The Brick Test is a method used to test students’ understanding of multiple approaches to problems. It encourages creativity and problem-solving skills. Teaching for creativity involves task design and collaboration, which are essential components of teaching. There are five ways to increase mathematical creativity: making problems open-ended, having students create their own problems, building divergent thinking skills, overcoming fixation, and encouraging analytical thinking.
To foster creativity, students should find multiple ways to solve problems and interpret their solutions. They should also avoid worrying about the impossible, as most problems are possible. To train their mind, they can engage in creativity exercises like teaching others what they learn, daydreaming, and utilizing both sides of their mind.
Creativity separates us from machines or robots, and to generate new ways to define and solve problems, students should read and proof extensively. They should also engage in competitive math books and engage in creative activities.
To improve their problem-solving skills, students should embrace curiosity and develop problem-solving skills through puzzles and brain games. It is important to remember that there are no wrong answers and that creativity is not a test, but rather a way to learn and develop skills and attitudes useful in mathematics.
📹 Are you creative or analytical? Find out in 5 seconds
The left and right brained idea is controversial. The research described in the video is here: Ida, Y.. The manner of hand …
Is dyscalculia a form of ADHD?
Dyscalculia is a learning disorder that affects an individual’s ability to understand number-based information and math. People with dyscalculia struggle with math-related concepts due to their brains’ inability to process them. Symptoms usually appear in childhood, but many adults may have dyscalculia without knowing it. They may also experience mental health issues like anxiety and depression when they have to do math.
A form of dyscalculia, acquired dyscalculia, can occur later in life and is often caused by other reasons like a medical condition. Both conditions are common, but most people with dyscalculia do not have the other.
How can I improve my math creativity?
A study by the US Department of Education found that 81 of 4th graders had a positive attitude towards mathematics, but this number dropped significantly to 35 for 8th graders. This decline in interest and performance can be reversed by recognizing and valuing mathematical creativity. Research has shown that creativity can help students acquire content knowledge. To encourage creativity in mathematics, researchers have found ways to make it more creative, fun, and engaging.
Make problems open-ended. Offering students open-ended problems with multiple solutions allows them to experience the first stages of mathematical creativity. Traditional mathematical problems can be converted into open-ended problems relatively easily. For example, students can solve the volume of an aquarium by finding its volume.
Encourage logical thinking. Analogical thinking can help students understand the world around them better and make better decisions. By incorporating these strategies, students can develop a deeper understanding of the subject and improve their performance in the future.
Can you develop a mathematical mind?
Practical Life and Sensorial curriculums indirectly prepare children’s mathematical minds. Practical Life helps children order their minds through sequential and logical activities, while Sensorial materials help bring order to sense impressions. Through exploration and manipulation of concrete materials, children develop observation, judgment, and reason skills. Mathematical concepts are unconsciously absorbed, as children learn to recognize similarities, differences, and gradations in size, width, weight, and length.
From concrete to abstract, understanding number-quantity correspondence is an abstraction that comes at a later stage of development, with Montessori math materials helping children develop this link.
How do you get a math mindset?
The article provides five simple ways to develop a mathematical growth mindset, emphasizing the belief that intelligence can be developed through effort and hard work. It emphasizes the importance of learning over getting the “right” answer, not giving up on trying new strategies, and reflecting on and learning from mistakes. The growth mindset is particularly relevant in education, where key characteristics include believing in the potential of intelligence, focusing on learning over getting the “right” answer, and not giving up.
How can I train my brain to think mathematically?
This blog post offers simple tips and tricks for improving math skills. It discusses various strategies to tackle math problems, such as brushing up on basic problems, using mental math games, practicing math in everyday scenarios, solving puzzles and riddles, breaking down complex problems into smaller ones, joining a study group, and using practice tests. The post also provides parenting tips to support children’s journey in learning math faster.
Despite the belief that practicing math is the only way to become better, there are many effective methods to improve math skills and support children in learning math faster through day-to-day practice. By following these tips and tricks, individuals can overcome the challenges of struggling with math problems and improve their overall math skills.
How to improve creativity in math?
The author shares their experience with math, describing it as a subject that they found pointless and tedious. They argue that many students, particularly in the K-12 grades, feel that math is pointless and boring, which can hinder their engagement and miss crucial knowledge. To infuse curiosity and creativity into math lessons, teachers should prioritize play, incorporate creative problem-solving through open-ended questions, and cultivate collaboration.
The author suggests that if we taught art the same way we teach math, we would use color-by-number worksheets, which can drain students’ imagination. Instead, teachers should focus on fostering curiosity and creativity in students, allowing them to explore their own interests and develop their own solutions. This approach will help students develop a deeper understanding of the subject and help them develop a deeper appreciation for the subject. By incorporating these strategies, teachers can help students develop a deeper understanding of math and its potential for growth and discovery.
