If you surveyed the population and asked, “How does someone get wealthy?” What answers do you think you would get? What would the most popular answer be? What would you say?

One of the responses that might be top of mind for a lot of people is, “Well…make lots of money.”

They’re not wrong. Having a substantial income certainly does contribute to making wealth building easier, and can play a huge role in accelerating how fast someone is able to accumulate wealth. But does that rule out middle income earners from realistically being able to make themselves independently wealthy? Is wealth a privilege of the “1%”?

One study that surveyed over 10,000 millionaires across the United States in 2017-2018 showed that one of the most important factors―if not the most important―in determining whether someone would become a self-made millionaire at some point in their lives was whether or not they made regular, consistent savings contributions, and for how long they were able to do that for. While some top earning professions such as engineering, accountancy, and law were at the top of the list, other middle-income careers were a significant presence as well. In fact, teaching was number three! And though medicine ranked high overall, doctors didn’t even make the top five careers in the survey.

How can a regular person, with a regular salary and regular responsibilities, kids, a mortgage, two cars, bills, college tuition, more bills...and all the rest, possibly get themselves into a position where they could consider themselves wealthy? How can our kids? Can they really pursue a career that they’re interested in, or should we be pushing them towards the top-earning professions at all costs?

First of all, as most of us would intuitively guess, very few people get to be wealthy without earning a steady living. There has to be enough to go around to meet basic bill obligations and needs, and there has to be a little extra to save, too. There should be a reserve for emergencies, because those will inevitably come up. This requires having a budget, so that you’re able to track regular expenses in order to save for a crisis and for the future, too.

And while life gets much more complicated than that―income sources get more muddled, and expenses get harder to track―in principle, the first step in wealth building is as simple as that: aim to spend below your income so that you can save, and have a way to make sure you’re doing it.

In a few words that we’ve all probably heard at some point or another from a cranky grey-haired voice: “Live below your means.” “Spend less than you make.” And while the demands of our modern, busy lives seem to make this an impossible, idealistic dream, the data seems to suggest that none of us can become wealthy until―and unless―we do.

Okay, but still? How much below our means can we really expect to live? I mean, we’ve all got serious obligations!

While the first ingredient in the secret wealth-building sauce is knowing to live below your means, the second ingredient is knowing just how little it takes to actually make a marked difference in the wealth and security of your future. Once it’s established that saving must be a priority and that it doesn’t take as much as you might think, the third critical secret is knowing that the absolute fundamental ingredient is saving regularly, and consistently, for a long period of time.

The fourth ingredient―and this is where the magic happens―is to have these savings in a safe, conservative investment so that they can grow over time.

Miss out on any one of these ingredients, and you might as well have forgotten to put the pod in the coffee maker. Yum.

Let’s work this out with some numbers.

Between you and your partner, let’s say you’re able to scrape together a nest egg of about $15,000 to throw into your safe, conservative investment. And let’s assume further that you’re able to contribute $400 per month.

You and your partner are both 30, and you plan to work for another 35 years before retiring together.

Pull up any old financial calculator online, and let’s see how wealthy you are at 65:

Lump sum: $15,000

Monthly contributions: $400

Annual rate of return: 8%

Number of years invested: 35

Total future value: $1,170,908.54

That’s right. Throwing just $400 a month at your $15,000 investment will make you millionaires when you retire.

And what if you’re able to do better than that? What if as you get raises over the next 35 years, you increase your contributions accordingly? What if your initial investment is $20,000? $50,000? What if you find a safe 10% return instead?

Needless to say, it can only go up from there.

And if you can only do less? That’s okay. Let’s try a new scenario. Let’s say you’re 22, and you can only imagine putting $100 a month in if you try really hard.

Lump sum: $0

Monthly contributions: $100

Annual rate of return: 8%

Number of years invested: 43

Total future value: $451,655.35

Still, not too shabby, considering your real cash contributions over that horizon have really only amounted to $51,600.

Wealth May Be PossibleSo what’s the moral of this story? Well, the moral, truly, is that almost anyone with a moderate income can improve their financial situation and financial prospects, making small decisions that make meaningful differences in the future.

It does take a little bit of learning, a little bit of sitting down to figure it out, not to mention a commitment to at least a little bit of budgeting and restraint. But this secret sauce really doesn’t need to be a secret―it should be something we get really, really excited about.

