Why am I especially good at problem solving and logical thinking but very bad at math?

You are missing the bigger context of all math. So let me help.

All math problems are a description of a set. Therein all math is division and the parts fractions. It is based upon sets of units which are arbitrary as their basis. And the numbers themselves are fixed in space and time - it is the infinite variety of math sentences that will get you there. Math is the specialization of sentence paths. So you may see the relations in patterns but missing the descriptors. Now, to be good, double check every answer, use check sums to gauge your efficiency in being accurate. that will get you most

You are missing the bigger context of all math. So let me help.

All math problems are a description of a set. Therein all math is division and the parts fractions. It is based upon sets of units which are arbitrary as their basis. And the numbers themselves are fixed in space and time - it is the infinite variety of math sentences that will get you there. Math is the specialization of sentence paths. So you may see the relations in patterns but missing the descriptors. Now, to be good, double check every answer, use check sums to gauge your efficiency in being accurate. that will get you most of the way. Do not learn more math until you know, or someone can explain how and where it fits into the math universe. Also go use Khan Academy which has robust analytics, you may just be stuck on one kind of problem and it will show you, then you might accelerate.

Logic is a very basic part of maths. It's contradictory to say I'm good at logical thinking but bad at math. Since you did say it, I guess you're not so good at logic. :P


Turns out, maths needs to be taught properly. You should try to get proper study material and introduction to mathematical topics in proper ways. I can't think any other reason than that to be bad at maths and good at logic.

(psychological issue? fear induced by teachers and classmates? pressure? traumatic experience from past about maths?)

  • If you are good in problem solving as well as logical thinking then maths is not a big deal. First think what maths is, if we break maths we will end up getting something not other than addition yeah ONLY ADDITION (not subtraction or division or multiplication because these are derived from the basic counting i.e. addition, Right) and story beyond that is all about logics. Even in computer science it is called as logical operation because complex computation implemented in computer is broken down into logical operation and manipulated at the bit level so this is how computer learns any kind of
  • If you are good in problem solving as well as logical thinking then maths is not a big deal. First think what maths is, if we break maths we will end up getting something not other than addition yeah ONLY ADDITION (not subtraction or division or multiplication because these are derived from the basic counting i.e. addition, Right) and story beyond that is all about logics. Even in computer science it is called as logical operation because complex computation implemented in computer is broken down into logical operation and manipulated at the bit level so this is how computer learns any kind of complex maths i.e. nothing other than counting and the logics given in program. We human, inventer of computer if you can make computer do that then why can't you. Logic is only the thing which have changed the entire world. So if u r good in logical thinking(assuming you are good in counting stuffs :p) then by a little bit of practice, maths would be in your fingertips.

4 or 5 minutes to add 22+33 and get 55?

The most likely explanation is that your sense of the time it takes you to do a problem is off (see 4 below). It almost certainly wouldn’t take you 4 or 5 minutes but you think it does because you are sensitive to how long it takes you. I would ask a teacher for an independent assessment of your calculation skills rather than relying on your own impression. You need a good picture of the problem to know if there is a problem and figure out how to improve (if you even want to).

A few thoughts on possible reasons if you really do arithmetic slowly:

  1. You are ab

4 or 5 minutes to add 22+33 and get 55?

The most likely explanation is that your sense of the time it takes you to do a problem is off (see 4 below). It almost certainly wouldn’t take you 4 or 5 minutes but you think it does because you are sensitive to how long it takes you. I would ask a teacher for an independent assessment of your calculation skills rather than relying on your own impression. You need a good picture of the problem to know if there is a problem and figure out how to improve (if you even want to).

A few thoughts on possible reasons if you really do arithmetic slowly:

  1. You are abnormally slow. There are certain disorders such as Dyscalculia. But if you are good at algebra, I’m guessing this isn’t the issue. Other reasons you may be slow are that your working memory is weak. That will hurt you when trying to add, say, 28+33, because of carrying. The good news is that you can work on this with the n-back game. Supposedly, it is the only brain game that actually can help you. If it really takes you 4–5 minutes to add 22 and 33, there very well may be something you need to look into.
  2. If I had to add 28+33, I would not do it by following the algorithm. Instead, I would note that 28+2 is 30 and 30+33 is 63 and then remove the 2 I added to get 61. This appears to be much faster, mentally, than 8+3=11 for the 1’s digit, carry the 1 to the 10s digit (2+3+1 = 6) then remember the 1 so that the answer is 61. The difference is that you need to remember 1–2 pieces of information in the first case and around 4 in the second case. Entire parts of the calculation are just sitting in your working memory (see point 1) waiting for you to finish up some other part of the calculation. There are many tricks for mental arithmetic that you can learn.
  3. You are doing algebra but you don’t really understand arithmetic as well as you think. Many students these days don’t get enough practice with basic skills. It is a shame that some of my college students, currently in calculus, can’t actually add fractions together, for example. You need to practice enough arithmetic to form an internal number line and, essentially, automate the processes as much as possible in your head (the same way you read without thinking about reading).
  4. You are actually well within the normal range of arithmetic ability. Many mathematicians and physicists I know are actually worse at arithmetic than many high school educated people. There’s nothing wrong with that.

