I Want My Students To Struggle

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Originally, it was a question on Quora that prompted this and got me thinking. The person asked if “math geniuses” struggled with math problems. Hmmm well first let’s answer that question.

Struggling is actually relative to the one solving the math problem. So, if you are asking if a math genius struggles with some of the problems that are difficult in basic classes up through calculus, then probably not. If, however, you are asking if such gifted individuals work through problems of their own without always knowing every step beforehand, then yes.

I provided the picture to exemplify my meaning here because it can be difficult to imagine problems that “geniuses” would find challenging, even for me with a math degree. While the first problem is hopefully easy for those reading through this, a student experiencing math for the first time can have a hard time putting together that one quantity plus another quantity gives a third quantity.

As a tutor and teacher, I have worked with students from the ground up, so to speak. It’s actually really cool watching little ones light up as they make connections and discover patterns. Getting there can be a struggle, though, and we all went through it at one point or another. In fact, the same struggle sticks with us all the way through our discovery and practice of mathematics.

There are problems out there that remain unsolved despite these brilliant mathematicians working together to arrive at a solution to benefit all of mankind. I would say that qualifies as a struggle since they haven’t been able to determine an adequate answer. But this is not a bad thing!

One of my personal education mentors asked me a question that has forever changed the way I approach math both as a student and teacher. Does struggling have to be a bad thing? While at first, of course I was opposed to ever having a student I was pouring myself into go through any distress in their attempts mostly due to the already negative association many people have with math, I came to understand that this is how individuals grow.

No matter how many times I explain a concept to someone, it will always seem easy when I do it because I already know how to perform the calculation or derivation. Until that person realizes for his or her self, they cannot repeat the process on a new problem. The struggle leads to discovery. Working through examples and then problems on their own helps foster both independence as well as appreciation for the effort needed to become a capable mathematician in their own right.

Granted, I don’t mean locking someone in a room and leaving them to their own devices. No, no. What I mean is a guided study that is equal parts help and discovery so that every student can feel that they understand the subject matter.

If you’re like me, then this revelation is one that does not come easy and can lead to a good deal of strife in terms of concern not only for your own progress but those you are responsible for. Hence, one of my favorite quotes from one of the greatest minds that has ever lived.

 

The famous math genius and physicist himself, Albert Einstein said not to let your struggles get you down because he was sure he had a much harder problem that he was trying to solve. Hard to get more authoritative than that!

Hopefully this not only answers your question but also serves as a springboard for any discouraged students looking toward the future for a little hope.

As always, thank you for letting me a part of your journey through math!

Kagan Love

I’m Bad At Math

Yet another answer I felt relevant for my blog. It’s questions like this that abruptly ended my pursuit of math for myself and tossed me headfirst into the sea of education to help keep others from drowning in fear of the subject that I adore so.

CaptureThere’s your answer, right there. Confidence is key!

Now, before you think I’m picking on you or doubting your assessment of yourself, please forgive the harsh opening. I want to let you know from the beginning that I believe in you and have no negative thoughts toward your intelligence whatsoever.

You yourself have said that your IQ is high, typically a great indicator of math ability especially! If I am to assume that you believe this, which I do, then the confidence you need is already a part of your personality, which is great news!

Unfortunately, I have seen time and time again students who lack the same attitude about their math skills. Fear not, you are definitely not alone. If you will allow, I would like to give you a few helpful tips in how to improve.

Confidence

No shocker there. In every initial assessment I’ve done with a student, either their parents lead with how their child doesn’t feel good at math or I will quickly discover that my new pupil is afraid to make a mistake.

That’s silly.

I made one small typo in an answer on here that had some 6,000 people read it. Was it embarassing? Perhaps a little. So what did I do with this situation? I pointed it out to every student I saw that day and online to my Facebook friends because I thought it was funny.

In all honesty, it is good that I made a mistake. Not necessarily for my ego, but for others to see that even though I literally do math more than I walk every day, I am not infallible. More than that, it wasn’t the end of the world. I still had numerous upvotes and support, so I corrected the typo and went about my day.

(And I can guarantee that I won’t make the same mistake again because now it has been cemented in my mind.)

I have no misconception about my math ability compared to others. My passion is in educating others, so there are definitely mathematicians out there and on here who are far more capable at computations, mind-boggling equations, and abstract proofs. But I continue on because I can see I’m making a difference every day in the students I teach.

You have an IQ, so the ability is there. Once you let go of the stress of making a mistake that might damage your intelligence (which it certainly won’t, or make others think less highly of your mind), I have no doubt you will begin to see improvements.

Practice

My favorite question for all of my students is this. Does knowing how to do a push-up make you stronger? No, of course not. Doing push-ups makes you stronger.

