Tag Archives: growth mindset

Growth Mindset: Our Mistake about Mistakes in Math

Does the expression “you can’t teach an old dog new tricks,” ring true for some of your students’ mindsets? Or “that’s just how I am,” or even the classic “I’m just no good at (fill in the blank),” ?

Photo by Chris Liverani on Unsplash

All of these statements are based on the assumption that knowledge is fixed and finite from birth, that one’s ability is pre-determined. From a perceived lack of creativity, mathematical aptitude, or basketball court prowess, a fixed mindset reinforces the idea that we are who we are, and no amount of effort is going to change that. A fixed mindset tosses aside any potential learning from life’s experiences and it creates a self-imposed world of walls within your brain.

This 20th Century ideology has seeped into the 21st Century even with clear neuropsychological evidence concluding that the brain is in fact malleable, as a recent study states: our “amazing ability of our neural connections to strengthen and grow as we interact with the world around us,” (Key Findings and Implications of the Science of Learning and Development). Jo Boaler supports this idea and pushes it one step further, saying in her book, Mathematical Mindsets, “every time a student makes a mistake in math, they grow a synapse” (Boaler, 11). That is, their brain learns something new. Quite contrary to traditional math teaching, where mistakes are to be avoided at all costs, often propelling a student’s belief that, “I’m just no good at math, and there is nothing I can do about it.” Good news folks, mistakes help you learn more…

“What separates the more successful people from the less successful people is not the number of their successes but the number of mistakes they make, with the more successful people making more mistakes.” – Jo Boaler

Photo by Roman Mager on Unsplash

Boaler further explains that one of the most valuable things parents and teachers could do for any child is “change the messaging” around making mistakes. Sounds easy right? Well, it really is… If a student is continually reinforced that mistakes are a crucial part of the learning process, then we can dampen self-perceived limitations and anxiety about getting the wrong answer, and instead, foster their growth and a love for learning. 

In doing so, math becomes real! Traditionally, math teaching tends to be very cerebral, abstract, and based on a textbook, with hundreds of methods and procedures to memorize, containing material that most will never use. Quebec’s situational problem competency in mathematics adds this “real-life” layer to the learning of math. Whereby it is not how quickly one can calculate that matters anymore – as we have 21st Century tools that can easily do such binary actions – but students “who make connections, think logically, and use space, data, and numbers creatively.” (Boaler, 31) Below are some suggestions on how to make math learning more meaningful for students, and how to get that brain elasticity stretching.

  • Open up the task – There is more than one way to find an answer.
  • Let inquiry flourish.
  • Start with a real life problem to be solved – Start big and break it down into its’ pieces!
  • Add a visual component…
  • Get students manipulating real-world materials (Boaler, 90)

It is possible to reverse years of a fixed mindset in math teaching. However, it doesn’t happen overnight – the strategies below will at least get teachers and students moving towards a better way of understanding how we really learn. I think one of the greatest actions any teacher or parent can take is modelling to our children that mistakes are super important because we learn from them.

We as parents, teachers, and leaders have to set our children free from the crippling idea that mistakes are to be avoided in math (and in life), that there is only one way to solve a problem, or only one way to see a solution, and that some students are just better at math than others. In doing so, we have limited their growth and bound them to a falsehood that never should exist in the first place. Old dogs can learn new tricks if you simply give them the time, space, and encouragement to learn from their mistakes in their own authentic way.

Boaler, J. (2016). Mathematical mindsets: Unleashing students potential through creative math, inspiring messages, and innovative teaching. San Francisco, CA: Jossey-Bass & Pfeiffer Imprints.

“Key Findings: Science of Learning and Development”. Competency Works. (2018, May 21). Retrieved March 12, 2019, from https://www.competencyworks.org/science-of-learning/key-findings-science-of-learning-and-development/

Fostering a Growth Mindset in the Arts Classroom

Guest post by Louise Campbell, Artist in Schools

What strategies can be used in the arts classroom to shift focus from ‘getting it right’ to exploring potential? Educators often refer to this as ‘fostering a growth mindset’. As an Artist in Schools, my first task in a music classroom is to use the skills students have developed with their teachers in a way that is surprising. I do this by setting up games. Games have rules, giving everyone clear guidelines that govern how and what to play, making it easy for everyone to participate, in addition to being fun.