How can I develop mathematical thinking?
Mathematical thinking is a crucial skill that involves using math to solve real-world problems. It involves thinking outside the box and offers infinite possibilities to pose new questions. Mathematics is a way to see the world around us and propose elegant solutions. It is essential to map all situations and problems in everyday life to relevant mathematical models to solve them. For example, during the pandemic, one major problem was to prevent the spread of the Coronavirus.
To develop mathematical thinking, focus on understanding concepts, approaching new concepts, practicing challenging problems, working on word-problem skills, teaching others, exploring math in practical life, and implementing daily practice.
Why can’t I think mathematically?
Dyscalculia is a learning disorder that affects an individual’s ability to comprehend number-based information and math. People with dyscalculia struggle with these concepts due to their brains not processing math-related concepts like those without the disorder. Symptoms usually appear in childhood, but many adults may have dyscalculia without realizing it. They may also experience mental health issues like anxiety and depression when working with math. A form of dyscalculia, acquired dyscalculia, can occur later in life, often due to other medical conditions.
How can I sharpen my mind in maths?
The article provides six mental math strategies for students, emphasizing the importance of practicing basic math in their heads. These strategies include rounding up to the nearest ten, working from left to right, using multiplication hacks, bumping the decimal over to find percentages, making guesstimates, and breaking down problems. By teaching these strategies, students can develop confidence to solve problems without the need for manipulatives or paper work.
How can I think more creatively in math?
Discussing alternative solutions is a crucial tool for introducing students to different thinking pathways. When solving a mathematical problem, encourage students to explain their method and relate their solutions to their classmates’. This helps students connect content with real-life situations and equips them with skills for unrehearsed problems. An example of a guided problem from BitMaths is SP803 Venn Diagrams and Two-way Tables (Australian Curriculum; Victorian Curriculum) and SP414 Venn Diagrams and Two-way Tables (NSW Syllabus).
How are mathematicians creative?
Wallas put forth the four-stage Gestalt model for mathematicians’ creative process, which provides a characterization but does not define creativity itself.
📹 Anyone Can Be a Math Person Once They Know the Best Learning Techniques | Po-Shen Loh | Big Think
Po-Shen Loh, PhD, is associate professor of mathematics at Carnegie Mellon University, which he joined, in 2010, as an assistant …
I like this argument. I was never good at math until I started taking my math classes online. I’m a slow note taker and it takes me a while to understand concepts, so in a traditional classroom setting I fall behind the curve really easy. But with online classes, I can rewind the lectures, pause them to catch up, and use multiple sources of learning to figure out a concept rather than just depending on the professors way of learning which may or may not work for me. There are some downsides to learning purely online, but in regards to math online for me, the benefits outweigh the costs.
Absolutely spot on. Math is pure reasoning and analysis, it always makes me laugh when people think that being good at math means being able to multiply insane numbers in your head in just seconds. People who can do things like that are certainly talented but there’s a lot more to mathematics than ridiculous computations lol
I was the worst in math but I needed to learn computer science. So I went on and started learning online from youtube khan academy etc and now I feel like a pro. From simple addition to integrals, probability and logic and It really opened my mind. My thinking process changed. I really recommend learning math. Its not just for school
One problem of the way that schools teach mathematics is that they focus too much on calculations and memorization of formulas and algorithms. Computers can do the calculations billions of times faster and they can store every single textbook you’ll ever need. Schools should focus more on translating important, everyday problems into mathematics, the construction of mathematical proofs, and the ability to spot errors in arguments. They also should test students’ abilities to intuitively explain their results. A simple 1 hr test doesn’t allow enough time for thinking in order to show understanding.
YES, exactly I have been telling students that if they miss one concept they will miss part of the chain. If you miss the class on the quadratic equation there goes your whole understanding of what to do when the teacher ask simplify using the quadratic formula. Good to know professors are teaching that it is important not to miss math class. 🙂
Wow! I wish I had known this. A good teacher makes all the difference! I finally understand some trig when I had a teacher who SPOKE NO ENGLISH, but illustrated the concepts with such clarity and enthusiasm that my brain caught on. I went on to take a theoretical calculus course and loved it, then I got lost in the mire again. This is such crucial information! Thank you!
Interesting, I came to a similar conclusion when I started delving into Advance maths and used Khan academy to catch up. It was amazing to see what I had a a weak grasp in and how, at my own pace, if could strengthen them. Lead me to believe that math is simply a poorly structured subject in our school systems, rather than something nefarious.