In order to get better at math, we must do it often. I said above that I do math more frequently than I walk every day. It’s true. I had some of my students in class help me do an experiment one day. The time I spent working through math problems with them and then tutoring in the evenings was almost quadruple the amount of time I spent walking.

Would you ever walk up to someone and say, “Wow, man, you are great at walking!” Probably not, because we all do it all the time. It’s more unusual when someone cannot walk well and typically has some underlying problem that prevents them from being able to do so.

Thus, when someone compliments my math abilities, I politely thank them and humbly offer that example as my reasoning. I am terrible at memorizing things, and know this about myself. So it was a lot of practice that got me to this math degree (thank you teacher who dared me to try to get one).

While I believe confidence may have the most to do with your struggles, you will still have a few years at least of practice in the wrong direction to rewire in your brain. All the time you spent thinking poorly of your math prowess set in your head to think a certain way when a problem came up. Now you will have to practice doubly hard to erase that time.

And don’t worry. In my experience, with a true attitude change, you will be surprised how quickly the fear dissolves away, and you realize just how intelligent you are.

Humility

Ask for help!

Seriously, find someone you trust and ask them to help you while you are improving. This serves two important purposes.

  1. Having someone who has an excellent understanding of mathematics there to guide you helps to feel like a team while initially overcoming your anxiety related to mathematics. They will be there to immediately help arrive at an answer when you get stuck. Over time, they should allow you to struggle more to develop independence until you feel confident enough to handle any problem on your own.
  2. They are going to see your improvements before you are. This is why you need to trust your math guru. If you believe their words and know they come from a place of genuine caring, you will know there must be something to their telling you that you are getting better!

This takes humility as asking for help can be difficult, especially for someone intelligent. I’m sure that so many subjects must come naturally for you, so to have to ask for help may be a new experience. I assure you that no real teacher or tutor will ever think less of you or degrade you for it.

Even people who struggle have an issue asking for help because no one wants to feel dumb. Let me tell you now so that no one else can ever take it away from you: Asking for help is the key to success, especially in academics. It does not make you dumb. Anyone who thinks or says differently has not yet overcome their own anxiety about asking for help in the areas they are aware of in their own lives.

Conclusion

Perhaps I’m wrong and you feel confident and are sure that the problem lies elsewhere. I do believe, however, that with these tips, any one or combination of them, can help you see improvements. Again, I believe in you and know that your future is bright in every academic area.

Thank you for letting me be a part of your math journey!

Quora Question: Why the 9-6 Schedule?

This answer is actually a rather fun one. In today’s society, especially since it’s the younger crowd that takes to the interwebs for answers, you may not see a lot of positive answers regarding the “daily grind.” That does not mean, however, that there are not advantages to working in a typical career with “normal” hours.

First, let’s examine some jobs that come to mind when we hear 9–6

  1. Administrators—These folks are the ones that are behind the scenes taking care of paperwork or ensuring that things run smoothly for other employees on the front lines dealing with customers or out performing whatever tasks are required in their company’s field. Though they have a somewhat tumultuous reputation for not caring about others, it is simply in their personalities to take care of the big pictures so that others can handle situations individually.
  2. Healthcare—Follow the link here for a whole list of medical specialists who maintain the 9–5 or 9–6 work schedule. This comes from a history of standard hours that these highly trained professionals maintain where emergencies are not the norm. Instead, you schedule times to meet with these guys and gals so they have the option of setting their hours (often exactly the schedule in question).
  3. Government—Many know this simply because of the frustration of getting off work or needing to utilize one of these services only to find they are closed haha! There are advantages though like holidays off, set schedules and a fairly predictable work day if you’re the one working for them though.
  4. Teacher—I’m adding this purely because I am a teacher. Though this is not exactly within the time frame of the question (I personally report in at 7:30 and am required to be on campus until 3:30 which turns into 5 after getting all of my stuff done), I believe it fits well enough into the vein of this topic as it is a “morning shift” job that has a set schedule around the hours listed.

At first glance, these broad categories don’t seem particularly appealing. The latest generations have found numerous ways to earn a very good living working outside of these norms and without necessitating the drive to a cramped space to churn out results, but still we have those who choose to remain in “white collar” jobs. Why is that?

I believe I have a unique perspective here as I straddle the line. I relatively young having not yet topped 3 decades, and yet I have both a standard morning job as well as a side-gig that I follow randomized hours. Every evening after I finish with the teaching portion of my day I maintain my own business tutoring math. Depending on how I am feeling that day, I may work until midnight or not at all. I have that freedom and sometimes double in a month what I earn at the school.

So why? Better pay. More flexible hours. No boss telling me what to do. Less hours overall. Quite a compelling argument can be made for ditching the 9–6 and is discussed at length all over the internet. Let me try to explain why I still keep both in order to shed some light on the situation.