The following is one of my favourite game pieces for use in the music classroom. It is a great start to a creative process, since long tones are a fundamental skill practiced in most music classrooms. The game starts out in a way that sounds familiar, and quickly evolves in surprising directions. Due to the process inherent in the game, the students can take the piece in any number of directions, leading them to more unfamiliar sounds and ways of playing.

Sound and silence By Louise Campbell

 

 

Instrumentation: for 4+ musicians playing pitched instruments

Instructions:

There are two choices of how to play:

  • a long tone( crescendo and decrescendo)
  • a silence

Long tones can be any pitch in any register on the instrument.

The long tones and silences can overlap in any way, shifting textures and timbres as different instruments come in and drop out at various times.

The next stage of this game is to consider pitch. Here are some variations, following the same rules as above. Musicians can play:

  1. An E in any octave
  2. Any note of a specific chord, such as C Major or E minor minor 7
  3. Any note of specific scale, such as pentatonic, or D Major
  4. Any note from a defined collection of notes, such as C, C#, D, F#
  5. Any note of the chromatic scale

Each of these variations sounds very different, depending on how students listen and respond to each other. The following excerpt demonstrates one version of this game as played by the Lindsay Place Music Étude students during a Culture in Schools workshop:

 

Sound and Silence,conducted by Louise Campbell. Co-composed, performed and recorded by Lindsay Place Music Etude students.

 

This is a fairly unusual sound for most students, and helps to create an atmosphere in which curiosity is at the forefront. In the event that a student understands the activity through a fixed mindset, this generally becomes evident when they point out a perceived ‘mistake’.  Hyper-focusing on mistakes can be quite detrimental to the creative process, as it can be quite limiting to what students are willing to try.

Let’s have a look (and listen) at one way in which a mistake may be identified, the self-talk that surrounds it and the way this situation was turned into creative potential.

 

The following audio track is a sketch I composed, played and recorded for clarinet and loop station (N.B. Loop stations repeat exactly what you play, over and over. So if you make a mistake…)

Sketch for Knitting Lessons, for clarinet and loop station by Louise Campbell. In the words of a wise woman who taught me both music and knitting, ‘If you make a mistake, do it twice. Then people think you did it on purpose. They won’t be any the wiser if you don’t tell them!’

 

The recording session is going swimmingly until:

ME TO MYSELF: Bah. I made a mistake.

(listens to 1:55 for a few loops and remembers knitting advice: if you make a mistake, do it twice)

Hmmm, actually that’s not bad, kind of foreshadows what I’m gonna do later.

(continues process for section, building new loop)

Now to work in that mistake…

(overdubs several loops 2:35-2:50)

… yeah, cool, that works…

Whoops! I didn’t mean that.

(listens to new ‘mistake’ at 2:50)

Actually that’s pretty cool. I wonder if I can use that…

(follows process to end)

 

In this case, my initial reaction to making a ‘mistake’ was frustration, as can be the case with a fixed mindset. I wanted the piece to come out the way I planned it. However, on remembering the advice to make a mistake purposeful, I was able to hear the potential in the ‘mistake’, and work it into the piece. In fact, the two ‘mistakes’ featured in this piece became ‘design features’ that are now integral to the piece. If I had stopped when I made the first ‘mistake’, I would never have found out where it would lead me. Re-contextualizing the ‘mistake’ as an unexpected event with potential allowed me to listen in a way that flipped a fixed mindset to one of growth.

This is only one example of the self-talk involved in a creative process, and resembles many discussions that come up with students in the art classroom. This was how I re-contextualized a perceived mistake for myself; listening to students and their self-talk shows the best way to re-contextualize perceived mistakes and help them see and hear the potential in unexpected events.

