Rebecca Zook - Math Tutoring Online

Get your free copy of 5 Tips You Must Know to Stop Freaking Out About Math!

Call me free of charge to discuss your situation, and we'll see if I can help.


Triangle Suitcase: Rebecca Zook's Blog About Learning rssfeed

Posts Tagged as "math tutoring"

Are you tired of watching your kid give up on math? Or, the secret of the tiny crumb of doability…

Thursday, January 5th, 2017

What do you do when you see a problem full of weird things you’ve never seen before?

Or a super-long problem?

Or just a problem that combines things you’ve learned in a way you’ve never encountered?

What MOST people do is look at the problem, and as soon as they register it as “unfamiliar,” they give up.

They think, “I don’t know how to do EVERYTHING in this problem, so I must not know how to do it AT ALL.”

Like, “If I don’t know everything, I don’t know anything.”

But my students and I have encountered a fascinating phenomenon.

Hidden inside most “seemingly impossible” problems is a tiny crumb of do-ability.

If you find this tiny crumb and you start there…

… a lot of times, that’s all you need to get started…

… and once you get started, a lot of times, that’s all you need to get going… and solve it!

For example, a student of mine came across a problem that combined a bunch of negative and positive integers with brackets and parentheses:


My student’s first reaction was, “I don’t know how to do this.”

Then she realized that she DID know how to do 8 times 5… (to quote her, she said, “I could do 8 times 5 like in second grade”)

…and then she remembered that negative 8 times negative 5 is positive…

…and by finding the “tiny crumb of do-ability”, she was actually able to get started and complete the entire “scary/impossible problem.” It actually took her less than a minute to do the whole thing!

And she observed, “All I had to do was use what I learned in 2nd grade,” just in a slightly more complex combination than before.

For another example, another student of mine got stumped when practicing translating English into math, a problem like, “The difference of seven times n and three is twenty-seven.”

Her first reaction was, “I haven’t learned this yet.”

She looked for the little piece she did know… which was that ‘is twenty-seven’ translates into EQUALS 27.

Once she got started with that little piece, she was able to build out from there, that ‘seven n’ is 7n, and ‘the difference of seven times n and three’ is 7n-3, all the way to the full translation, 7n-3=27.

To quote one of my students on how she felt after we worked on this approach together, “Problems are never so hard when you break them down. You can’t judge a problem by its length or numbers. Even if it just looks really hard, you have to break it down.”

So the next time you encounter a problem that just stops you in your tracks, looks super long or complicated, or overwhelms you with unfamiliar symbols, look for the tiny crumb of do-ability.

Even if it seems insignificantly small, a lot of the time it’s all you need to get on your way to the solution.

This is also a great way to practice deliberately being with the UNKNOWN and setting yourself up for revelations and lightbulb moments, like I wrote about in “Do you wish your kid could feel like Albert Einstein while doing math?”

Do you wish your passionate, unique, visionary kid could be supported in breaking things down and experiencing math as fun, do-able, and creative? Then let’s get you started with your application to my powerful private tutoring programs!

This application includes the super valuable opportunity to speak with me one-on-one and get clear about exactly what’s going on in your family’s math situation.

Just click here to get started with your special application.

Once your application is received, we’ll set up a special phone call to explore whether or not my magical math tutoring programs would be a fit for your family! I’m excited to connect with you!

Related posts:
How to help your kid with their math homework
How to get your kid talking about math
What changes when someone believes in you?
A 5th grader goes from believing “math doesn’t like me” to singing and dancing about math while wearing a purple tutu

Posts Tagged as "math tutoring"

Do you wish your kid could feel like Albert Einstein?

Thursday, February 18th, 2016

My student who loves to sing and dance about math boldly announced to me during our tutoring session, “I feel like Albert Einstein!”

Ok, so let’s back up for a second. How did this happen?

When she told me she felt like Albert Einstein, I told her, “I think this is really important. Let’s look at this together for a minute.”

What was the process that led to this lightbulb moment?

Here’s the breakdown.

We were working on a problem that combined multiple circles shapes to make a complicated-looking shape that LOOKED super scary and weird – but was actually just a bunch of circles combined in an innovative way.