SECURITY

Not exactly like that. I mean financial security and peace of mind. So many side gigs or online avenues require a certain level of risk. While I clearly found it worth venturing out of my comfort zone in order to earn money with my own tutoring business, I also had the back-up ready to pay the bills.

Many people either do not believe they can start a business or have fluctuating income due to families they have to support or as a result of poor money management. Older generations may not see the value in such crazy ideas, and younger folks who lack confidence to put their ideas out into the world remain happy with their salaries because they know at the end of the day they will be able to eat and have a place to sleep.

There is absolutely nothing wrong with individuals who choose to pursue their security this way as it is tried and true and has functioned well for a very long time. As we will discuss in other reasons, these people usually have more purpose in choosing this lifestyle than fear of leaving it which means their motivation rests elsewhere.

I can personally attest to the frightening aspect of having alternative work schedules. I have had great months where I’ve earned as much as $7000 just working part time tutoring, but I have also seen months where I brought in only $500. With a little saving skills and budgeting, the lean months aren’t so rough, but for the sake of argument here, it is an example worth noting.

Personality

A key to consider here is how others think. Many who find themselves in this thread are probably opposed to the idea of such a work schedule on some level due to the way they think. Unfortunately, everyone in life thinks a little differently, though wide patterns in behavior certainly exist. For example, people who like to work 9–6 for a salary.

Personally, I do prefer my open schedule and higher potential earnings due to the way I’m wired and the values that I hold. I was raised to take risks and always attempt to make the best of myself in every situation. To me, this took on the form of beginning a tutoring business to help others in math where they were struggling in the standard educational setting.

Many, though, find comfort in stability. This goes beyond the security detailed above and refers to where people find enjoyment. A comfy chair after a drive chilling to music might be a calming way to start the morning for some rather than viewing it as stuck in traffic then trapped in a cubicle. Working on approving a new policy with a team then returning to your own life with a definitive time to separate work and play every day might be just what certain personalities need.

Schedule

How could anything be easier to work around than a flexible schedule you control? Those writing jobs you see online aimed at stay-at-home parents who hustle the kids to and fro for school and practice fit perfectly in the down times. Yet the 9–6 crowd also usually has kids that they seem to raise fairly well and even allow for some extracurricular activities. How?

When you know that Monday-Friday you will be occupied for a given time, you schedule everything else around it. In rare instances you take time off for a special event or emergency. You have the advantage of relying on the fact that every day until the end of time, you will have the exact same hours of the day you will work. That leaves the rest for you to do whatever you need to or want to with.

Planning evenings with friends or nights out with the significant other become simple tasks that require very little thought. Personally, my friends make fun of me quite often saying “Kagan isn’t alive during the week.” This began when I had a terrible stomach issue that I couldn’t make time to go to the doctor for. It was silly of me, but having to move around tutoring when I had every single second booked from 7 am to 11 pm Monday through Friday, shifting things around became a nightmare.

For those who enjoy their 9–6 schedules, the idea of having the added responsibility of setting all those sessions up and having every day present a new challenge or whisk me off to a new location to tutor can be a nightmare. It certainly is to me on some days, and I enjoy it! The monotony we see can instead be a different kind of security and comfort for those other personality types.

Reward

The ultimate determination of anyone’s career choice is the reward involved. For some, this may be compensation. How much does it pay, and will it cover the lifestyle I want to live. Others may require the balance between work life and home life. This is the group who typically are “content with just earning a salary and working 9–6 their entire adult life.”

One of the highest rated job satisfactions is securely in place with actuaries. These guys earn a pretty darn good living working the 9–6 schedule, and most report this is due to exactly that balance between work, home, and pay.

Still others do what they do because they believe it is right or for the personal rewards involved. I fall in this category as a teacher. There are so many other things I could do with a math/physics degree, yet I choose to teach. Even then, I have already stated that I earn far more and even find more enjoyment tutoring. So why teach? Just for the security?

I grew up poor and dreamed of having a tutor so that I wouldn’t be so bored academically. (Weird right?) Because of that, I teach so that those who can’t afford private tutoring still get to see me. I still get to have an impact on their lives and hopefully alleviate some of the fears they have about mathematics. Further still, I am able to utilize that secure income to offer a few sessions privately for free to help make a difference that I never got to experience as a kid.

Many find there contentment in believing what they do makes a difference, which keeps them where they are happily working the 9–6. That’s not to say the same satisfaction cannot be had from us entrepreneurs who sought a different avenue. Instead, it simply means these others found their calling in a sector that utilizes a different schedule.