And that’s not to mention, at Mentorhood Math, we believe that math is something relatable, that we interact with daily, and that has a real effect on us as we move through our own little worlds. Wealth building is one of the most tantalizing forms of impactful math―and we don’t mind sharing just how giddy it makes us, so that maybe you can get a little giddy, too.

(And so that you can giddy up, partner, towards your own wealth building journey.)

1. This is not investment advice, but an illustration for the purpose of arguing a certain point. Speak with your professional of choice about what’s right for you.

2. Such as https://www.calculator.net/annuity-calculator.html, for example

3. There are plenty of resources out there, if you’d like to learn more about financial calculators and calculating how much your investments might be worth over time! Hop on to YouTube or speak with a professional of your choice.

4.You’re dying to try this with your own financial situation. I know you are. Please do―and have fun!!

“Honey, let's crunch the numbers,” is a less-than-popular conversation starter in many households. Balancing the chequebook "at the kitchen table" used to be a common trope describing how families manage their household budgets, but today, it’s less than common. Studies show that one half to two thirds of people in the United States and Canada self-declare having a budget, and yet other studies show that the primary factor determining wealth in retirement is as simple as saving consistently over a long period of time. So, if regular maintenance of a budget continues to be a vital part of wealth management and prediction, why is financial literacy so under-discussed?

Budgeting, at its core, isn’t chock-full of groundbreaking arithmetic concepts. It’s addition and subtraction: income minus expenses equals either a surplus or a deficit. That's it! That’s the heart of it. So, is the math really over our heads?

**Why Don’t We Budge on Budgeting?**

Our modern lives are much more complicated than the aforementioned equation might imply. People often have multiple income sources, or double income households, and many people don't have a good metric for tracking expenses. Where did I put that cash? How come my bank account is lower than I budgeted for? Which card was that on? I have so many transactions. How can I possibly categorize them? This is where things get a little more complicated, but these questions are not unsolvable without a little bit of confidence and organization, and the math itself, if isolated, would typically be easy-breezy to an average person.

Perhaps we don’t see universal acceptance of budgeting because our busy modern lives have left us with little time for financial reflection. Couple that with the availability of credit that lets us tap into tomorrow’s savings today, and we might have created the perfect environment where we grow up without seeing the impact of personal financial management on daily life, and we may have little desire to discover it for ourselves when we grow up. Our children, likely, will follow suit. It’s possible, then, that lack of budgeting is partially because budgeting seems unfamiliar, foreign, even enigmatic. Having never been taught how to budget, we feel intimidated, which creates a lack of confidence, which short-changes our motivation to begin.

**The Intimidation Factor**

We see children confronted with unfamiliar, intimidating math every day at Mentorhood. And our philosophy is to take that intimidation factor directly out of the mathematics. Math is not mystical, and it’s not reserved for the most acute minds who can perform mental gymnastics on a dime. Rather, math is an observable reality that we can relate to in our everyday lives, and as such, can be taught from a relatable perspective. And that’s why we believe that math can be mastered at an intuitive level―that when broken down, even the most difficult concepts can be swallowed by the most math adverse individuals.

Budgeting is about rolling up your sleeves and believing that if you sit down, open up the computer, check the credit card statements, and plug some numbers into your spreadsheet or app, you’ll be able to get to the bottom of your financial situation and do something to influence it. If we can empower our children neutralize the intimidation that often surrounds things like math, we could see more willingness to approach mathematical activities, such as budgeting, in daily life. This effect can proliferate itself into a whole host of economic decisions they make as they grow up: how they choose their careers, how they save and plan for the future, how they pay for education and expenses along the way, how they manage credit, and how they build into their lives the freedom to pursue the things that satisfy them.

**The Simple Secret**

Math can be intimidating. But turn that on its head, and a confidence to apply mathematics in daily life can be incredibly empowering. Budgeting is not a tool for being miserably miserly. Budgeting celebrates the resources you have, and puts you in the driver’s seat to decide how you are going to allocate those resources. Budgeting creates a policy of full disclosure between you and yourself, allowing you to fully see how well your financial bloodstream is supplying resources to all the vital parts of your life. Budgeting is about peeling back the curtain―which can be incredibly scary! And that’s why we believe that the first step towards good financial management for the kids that we teach is to take some of that “scary” out of the math.