Interesting article. I liked the contrast between learning history and math. After a career in industry, I taught high school chemistry and physics for several years in the city of Chicago. I was very dismayed by the level of math knowledge in general. What I would like to add to the discussion are two points: first, because a student is “bad” at math, doesn’t = they are “stupid” or unable to learn it. They need to see and understand the importance of knowing the subject. Second, education does not need to be torture. For anyone interested, a great book on education is “The Smartest Kids in the World and how they got that way” by Amanda Ripley. Last thought: find a reason to learn. The future belongs to you.
I completely agree. I think he nailed down the problem exactly. The most upsetting thing for me, is that the link that most people seem to be missing in their mathematical thinking is somewhere around second grade. I TA for undergraduate math, and one of the difficulties I have noticed most often is that students have a poor understanding of fractions and ratios, which goes back to second grade. This is something I have noticed throughout my education at every level. Without an intuitive sense for fractions and ratios, higher level mathematics becomes just a manipulation game that is more akin to how a computer works than to real understanding.
This article is very useful. I would add one more thing. math is beautiful, and very challenging, so enjoy the challenge! See it as taking a difficult hike, playing Chopin, or learning a new language (which it is, in a way). There is much pleasure to be gained in tackling a challenge meticulously, gradually, and with dedication, and seeing the slow but gradual progress that takes place, until one day you see that you finally reached the top. I have learned much math on my own, and at my own pace, and it gives me great pride and confidence to be able to do it. No matter what your particular case is, try to be able to enjoy this wonderful challenge!
I’m not going to say school was useless, because I did have some good teachers and still have some good memories. But being forced to learn at a pace that I don’t feel comfortable with, and using a set of stupid rules that don’t aply to my way of thinking just ruined my whole school life. My real school is my bookshelf and the Internet, and my teachers all those who took the time to write something useful to learn. Almost everything I was bad at I learned by myself and scored the higher grades when I finally had a window to be at peace and study by my own, instead of being shamed in public for not being able to comprehend.
I totally agree with Po-shen Loh. The difficulty in math is the chain of dependencies. If one link is poor your understanding is severely hampered. What Loh however neglects is: One must have the DISCIPLINE to go back, FIND AND FIX ALL THE MISSING Links. This takes extreme perseverance. To find all these gaps, one needs also to do as many problems as possible. I.e. HOMEWORK. It aggravates me when schools/teachers are reducing homework and in fact are considering it’s abolition. It’s analogous trying to be a great athlete but NOT Training at all – egregiously ignorant. So did Stephen Curry or LeBron James just become great basketball players with ZERO practice??
I feel lucky on having a great teacher who introduced common sense in math and made it enjoyable in 7th grade. I always took my time on my homework and would work on a question till’ 12am if I did not understand it. Math was something I liked because I could be in my own little bubble and problem solve. The flexibility of math due to its connections gives me freedom in learning. To see results after working hard and pushing my brain is amazing. Now math comes easy to me and I have A’s in all my math courses in my time in high school.
One of the most valuable things I learned at university was “The order in which to learn each topic”. Exactly as is described in this article, you need to know about certain concepts before you can grasp some others. Even having all the right books won’t help you if you don’t know in what order to read them.
Thank you, sir. I can completely agree with this statement. I, for all of my early life, felt I was just doomed to be bad at math. As I learned, I learned every subject I love comes back to math. I finally decided to at least learn some math. I went in not expecting anything and came out thinking about everything. Once you have the connection with math click, and I do believe everyone can with the right approach, it almost becomes easy. I am saying this as someone who originally thought I could never, ever be good at math. Math is actually really cool, once it starts to click.
I am a full-time math tutor for an accelerated high school and this is 100% correct. More specifically, I noticed that there are about three locations in math knowledge that generally destroy a student’s comprehension. The first is the memorization of times tables. Now, usually, I am against memorization in math, but I think basic times tables are an absolute must for higher level mathematics. Too often I see students pull out a calculator for things like “8 x 7”. I think times tables should be memorized through comprehension, but this memorization plays a bigger part later. The second area, which I think is also the most beneficial to our rational thinking, is order of operations. In America, students usually learn this right before high school, so even if they don’t grasp the concept, the teachers will still simply pass them. Now, the pattern I noticed while working with students is that these two areas compound once they get to factoring in Algebra 2. I’ve also noticed that this is where students start to give up on math. I think it’s because factoring, in my opinion, is easiest to solve using mental math. But, because a lot of students don’t remember their basic times tables and have a loose grasp on orders of operations, they’re forced to use idiotic workarounds that only complicate matters.(diamond method, box method, etc.) It’s at this point that the shaky foundation of mathematics finally falls apart as further curriculum is dependent on the ability to factor. But, that’s just what I’ve noticed.