When facilitating creativity in the arts classroom, establishing an atmosphere of curiosity and exploration is the first step to fostering a growth mindset, and lays the foundation for contextualization of ‘mistakes’ as unexpected events that provide potential for the new and unexpected. Fostering a growth mindset makes for surprising discoveries for everyone, and keeps fun and play at the center of learning, creativity and making art.

 

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Louise Campbell is an Artist in Schools. You can read her other guest posts:

Cell Phones in the Classroom: Music education in the BYOD era
Music, Memory and Making the Most of Earworms

The Power of Our Words! Dismantling the Fixed Mindset Redux

I previously wrote about the Power of Words here. This is a follow up to that discussion, with even more concrete suggestions for changing the language we use in classrooms.

“It’s unbelievable how much you don’t know about the game you’ve been playing all your life.” Mickey Mantle

Why would a baseball legend, arguably the best all-time switch hitter in the game not consider himself an expert in baseball??? What does being an expert mean? Is perfection ever possible? Can one ever know all there is to know on any given subject? Does getting 100% on a test mean I’m done learning?

As educators, we know that our words have an impression on our students. We often hear our words coming out of their mouths, for better or for worse. What we might not always be aware of is how our words can topple dreams, change the course of history or even influence a student’s future career path. Dramatic? Consider that the student-teacher interaction is “the primary determinant of student success” according to Darling-Hammond (2000).  In fact, this interaction – in particular the words teachers use when addressing students – “is seen as the most important variable affecting student achievement, even more so than demographic factors” (Darling-Hammond 2000).

“No matter what anybody tells you, words and ideas can change the world.” -John Keating

Which brings me to the crux of it all: Our words matter! The words we use can limit or set our students free; it is really that simple. Carol Dweck has labeled the fixed mindset often seen in schools as the “CEO disease,” i.e. striving for success and avoiding failure at all costs. The typical language that accompanies such a mindset goes some like, “I can’t…” “I’m no good…” “I’m not creative at…” “I failed…” Dweck’s extensive research into brain psychology suggests that developing a growth mindset in our educational system “requires not just maintaining a positive attitude, especially in the face of adversity, but developing the determination and self-confidence to try and keep trying.” Transforming our perceived limitations into ” I’m not there YET but I will get there eventually.” An open mindset and the words we use can “create a passion for learning rather than a hunger for approval”. What educator doesn’t want that?

“The purpose of adopting a growth mindset is to encourage the children to reflect on their learning and progress.” – Carol Dweck

From the hallways at Pierre Elliot Trudeau Elementary school (EMSB) 

As an educator, opening your mindset can be as simple as using the word YET more amongst your peers and students. Put up a poster in the hallways of your school or classroom, and keep coming back to it with your colleagues and your students, and watch how it starts making curious, innovative, and creative learners.

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Denton, P., EdD. (2015). The power of our words: Teacher language that helps children learn (2nd ed.). Turners Falls, MA: Center for Responsive Schools

Darling-Hammond, Linda. (2000). “Teacher Quality and Student Achievement:” Education Policy Analysis8(1). Accessed on 7 May 2018; http://epaa.asu.edu/ojs/article/view/392/515>

Dweck, Carol. (2006). “Mindset: The New Psychology of Success.” New York: Ballantine.

The Power of Words: Dismantling the fixed mindset

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If you believe, “It’s hard for me to learn new things,” “I’m not good with science,” “I’m not a natural dancer,” “I’m not creative,” “I’m a pessimist,” you’re probably living with a fixed mindset. Such a mindset locks your abilities in place, boxing your learning within the constrains of what you think you know and are good at, and that’s it! How can you free yourself from the shackles of these perceived limitations? Is it possible to grow your mindset? Can I as an educator instil an open or growth mindset into my children and students? Let’s explore how the power of words can lead teachers and students alike to becoming life long learners.

