However, our brains haven’t evolved fast enough to catch up and process all the information and impressions inundating us daily. Sometimes (ideally each day) we need to slow down, pause,  be still, and be left quietly alone for self-reflection because this will ground us in reality.

This applies to your teen as well, especially after busy day or week. If your teen is more introverted, he prefers to spend time alone and you should respect his need. However, you might suggest that exploring and learning different ways to self-reflect could be beneficial for him. If your teen is more extroverted and doesn’t like being alone, you should teach him the advantages of slowing down and self-reflecting every now and then.

This could mean taking a walk outside or just sitting or lying down in your room and doing nothing. Though it may appear we’re doing nothing, we are consciously and subconsciously processing information and getting closer to our true selves.

You can simply offer a  gentle suggestion. For instance: “Honey, why don’t you go for a walk, write in your journal, or just spend some time processing this so you can figure out your true feelings and what you should do next.”

Keeping a journal

This is another form of self-reflection, but it is especially beneficial for teenagers.

Writing our thoughts down can help us explore what is going on in our minds – what we think, how we feel, what inspires or frightens us. Writing provides a sense of clarity especially for confusing and complex feelings we don’t yet understand.

For the emotionally loaded or conflicted experiences teens face as they grow, writing a journal is particularly useful since it provides a safe space for expressing their feelings, and there is a greater chance that creative solutions will emerge in the form of new decisions and actions.

If you had a diary of your own when you were young, you can share it to encourage your teen to start his own.  Journals can take many forms. Besides the classic diary, they can combine words with drawings or images if your teen is more visually inclined.

Mindfulness practices

Mindfulness practices develop full awareness in the here and now, promote non-judgmental observance and acceptance of our inner thoughts and feelings and help us release and overcome emotional pain. Watch this short movie to find out how mindfulness empowers us.

Inspired by the wisdom of the East, particularly the Buddhist tradition of meditation, Jon Kabat-Zinn was one of the first to introduce and adapt mindfulness practices to the Western world.

Due to its proven clinical effects on stress reduction, enhancement of self-awareness, inner balance and general well-being, a variety of mindfulness techniques has been developed for application in daily life and school programs.

You can find available mindfulness programs in your area or even find some guided online sessions and practice it together with your teens.

Emotional learning

Emotional awareness, understanding why we feel a certain way and knowing how to handle these feelings is crucial to success and happiness in every aspect of our lives.

Psychotherapist Claude Steiner defines this ability as “emotional literacy”. We learn how to manage our emotions, develop empathy for other people, repair emotional damage when we’ve done something wrong, and succeed in interacting with others effectively.

The importance of emotional awareness has brought emotional learning programs into schools and hopefully your children have already had the opportunity to develop this competency. If not, look for available lectures and workshops in your community that are oriented towards developing emotional awareness and literacy, either for youth or adults. Let’s not forget that as parents, we are pivots of our children’s emotional health and emotional learning, and personal development should always be a priority.

You can also check available online programs. Here you can find more about emotional literacy and even download a full book by Claude Steiner. In one of our previous articles, we wrote about how we can enhance teen’s emotional development through the use of movies.

Learning to have an accurate self-image

Self-image in teens can often be biased or fluid and they need to learn to evaluate their own strengths and limitations objectively. Constructive feedback, both positive and negative, is essential in learning this ability, which is part of self-awareness and development in general.

Foster an atmosphere in your family where providing honest feedback is natural both for you and your children. Here you can check some of the principles to deliver effective feedback.

Try this interesting exercise along with your teens from time to time. Each of you should write down three positive and three negative aspects of yourself. These can be your personality traits, habits, abilities or physical appearance. Then share and discuss what you all wrote down, suggesting how strengths can be used and limitations overcome.

Pay attention to how realistic your teen has been in his/her estimation. Has she written positive or negative first? Did she have problems listing positive or negative qualities? These indicators, if any, will be the basis for your further interventions.

The mind-body connection

Long a tradition in Eastern cultures and advocated widely by current holistic practitioners, mind-body awareness or the ability to “listen” to your body through sensory experiences can enhance the development of full self-awareness.

Besides yoga, there are numerous practices that can help us integrate mind-body experiences.  Some are spiritual in nature while others are more physical. Free dance practices with elements of improvisation, such as 5Rhythms, Open Floor or Authentic Movement, also referred to as “moving meditation”, are good examples. All these can help us focus on our inner selves,  become rooted and more fully present.