In my experience, you need to be able to grasp enough of one small part of math to begin to appreciate it and start thinking deeply about it, desiring to know from pure intrinsic curiosity rather than extrinsic goals. Then you will naturally be drawn to other areas of math because its subjects are deeply and surprisingly interconnected. Math is simultaneously art and science: it is intrinsically beautiful; it just takes some time and help to be able to look at it in the right way. All of this is completely and monstrously ignored in conventional schooling thanks to ignorant and shortsighted bureaucrats. Self-learning techniques are really the best option. Even conventional learning with the best teachers must end eventually. Moreover, bad teaching must be overcome via self-learning if the student wants to progress despite failures of the educational system. So I applaud all those attempting to democratize education online and make lifelong learning easier. Thank you for all you do.
I flunked out of calc 2 at one point (two actually). I then went 3 years without doing math at all. Then I got a job tutoring at a community college while I got an electrical certificate. I learned from other tutors and also from helping other students. This filled in the missing links described here. I am in my last two semesters of a physics and applied math degree, and I do very well. It’s not easy by any stretch of the imagination, but I still give most of the credit to my tutoring experiences. We need to allow people to discover math at their own time and pace. Math should be explored, not force fed. I really enjoyed this professors insight.
I was not really good at math throughout middle school and high school, but still made it into Engineering school. So to prepare myself for college, I was able to develop a study method to review all my deficiencies before the start. I learned that being put in an accelerated class in middle school may have resulted in me picking up those deficiencies. I really do agree with Po-Shen Loh, and by using these principles my math reasoning in my Mechanical Engineering courses has become a powerful beneficial tool. I am also taking my final math course, Differential Equations and happy to say I’ve become more of a math person.
I think of Math as bricks. For example, Algebra is one brick Diff Eq another brick. You have to begin by laying down the foundation and eventually building upon it. If the foundation is bad, your building will collapse. Same thing with math. My foundation was pretty good for Basic Algebra and Geometry. Once I hit pre-calc and Calculus, I simply slacked off. Math became a mess for me after that because they were also fundamental to understanding Differential Equations. I regret doing average in math. As a physics major, math is the language and my god it sucks not knowing how to do simple stuff.
That was well explained and very logical and helpful. It was easy to follow while explaining a link left out can derail an entire train. Something teachers don’t have the time to assistant a struggling students, they’re simply left behind in frustration. Here is where a teacher’s assistant would have a positive impact repaired the link. People don’t always grasp these concepts at first, but can with a little help they will. School are not usually structured to give the necessary help when needed, if to have a successful class.
I used to be pretty pathetic at math because until my junior year in high school, all my tutors had no faith in my ability to do math. They didn’t realise I was bad because I missed out on some building blocks. And their constant shaming convinced me that I was dumb. Then in junior year I went to an after school tuition teacher who believed in me a loooot and saw that my reasoning was good but I didn’t know some fundamentals which is why I was sucking at it. He made me fall in love with math tbh.
Not many think that memory parts a essential parts of programming and Maths ? What Memory and maths ? Maths and programming both Involved Intelligence but Memory plays a key role,because in maths and programming you have to chain the smaller concept to solve the bigger . This chaining of smaller parts is where memory is involved.
This is a great insight. Here in Spain when I was studying for my written driving exam the classes were actually circular. You had one book with every chapter you need and a few teachers who would cycle through the book. You could join the class any time you wanted, start with any chapter, and stay for as long as you need. You can repeat the chapters as many times as you need before the test just by waiting for the class to cycle back to them. It seems like this would be a good model for teaching maths. I wish I could have a teacher like this for maths, but I am older now and it’s hard to find tutors for people my age.
For basic mathematics, everyone could do it with hard work but to actually have a successful path to get a Phd on Mathematics. You need to be a special person to actually understand the patterns and generic rhythm to have a constant success in math problems. That is why you don’t see many people with phd in mathematics. Science is different, it is all about discipline. You actually see if you are good in math, if you compete at national level and score 70% in every math test for the competition.
Now I feel like what was lacking here is how to properly get started. I definitely feel I have some missing links, but how to find what they are? What are some good resources out there to help myself get back on track and keep moving in the right direction. That would have made this message more powerful.
As a self taught software engineer who picked up on crypto analysis for fun, I fully agree. I used to suck at advanced math when I was in high school. It wasn’t until I started to pick up on engineering things outside of school that concepts started to click and advanced math became easy as hell. That being said, the main issue at hand is our garbage ass school system. It’s set up to not care about your education as a student, but rather, just get mass results. Which I understand, teachers can only do so much and it’s a solution that is monetarily feasible. But it doesn’t produce meaningful results. It’s set up for a learn and forget system, profit gains, and wasteful efforts. School does not work for people like me. I am already a salaried engineer without a degree because school failed to teach me. It’s mostly a waste of time and if we really cared about kids education, we would reform the system. Does this mean I know what to do? No. I just know it doesn’t work but we need a change.
