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!
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.
There’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.
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.
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.
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.
Ask for help!
Seriously, find someone you trust and ask them to help you while you are improving. This serves two important purposes.
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.
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.
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!
As I have been getting quite a kick out of answering these questions I find online, I would like to attempt to shed some light on this area. This answer, like so many others pondering a monetary value assigned to a skill, is largely dependent on a number of factors:
Your Tutoring Medium
Your Subject Area
Let’s look at each in just a little detail so as not to make a monster wall of text but still provide some meat to dig into. (I personally tutor math, so the example numbers I use will be based on that information.)
As with any job, the more capable you are, the more people are willing to pay you. As a general rule of thumb, high school students charge $15–20 per hour, college students charge up to $30, individuals with a bachelor’s degree move up to $40, and master’s degrees go to $50+ per session.
Typically, this would vary slightly due to geographic location. Large, more affluent cities will be willing to pay higher rates on average than smaller towns. Conversely, areas with less tutors in your specialty may let you set your own rates. Buuuut, the online world doesn’t care about any of that.
In my mid-sized city with one of the lowest costs of living in the United States, families couldn’t care less that some New York tutors charge up to $150/hr because they are paying $40/hr for excellent teachers. My advice, figure out what your specialty averages overall, and charge that.
Your Tutoring Medium
This could honestly be the largest deciding factor in this list. What I mean by medium is how you choose to go about offering your services. Should you choose a tutoring service such as Wyzant to simply list yourself as an in-person tutor, the values would be very similar to what I stated above.
Other sites such as tutor .com pay out somewhere in the $10-$15 range as they take their cut and have to make money as a business. The most profitable, however, are those who have their own websites and promote themselves there. Taking into account the other factors on this list, you could earn quite a good living.
Taking things a step further, you could also offer lessons coaching other tutors or hopefuls dreaming of making a fortune charging upwards of $500 for a specific online course package where you meet with clients.
Your Subject Area
Again, I personally make my supplemental income through tutoring math. The numbers I have been quoting through personal experience. Few academic subjects other than physics or specialty courses will earn you more. That said, there is oh so much more you could do other than simple academic tutoring.
I mentioned above that some internet gurus offer training to emulate their success. Perhaps you’ve heard of copywriting and it’s potential to earn you tens of thousands of dollars for a few hours of work. It isn’t a scam. It is completely possible, assuming of course you are very very well known with outstanding results. But those who are well known are happy to train you for your shot…for a high price.
Add to this skills such as playing a musical instrument or sports coaching one-on-one and you can see just how diversified tutoring can be.
Just how good are you? What can you offer that no one else can? You should be readily able to answer these questions in order to land clients. Perhaps you are just as good as the next mathematician but offer quick wit an humor. That can be your catch for students. Maybe you are an excellent storyteller or have a knack for empathizing to help alleviate stress before tests.
Whatever makes you you is your highest selling point because there isn’t anyone else that can do it the same. Granted, you do need to be skilled at your specialty in order to teach others. Figuring out the demand for your skill as well as your specific ability to teach it will help you determine what you are worth usually through experimenting with different prices.
No answer will be a one-size-fits-all here which is hopefully apparent just with the four extremely broad and over-simplified factors that I mentioned here. In the end, it is up to you to set your prices and come to a justifiable amount for your own services.
What I aim to provide through blogging about this topic is a guide to getting started on your own. Even though every case is unique, researching the successes others have seen can help you to discover your own path to achieving similar goals.
The answer is of course that it really depends. I am sure that isn’t the response you were looking for, however, so I will do my best to toss in my two cents.
First I am going to assume that you mean tutoring privately as yourself and not through a business such as Mathnasium or Sylvan, both of which I have been employed by and even run at some points. At either you can earn anywhere from $9/hr to $20/hr for private lessons. The advantage to such employment is guaranteed income at 5 to 20 hours per week with the possibility of more as you devote more time to them and rise in ranks.
The next factor to consider is what you are charging. This will rely on both your qualifications and location. I live in a mid-sized city where math tutors charge from $15/hr as high school students to $50/hr as teachers with masters degree or higher. I personally charge $20 to $30 for each hour.
Finally, you must take into account the time you are willing to invest in tutoring. As a teacher, much of my day is naturally devoted to my job in addition to planning lessons and grading. Thus, I typically only have from four in the afternoon until whenever I feel like is a good time to stop. A word of caution here, however. It is very easy to get burned out working late into the evening and pulling consistent 13 or 14 hour days, so if this is a part-time endeavor on the side, mind your health.
On average, I once read somewhere that tutors can make an extra $500 a month as a simple side gig. Personally, I average around $2000 tutoring with some months as low as $600 and others as high as $2800. (My all time record was a month where I brought in almost $7000.) I have been told that I am a more rare case, to be fair.