Logical thinking and problem solving skills, contrary to much public opinion and even college classes, etc. has nothing to do with how much knowledge or information is in your head it also isn’t just a trick in the way you think… it takes serious wisdom and understanding the big-picture about how things work, in reality, generally and specifically. You can’t ever get that from anyone else. The best teachers are people who guide you to discover truth. Actual teaching is becoming extinct in our society. Our schools, k-12 and even colleges are filled with “tellers” and very few actual “teachers”

Logical thinking and problem solving skills, contrary to much public opinion and even college classes, etc. has nothing to do with how much knowledge or information is in your head it also isn’t just a trick in the way you think… it takes serious wisdom and understanding the big-picture about how things work, in reality, generally and specifically. You can’t ever get that from anyone else. The best teachers are people who guide you to discover truth. Actual teaching is becoming extinct in our society. Our schools, k-12 and even colleges are filled with “tellers” and very few actual “teachers” any more.

For that reason, serious problem solving and logical thinking skills, are some of the most rare virtues around. Working in nature, where you begin to reap the cause and effects of your own labor, is one of the best habits you will ever develop. Plant a garden, learn how to build things, work with animals, work with your hands and discover for yourself how nature works and the universe operates… but then relate everything to your own life in practical application. It is a good thing to learn from others but learning is not about memorizing, it’s about discovering.

What you want to focus on is discovering principles. Principles are the most precious treasure on earth. they are always hidden beneath and in between what you think you already know. That doesn’t mean that simply working with your hands is the magic. Most people who work with their hands, still haven’t discovered principles.

Only wise and worthy mentors can help to uncover principles for you and then guide you how to discover them through your own practical experience with life. But you must be willing to do the work and discover them for yourself.

Unfortunately, even the vast majority of people who make a living helping to solve problems actually end up creating more problems than they solve because they lack the big-picture of life and reality. That only comes to a small few who have discovered that wisdom is a totally different thing than knowledge. The two are acquired in very different ways. Knowledge is based on information that can be memorized and passed from one person to another. You can stumble upon knowledge through experience but knowledge is all about “answers,” it breeds arrogance and inflated, false pride (most assumed knowledge today is not really knowledge at all but only naïve assumptions, which is really foolishness).

Wisdom on the other hand, is founded on principles. Wisdom is never contented with “answers,” because it knows there is always more…. Wisdom is entirely based on discovering better questions. Answers stop growth, questions demand and perpetuate growth… Since every piece of real truth is totally interdependent on every other truth, there is always more, better, greater improvements to make, regardless of whether you are at the bottom, top or anywhere between-of what you are trying to understand.

The great masters through time, became great masters because they never stopped learning, discovering and evolving. The only way they remain great masters is by never losing track of their leaders, mentors, masters….

Beware, however many, many today believe (and/or try to convince you) that they are wise and flaunt their money, positions, knowledge, influence, etc. Many even believe they have risen above ordinary mortals (talk about ego). But the truly wise and their followers are the ones willing to do what the masses are not willing to do… the hardest work they will ever undertake—their own self evolution. Even though difficult at first, it is only way to live with real fulfillment and genuine happiness that doesn’t fade with the lights and the music….

I have come to call, what everyone wants, but only a few have been willing to discover, the most valuable and precious treasure on earth… “The principles that birth intelligence, lead to wisdom and harness the laws of creation.”

Since you are a creator—that’s what you do, every moment of your life—create your own future reality, You can learn to create something much greater than you have done so far, regardless of how little or far you have come.

Once on that path, you will naturally see what is, over ride your ego that desperately tries to get you to find what will pacify you for the moment, so you don’t have to risk failure, and claim whatever rewards you want most. Intelligently taking those risks is the only path to wisdom and wisdom is the only environment that enables one to solve problems and see the perfect logic in the universe—and align your thoughts and behaviors with it…

There is no way to cut corners to gain wisdom—but it is the great shortcut to super success. Everything else is settle-for. You just must make the decision.

The efforts will pale by comparison to the rewards—IF you recognize and accept that it is all up to you, no one can ever come to your rescue, and then make it a life-style. There is no gimmick or tactic or trick, but once you make those commitments, the right mentors will show up and make all the difference.

Learn to love being uncomfortable, pushing yourself out of your comfort zones IN THE RIGHT DIRECTION and the world will be yours.

Let’s go catch your dreams .

Eldon Grant

Logical reasoning is an intellectual ability which includes abstraction and often requires imagination and mental courage (open mind) to think about what if -situations. Most mathematical skills also need this ability to use your reason abstractly, but they can also involve some other kind of thinking. For example, in geometry it is good to have an ability to think about objects in space and to mentally see 3-dimensial objects from different angles.