When my student first saw the problem, her first thought was, “I don’t want to do this. This is too complicated.” (Initial resistance to the problem.)

Then, she thought, “OK, why don’t we just try it, because if we skip it, I might forget to do it and then I won’t ever get it done or learn from it.” (Willingness to engage with the problem.)

As I was talking to her about the problem, this student started playing around with the diagram, trying to break it into smaller shapes.

Without freaking out or trying to force anything, she just playfully engaged with the problem, without being worried that she “didn’t know how to do it.” (Willingly engaging with the unknown with a sense of playfulness and lightheartedness.)

While she was listening to me, she started getting a mental image of Mickey Mouse ears, and a Mickey Mouse cartoon she had seen where Mickey lost his ears. Then, when Mickey found his ears and put them back on his hat, half of the full circle disappeared into the hat, so only a semicircle stuck out to make the ear.

(Her subconscious started to make non-linear connections. She let her subconscious flow without shutting it down.)

Then my student realized that the same thing was going on in the diagram we were looking at – the little circles were being “stuck” into the big circle and half of them were disappearing.

(Her subconscious/visual mind clearly showed her how to solve a problem she “didn’t know how to do.”)

Then she knew exactly what to do and was off and running! (She immediately applied her flash of insight to successfully solve the problem.)

What makes me SO HAPPY about this is… very advanced scientists, mathematicians, and inventors often rely on their creativity and their subconscious mind to solve the problems that really stretch the limits of their current understanding.

But you don’t have to wait until you’re in graduate school or interning at CERN to start working with your creativity and subconscious to solve problems.

In fact, you can start right now… even if you’re “just” a rising 7th grader!

Here’s how you, too, can start to invite more Albert Einstein moments into your math learning:

1. Be willing to engage with the unknown. When you see a scary problem that looks unfamiliar, instead of shutting down and saying, “I don’t know how to do this,” or, “I need someone else to show me what to do,” just say to yourself, “Why not just take a look at this and see what happens?”

2. Let yourself play with the problem and explore. You don’t have to know what to do. Try to break it down into something you do know how to do. Look at it from different perspectives. It doesn’t have to make sense immediately.

3. Remember that it doesn’t have to be linear and you don’t have to force it. Just hold the problem lightly in your mind while you are exploring.

4. If you start to get some unrelated images or ideas, let them come through. Maybe they will show you how to solve the problem!

5. If you do have a lightbulb moment of insight, go ahead and apply it to the problem and solve! This is so satisfying!

6. VERY IMPORTANT: If you don’t solve the problem right away, it’s OK to take a break and come back to it later. (In fact, professional mathematicians and scientists do this on purpose! And many of the most important problems of their careers took them months or even years to solve.)

7. ALSO VERY IMPORTANT: Even if you DON’T solve the problem, practicing deliberately being with the unknown is incredibly valuable.

I’ve come to realize that deliberately being with the unknown and having the courage to experiment is maybe the most important skill we can learn in math and in life. To me, it is an incredible meta-skill that allows so many other beautiful learnings, creations, and opportunities to come through. Unfortunately, it’s something that is not mentioned or encouraged in most educational environments.

Just as an example of how this skill is developed as part of my work, when this student first came to me, what was going on was if she didn’t immediately know what to do, she would give up right away and ask her Mom to show her how to do the problem.

Now she her instinct is to explore, instead of give up, and she is living in a completely different world.

Is this a transformation you would like your child to also experience – from giving up as soon as they don’t know what to do, to having their own moments where they feel like Albert Einstein after a blinding flash of insight?

Then I invite you to apply to my super powerful one-on-ones tutoring programs.

Just click here to get started with your special application for my one-on-one math tutoring programs.

Once your application is received, we’ll set up a special phone call to get clear on what’s going on in your kid’s math situation and whether or not it’s a fit for us to work together. (This level of attention to incoming families is unparalleled in the tutoring industry!)

I’m excited to connect!

Related posts:
Does having a math tutor make you a “loser”?
Case study: a 5th grader goes from thinking “math doesn’t like me” to singing and dancing about math while wearing a purple tutu
I just can’t keep this a secret any longer
How to experience math as your own unique creation
Is your kid a creative, passionate, unique visionary of the future?