By providing classroom environments where children are encouraged to explore mathematics from a concrete and visual perspective, where they can build their intuitive understanding and be celebrated as they make strides, we’re paving the way for tomorrow’s adults to approach their lives―and their pocketbooks―with courage, confidence, and good cents.

References

Backman, M. (2016, October 24). Nearly 3 in 5 Americans are making this huge financial mistake. CNN Money. Retrieved October 27, 2021, from https://money.cnn.com/2016/10/24/pf/financial-mistake-budget/index.html.

Debt.com. (2019, April 4). Fewer Americans are budgeting in 2019 -- although they think everyone else should. Cision PR Newswire. Retrieved October 27, 2021, from https://www.prnewswire.com/news-releases/fewer-americans-are-budgeting-in-2019----although-they-think-everyone-else-should-300824384.html.

Financial Consumer Agency of Canada. (2020, May 29). Canadians and their Money: Key Findings from the 2019 Canadian Financial Capability Survey. Canada.ca. Retrieved October 27, 2021, from https://www.canada.ca/en/financial-consumer-agency/programs/research/canadian-financial-capability-survey-2019.html.

Ramsey Solutions. (2021, September 27). The National Study of Millionaires. Ramsey Solutions. Retrieved October 27, 2021, from https://www.ramseysolutions.com/retirement/the-national-study-of-millionaires-research.

]]>Budgeting, at its core, isn’t chock-full of groundbreaking arithmetic concepts. It’s addition and subtraction: income minus expenses equals either a surplus or a deficit. That's it! That’s the heart of it. So, is the math really over our heads?

Perhaps we don’t see universal acceptance of budgeting because our busy modern lives have left us with little time for financial reflection. Couple that with the availability of credit that lets us tap into tomorrow’s savings today, and we might have created the perfect environment where we grow up without seeing the impact of personal financial management on daily life, and we may have little desire to discover it for ourselves when we grow up. Our children, likely, will follow suit. It’s possible, then, that lack of budgeting is partially because budgeting seems unfamiliar, foreign, even enigmatic. Having never been taught how to budget, we feel intimidated, which creates a lack of confidence, which short-changes our motivation to begin.

Budgeting is about rolling up your sleeves and believing that if you sit down, open up the computer, check the credit card statements, and plug some numbers into your spreadsheet or app, you’ll be able to get to the bottom of your financial situation and do something to influence it. If we can empower our children neutralize the intimidation that often surrounds things like math, we could see more willingness to approach mathematical activities, such as budgeting, in daily life. This effect can proliferate itself into a whole host of economic decisions they make as they grow up: how they choose their careers, how they save and plan for the future, how they pay for education and expenses along the way, how they manage credit, and how they build into their lives the freedom to pursue the things that satisfy them.

By providing classroom environments where children are encouraged to explore mathematics from a concrete and visual perspective, where they can build their intuitive understanding and be celebrated as they make strides, we’re paving the way for tomorrow’s adults to approach their lives―and their pocketbooks―with courage, confidence, and good cents.

References

Backman, M. (2016, October 24). Nearly 3 in 5 Americans are making this huge financial mistake. CNN Money. Retrieved October 27, 2021, from https://money.cnn.com/2016/10/24/pf/financial-mistake-budget/index.html.

Debt.com. (2019, April 4). Fewer Americans are budgeting in 2019 -- although they think everyone else should. Cision PR Newswire. Retrieved October 27, 2021, from https://www.prnewswire.com/news-releases/fewer-americans-are-budgeting-in-2019----although-they-think-everyone-else-should-300824384.html.

Financial Consumer Agency of Canada. (2020, May 29). Canadians and their Money: Key Findings from the 2019 Canadian Financial Capability Survey. Canada.ca. Retrieved October 27, 2021, from https://www.canada.ca/en/financial-consumer-agency/programs/research/canadian-financial-capability-survey-2019.html.

Ramsey Solutions. (2021, September 27). The National Study of Millionaires. Ramsey Solutions. Retrieved October 27, 2021, from https://www.ramseysolutions.com/retirement/the-national-study-of-millionaires-research.

You don't have to look too closely to see math at work in everyday life. From calculating transaction change and sale prices, to looking at the percentage of probability on a weather forecast, to setting timers so that your Christmas lights will turn on at a measured level of darkness, math is arguably irremovable from every experience on Earth. Even nature falls into patterns, routines and life cycles, down to the most micro ecological organizations.