In a fixed mindset, students believe their basic abilities, their intelligence, their talents, are just fixed traits. They have a certain amount and that’s that, and then their goal becomes to look smart all the time and never look dumb. In a growth mindset, students understand that their talents and abilities can be developed through effort, good teaching and persistence. They don’t necessarily think everyone’s the same or anyone can be Einstein, but they believe everyone can get smarter if they work at it.   – Carol Dweck, Stanford University

Learned Helplessness

Professor of Psychology at Stanford University, Carol Dweck’s research into fixed vs. growth mindsets shines a light on the words we use when interacting with our young people, and shows us how these words can affect a child’s perception of their abilities. One might think that praising a child for a good exam result, or highlighting how amazing a student’s talent in adding up numbers is would be the right words of encouragement, right? Actually, they do quite the opposite. Dweck explains, “When you let the results define you — your talent, your test scores, your weight, your job, your performance, your appearance — you become the victim of a fixed mindset.” This phenomenon is referred to as learned helplessness, in which words of praise, such as “you’re so smart, you always get it right, you’re the best writer ever!” actually hinder a learner from believing in one’s full potential. They will tend to shy away from challenges for fear of being wrong, shy away from problems so they are not perceived as dumb, making a fragile and defensive learner fixed within their limited perception of self. Dweck further states that “those afflicted with this lack of perceived competence adopt lower standards for success and expect less of themselves. They underrate the importance of effort, and they overrate how much help they need from a parent.”

More than 35 years of scientific investigation suggests that an overemphasis on intellect or talent leaves people vulnerable to failure, fearful of challenges and unwilling to remedy their shortcomings. – Claudia M. Mueller and Carol S. Dweck

IMG_2294

Words matter

The power to begin shifting learners away from a fixed to growth mindset begins with words! Simple words with powerful implications. One such word is yet! Yet allows for constructive feedback, with trust in growth, for example, “Your program still needs some tweaking when you are using turning angles. You’re not there yet, but I know with some more trial and error you’ll get there.” Process oriented praise is our best friend when addressing small successes. This way, mistakes can be seen as opportunities for further learning, and persistence is embraced by giving learners time to explore and figure it out. Praise is most effective when focused on effort, strategies used, focus on task, persistence, cooperation, willingness to take on challenges.

Sustained higher achievement is possible when teachers use pedagogical approaches that enable students to take charge of their own learning.  Quality Teaching for Diverse Students in Schooling: Best Evidence Synthesis Iteration (BES)

Look at Sylvia Duckworth’s infographic on comparison similar statements in two different mindsets:

sylvia-grown-mindset-statements
https://sylviaduckworth.com

Adults in the building have to be very clear that you can’t have a focus on growth mindsets if all you’re going to be focused on is grades. – Stephen Mahoney, principal of Springfield Renaissance School

Where fixed mindsets see barriers and lack of abilities, growth mindsets see lifelong learning and unlimited potential. The fact is: learners will struggle at some point in their lives. Simply by the words we choose to use when addressing adversity in learning, we can begin to see a shift away from the fixed mindset that is so damaging to perseverance and self-esteem. Words are a good place to start, but ultimately, what is also needed is a shift away from performance oriented goals and into process oriented learning goals. After all, no amount of exams, tests, worksheets or quizzes will lead an individual to knowing how to be a learner. Rather, individuals build an identity through experiential learning rather than worrying about getting the right results. So the next time your child or student says “I’m horrible at math,” reinforce growth, ” Well, Chris, you have a good understanding of fractions, you’re just not there yet when it comes to decimals. Let’s look at the strategies you’re using for fractions and see how they can apply to decimals.”

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Alton-Lee, A. (2003, June). Quality Teaching for Diverse Students in Schooling: Best Evidence Synthesis Iteration. Retrieved February 20, 2017, from http://www.educationcounts.govt.nz/publications/curriculum/2515/5959

Claudia M. Mueller and Carol S. Dweck Praise for Intelligence Can Undermine Children’s Motivation and Performance.  Journal of Personalityand Social Psychology, Vol. 75, No. 1, pages 33–52; November 1998.

Dweck, C. S. (2014, December 18). The Secret to Raising Smart Kids. Retrieved February 20, 2017, from https://www.scientificamerican.com/article/the-secret-to-raising-smart-kids1/

J. A. Mangels, B. Butterfield, J. Lamb, C. Good and C. S. Dweck. Why Do Beliefs about Intelligence Influence Learning Success? A Social Cognitive Neuroscience Model. Social Cognitive and Affective Neuroscience, Vol. 1, No. 2, pages 75–86; September 2006.