Posts Tagged as "math tutoring"

The secret to getting straight As in math (it’s not what you think)

Wednesday, February 17th, 2016

I was recently talking with one of my favorite students about her goals for the upcoming school year.

She told me her big goal was to make straight As.

This actually made me kind of worried!

You might be thinking, what, Rebecca, are you CRAZY? Why would it be BAD for a kid to WANT to get straight As?

So … let me explain.

The reason why this made me a little worried is because what is most important to me as a math mastery mentor and joyful learning expert is that the students truly master the material.

I’ve found that when students are committed to the process of mastery, and receive aligned support, everything else just happens naturally – the confidence, the grades, successful classroom participation.

It’s all just a byproduct of the true foundation, which is the mastery process.

So I’m going to share a big secret with you – the same big secret that I shared with this student.

If you want to make straight As in math…

…focus on the habit, not on the goal.

I explained to this student that her success in math up to this point is all because of incremental habits that she’s been developing.

If she keeps doing these little incremental habits, those grades will come, whether or not she’s focused on them.

So here are the exact incremental habits that are the secret to getting As in math.

If you want to get straight As in math, this is what to focus on:

1. Keep track of your assignments so you know what’s due and when.

2. Give yourself plenty of time to complete the assignments and study for tests.

3. Practice new concepts until they are automatic (even if this means doing more practice than is assigned for homework).

4. ALWAYS make sure to get feedback on your work (like checking your problems in the back of the book) so you know whether or not you’re on track.

5. When you miss something on a test or quiz, go over it and figure out exactly what wrong and what you need to do differently next time.

6. Do extra practice of those types of problems you missed on the test or quiz, so they won’t be confusing when they come back in the future.

7. When you don’t understand something, keep a running list of problems, concepts, and vocabulary that aren’t clear and you want help with.

8. Ask for help with the things you don’t understand.

9. If the help you receive doesn’t work, keep looking until you find help that TRULY makes sense to you.

Do you want your creative, passionate kid to receive math help that actually makes clicks with their individual brain? Help that supports them in truly mastering math (and getting great grades and having awesome confidence as a result)?

Just click here to get started with your special application for my one-on-one math tutoring programs.

This application process has been meticulously designed to help us both get clear about whether the special, magical way I work is a match for you.

Once your application is received, as part of the application process, we’ll set up a special phone call to get clear if my approach would be a good fit for your child. I look forward to connecting!

Related posts:
On optimal challenge
What to do when your kid makes a math mistake
Tips for a happy math year – #1
Tips for a happy math year – #2
Tips for a happy math year – #3

Posts Tagged as "math tutoring"

How much do math grades really matter?

Tuesday, December 2nd, 2014

Photo on 9-5-14 at 8.56 PM #2
“Practicing” wearing a sparkly new outfit!

So you may have gathered… I’m like, all about practice.

And I just can’t stop thinking about the student I told you about last week… the one who was focused on getting straight As.

What do you do when your unique, visionary kid is SUPER FOCUSED on grades?

Is this a practice to encourage, or something to fear?

Especially with kids who are usually very intrinsically motivated – who have their own plans, ideas, and passions – a sudden focus on grades can actually be a red flag that they are terrified of falling behind, not measuring up to their peers, or being excluded from the “smart kids group.”

When this happens, it’s really important to redirect the focus back to where it belongs – on the mastery process.

Grades CAN work like a thermometer. They have the potential show you what you’ve learned, and what you haven’t learned yet. In this way, they can give very helpful information.

But grades in and of themselves don’t give you the full picture.

Did you get an A because you really understood the material, down to your core, so much that it’s part of you? (True mastery?)

Or did you get an A because you turned in your homework, showed up in class, and raised your hand even when you knew you didn’t know the answer? (Being rewarded for appropriate behavior, even if you have no clue about the math?)

Did you get a D because you made a silly mistake, but you get the concept and you can figure out exactly what went wrong once you look over your work?

Or did you get a D because you have no friggin’ clue and you just wrote something down so you wouldn’t leave it blank?

Did you “complete” the worksheet by passively watching the teacher review a problem, thinking that this means you “get it” because you “got it done”?