But what about the Earth, high in the air? Birds and other flying creatures have long been making use of Mother Nature’s carefully attuned laws of physics to carry themselves from Point A to Point B. It turns out that the airline industry is also a great borrower of such universal mathematical and physical principles, and given the high economic and human stakes associated with flying, aviation is arguably one of the industries for which reliance on mathematics is the most critical.

High-Flying Formulas

It is easy to see how critical it is that a pilot is capable behind the controls. With thousands of pounds of metal and flammable fuel careening through the atmosphere at extremely high velocities, carrying human or economic cargo over invaluable infrastructure, civilizations, and natural environments, the stakes for safe airline operation are extremely high. Airline pilots are rigorously trained in countless formulas, models, and principles of physics. On the other side of airline training, students are equipped to see the world as a series of grids and graphs, and to understand how a whole host of calculable variables interact with each other in three-dimensional space.

Pilots must be proficient in formulaic calculation and must have a keen mind for deviation. They must be able to account for routine and circumstantial factors as well as safety buffers, to calculate fuel requirements and to know the mathematical limits of their resources in case they need to make emergency adjustments to their plans. Pilots have to know how different levels of cargo weight will affect their instruments and handling. Altitude, velocity, and pitch will have significant impacts on how the vehicle operates and where it ultimately goes. It’s the pilot’s responsibility to make sure that from a numerical standpoint, everything is in tip-top shape before taking off or landing.

From Creation to Transportation

Every single component of an airplane is optimized for maximum performance in the air. Decades of research and experience have gone into curating every bolt, every panel, every cavity, and every instrument to deliver the safest flying experience possible. Deviations of fractions can have detrimental consequences, which is why mathematicians and engineers are part of every stage of the development process.

Moreover, maintenance schedules need to be designed and followed meticulously for assurance that the vehicle is operating within its safety margins. These need to be mathematically optimized to calculate the exact amount of variation that can still provide a safe experience. Maintenance operators need to understand how to measure these variables and metrics in order to properly mark an aircraft as safe or unsafe.

And once in the air, safety is not just the responsibility of the cockpit, but it is also critically in the hands of air traffic control. Air traffic control operators manage a series of complex geometric representations of their air spaces. They must have a vivid understanding of flight trajectories, velocities, and geometry, and be able to extrapolate that information to prevent disasters in the air. Pilots and air traffic controllers operate on universal principles to measure and curate safety, and those principles are based on mathematics.

The Fabric of Space

Fixed mathematical principles define and explain how the world works. Math does not change, though our understanding of how to operate within its principles allows us to advance higher than was ever possible before. A constant reliance on math governs our travel in the air, allowing us to catapult forward in our understanding of how humans can move around this planet―and even unlock the potential we are currently exploring for traveling beyond it. Without an insatiable curiosity to explore physics and math when engineering rocket ships and space travel missions, international space travel efforts would simply fall flat.

These principles have helped us optimize all kinds of transportation on the ground, too. Cars and vehicles have gotten safer since we’re better able to mathematically measure risk and adjust accordingly. Roads have been optimized for traffic flow and stoplights have been timed for pedestrian safety. This is math at work, getting us from our everyday Point A to Point B. As we continue to dive into what math has to offer, and how we can creatively apply that to our insatiable desire to explore, perhaps math will one day get us all the way to Point Z, as well.

]]>But what about the Earth, high in the air? Birds and other flying creatures have long been making use of Mother Nature’s carefully attuned laws of physics to carry themselves from Point A to Point B. It turns out that the airline industry is also a great borrower of such universal mathematical and physical principles, and given the high economic and human stakes associated with flying, aviation is arguably one of the industries for which reliance on mathematics is the most critical.

High-Flying Formulas

It is easy to see how critical it is that a pilot is capable behind the controls. With thousands of pounds of metal and flammable fuel careening through the atmosphere at extremely high velocities, carrying human or economic cargo over invaluable infrastructure, civilizations, and natural environments, the stakes for safe airline operation are extremely high. Airline pilots are rigorously trained in countless formulas, models, and principles of physics. On the other side of airline training, students are equipped to see the world as a series of grids and graphs, and to understand how a whole host of calculable variables interact with each other in three-dimensional space.