Lisa S. Blackwell, Kali H. Trzesniewski and Carol S. Dweck. Implicit Theories of Intelligence Predict Achievement across an Adolescent Transition: A Longitudinal Study and an Intervention. Child Development, Vol. 78, No. 1, pages 246–263; January/February 2007.

Living in a World of “Not-Yetness”

Last week, Amy Collier and Jen Ross talked about the idea of “not-yetness” at the #OpenEd15 Conference in Vancouver, BC. They connected the idea of not-yetness in terms of the messy, risky and frustratingly hard experiences that educators and learners go through with emerging digital learning.

When I asked my son, “What does ‘not-yet’ mean to you?” he responded, “Don’t do whatever you are doing”. Alternatively, when I asked my daughter the same thing, she said, “You can’t do whatever you’re doing right now, but you can do it later.”

Different reactions to the same words.  Like my son, when I hear “not yet,” I hear, “Stop doing that!” In fact as an innovator and teacher who thinks outside of the box, I was often told, “not yet” when I told others about an idea. Although curious by nature, I feel hesitant and lose confidence when I hear the words, “not yet”.

However, my daughter’s response intrigued me. Why did she hear something else when she heard the words, “not-yet”?

I thought about my favourite t-shirt with the following image on it:

CC BY-SA 2.0
https://www.flickr.com/photos/rodtnytt/18585507373/in/photolist-6ovXhu-ujkzQi/ – CC BY-SA 2.0

 

My daughter laughs when I wear the t-shirt. She loves the idea of no boundaries and always thinking outside the box. My son has asked me to take the t-shirt off because it breaks all the rules and it isn’t right.

The best thing about the topic of “not-yetness” for a blogpost, is that the chapter Complexity, mess, and not-yetness: Teaching online with emerging technologies (Collier & Ross, in press), is “not-yet” published in the forthcoming second edition of Emerging Technologies in Distance Education. So I can write about the possibilities of “not-yetness” ahead of time, I can break all the rules and I don’t have to be right.

Based on the context of messiness and not-yetness in digital learning, in her ET4Online Plenary talk Ross said that, “We can use (not-yetness) to tell new stories about what teachers, students, developers, designers and researchers are doing in our digital practices, and why it is hard, and why it matters. We can take better account of issues of power, responsibility, sustainability, reach and contact in digital education. We can be more open about the work of education.” (2015)

The idea of, “not-yetness” appears to encourage learners to learn without barriers, take leaps of faith and trust the process. Learners are encouraged to be independent and driven by self-directed inquiry while using collaborative learning strategies when they need some extra support or want to discuss an idea.

“Not-yetness” reminds me of the idea of the Growth Mindset. “In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment. Virtually all great people have had these qualities.” (Dweck, 2006)

When my daughter defined “not-yetness” she added, “My teachers tell me, “Instead of saying ‘I can’t do it’, say ‘I can’t do it yet’.”  

I didn’t learn to teach using digital tools by following the same set of rules and guidelines I used when I learned how to teach in a regular f2f classroom. I learned by trial and error, hours of practice, development of skills I never knew I had, knew I needed, or even knew existed. I learned to code, embed, ask questions, collaborate, connect, and trust the process. I learned that it’s ok to fail one day and succeed the next and that failure can feel good and success can feel bad. I learned to give up control and focus on listening to others. I learned to push boundaries and look for alternatives. I learned that there are worlds out there in which I can learn – that I don’t know anything about, and that’s ok.

Whether you are a believer in “not-yetness”, growth mindset, or otherwise, the power of the unknown can motivate and challenge learners. It is wrong to take away the magic of the “not yet” when it is full of potential learning energy. Next time you hear or say, “not-yet” take a moment to think about the context and consider if you are encouraging or preventing new learning from happening.

Dweck, C. S. (2006). Mindset: The new psychology of success. New York: Random House.

Onward and Upward: Fostering a growth mindset

kids_gardenWelcome back, learners!