Or did you complete the worksheet by truly understanding what is going on and practicing it until it’s automatic for you?

Did you get the GPA to be accepted to your dream college by flagellating yourself every night and focusing on fulfilling other people’s expectations, miserable, sleep-deprived, and constantly anxious that you won’t measure up?

Or did you get that GPA and receive that acceptance letter by pursuing your passions, taking care of yourself, and being intellectually nourished?

On the surface, it looks the same, but underneath, it’s much more complex.

This is why I find it’s so important for creative, unique, trailblazing kids to be focused on the true process of mastery, instead of just grades.

Just getting straight As alone doesn’t mean that you actually understand what’s happening.

It doesn’t mean that your dream college will accept you.

It doesn’t mean that you know yourself.

It doesn’t mean that you are prepared for life – especially if you are blazing your own trail.

Focusing on perfection (like getting straight As) can be extremely debilitating and discouraging.

It can make it harder to grow and learn and even suck all of the joy out of life.

But focusing on mastery, regardless of what’s happening with grades, is energizing.

You feel the thrill of understanding something new.

You focus on learning from your mistakes and understand that mistakes are just part of the process.

By constantly engaging with the process of learning – asking yourself, what makes sense to me here? what do I not understand yet? – you develop deep self-awareness.

You come to know who you are – not just how to “get through it” or “churn it out” for a teacher or requirement.

You are resilient in the face of challenges, because you are in the practice of joyfully engaging with challenge just as part of your routine.

You trust yourself.

You understand how you do your best work.

And paradoxically, by focusing on the immediate, incremental process of mastery, the great grades, with time, will just naturally happen.

Just to share, from my own personal experience, in college I had to take French in order to fulfill a requirement, and I had to maintain a certain GPA or I would lose my full tuition scholarship.

I got through it, and I learned French, but the process wasn’t that meaningful to me.

I remember feeling so frustrated that I was expected to speak French perfectly and it made me afraid to open my mouth. This wasn’t how fluent speakers mastered the language! It was so artificial and hollow to me.

In contrast, when I was 23, I studied Indonesian language (in Madison, Wisconsin, of all places) in a total immersion environment. Four hours, every day, all Indonesian, no English. We HAD to make mistakes in order to learn. The focus was just on communicating and being playful…on the process of mastery, rather than on being perfect.

It was the most incredible language learning experience I’ve ever had. I felt so confident and secure!

And when I went to Indonesia the following summer, I was completely prepared to speak Indonesian with the musicians and dancers who I truly wanted to study with – who happened to not speak English at all.

And the Indonesians I met on the street thought I had been living in their country for years because of how comfortable I was with the language – when I had only studied it for 8 weeks.

This astonished me. And it was all because of focusing on the process rather than on perfection.

So if you find your creative, unique, trailblazing kid is coming to you with goals like “I want to make straight As,” shift the focus back to the ongoing process of mastering math.

Do you want your passionate, visionary-of-the-future kid to receive totally aligned support with the process of true math mastery? (And to experience the awesome confidence and great grades that happen as a result?)

Then I invite you to begin the application process for my individual math tutoring programs.

Just click here to get started with your special application. This application process has been meticulously designed to help us both get clear about whether the special, magical way I work is a match for you.

Once your application is received, we’ll set up a special phone call to get clear if my approach would be a good fit for your child. I look forward to connecting!


Dancing with my Indonesian dance teacher (who only spoke Indonesian to me)-
this is what can happen when you focus on the mastery process
instead of on “being perfect”!

Related posts:
What a Balinese dancing queen taught me about praise and encouragement
What I learned in the streets of Paris, and in a Dutch grocery store
It’s eraser time! (And other math mantras)
Is your kid a creative, passionate, unique visionary of the future?

Posts Tagged as "math tutoring"

Can math be a sanctuary?

Thursday, November 13th, 2014

I went on an adventure this week. I did my first recording session with my cello.

Me and one of my best friends went to my “power place,” this magical, beautiful tunnel in Central Park covered in beautiful mosaics that has amazing acoustics. We purposefully went late at night so it would be quiet.