Pilots must be proficient in formulaic calculation and must have a keen mind for deviation. They must be able to account for routine and circumstantial factors as well as safety buffers, to calculate fuel requirements and to know the mathematical limits of their resources in case they need to make emergency adjustments to their plans. Pilots have to know how different levels of cargo weight will affect their instruments and handling. Altitude, velocity, and pitch will have significant impacts on how the vehicle operates and where it ultimately goes. It’s the pilot’s responsibility to make sure that from a numerical standpoint, everything is in tip-top shape before taking off or landing.

From Creation to Transportation

Every single component of an airplane is optimized for maximum performance in the air. Decades of research and experience have gone into curating every bolt, every panel, every cavity, and every instrument to deliver the safest flying experience possible. Deviations of fractions can have detrimental consequences, which is why mathematicians and engineers are part of every stage of the development process.

Moreover, maintenance schedules need to be designed and followed meticulously for assurance that the vehicle is operating within its safety margins. These need to be mathematically optimized to calculate the exact amount of variation that can still provide a safe experience. Maintenance operators need to understand how to measure these variables and metrics in order to properly mark an aircraft as safe or unsafe.

And once in the air, safety is not just the responsibility of the cockpit, but it is also critically in the hands of air traffic control. Air traffic control operators manage a series of complex geometric representations of their air spaces. They must have a vivid understanding of flight trajectories, velocities, and geometry, and be able to extrapolate that information to prevent disasters in the air. Pilots and air traffic controllers operate on universal principles to measure and curate safety, and those principles are based on mathematics.

The Fabric of Space

Fixed mathematical principles define and explain how the world works. Math does not change, though our understanding of how to operate within its principles allows us to advance higher than was ever possible before. A constant reliance on math governs our travel in the air, allowing us to catapult forward in our understanding of how humans can move around this planet―and even unlock the potential we are currently exploring for traveling beyond it. Without an insatiable curiosity to explore physics and math when engineering rocket ships and space travel missions, international space travel efforts would simply fall flat.

These principles have helped us optimize all kinds of transportation on the ground, too. Cars and vehicles have gotten safer since we’re better able to mathematically measure risk and adjust accordingly. Roads have been optimized for traffic flow and stoplights have been timed for pedestrian safety. This is math at work, getting us from our everyday Point A to Point B. As we continue to dive into what math has to offer, and how we can creatively apply that to our insatiable desire to explore, perhaps math will one day get us all the way to Point Z, as well.

It’s a common complaint from math students all over the world, learning a new concept or practicing a particularly tricky one: “But when am I going to use this?”

While every student may not use every facet and formula from their math education on a daily basis when they reach the working world, we emphasize at Mentorhood that teaching math is about far more than simply teaching calculable numerical solutions.

Math and intuition are self-reinforcing: teaching math intuitively empowers students to smoothly advance to more complicated math topics―and the more mathematically a student can fluently think, the more intuition, critical thinking, pattern recognition, and analysis skills become second nature.

It’s those soft skills, paired with a mathematically logical framework for thinking, that fuel some of the highest paying careers in today’s modern economies. And globally, there’s no industry with a greater association to higher pay than the medical industry.

Math in Medicine?

From dentistry to surgery to anesthesiology, there is no doubt that the field of medicine boasts of highly skilled, highly specialized, and highly paid professionals. And up to a certain degree, the specialists of today’s medical sector share a similar educational background: a rigorous post-graduate medical degree, undergraduate studies that equip them to pass the competitive application process to medical school, and primary and secondary studies at a public or private institution, when they were just regular kids in regular classes.

While science is the primary academic thrust of medical training, math is inarguably linked to that science in a critical way. Many math and science studies are inseparable at the post-secondary level and are often packaged together on admission requirements. But why are they so connected when it comes to medical science? Don’t medical professionals need biology a lot more than binomials?

The Mathematical Foundations of Medical Science

The average emergency or family physician might draw on their years of studying, recognizing, and diagnosing biological anomalies a lot more than they draw on what they remember from high school calculus. But no branch of medicine can be separated from the math that helped it come to be.