So if your teen is more inclined to work through his thoughts and emotions  through body/movement, seek out those activities and practices that best match his channels of communication with himself.

“Know thyself” – it was inscribed at the Delphi temple. This virtue was as valued in ancient times as it is today. Let’s help our kids acquire this wisdom and prepare them to be able to lead fulfilling lives.

Need additional support in helping your teen develop self-awareness? Don’t hesitate. We can help. Schedule an appointment with our coach.

References and useful links:

  1. Self-Awareness: The Foundation of Emotional Intelligence by Daniel Goleman
  2. New Study Shows Nice Guys Finish First by Shari Lifland (American Management Foundation)
  3. How Mindfulness Empowers Us: An Animation Narrated by Sharon Salzberg
  4. Emotional Literacy: Intelligence with Heart by Claude Steiner (2003)
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MATH THAT EXCITES AND MOTIVATES? YES, IT’S WITHIN YOUR REACH

Our founder has a long history of interest in mathematics. Here, he reflects on how, congruent with the Growth Mindset [1] approach to teaching, interest, and motivation awakened by teachers and parents, and not innate ability, led to his efforts and achievements. Mathematics, including statistics, is a foundational element in navigating life well and excelling in many careers. The founder details techniques parents and teachers can use to help students of all abilities activate their interest and maintain their motivation for learning mathematics. We have found that these techniques help create mathematically accomplished learners.

The Challenge for Parents and Teachers – How to Excite and Motivate

My first recollection of being interested in mathematics comes from second grade. We had a self-paced mathematics workbook and I found myself competing against a classmate named Wally to see who would finish first. I don’t remember now who won, but I realize that, even as a second grader, that feeling of competition pushed me to try harder and do more. Reflecting back, I am guessing that I was guided by a wise teacher who knew how to get the most out of me while also keeping me out of trouble.

Parents and teachers today are challenged with exciting and motivating their students, with their varying levels of abilities and motivations, to achieve in mathematics and other subjects. Today, I find myself the coach of a math team comprised of amazing students of varying levels, all really interested and excited about mathematics, and I wonder how their learning path led them to join the math team. Psychologists tell us that, to understand this subject, we should take a step back and review motivation for cognitive tasks such as learning and, even before motivation, understand how an interest in a subject starts.

Why the focus on interest and motivations? Because it matters. While, for years, America has focused on the teachers’ capabilities and depth of knowledge in the materials they are teaching, no surprise, students’ own beliefs and motivations form a significant part of effective learning. Carol Dweck’s Growth Mindset research shows that, like compound interest, differences in attitude can accumulate to significantly different accomplishments over time. This research holds true across different ability levels, cultures, and socio-economic groupings.

First, Activate Interest

Researchers, such as Paul Silva from the University of North Carolina, have been making progress on examining the science of interest, understanding what interest is, determining how topics become interesting and learning how we can cultivate interest in ourselves and those around us [2]. Interest helps the brain to focus and can drive everyone to think more clearly, focus better and achieve more in any particular area, regardless of their ability.

Paul Silva’s research details how, for a subject to be deemed interesting, it must be novel, complex, but still comprehensible. The tools to help make math interesting can take many forms, including:

  • Make mathematics relevant to the family [3]- Can you estimate how much money is needed to purchase a group of items? Which is cell phone plan right depending on how much data everyone uses? What is the effect of just a 0.2% expense charge on your retirement after compounding for 30 years?
  • Mathematics through logic puzzles and workbooks – A huge array of math and logic puzzles and workbooks is available for all levels. Browse in the library or bookstore and bring home what captures your student’s attention. These are some of the founder’s favorites: https://goo.gl/d66ji4.
  • Amazing Results, Paradoxes & Fallacies [4]- How much is $0.01 doubling each day for a month [5]? Prove that 1 = 2 [6]. And, consider this favorite of my nephew Mitchell, prove that 1+2+3+… infinity = -1/12 [7].
  • Crazy Math Challenges [8]- How many marshmallow bags would we need to fill up your brother’s room? How fast must Santa be traveling to deliver presents to all those homes within 24 hours?
  • Math using projects – This is probably the most useful form of instruction as the retention rate for hands-on learning achieved through projects is very high. Consider this example: If you built a marshmallow cannon, how fast would the marshmallows have to travel to go up two stories [9]? How high must a track’s starting point be to accomplish a 2’ diameter loop-de-loop for the racers [10]?