Walking through the park, I saw that a film shoot was set up next to the tunnel, with this huge floating dirigible light and all this film equipment. And I was afraid that they would kick us out or tell us to not make any noise.

I thought, OK, well, the worst thing they can do is tell us to stop. So we went down into the tunnel, and I said out loud to my friend that my intention was for both us and the film shoot people to peacefully do what we needed to do without disturbing each other.

I had brought some special gluten free pastries, and before we started recording, we sat and ate our dulce de leche eclairs. My friend observed that she felt like a queen in a beautiful palace, and I had to agree. I felt like we were queens, too.

After our little pastry feast she set up the recording equipment and I started playing. My intention was to record my own original material, and then two covers of me singing with my cello, which is scary and new for me.

It was totally magical. My friend took care of all the recording details, and she even did this amazing spontaneous backup harmonies. Which really made me feel like a badass, to have backing vocals!!

Somehow, the movie people right outside the tunnel were utterly silent, and didn’t bother us at all.

They even shone a spotlight down into the tunnel, which looked and felt amazing to be illuminated like that.

At the very end, for the last song, I was like, what the heck.

I turned to my friend and I said, “Please promise me you’ll still be my friend no matter what you think about what I’m about to do. This is hot off the press and I feel really vulnerable sharing it.”

Then I played what I know is the next level for me – the most exciting, and the most scary thing of all – which is to sing my own original material.

Afterwards, my friend said, “That was gorgeous! Who wrote that??” And I was so excited and gratified that I jumped up and down.

I told her, “I wrote that. This is the first time I’ve ever sung a song I created myself in front of another human being. And I’m so glad I got to sing it in front of you.”

Can I tell you a secret? Recording myself used to be one of the things I dreaded most in the entire world. Listening to recordings of myself playing would rip my belief in myself to shreds. It was so completely stressful for me – a lot like how math used to be completely stressful for me.

How the heck did I get from that place, to where I am now? How do you get from a place where you’re completely struggling, ashamed, in tears, stressed out of your mind, to feeling confident, spacious, and like a queen in your own beautiful palace?

I am still in the process of figuring this out, but here’s what I think it’s about.

Stake out your own territory. If you’re in a really agonizing classroom or math learning experience, you have to stake out your own territory, outside of the awfulness of what you’re currently experiencing. You can’t keep dwelling exclusively inside the “meltdown/panic” zone of what’s currently being offered to you. You have to create a new space for yourself outside that experience, because that meltdown/panic experience isn’t going to give you what you need to move forward.

For me with my music, this meant exploring territory completely outside the classical world, learning how to play by ear, traveling to Cuba and Bali, even taking acting classes. For me with math, this meant learning how to take things apart, go slow, find my own way of understanding. With my clients, in our tutoring time, we very purposefully create a new math zone where math is comfortable, enjoyable, and meaningful, no matter what’s going on in the classroom.

Do it your way. If the way you’re being taught or trained doesn’t work for you, it’s not the only way. So much of the way I was taught and trained in the classical music model made me feel so awful about myself and didn’t help me create good work. “My way” happens to be performing in a beautiful mosaic-ed tunnel next to a fountain with an angel on top.

Same thing with math. You can do it your own way, relying on your own strengths, your own fascination and creativity. With my clients, we find ways that really work for each individual so they can start to experience math as a source of joy and strength, even a way to express themselves creatively.

Surround yourself with true companions. That evening of recording in the tunnel was so magical. And at the end I told my friend, wow, it felt so effortless. But I know so much of it had to do with the fact that I picked my recording engineer – my friend who came with me to record – so very carefully. Not only is she one of my closest friends and an amazing musician, but I had also sang to her as an audience member in the tunnel over the summer, and I already knew I felt so comfortable and safe with her, and encouraged, even when I was doing the most vulnerable thing musically that I’ve ever done.

Having her there with me completely transformed the experience and made me feel so strong and safe. And this also happens in my work with my math tutoring students – finally having a true companion, a truly matched math mastery mentor, allows them to completely transform their relationship with math, and even with life.

Are you ready to have a true math companion who will support you in transforming your relationship with math from agonizing to euphoric?

Just click here to get started with your special application for my one-on-one math tutoring programs.