I am honoured, for the fifth year in a row, to write the official back-to-school post on the LEARN blog.  How do I always come up with something fresh(ish) and new(ish) to write about?  Believe me, every September I struggle and I do feel a certain amount of stress. Despite those feelings,  I accepted the request of our blog editor when she asked me in August if I would uphold my “first post of the school year” tradition.  My response:  “I don’t have any ideas for this year…YET!”

That one word, yet, is very powerful!  What does it signify?  For me related to this blog post, it meant that even though in mid-August, I didn’t know something, I had faith that “not knowing” was a temporary state.  I wasn’t giving up after coming up blank on topics for thirty seconds, or even a few days.  I had the belief that, by putting in several days of thought, and planning a professional learning day for the online teachers, I would find a good topic.  By putting in the time, reflection, effort, research, and discussion with colleagues, I knew that the topic would come to me.  Happily, I have a GROWTH mindset.

Growth Mindset vs. Fixed Mindset

For those of you who are familiar with the work of Stanford University psychology professor Carol Dweck, growth mindset is not new to you.

According to Dweck’s definitions, “In a fixed mindset students believe their basic abilities, their intelligence, their talents, are just fixed traits. They have a certain amount and that’s that, and then their goal becomes to look smart all the time and never look dumb.”

“In a growth mindset students understand that their talents and abilities can be developed through effort, good teaching and persistence. They don’t necessarily think everyone’s the same or anyone can be Einstein, but they believe everyone can get smarter if they work at it.”

Or, to use that word yet,

  • With a fixed mindset, a learner might think, “I can’t do that!” and stop trying.
  • A learner with a growth mindset, would instead think, “I can’t do that YET,” and put in place all available strategies to tackle the problem.

Looking at one study in Dweck’s research, students were asked to complete a puzzle.  After completing the puzzle, all of the participants were praised.  One group of students was told they must be very smart and talented to have completed the puzzle.  The other group was praised for the hard work and effort put into the puzzle.  As teachers, when we use praise, our intent is to encourage students and instill them with confidence and self-esteem.  All good, right?  That’s not what the study found.  It turns out, not all praise is necessarily good praise.

After being praised, the participants were offered a choice in the puzzle they would work on next.  When given the choice between puzzles described as being within their comfort zone (they would certainly succeed) or puzzles that would challenge them (they would make mistakes but learn), most students who had been praised for their intelligence selected the easier puzzle, whereas the majority of the students praised for hard work selected the more challenging one.

The study was repeated several times with the same results. You can read more about Dweck’s fascinating and revealing research by following the links below, but what I really want to consider is how her findings might impact us as teachers and learners.

Pause before you praise

Listen to how you praise students (and your own children).   If you start to give a student feedback that focuses on his/her talents and intelligence, wait a moment.  Consider instead the effort and process that the student has put into the work and try making encouraging comments related to that.  If the student had no trouble completing the work and made no mistakes, encourage them to try something more challenging that may even allow the student to struggle a bit.

growth_statements

Check your own mindset

Do you believe in the power of your own attitude and effort, or are you limiting yourself to your own teaching comfort zone?  Yes, trying something new leaves us open to making mistakes, struggling, and feeling stressed.  Believe me, I have made epic mistakes when tackling new things.  I do get frustrated when trying to figure out something challenging for the first time.  However, I have learned from most of my mistakes, and felt the exhilaration of FINALLY being successful with something that had previously seen me pulling my hair out.  Staying in one’s comfort zone rarely gives us those same amazing highs and real feelings of accomplishment as when we take on, and finally conquer, a new challenge.

I will leave you to consider the question posed to our online students this year in their first assignment in which they introduce themselves to their new online teachers:  Describe a situation (not necessarily at school) where you had to work hard at something to succeed.

Feel free to comment below to answer this question for yourself, or consider how a growth mindset may have helped you or your students succeed.

Wishing you an exciting year of growth and learning!

An interview with Carol Dweck

The Educator and a Growth Mindset – Jackie Gerstein’s thinglink (click on dots on the infographic for more resources)

TEDx video: The Power of Belief: Mindset and Success, Eduardo Briceno