Rebecca Zook - Math Tutoring Online

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:

[(-8*5)-(6*-9)](-2*3)

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

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?

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

Yesterday I was working with a student on some very sophisticated geometry problems that require a lot of synthesis and creativity. She had come to me with the questions she hadn’t been able to figure out from her summer geometry homework assignment.

For a second I thought she meant she hadn’t known how to start on the problem, but while I was putting the diagram up on the whiteboard for us to refer to together, she said, referring to her preparation, “I was just doing this big thing, and I don’t even know if it’s right.”

I was like, awesome! I was so happy that my student dove in and explored, even though she wasn’t sure if she had done the right thing.

When math becomes more demanding, it frequently requires two completely different skills: really internalizing everything you’re learning so much that it’s completely automatic, (like writing your name or eating with a fork); and THEN, being able to creatively combine those ideas, concepts, and strategies in ways you’ve never done before when you’re faced with something mathematically completely unfamiliar.

I told this student how proud I was of her that she had tried to solve the problem so extensively even though she wasn’t sure what to do – instead of just giving up or waiting.

I explained, “It just means that you’re in the exploration and experimentation zone, instead of the repeating and recycling zone.” We go through the process of internalization in order to flourish when faced with the unfamiliar.

And then, we train ourselves to be comfortable – even lighthearted and jubilational – when faced with something we’ve never seen before. To be comfortable with being uncomfortable, and to ask ourselves questions like:

What could I try here?

OK, if that didn’t work, what could I try instead?

So, is it OK to not be totally sure? Absolutely! In fact, it is an extremely important space to become acquainted with, and to befriend: “the not-totally-sure-if-it’s-right space.”

Are you worried that your kid’s current math issues will prevent them from understanding math in their own unique way and being able to live their dreams?

Do you deeply desire that your kid receive high-level, super-customized math support that feeds their autonomy and helps them really do what they’re here to do in the world?

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 if my approach would be a good fit for your child.

I’m here for you, and I’m so glad we’re connected!

Sending you love,
REBECCA