If your purpose in asking this is to begin supplementing your own income through tutoring, I have a few suggestions.
Start Now — I managed to make a name for myself in college by having my name on their tutor list to be provided to local parents who inquired about help for their children. The ultimate key to building up a steady stream of students is through recommendations made over time. I know everyone hates to hear that nothing is a “get rich quick scheme,” but I can attest that anything worth doing takes time. As you work with more and more students, you will slowly gain a following.
Get a Facebook Page — This one is actually unique from what many professionals would suggest purely because I mean to have the page as your primary source of contact. I purchased a website and maintained it for two years with zero response even from the fairly decent number of pupils I had already. My Facebook page, however, continues to bring new customers. Perhaps others have had different experiences, but this is what worked for me. (And it is completely free! I wouldn’t even recommend running their ads!)
Make Every Session Your Best — Ultimately, your best qualification and source of new clients will be word of mouth. This is especially true for any city with a population of less than 100,000. Be your own unique self. Personally, I live by the philosophy that math terrifies people, so I make them laugh and boost their confidence. I promise that if you can get a student to laugh even once, their mindset will change, and their parents will notice. Associating any academic venue with happiness instead of pain for a family that has been having struggles is sure to have them talking about you to their friends.
Figure Out Where to Advertise — Alas, even though this is surprisingly the least important part of the puzzle, it is just as necessary. Where else are you going to find your first student to start making your recommendations? I have found success in Craigslist, Facebook (as mentioned above), college campuses, and math departments. Anywhere that will let you post a flyer will help get your name out. Talk to others in your area to see the most visited spots both online as well as in physical locations. The most useful areas are those where you would find your prospective clientele. You’d be surprised how helpful people can be with a simple conversation about what you are wanting to do.
These are only four of dozens of tips floating around in my head as well as making rounds on the web, but they are broad enough to help get you started. Everyone’s experience is unique, so as you begin to get a feel for how you would like to work you will undoubtedly find your own successful route. What helped me was my experience at Mathnasium and Sylvan honing my ability to break topics down all the way from pre-K through Calculus. This lead to building relationships with parents who sought me out after a center closed and they still desired math help.
Some of those parents recommended me to a private school where I found my dream job and continued to make more contacts. And the success snowballs from there as long as you remain honest and love what you do. That is where the time part comes into the equation.
At the end of the day, the best advice is to begin tutoring because you want to make a difference in students’ lives. This passion will drive you to become better which will draw the attention of the clients you need. I wish you the best and hope that I didn’t drone on too long as well as managed to answer your question adequately. Good luck!
Well, does it? As I said in my last blog Why Buy a Book, I already know that I am an unknown author without a huge following trying to get my first novel noticed in a crowded market where anyone can publish anything. Sure there are success stories out there where a “nobody” made a name for his or her self and quit their day job to write full-time, but most of us realize that this is the exception rather than the norm…So then why would I continue to write despite this unfortunate understanding?
To answer both questions simultaneously, it is because I believe that writing does matter! There, blog finished.
You’re still here? Ah, you’re curious as to why I nurture this belief. Well, I suppose since you did bother to scroll down and check if this thought was fully founded rather than just hastily thrown up that I do owe you a bit more. As always, my primary purpose in writing this is to encourage others to continue the fight and persevere through any creeping negative thoughts that attempt to prevent them from realizing their potential.
I know I am not alone in suffering these thoughts and discouraging questions, so I wish to remind us all, myself included, exactly why what we do is so important in shaping the world. Furthermore, as I am a selfish reader incessantly searching for the next series to devour and obsess over, I hope that by writing this that even if I continue to write merely as a hobby, one of you will stay true to your passion and finish that masterpiece so that it can be my next world to dive into.
So why do I believe writing matters? Of course, I hope that each one of you has a thousand different answers personalized to your own experiences where you have seen the difference the written word can make in someone’s life. I will attempt to narrow these down in order to generalize my own reasons for carrying on in terms of the past, the present, and the future.
Where We’ve Come From
In ancient times, knowledge was passed down from one generation to the next through the telling of stories and later on through lectures where a massive audience would gather around to witness another’s insight. Eventually this evolved further still to translate to written texts in terms of pictographs, carved tablets, and eventually ink. The transition from spoken to recorded allowed for a greater preservation of the discoveries made by great minds as well as accurate recollection of important historical events.
Initially, only important people were allowed to learn the skill of reading and writing as it was understood that such skills brought power that elites wanted kept to themselves. The reasoning behind this was that allowing commoners to communicate with one another or to study and gain knowledge meant the possibility of being overthrown or undermined in the very least. How could something as simple as written words which we take for granted every day pose such a threat to royalty?