To make these activities novel and complex, present content from a wide variety of sources and levels to see what engages students and challenges them. For classroom teachers, this means having items at all levels available. Parents can more precisely gauge their child’s interest and abilities by trying different content at different levels.

As parents and educators, we soon find the delicate balance in keeping content comprehensible. We must encourage persistence and innovative thinking, but not frustrate the student at the same time. We can subtly monitor progress and ask our students leading questions, and help them understand the material while not taking away from their achievements. While the student may need hints to reach the right solution, the key is that the student can approach the problem on their own.

Then Maintain Motivation

“If Kids Don’t Want to Learn You Probably Can’t Make ‘em” – Jack Frymier

My wife, a very talented classroom teacher, sees her job, at the beginning of each school year, as getting to know each child, discovering what motivates them and then using that knowledge to teach them more effectively during the year. As humans, parents, and teachers, evolution has left many of us with instinctual approaches to motivation better suited for motivating physical tasks and encouraging behavioral modification, e.g. take out the garbage or you don’t get your allowance. While effective for simple tasks, this form of motivation falls short in motivating us in highly cognitive tasks such as learning. We need to take care. Pressure, unfair competition, threats, or punishments can all disrupt the learning process. Teachers and parents can accelerate the learning process by weaving in techniques such as autonomy, rewards for effort and achievement, and the delivery of more positive than negative feedback. Students respond well to our genuine interest in their learning pursuits and our reinforcement of the relevance of their study materials too [11].

James Middleton goes a bit further and details how, to maintain interest, the student must continue to see how the activity provides continued stimulation while also remaining in their control [12]. In practice, that means letting the student choose. All parents and teachers know how addictive and enticing electronic devices can be; so, for most students, all this must be accompanied by some sort of non-electronic relaxation time, where playing Call of Duty on your phone or texting friends is not an option.

A very useful tool for parents can be to utilize the Pomodoro technique and combine study time, e.g. study for the first 45 minutes of the hour, and use the remaining 15 minutes for non-electronic relaxation and explore some of the learning activities explained above. Teachers can ask students to select from these activities during these breaks from structured learning. Even though it’s the equivalent of asking your child: “would you like to take a bath or go to bed?”, it still allows them to retain control.

Parents and teachers may want to try some of these motivational tools:

  • Learning Gamification – Reward for progress and efforts – While sourced from the mortal enemy of learning, gaming, the techniques work just as well in incentivizing learning as they do in encouraging gaming addictions. In this case, at least, the student might find him/herself hooked on something useful [13].
  • Reward Systems that work in a student’s home – A properly designed reward structure can help bring focus to students who find it hard working for longer-term goals (e.g. ADHD/ADD). Teachers can convey home the students’ awards while parents can deliver the actual reward. These rewards can take the form of money, screen time (with limits), or even tasks performed by the teacher/parent such as doing the dishes at home or cleaning up their students’ desks.
  • Drawing practical inferences – Students can benefit from periodically linking the learned material back to real-world applications, e.g. using probability to determine if you should bother checking Google Maps for traffic on the way to school.
  • Project-Based Learning [14]- A huge subject beyond the scope of this article, it’s been shown that accomplishing learning through projects is one of the most important elements in maintaining motivation. The theory is that the project learning helps link the learning to practical inferences.
  • Demonstrate genuine interest in their learning – We need to show a genuine interest in what our students are learning. This recognition and attention will provide much-needed reinforcement for students.
  • Engage in well-matched competitive efforts – Competition is a motivator. When engaging our students in a competition, we need to make sure that both students believe that, with effort, they could succeed. This could be tiered competitions in the classroom, competitions formed through a website like chesskids.com, or even employing a system of handicaps so that the less accomplished learner can still win.
  • Engage/relate items they are already interested in – This could be as simple as labels. E.g. How many phases does it take to burn a …
  • Encouraging revision and learning from initial mistakes – This is quite simple to do at home, but a real challenge for the traditional classroom environment. Allowing students to revise their work is a significant learning and motivational tool.
  • Value/Reward/Recognize the knowledge acquisition itself – Have acknowledgments in the family or classroom for knowledge progress regardless of level. Psychologically, it is quite simple to fall into the pattern of always recognizing the most accomplished students, but implementing some tools that help force you to spread the praise can combat this tendency, and motivate the students who really need it.
  • Address anxiety surrounding tests or studying – Sometimes, anxiety due to previous failures, whether perceived or real, can interfere with future progress. Work with a teacher, coach or other professional to help with organizational abilities and study habits. Addressing anxieties and providing encouragement can go far in removing this blocker of motivation.