Anesthesiology is the study of how anesthetics affect the human body. Working with something like anesthetics can have grave consequences if it is not administered properly. Every patient brings a unique set of variables to the operating table (pardon the bun), from basic metrics and vitals such as age, heart rate, oxygen levels, blood counts, and the like, to medical history, environmental factors, family medical risks, and countless more. The decision to administer anesthetics and how much must be fine tuned for each individual patient, and anesthesiologists must be able to predict and adjust for the resulting outcomes.

Continuous improvement of the study of anesthesiology cannot be done without complex empirical research and statistical analysis, measuring a plethora of variables that may or may not turn out to be relevant to the final conclusions. Moreover, practicing professionals must be critically aware deviations from the norm and will build up their own banks of pattern recognition experience over time.

In fact, any empirical justification of a medical intervention must be founded in reliable analytical studies of complex statistics before it can be considered both safe and recommended. Observable results must not only be non-harmful but must also be statistically significant. This cannot be understood without advanced knowledge in how the mathematics of statistics works.

Epidemiology is the study of viral spread in human populations, and its role has become increasingly more visible as the world faced the COVID-19 pandemic. Decision-makers continue need accurate data on case spread, symptom changes, mutations, effectiveness of policy measures, vaccine risk factors, treatment efficacy, and more in order to make informed policy decisions, and this is fundamentally rooted in statistics.

But statistics is just the start. With accurate statistics, medical scientists can develop formulas, charts, and data tables that enable radiologists to advise hospitals on radiation and magnetization levels for imaging technology. Oncologists can make decisions about how much chemotherapy to administer to a patient. Cardiologists can measure the variables in a proposed heart surgery and have a framework for maximizing the probability of success.

An Inseparable Pairing

Medical science is inseparably dependent on mathematics. Whether its the analysis of a revolutionary new technology, or the determination of correct doses of paediatric medicines, we would be far more behind in the medical capabilities of the modern world without the contributions that mathematics has made to the medical world. If you’ve had a major surgery or have seen a loved one recover from a serious illness thanks to the administering of a life-saving treatment, you’ve witnessed math-fuelled medicine at a personal level. In many ways, all of us, either directly or indirectly, owe our lives to the influences math has had on our advancements in medical science.

Future Career Math Career

We’ve spent a lot of time at Mentorhood Math creating a curriculum that teaches math through concrete, relatable methods, because we believe that’s the best strategy to building mathematical intuition. When it comes to building a solid foundation of understanding that gives our learners the ability and the confidence to advance to higher topics, we believe that teaching slowly, systematically, and intuitively is far superior than teaching through repetition, rote training, or spoon feeding.

Spoon-feeding and rote training give students mechanical answers to math problems, and repetition reinforces its memorization. Students have the option to copy and repeat the solutions without really understanding what they are doing, or without being able to extrapolate the principles to slightly different situations.

At Mentorhood, we want students to understand the problem, know how to arrive at the solution, and proceed to calculate it.

If repetition can take the thinking out of the equation, should it be done away with all together? Is it destroying our children’s ability to think through math for themselves?

**Building Mechanical Understanding**

As stated above, repetition reinforces the ability to repeat mechanical answers without spending too much time thinking about it. Repetition ingrains mathematical processes into a student’s mind and body so that they can repeat the mechanics with almost no hesitation.

This can be highly advantageous―so long as you don’t skip the thinking from the start.

The Path to Mastery

Mentorhood believes that understanding is the first step on the path to mastery, but that memorization falls on the path too. We believe that repetition should be something students work towards, not work from. We don’t train through memorization; we reinforce through it.

Our three-step approach to teaching mastery in a topic begins understanding and builds up in skillfulness:

Building their skillfulness from understanding to memorization not only makes them more efficient calculators, but gives them confidence that they have mastered the topic. They understand what they are doing so well, and how to apply it to different situations, that they don’t need to think about it anymore, and can focus on efficiency instead. They know that if required, they could pull out the knowledge underneath their memorized solution at the drop of a hat.

**It’s All About the Numbers**

Math really is a numbers game. It’s about speaking numbers, breathing numbers, and drawing inferences from how numbers operate and interact with each other in the real world. Math is the language of numbers, and like learning any new language, sometimes you have to memorize a few new words.

We believe in first helping students understand that mathematical questions come from tangible problems that they can relate to in their lives. We seek to help learners develop intuitive visualizations so that they can see how numbers relate to one another. And we believe that once understanding is achieved, the next step on the path to true mastery is expediency.