People, in my opinion, are biologically inclined to connect with one another for survival. (You can read one of the many reasons why I’ve come to this conclusion based purely on how our brains are wired here.) Keeping others from effectively communicating eliminates their ability to express their grievances to one another and come to the conclusion that they are not alone in their distaste for being taken advantage of. Without the subtle nuances of higher-level learning that writing and reading foster, under-educated people could not secretly plot or discuss among themselves.
As time passed and these skills became more and more necessary for daily living throughout the social classes, education increased allowing for a greater exchange of information. Though we certainly do not live in a utopia free of problems or social disparity, we are closer than we have ever been due to the free exchange of information posted online. As always, I will qualify this with the fact that I understand the dangers of anyone being able to post their ideas online without proof which can lead to entire groups of people jumping to conclusions before cross-referencing, but such misunderstandings have prevailed throughout history regardless of the medium
If royal elites could see the importance of writing to influence or control others, shouldn’t we still value the abilities we learn at such a young age and later come to accept merely as basic strengths most people in developed nations possess? Clearly, the past has held this skill in high regard, but let’s move on.
Where We Are
These days, we have books, newspapers, internet articles, and newscasts constantly influencing us whether or not we want to heed their words. This rapid transit of ideas has allowed for monumental increases in scientific areas such as medicine, architecture, and technology as well as more artistic avenues such as literature, movies, and philosophy. Without the necessity of delivering snail mail as the primary means of conveying information from one mind to the next in solving a puzzle, we are at the peak of information exchange.
Writing provides a way for common folks such as myself to be heard in their encouragements, complaints, and victories. It allows for anyone to dream of accomplishing more and, perhaps most importantly, to make friends with similar passions. I keep saying again and again just as in my first post Aspiring to Aspiring Writer, the opportunity to love others and help one another along in the journey of life should be a key component of everyone’s purpose. Now we get to digitally “meet” others from geographic and even socioeconomic areas we have never experienced.
Simply being able to enter a chat requires the use of written words or even online translation software, because the world is just that cool now. All of these friendships, business partnerships, and even romances are possible through others’ belief that writing today does still matter in terms of connections and paving a way for the future, which transitions nicely to my final category.
Where We Are Going
As a teacher, hopefully it is understandable that I couldn’t go forever without speaking to this highly influential area of my life. Tomorrow is what I spend every day working on, tirelessly working to prepare young minds to tackle issues that I can’t even imagine they may someday face. Though I am a mathematician/physicist, I try to maintain that communication is the most important skill that my pupils can pick up during their time in school
In a world where the means of communication are forever evolving even to the point where texting is beginning to die off in favor of video chats and messages, it has never been more important to emphasize the power words hold in written form. Thus, I implore anyone reading this who feels called to write as a hobby, profession, or any other desire to hone your craft and demonstrate to the next generation how ideas immortalized in digital or printed form will forever drive our world forward.
Furthermore, for those who disagree that the pros of being able to freely express ourselves via our writing do not outweigh the cons, shouldn’t that spur you on even more fervently to produce the facts you see so that impressionable minds have multiple sources to digest before coming to a conclusion that could mold the rest of their lives? If anyone fears that the “crap people can put on the internet” is dangerous for others who are still being exposed to a new topic, and I agree that it very well can be, I charge you with the task of ensuring our future politicians, scientists, philosophers, and yes, even writers have a varied knowledge pool to dive into when discovering their passions.
It Matters to Me
And I believe it matters to you. I believe that even if my words only reach the few people I am honored to read my work regularly, they will see my passion so that it spreads and reaches others through their filter. I love to write to organize my thoughts, express my love to those closest to me, and hopefully entertain those crazy enough to take the ride through my series Across The Breach with me.
And I like to sit in bookstores while I’m writing, so typical selfish Kagan, haha.
As a private math tutor, I am called upon for a number of reasons. Some parents contact me out of concern that their child is falling behind. Others reach out to me in the hopes that I can help get their kid to the top of their class or achieve the scores they need to get accepted to the prestigious school of their choice. Lately, however, I have been approached to simply help students with their homework. It is not necessarily that the student is behind or looking to expand their knowledge and jump ahead. Instead, the parents see the methods being used and come to me in frustration to answer the questions that their children have.
While it is true that this is good for business, and it is nice to make a living doing what I love helping people better understand math…I would feel too guilty charging for something that I can remedy in less than an hour. That is why I am hoping to simplify some of the “crazy stuff” that kids are bringing home these days so that parents aren’t left scratching their heads wondering what is is that a teacher is looking for.
First of all, let’s start with the basics. If you have a kid who’s in Kindergarten through Second Grade, they are most likely working on adding and subtracting numbers to begin with. Now many reading this might scoff and say, “Addition? Subtraction? Why can’t they figure this stuff out?” Well, let me show you a few things.