I’ve been saying this sh for years! More than understanding the concept, it’s about understanding the logic, the reasoning behind the mathematical language used to systematically calculate or solve problems. Most people just accept the concepts even if they don’t truly feel aligned with its foundational reasoning.
Ok, so if this is true, everyone can be the coolest person in Highschool because all the basketball proficiencies and soccer mastery is all coming from an internal —inborn understanding of maths. Also juggling and any kind of art Manouvre is really easy then because it’s just a combination of various math concepts.
To understand is to love. To understand mathematics, you need to have reasons why you love math. To me personally (although I’m starting to get interest on math), math requires thinking skill same as to philosophy (subject that I love). That’s what makes me interested in math. Besides, math is an art. You learn the formulas, crush them and remake for your own comprehension. That’s my way on how to get comfort with math.
I don’t understand math’s because I don’t even understand what the concepts are used for. I know what linear algebra is, but why the f… am I learning it? what is it used for?. This goes for almost every f.. subject in math. I don’t even know why I am doing it at the first place and you expect me to adapt to it. (I am not blaming you lol, just a way of saying to a teacher that teaches math)
There is a useful term to describe what he is trying to get at. The discipline of mathematics is ‘hierarchical’ in its knowledge structure in ways that are similar to say physics and many other STEM fields, but other fields are not hierarchical. Another key feature of the structure of knowledge is the amount or degree of consensus. Math and Physics are “high consensus” disciplines in which members of these communities agree on quite a bit, especially the fundamentals. Sociology, anthropology, history and others are “low consensus” fields. They do not agree on the methods, do not prioritize topics, and do not conceptualize the field in homogenous ways. The members of the field actively contest how to think about and “do” these fields. Consensus of the field matters, because high consensus field will be taught in similar ways, thus students can reasonably be expected to have encounter similar content in classes on calculus, but not in classes on intro to sociology. Multivariable calc professors then assume far more and expect more background knowledge as a result, which makes it hard for students without that knowledge to follow along or even catch up.
Pls don’t use Lagrangian mechanics to describe laziness or principle of least action I know,you know everybody know, Human has too share his knowledge not his ego I am not saying that you are egoistic you aren’t but the world has too much ego because it can break their so called filthy beliefs so break everything and start learning. Happy learning……….
No. Not everybody can be a math person. I’m affraid this professor has been living and working for too long in the bubble of intelligent, determined, hard-working people and slightly lost connection with the less-blessed part of the society, which in fact is the majority. There are people who simply don’t know how to be rational and even if you showed them a number of times examples of rationality, they would maybe learn to repeat it in those exemplary cases, but would struggle to be rational on their own. The professor mentioned the condition: “if they wanted”. One problem is, wanting is not really independent from the abilities. Usually, the desire to do sth and the abilities mutually reinforce each other. I want sth. because I already found that easy. But those who struggle at sth. in the beginning will not find the desire to pursue this. Some people are simply not into long, analytical thinking, like others are not into dancing or risk taking. People differ and we should accept it instead of making false claims that everyone can be like someone else. Some of you say: “I sucked at math, but then I found my way (online course/good tutor/sth. else), and now I understand it”. Good for you. But being a math person is not about it. Ask yourself: “Has this taught me sth. more than just math? Can I now go on another level but this time on my own?”. Being a math person is not about understanding math. It is about shaping yourself to be able to perform long, tedious and solitary mind-work and gain knowledge out of it.
There is a cognitive component that can’t be glossed over; chain (linier) thinking is a left-brain function. I am right-brain. 15 minutes of forcing myself to work math problems and my brain starts forcing me to want to sleep. After thirty minutes in a math class, and I get something like highway hypnosis where I am in a fog and can barely feel my body. Then, I cannot comprehend anything without taking a ten-minute break. It also means that I lose the latter half of any math class I take.