Conlcusion

There are dozens more ideas that could lead to an individual working with the philosophy you asked about that may not fit under the broad categories I mentioned. In the end, however, I hope that this has shown that different ideologies, though potentially foreign to us, can hold just as much meaning to those who hold them.

Thanks!

Common Core Rant

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As a private tutor, I am incessantly met with complaints about the current method of educating students in mathematics.  In many cases, when I meet with a student and parent for the first time, the topic of the dreaded Common Core methods come up.  Time after time I hear the same frustrations.

“Why do they make it so much more difficult than when I was in school?”

“What’s wrong with the old way they taught it?”

“If I can’t understand it, then how can my kid?”

“Why do all these steps when you could just do it like this?”

These concerns are very real, and it is never a bad idea to be involved in your child’s education.  Taking an interest in how your son or daughter learn lets them know that you care, that you’re there to help them should they get discouraged, and helps them realize the importance of practicing their academic skills.  However, I take the unpopular position that the Common Core methods are not inherently bad.

What many people do not realize is that math builds on itself.  It is very difficult to comprehend a topic without the foundation beneath it and fully grasping the necessary prerequisite skills.  What many Common Core strategies address is not only how to arrive at a correct solution, but also how best to build up the techniques that will be used later on in math.  Let’s look at an example.

Say we want to multiply 364 by 12.  One of the Common Core methods for this is to use something called partial products.  Instead of brute forcing it with the algorithm that many of us know, we do it in pieces.  One way would be as follows:

364 x 10 = 3640

and then,

364 x 2 = ?

Here again we break into pieces:

300 x 2 = 600

60 x 2 = 120

4 x 2 = 8

All together we have:

600 + 120 + 8 = 728

So our final answer would be 3640 + 728 = 4368.

I know what you’re thinking (because I’ve had it yelled at me before), “That’s so many steps!  Why bother?”  Well, what do you really do when you line up the numbers and follow the algorithm?

   364

x   12

You would multiply 2 by each part on the top, and get 728, then you would go down, put your zero because it’s in the tens place, and then come up with 3640.  Hmmm.  Hopefully it seems a lot more similar now.  It’s the same concept, just the way it has been written is different.

Unfortunately, people are creatures of habit.  I will be the first to tell you that if you know how to do something in math, good for you.  By all means stick with it, and keep practiced!  Where we run into a problem, however, is when a student does not understand how to do the algorithm the way you do.  What then?  Should I simply keep telling them to do it until he or she might finally accept the process.  How many of you knew why to put the zero in the second line when you first learned multi-digit multiplication?  How many of you just thought about it now?

Is it important to be able to simply arrive at a correct answer?  Of course it is!  Wouldn’t it be far more useful later on to have the knowledge of why a process is happening?  You be the judge.

The reason I tutor is so that I don’t have to stick to one method only.  (More on that in a little bit.)  I get the opportunity to find out which method makes more sense to a child rather than only staying stuck, nailed, and riveted to the same techniques regardless of what helps a child learn.  Because of this, I have taught both ways to multiply on numerous occasions.  Here is what I’ve noticed.  When I teach the algorithm to someone who is struggling and it takes hold, they can usually get it and very soon are having no problem.  Then I ask them to multiply by a three-digit number and….they get stuck.  No idea what to do on the third row with very few exceptions.

The kids who happen to like the partial products method more, however, rarely get tripped up when moving into three digits.  Why is this?  It’s simple really.  The students who do the longer steps don’t need to learn a new rule.  Instead they are prepared to extend their knowledge and tackle a larger problem.  With the algorithm, it must be taught to put two zeroes on the third line as you are now in the hundreds place.  Usually at this point, the child sees a pattern and can move into 4 and 5 digit numbers with little trouble.

Does this mean that one way is superior to the other?  Nope.  Whichever way makes more sense is the way to teach it.  The ability is more important than the method for sure.  Once understanding has taken place, then other methods can be taught to help improve speed and efficiency.

But that brings us back to our initial complaint.  Why does the school force everyone to do the first way then?  Now we are asking the correct questions.  There is nothing inherently wrong with the Common Core methods.  In fact, they are better for preparing students for more advanced topics later on, if any comparison needs to be made.  Where we run into trouble is that the school system has made the mistake of assuming that every person needs to perform calculations in the same manner.

Every person learns differently, and the key to education is figuring out the best way to convey a topic to a student.  When the schools only teach one way in order to attempt to reach the majority, there will always be those who are left out.  The problem with the new Common Core system is not necessarily the methods being used to teach, but rather the ideology behind when and how to use those techniques.  So the next time you have trouble with a topic, or you see your child working through a method that you question the usefulness of, try another approach instead of complaining.  I think you’ll be surprised how it takes away the frustration and helps kids grow in leaps and bounds.