Let’s look at an example of a fairly basic problem:
I would hope that this looks simple to the majority of us. Now consider this, how do you know that 4 added to 8 results in 12. In the beginning we were given pictures; one group of 8 somethings then a group of 4 somethings and told to count them all up. Of course, we would count 12 somethings in total. The problem with this is that counting is slow and we would like to eventually move into memorizing this as a basic addition fact. How then can we help a young student to internalize this idea that 8 plus 4 equals 12?
This is where some of the Common Core strategies come into play. Now, let me just preface this with a disclaimer. I like the methods for helping students to learn concepts that are having trouble with more “old-school” techniques, but these are not useful for everyone. I believe I made my stance clear on the matter in my other post here (Common Core Rant). We good? Ok, back to delving into some of these things.
If a child is having trouble quickly remembering that 8 and 4 make 12, then we have to come up with another way to come up with the answer that is more efficient than drawing objects and counting. The first step would be to recognize which number is larger. In this case, 8 is bigger than 4, so we would begin with 8 and count up by 4: 9, 10, 11, 12. So 12 is our answer. This is still slow, but it is slightly quicker than counting up to 12 with two groups. The reason this step is important is for problems like this:
Though this is the same problem, initially, students don’t realize this. Showing young children that a group of 4 and a group of 8 is the same thing as a group of 8 and a group of 4 is another building block that helps with fact families and more difficult problems later on. For a student to realize that he or she can start with the larger number will also save time as counting up 8 from 4 will take longer than counting up 4 from 8. This idea of addition being Commutative is a concept that we get to show students even though they may already have memorized 8+4=12, which is one reason that a teacher may spend extra time on some of these facts.
After establishing that we can count on from the bigger number, we can extend this further. Knowing something called Ten Facts, we can help students to break problems down into easier pieces. For instance, we know:
Since we are adding 4, we need to add two more to get to our answer 12. Ok, there is a lot going on here. Our number system is based on tens, so being able to recognize how to get to ten, and later to multiples of ten, can help improve students’ efficiency later on in life. So recognizing all the tens facts,
will help with knowing how to make it to ten for the first step in addition problems involving answers over ten. Again, notice that both 8+2 and 2+8 are listed as facts. This is a chance to reinforce the idea that addition can be performed in any order so that with extra practice, students are more likely to internalize the concept. The second important skill necessary here is to know that 2+2=4. With the tens facts, a child can see how to get from the larger number up to ten, but that won’t do any good if he or she doesn’t know how much left to add.
Being able to decompose numbers into parts or groups is not only a way for children to perform the rest of this problem and others like it, it also helps to lead into subtraction later on. Knowing doubles like 2+2=4, or being able to see facts like 1+3, 2+2, and 0+4 all equal 4 will help a student to figure out how much more must be added after figuring out the distance from 8 to ten. All these methods are explained in school, and the student decides which is easiest or which he or she remembers the quickest to know that 2 more must still be added.
This brings us to the final step of adding 2 to 10. Being able to add single-digit numbers to ten is useful because it is one of the more quickly learned skills (which builds confidence in students who are struggling) and can carry forward to adding to multiples of ten like 20, 30, 40, and so on. One of my favorite ways to show students how to add numbers is to say them close together. For example with 3 and ten, if you say them quickly, you get “threeten,” which sounds a lot like thirteen. The same with “fourten” and others. With 11 and 12, the sound doesn’t play out so well, but after practicing the others, the student usually pics up the pattern (and finding a pattern is the best we can hope for our students as a teacher). Whatever the path, the student will find a way to finish up to see that 10 +2 =12. So let’s review:
hmmm… I know:
so if I added 2 to 8 already, I need to add 2 more:
Phew, that’s a lot of steps, but look at all the good things we learned to get there. In the end, memorization is the goal. However, simply memorizing isn’t always the best. As I stated in Common Core Rant, students who have a deeper understanding of more basic concepts are better prepared to extend that knowledge when working on more difficult problems later on. Yes, this takes more work, but it could be the only way that your child is capable of getting to the answer if he or she just isn’t remembering the fact initially.
Ultimately, if you prefer that your child learns in a different way, that’s what tutors such as myself are around for, to supplement the education that they are receiving. However, my goal here is to show the method to the madness and help explain away some of the confusion that many parents have come to me with. Hopefully, next time your young student comes home with this “crazy new math,” you’ll have an idea of what is going on and what the teacher is trying to convey through these longer processes. Again, not every student learns the same way, which is my problem with Common Core, since teachers are required to teach the entire class the same methods even though it may not be the most effective. The techniques are useful, however, and we should appreciate the thought that has gone into helping all children better understand math.
I will continue on with some of the subtraction techniques in my next post, and from there I will go on to cover multiplication and division. Thanks for reading, and be sure to like or subscribe as this will most likely become a series I am writing!
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
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?
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.