He’s 100% right. Education should be catered to the kids needs and interests, that’s why Khan Academy is so successful everybody learns at their own pace. I predict in the next decade or two homeschooling will be more prevalent because the public school system isnt designed to cater to a child’s learning needs or interests. But if you homeschool odds are you can get a child to learn about anything they want in a smaller time frame than a 7 hour school day for example. I think the downside of homeschooling is that most people cant do it or dont think they can do it, half of the us are dual-income households and a third are single income. If there wasn’t that barrier to entry, I’d imagine 50+% of people would already be homeschooling if they had the means
He is lucky he was born smart and it’s easy for him to assume that everyone is like him, if you don’t believe me try benching 2000 tons, you will never bench that amount no matter how hard you train, the same applies to the brain, if I tell you to learn quantum mechanics and argue that Albert Einstein learned it so that means that anyone can learn it, while ignoring the fact that he had an IQ of 160 and could memorize photographically
Alright first and foremost, the first damn week of Algebra I should be learning the history of it, and all of the interesting things you can actually do with the knowledge. plotting out lines on a meaningless graph is pretty pointless without first learning what in the hell you can utilize that for… we’re failing our students… badly.
The problem with math is that many people don’t end up using it. Especially algebra. I’ve talked to many successful people and they all agreed that most of the math being taught in high school and in college are a waste of time. Math has also been proven to be the one subject that drives people of school.
This is so true…I was very poor in mathematics till 7th grade(So poor that I wanted to take arts in senior high school )…In 8th grade I started talking extra mathematics classes..Our tutor used to beat the shit out of us when we used to make mistakes….Eventually I ended up qualifying at maths olympiad at national level without even knowing the syllabus for the exam…
This garbage article should be taken down. There are solid studies concluding that most advances in math come from a tiny % of geniuses who mostly graduate from elite schools. The fact that some math concepts build on previously learned ones is something every math teacher from first grade up points out, not anything new or enlightening. Watch the interview where Jeff Bezos talks about the moment he realized he wasn’t going to be a theoretical physicist at Princeton. I’m so glad that Bezos founded Amazon instead of becoming a mediocre physicist, and Bezos is intellectually at least 1 in 1,000, maybe even 1 in 10,000! It’s better for people individually and the world if people pursue the things they enjoy and are talented at. For the vast majority of people this is NOT math. Most people don’t need anything above algebra as adults and lots don’t even need algebra. Plenty of people just aren’t interested in math and that is OK. Telling everyone they can be a math person, and the implication is that everyone SHOULD be a math person, is terrible advice for the vast majority of people, wasteful, and utterly false. Encourage people to pursue what they are talented in instead of making them feel bad for not liking math. You’ve gotta be realistic about these things. This article is false garbage and should be taken down.
I’m still waiting on the neural link, where I have a USB adapter attached to my brain, and I can just upload what I need to know! However, that’s the first version, eventually there be an upgrade with a Bluetooth link, and I can just send whatever I need to know to the neural link via phone or computer, tell eventually an upgrade, reaches a point, where I can just think about it, and then the rolling basically be an intermediary between my brain in the Internet of knowledge!
I was always bad at math but I saw this article a year ago (around December 2022 and January 2023) and decided to challenge this belief of his that everyone is a math person. So I started learning math from scratch, I did take some breaks here and then but one year later I’m now on algebra and I’m SO much better at math that I ever was in school. And what’s crazy is that I also enjoy doing it. So I can say he is right
Once again you are right, when I tutor students they always will tell me that they do not understand math or that they hate it ect., especially girls, but boys don’t respond due to the fact they do not want to look dum. Another thing I have seen through the years that students in middle school do not know Algebra or any other part of math is because they do not know their multiplication tables. I also notice that many student including adults do not know how to work with Fractions or math sentences. 🙁
I skipped preschool because of my age and didn’t speak any English in my 1st grade class. I remember doing math in 2nd grade and it being very difficult for me. I was too slow. I still struggled in 3rd grade, but fortunately in the 4th grade we just repeated what we learned in the 3rd grade. It was the same stuff on repeat. That allowed me to catch up and I eventually ended up taking math courses one grade above me. For much of the same reason as described in this article.
In my elementary days, i hated math, i don’t know a thing, and I sleep on purpose because I can’t even learn anyway. But when in high school days, i suddenly had a click on math, I easily understand math, i get perfect scores on math exams, even in college i managed to graduate with a physics degree with flying colors. At some point I suddenly loved math, it became easy for me. Until now I don’t know how I came to be this way.
Good conclusion. Though I’d add that mathematical knowledge isn’t exactly built as linear chains, everything is more like a net. So there’s always multiple possible routes you could take to acquire a new piece of info. Obviously some routes are easier, but the preference can change from person to person. This also means you aren’t strictly required to fill the holes in your knowledge with exactly the same tools you’ve forgotten. Any other will do that can bridge the gap. If you have good enough reasoning skills and didn’t forget too much, simply deducing lost materials is an option too. What I think could help people study math better is to give them more learning options, and not limit mathematical growth into narrow predifined confines. Education should be more flexible. And also more supportive in helping people pursue their math related interests in any topic, even if it goes further than the planned curriculum. We could list the shortcomings of public education for a long time, thankfully we don’t have to wait until it improves. With the internet self-teaching is easier than ever before, you can find forums, articles, download textbooks to satisfy your interests. Treat math learnig less as an obligation, more like a hobby. Whatever you learn make sure to practice it properly. Keep learning deeper and deeper subjects, and in practice find harder challenges. Your mastery will only grow.