The more expedient students become at arriving at solutions that they have calculated over and over (rather than answers that have been fed to them), the more confident and quick they will be in integrating those calculations into more complex topics. They will be quicker to recognize patterns and relationships because their memory banks will be full of similar problem and solution sets that they have seen before. This can make them even more capable of drawing inferences and conclusions based on the numbers they see.

It Starts With Understanding

That’s the difference between our approach and the traditional methods of rote training. Memorizing through rote training fails to link these numbers into relationship with one another because questions-and-answers are memorized individually, and are stored in little memory banks as isolated instances.

Memorizing based on understanding allows students to draw on a well of related information that bubbles up into memorized answers. It allows students to tap into an interconnected network of mathematical relationships underneath the surface of what they can repeat without hesitation.

So, is there room for memorization at an institution that stresses learning through understanding and building intuition? Absolutely. Memorization is just one more step towards building a more thorough and robust mastery of mathematics. And with enough time and the right understanding-based approach, memorized math can feel just as reliable and comfortable as intuition, too.

#SingaporeMath #MathMastery #Singaporemathematics #barmodels #visualization #Mathclasses #Mathtutor

]]>Spoon-feeding and rote training give students mechanical answers to math problems, and repetition reinforces its memorization. Students have the option to copy and repeat the solutions without really understanding what they are doing, or without being able to extrapolate the principles to slightly different situations.

At Mentorhood, we want students to understand the problem, know how to arrive at the solution, and proceed to calculate it.

If repetition can take the thinking out of the equation, should it be done away with all together? Is it destroying our children’s ability to think through math for themselves?

As stated above, repetition reinforces the ability to repeat mechanical answers without spending too much time thinking about it. Repetition ingrains mathematical processes into a student’s mind and body so that they can repeat the mechanics with almost no hesitation.

This can be highly advantageous―so long as you don’t skip the thinking from the start.

The Path to Mastery

Mentorhood believes that understanding is the first step on the path to mastery, but that memorization falls on the path too. We believe that repetition should be something students work towards, not work from. We don’t train through memorization; we reinforce through it.

Our three-step approach to teaching mastery in a topic begins understanding and builds up in skillfulness:

- Teach the students to know how to solve a question, using our CPA approach, working from concrete representations all the way to abstract numbers. This will build the students’ understanding of the problem and the solution.
- Help the students practice remembering how to solve a question, especially with slightly modified scenarios, to strengthen the accuracy of their approach to the solution.
- Train the students to memorize the solution to that type of problem, or to a handful of common problems, improving their speed.

Building their skillfulness from understanding to memorization not only makes them more efficient calculators, but gives them confidence that they have mastered the topic. They understand what they are doing so well, and how to apply it to different situations, that they don’t need to think about it anymore, and can focus on efficiency instead. They know that if required, they could pull out the knowledge underneath their memorized solution at the drop of a hat.

Math really is a numbers game. It’s about speaking numbers, breathing numbers, and drawing inferences from how numbers operate and interact with each other in the real world. Math is the language of numbers, and like learning any new language, sometimes you have to memorize a few new words.

We believe in first helping students understand that mathematical questions come from tangible problems that they can relate to in their lives. We seek to help learners develop intuitive visualizations so that they can see how numbers relate to one another. And we believe that once understanding is achieved, the next step on the path to true mastery is expediency.

The more expedient students become at arriving at solutions that they have calculated over and over (rather than answers that have been fed to them), the more confident and quick they will be in integrating those calculations into more complex topics. They will be quicker to recognize patterns and relationships because their memory banks will be full of similar problem and solution sets that they have seen before. This can make them even more capable of drawing inferences and conclusions based on the numbers they see.

It Starts With Understanding

That’s the difference between our approach and the traditional methods of rote training. Memorizing through rote training fails to link these numbers into relationship with one another because questions-and-answers are memorized individually, and are stored in little memory banks as isolated instances.

Memorizing based on understanding allows students to draw on a well of related information that bubbles up into memorized answers. It allows students to tap into an interconnected network of mathematical relationships underneath the surface of what they can repeat without hesitation.

So, is there room for memorization at an institution that stresses learning through understanding and building intuition? Absolutely. Memorization is just one more step towards building a more thorough and robust mastery of mathematics. And with enough time and the right understanding-based approach, memorized math can feel just as reliable and comfortable as intuition, too.

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