Summary

Teachers and parents have many available tools to activate interest and maintain motivation for learning in students. Research shows that applying just a few of these techniques regularly can result in a significant difference in student engagement and, ultimately, accumulated learning. Teachers can engage parents to educate through these tools and activities and personalize them for their children while parents can assist teachers in complementing classroom efforts. Parents and teachers must keep a constant eye on the tools they deploy, ensuring they stay positive and work well with encouraging cognitive tasks while being specific to the motivators of each student.

While these tools can be used to activate, or re-activate, a learner, regardless of level, in any subject area, the focus on math is because of its criticality for other subject learning, the long-term usefulness of education in life and careers, and the history of math in being a source of challenges. Not learning the state capitals has few long-term effects, but not knowing your multiplication tables can trip you up for life.

The astronomer Galileo Galilei observed in 1623 that “[the entire universe] is written in the language of mathematics” and that science and society are governed by mathematical principles and ideas. From counting and sets to systems theory and practice, understanding mathematics helps us, as humans, overcome our genetic programming, and function better as a society.

Postscript and Thanks to …
In writing this article, I did a little self-reflection on my own mathematics learning journey. I was lucky to have parents, teachers, and colleagues who gave me many of the above items. Here are a few key people that I could remember who helped me on that journey:

  • 2nd Grade – Ms ??? for letting me compete with Wally P. to finish that workbook first.
  • 3rd Grade – Scott S. for being a worthy, nearly unbeatable competitor in “around the world”.
  • 7th Grade – for Ms.??? for working with me 1:1, and encouraging me to compete in and study for the county math exam.
  • 9th Grade – Dr. Zalewski – For allowing me to earn my first C in math [15] and teaching me to work hard at math again. I also remember waking up in class after being hit by chalk. I guess I knew he cared and knew I could do better.
  • 10th Grade – Mr. Philips – For “bet A points”, “minus B”, and more contagious enthusiasm contained in one teacher than I thought was possible.
  • 11th Grade – Ms. Potrikus – For 3/11 day, having purple as my favorite color again and an understanding of how Newton got to inventing calculus.
  • 12th Grade – To the ‘ov people’. I took the AIME exam that year and got clobbered by all these people whose last names ended in ‘ov’ (e.g. Kasparov) from the New York City area. I began to think about how a whole culture can bring about an accomplishment.
  • High School – Dr. Swanson for encouraging my efforts at leadership on the math team. We really managed to get kids excited about math and make it a team sport.
  • The entire MAA/AIME/Mathematics Olympiad team that created the tests every year that I would get excited about. Yeah… I was that kid and still have a stack of the old tests.
  • Stevens Institute of Technology – Dr. Roger Pinkham – For introducing me to Apostle’s Calculus book, deep mathematical thinking and an appreciation for how math describes the universe. Ohh.. and to Vivek and Henry L. who showed me what real math-smart people could accomplish.

References:

  1. https://www.edutopia.org/article/growth-mindset-resources
  2. Silvia, P. J. (2005). What is interesting? Exploring the appraisal structure of interest. Emotion, 5, 89-102.
  3. http://illuminations.nctm.org/uploadedfiles/activities_home/familyguide_fulltext.pdf
  4. Some favorite paradoxes, fallacies, and amazing results:
  5. http://www.bloomberg.com/news/videos/b/92966fc7-c54d-4405-8fa6-cbefd05bbd6f
  6. https://www.math.toronto.edu/mathnet/falseProofs/fallacies.html
  7. https://www.youtube.com/watch?v=w-I6XTVZXww
  8. E.g. http://www.eduplace.com/kids/mhm/brain/gr6/index.html
  9. http://community.homedepot.com/howto/DiscussionDetail/Marshmallow-Cannon-9065000000008MO
  10. This was used by the founder to teach his son calculus
  11. https://www.edutopia.org/blog/strategies-helping-students-motivate-themselves-larry-ferlazzo
  12. James A. Middleton, “A Study of Intrinsic Motivation in the Mathematics Classroom: A Personal Constructs Approach,” Journal for Research in Mathematics Education, Vol. 26, No. 3, pages 255-257.
  13. https://www.lynda.com/Higher-Education-tutorials/Gamification-Learning/173211-2.html
  14. https://www.edutopia.org/project-based-learning-guide-importance
  15. This sentence initially read “..gave me my first C..”. My teacher wife corrected it. 🙂