We desperately need an individualized, mastery-based educational system – the “traditional” pass/fail class system is failing us. It leaves many students with “missing links in the chain” which leads to confusion and disengagement. And it often puts a brake on the potential speed of progress of exceptionally gifted minds. The technology is already available to facilitate fully customized learning progressions for each individual student. We simply need to implement it, as some schooling systems are already doing.
If i could tell teachers one thing it would be to explain earlier what the equal sign actually is. We are trained to see it as a symbol for answer, and not as “this is literally the same numerical value on each side”. Then show extensive examples and “proving” it, all the way from easiest to hardest. I think this would help a lot
I think something similar happens with Organic Chemistry: you must be aware of the fundamentals to get through harder topics. However, my relationship with math is a little strange, to me is very easy to understand once someone explained the topic to me, i watch a article and the like, but i, usually, forget everything in a few weeks and i think it has to do with the level of processing of the information and that im no able to associate math concepts in a way that i do with Organic Chemistry, for example. Also, it makes no sense to me bc i never apply most of the math conecepts, however, i do know the importance of math in terms of thinking so, does anyone is going through the same?
I’ve always liked math, but hated school. I graduated high school with only a very basic understanding of the subject. A few years later I bought some books and started teaching myself, and it was very enjoyable. I taught myself basic calculus first, then higher calculus, linear Algebra, vector analysis, and even some tensor analysis. I learned waaay more in 6 months on my own than I would have sitting in classrooms for who knows how many years.
Absolutely right, about the “chain”. Miss a few history lessons, you can still understand the rest. Not so with maths. In my first year of secondary school I started to not understand what was being taught. Weeks went by and it got worse. I got nothing but bad marks. By the time they realised I had a real problem I was at the “bottom” of he class, with marks averaging 2 to 4 out of 20. I never recovered. I understood nothing in Maths lessons, I dreaded them, maths was a threat (of not getting into University), and it was a constant source of bad marks. I realised that results were the same whether I made an effort or not, so I gave up, became bored and loathed maths. To this day, more than half a century later, I still do, and my level is still what it was when I started secondary school, aged 10. On the other hand I doubt whether everybody can really be a “maths person”. Some of us are better than others. But most people seem to be able to achieve levels higher than mine.
I was always a pretty decent math student, I enjoyed math and logic, which is why I decided to become a computer scientist, but I was never great in college math classes because of the speed that they moved. I felt like I never quite picked up everything and was being dragged behind that math train falling into many holes along the way. I would technicality finish the classes with decent grades, but I didn’t actually learn the math, I just learned some basics to get s enough of the problems on the test correct to pass a class. I had to go back at my own pace much later and fill in things myself.
I got the same situation when I recently started with data analytics. I just wanted to learn how to clean data. But then I discovered that data cleaning is like the chapter 7, and that I skipped the other ones. So I restarted at chapter 1. Now data cleaning with pandas doesn’t seem so difficult anymore.
I actually knew this problem of mine from a very long time, I wasn’t able to solve complex problems in High School since my base wasn’t clear. It was like trying to climb a ladder that had few bars missing on it. Some of the tutors did not care about trying to fix my gaps in these basic concepts all they did was make me a robot and do exactly how steps are described in books without trying to understand how the base behind it works. One tutor in High School really helped me a lot with clearing my base and filling the gaps in Mathematical concepts it really did help me. I was able to solve complex problem without much problem. However, I still do think I have some of the gaps left behind though. But taking in account of what you said and what I experienced and how I was able to catch up, this is 100% true most of my classmates exactly had this problem of base. They weren’t able to solve complex problems because their base wasn’t strong and because of it they relied on stupid memorization methods that included memorizing the questions practicing questions to memorize the steps without a strong base and so on … I personally think when the students are being taught mathematics and their bases on how actually it works. I think the students at that period of time should receive some special treatment so they can have those mathematical concepts engrained in their mind which will help them to guide through complex problems throughout their life without having to rely on stupid memorization tricks and they will love doing Maths from the bottom of their heart and also if teachers find their students being this way.