This application process has been meticulously designed to help us both get clear about whether the special, magical way I work is a match for you.

Once your application is received, we’ll set up a special phone call to explore whether or not my magical math tutoring programs would be a fit for your family! I’m excited to connect with you!

Posts Tagged as "math tutoring"

Don’t back down

Thursday, October 16th, 2014

So I recently flew to LA for a workshop with my super special acting teacher.

It’s my fifth time taking a class with him in about 18 months. Every time it’s amazing and every time it’s totally different. (Which is why I keep going!!)

At the very end of the workshop, we did this special exercise to access an “inner superhero” we could call upon in the future.

Usually I jump up in front of the group, eager for my turn. But for some reason this time I was dreading going up there.

Sitting and waiting was so intense. Like every cell in my body was going crazy.

The longer I waited the more intense it was. And I waited until no one else was left.

When I got up there to embody my inner superhero, I didn’t know what to expect.

What happened was it felt like I was channeling something huge, something so powerful. I found myself giving the audience loving advice, telling them, “DON’T BACK DOWN.”

I singled out one classmate who was a “struggling actor” and told him the truth, that I saw him as a leading man and he couldn’t stay in his cave.

I felt so connected to the people in the audience. I felt so strong, so direct, so clear. I felt way different than I normally feel.

Afterwards it felt like whatever I had just channeled was still happening in my body.

And where my mind started to go was, “How could I possibly be strong enough to be this big, this clear, this direct, all of the time?”

And also, “What if that was the peak of my entire life? What if I never experience that again, and that’s as good as it gets?”

I brought this up in front of the group and asked these questions to my teacher, and he told me that this was always accessible to me, that what I had just channeled was me, and was always inside me.

And the doubt was still there. How do I stay connected to this huge amazing breakthrough? How do I go forward from here?

Let me tell you, it does NOT always feel good to be called to the next level of growth.

It does NOT always feel comfortable, even when you are having an incredible breakthrough.

It doesn’t always feel safe. It doesn’t always feel like you know what to do next.

So…. flash forward. I’m back from LA. Someone who saw me playing my cello in Central Park this summer is emailing me asking me to play my cello for a private party after his dad gets knighted (??!!) and was wondering if I could send him some video clips.

I’m going through videos of my cello performances… one from the very beginning of the summer, right after another huge breakthrough, but before I started performing regularly in the magical Central Park tunnel. Another clip from my last performance of the summer, after I’d clocked dozens of hours in front of people.

When I was performing in the first clip, I remember it felt like a major peak. A big deal. But watching it now, I could see how uncomfortable I was, still, even after my breakthrough.

Performing in the second clip from the end of the summer, I remember feeling tired and pissed off. It didn’t feel like my best performance ever. I didn’t feel like anyone was connecting to what I was sharing.

But that’s not what it looked like on video.

On the video I was shining, beautiful, playing from my heart.

What the heck happened?


Back right after my huge breakthrough in May, that performance felt like the best I’d ever played.

But instead of staying at that level, or retreating out of fear that I’d never “hit that level” again, I kept going. I played every weekend. I played for hours. I played for strangers.

And the things that had felt like a huge breakthrough in May became second nature. They became automated. They became integrated.

And now I’m being called to go through the whole cycle AGAIN!!

And it’s scary AGAIN!!

What I’m here to do is create transformation – in my own self, in my performances, for my audiences, and for my students’ relationships with math, mastery, and themselves.

But people don’t always talk about what to do after the breakthrough.

Here’s what I see needs to happen….

After the breakthrough…

1. …keep going. Just keep going.

2. Remember that there is always another loop on the upward spiral of growth. This is part of what it means to be a trailblazer. It’s OK if it feels scary and uncomfortable.

3. Stay connected to community. Stay connected to people who are also committed to their own transformation. Let them reflect your growth back to you. Let them celebrate where you’ve come from and lovingly remind you what it was like before. Let them hold the vision of where you’re going and travel through the next steps together.

4. Stay connected to your mentors who are farther along the upward cycle of growth, and who can help you through what they’ve already been through. Being guided by aligned people who have walked their own path with heart is an incredible transformation accelerator.