But….most high school math curriculums are “spiral” in nature i.e. they return to previous topics (but usually at greater complexity), thus giving the opportunity to revisit possible missing links and yet some people still struggle? I agree with the “chain” metaphor and the notion of having the will to tackle the topic of maths but there are still brains that process this topic better and some people are literally flogging the dead horse for little gain! As for “anyone” being able to tackle maths, what about dyscalculia (cognitive processing issues) or cognitive deficits? Having struggled myself I would say stick with it if you relish the challenge! I’m in my 50’s and have just enrolled in a full time Engineering degree. so I’ll be trying to master higher math for the 3rd time (and by “master” I mean learn to a deeper level the math involved). Great website and content, so thanks!
the crazy thing is when i took calc 1 in college i remember after i put in the 10 hour study days i really started enjoying it and my reasoning skills were permanently improved in my life. I ended up switching from premed to engineering because i fell in love with math, which is crazy because i first attended a community college starting at ALGEBRA 1 LOL
Exactly what I think, but unfortunately, here in Bangladesh and in many Asian countries failing, or repeating a year is looked down upon. I think that kind of mentality needs to go way. Math used to be my favorite subject, and now I find it troubling to understand. On top of that, I was a “gifted kid;” unlike others, I never learnt, how to learn. Being born in a poor family doesn’t help either. This may sound like a lot of excuses, and I guess these are.
I enjoy math, but the question I have to ask is, “Just because you CAN do math, does it mean you SHOULD do it?” Riemann definitely should have, but in general I’m not sure if it’s a good idea. Theoretical math is exciting but not lucrative, and applied math is lucrative but not exciting. At least that has been my experience.
Havent watched the article. But I have sth to say about the title. In general, math or any other intellectually compelling task, You cannot know what works best in advance. You start doint it and you learn on the way what works best. Planning in advance how to work does not work, again, you start and learn what works for you on the way. It took me literally years to understand this. I am always planning what to do and how to do it. Let it alone to decide what to do, lets say you decide it and searching the best effective way possible on how to do it, you cannot understand. Just take the first step on the way, you will learn on the way.
Okey, what you re trying to say is that MATHS is nothing else than CHESS ? ..meaning that this is just a GAME of learning how to LEARN TO REASONABLE Thinking ? (Which is basicly the art of breaking down of things) If so..than what you re saying is that we should change our approach to maths to understand maths, Iam asumming this correctly ? Then what you re saying is that IF you understand the basics of MATHS in order to BE A MATHS person..which means not necessarly to be stricly a numbers person but a BREAKDOWN APPROACH professional..
I totally agree with him! During school, I lost my way by missing certain key links in my chain. So recently, at the age of 28, I started to teach myself basic Pre-Algebraic Mathematics. A month ago, I didn’t know how to do really basic Arithmetic like long division or my 7 times table, but now I’m working through arithmetic operations with ease! Fractions have started making a lot more sense for me too! Hopefully I’ll keep this up and eventually get good at Algebra, Trigonometry and maybe even Calculus! 😁
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People tend to think mathematics as a subject having complex, symbols, iterations and formulas that we just need to read remember and understand, but in reality, mathematics acts as a language of link between different corelatable concepts altogether, for, example, for clearly understanding concepts that are related to physics via, chemistry, we need to have a knowledge of mathematics, because the total explanation of the physical theory in chemistry is dont with the help of mathematical concepts altogether.
Very true! I used to never comprehend math at all. I saw Richard Feynmans Physics & Mathematics lecture (black n white article), and he broke down how math is reasoning within physics. But he did it with such simplicity I felt like a genius within my new found understanding. Math is pretty to understand, when you want to understand it that is.
I wanted to be a math person, now I am one, you will be the judge 2021’s Biggest breakthrough in Mathematics Hot off the presses : We can pair every positive floating point number using up only about 20% of the integers Algorithm #1 : Convert a float with a zero whole part into an integer 1. Reverse the character sequence representing this float 2. Remove the decimal point to obtain the desired integer Example : Convert the float 0.002743 into its integer equivalent 1. Reverse the float string to obtain 347200.0 2. Remove the decimal point to obtain the integer 3472000 3. Note : All corresponding integers will be terminated by the character “0” Algorithm #2 : Convert a float with a non-zero whole part into an integer 1. Count the number of whole digits or NWD (those preceding the decimal point ) 2. Append a number of “0” digits equal to NWD to the float. 3. Append a digit “1” to the resulting float 4. Remove the decimal point to obtain the desired integer Example : Convert the float 1230.0098 into its integer equivalent 1. Count the number of whole digits : NWD = 4 2. Append NWD = 4 “0” digits to obtain 1230.00980000 3. Append a digit “1” to obtain 1230.009800001 4. Remove the decimal point : this gives us the final integer of 1230009800001 Note : We append a digit “1” to distinguish the integers derived from floats with non-zero whole parts from integers generated by floats with zero whole parts . This can be done for every float (whole.fraction) where whole > 0 !!! AMAZING!!