Do you want your trailblazing, outside-the-box, creative, passionate kid to be mentored in creating math mastery breakthroughs by a fellow trailblazer?

Just click here to get started with your special application for my one-on-one math tutoring programs.

Once your application is received, we’ll set up a special phone call to explore whether or not my magical math tutoring programs would be a fit for your family! I’m excited to connect with you!

And here’s the video I was talking about…

Related Posts:
What changes when someone believes in you?
Does having a math tutor make you a “loser”?
Failure is not the enemy
Is your kid a creative, passionate, unique visionary of the future?

Posts Tagged as "math tutoring"

Will guessing move you forward, or throw your hard work out the window?

Thursday, August 21st, 2014

Have you ever been working with your kid on a math problem and they just throw a number at you out of nowhere?

When this happens to me, I usually ask diplomatically, “Is that a guess?” or make the observation, “That sounds like a guess,” with a little smile.

The thing is, guessing is a super powerful problem solving technique – but most kids don’t realize that there are different kinds of guessing, and that certain kinds of guessing can move them forward confidently, while others can throw all of their hard work out the window.

Let’s break it down.

1. The first, and least helpful, kind of guessing is WILD GUESSING.

WILD GUESSING is NOT a helpful kind of guessing. It’s like if someone asks you what the capital of New Jersey is and you just open your mouth and name any geographical location that comes to mind. (“Poughkeepsie, Montreal, the Cote D’Azur…”)

Sometimes wild guessing happens at the beginning of a problem, when a student doesn’t know how to get started, so they just start doing random operations with the numbers in the problem. (“Hm, I have no idea what to do, there is a 5 and an 8 in the problem, let me multiply them together, then at least I have ‘done something’…”)

For some reason it also tends to happen when a student is almost done with the problem – usually almost at the very last step – and for some reason, instead of actually doing the tiny bit of work remaining, they’ll just throw a number out there.

This kind of WILD GUESSING – whether with guessing a number or just doing random operations – is important to recognize, because it usually means the student is not connected to what is going on in the math.

2. Another completely different kind of guessing is ESTIMATING. This is a great way to quickly predict an answer and then be able to confirm at the end of the problem whether or not you’re in the right ballpark, or if you made a calculation/computation error and are way off.

Frequently, estimating involves rounding the numbers and then making a mental calculation, before you dive into the nitty-gritty EXACT computation.

Estimating is a powerful tool and also a great way to practice mental math!

3. The third kind of guessing is DELIBERATELY TESTING A HYPOTHESIS.

This type of guessing is SUPER POWERFUL, and it’s something that professional mathematicians and scientists do all the time to move human knowledge forward!

For example, today I was working with a student on graphing a straight line.

She said, “What would happen if I flipped the xs and ys? Would they just be all over the place, or would they form a straight line?”

Though I knew the answer, I told her, “Why don’t you try it and see what happens,” because I knew that would be more impactful than if I just told her without her actually doing it.

Then she got to see that the points she was graphing DID still make a straight line – just a completely different line than the original one.

DELIBERATELY TESTING A HYPOTHESIS is also a great as a way to get started when you’re not quite sure what to do, but you have a hunch that you could try a particular approach, but you’re still not sure.

It is most helpful when there is some way to check your answer. Otherwise there’s no way to tell if your test was correct!

So guessing can either be a super powerful and savvy sophisticated tool – or the sign that a student is flailing and not yet connected to the meaning of material. That’s why it’s so important to know about the three different kinds of guessing, and discern between them.

Would you like your innovative, unique kid to experience math from the powerful position of being able to deliberately test out their own creative hypotheses? If so, I would love to talk to you!

To make sure it’s the right fit, I accept students into my magical tutoring programs by application only, and the application includes the extremely valuable opportunity to spend 90 minutes on the phone with me so we can getting super clear on what’s going on with your kid’s math and whether or not it would be a fit for us to work together.

Just click here to get started with your special application for my one-on-one math tutoring programs.

I’m excited to connect with you!

Related posts:
Case study: a rising eighth grader masters her summer math packet
When in doubt, talk it out
What to do when your kid makes a math mistake
How to experience math as your own unique creation