Formal logic is usually learned rather late in school because you have to have the capacity of abstraction, making formal operations and following

Logical reasoning is an intellectual ability which includes abstraction and often requires imagination and mental courage (open mind) to think about what if -situations. Most mathematical skills also need this ability to use your reason abstractly, but they can also involve some other kind of thinking. For example, in geometry it is good to have an ability to think about objects in space and to mentally see 3-dimensial objects from different angles.

Formal logic is usually learned rather late in school because you have to have the capacity of abstraction, making formal operations and following the rules literally. Most children have learned to do something with numbers by this age and laymen call this counting mathematics. Some of these kids have not been very good in these early exercises and they may have math anxiety: they are too anxious to perform. The same children can become decent at logical thinking later, but their basic understanding of mathematical thinking can be too limited for them to learn new things. And the anxiety is still their, constant failing does not help in erasing it.

In the brain there are separate areas for understanding number concepts. Some people have difficulties in undertanding even the relationships between smaller and bigger digits and this kind of brain makes it hard to do any algebra. Those kids and adults still can perform in logical tasks. Therefore, at least some parts of thinking is not the same.

There are IQ tests which claim to test logical and mathematical reasoning but test only a part of the skills required in those areas. Algorithmic thinking might be a better test for abilities required in both logic and mathematics than mental rotation tests, especially because mental rotation tests may cause test anxiety and some people underperform in them.

“Logical thinking” is ambiguous: it can refer to (what I’d call) common sense abilities to solve practical problems in daily life, or it can refer to rigorous analytic abilities to distinguish valid, sound, and complete systems of inference and argumentation from those that lack those properties.

Perhaps surprisingly, being “excellent” or exceptional in either one does not always entail being equally “excellent” or exceptional in the other. Very gifted logicians and mathematicians are often notoriously inept at many of the mundane tasks of daily living, from poor hygiene and money management to

“Logical thinking” is ambiguous: it can refer to (what I’d call) common sense abilities to solve practical problems in daily life, or it can refer to rigorous analytic abilities to distinguish valid, sound, and complete systems of inference and argumentation from those that lack those properties.

Perhaps surprisingly, being “excellent” or exceptional in either one does not always entail being equally “excellent” or exceptional in the other. Very gifted logicians and mathematicians are often notoriously inept at many of the mundane tasks of daily living, from poor hygiene and money management to casual conversation and personal relationships, and much more that many of us easily navigate by common sense abilities.

At the same time, many who rise to various pinnacles of material success in daily life, guided by common sense and little or not formal logic or mathematical training or study (such as physicians, attorneys, financiers and bankers, politicians, and others) are often at a loss to explain just how their success can be “logically” explained or how they can discern between “logical” or “reasonable” decisions and actions in general.

So the bottom line is that neither common sense reason nor rigorous analytic logic is is necessary or sufficient for success or excellence in the other. As a formal analytic discipline, however, I think it’s safe to assume that advanced mathematics requires at least an exceptional intuitive capacity for rational, logical thought that is significantly above average.

Improvement in common sense abilities is perhaps best achieved through puzzle and problem solving, whether or not they involve math. Playing complex games like chess and go, for instance, and reading detective mysteries with challenging plots to solve may also hone those skills. Improvement in rigorous (formal) analytic abilities, by contrast, is best pursued through academic studies, either self-directed or in college or university courses, online or on campus.

There are several ways a prior grasp of Logic can help one learn maths with greater confidence: It can give one a deep understanding of the use of quantification; it can give one a deep understanding of the logical structure of different proof strategies; it can help you understand how to structure natural language assertions to reflect their logical structure more clearly; it can help you understand how to unpack the language of a theorem’s antecedent(s) and use them to satisfy the antecedent conditions of another theorem that could help you in your current proof; finally, it provides an oppo

There are several ways a prior grasp of Logic can help one learn maths with greater confidence: It can give one a deep understanding of the use of quantification; it can give one a deep understanding of the logical structure of different proof strategies; it can help you understand how to structure natural language assertions to reflect their logical structure more clearly; it can help you understand how to unpack the language of a theorem’s antecedent(s) and use them to satisfy the antecedent conditions of another theorem that could help you in your current proof; finally, it provides an opportunity to become versed in the language of proof.

One major challenge for students new to post-school maths is the structure of proofs. Logic can help you with this challenge by presenting you with the opportunity to understand quantification deeply. For example, “For each x, there exists a y such that…” is a common type of assertion. To prove it, one sometimes assumes its negation (assumes that its false) and derives a contradiction from this assumption to show that it can’t be false (therefore, it must be true). In logic, you would learn the forms of the negations of such assertions.

Another challenge is to disprove assertions. Sometimes after attempting mightily, yet unsuccessfully, to prove an assertion that seems obvious or likely to be true to your intuition, you suspect that it might not be true, after all. To prove the negation, you need to understand the structure of the quantifiers, which can be learned by studying logic.

A third challenge arises when, while proving some theorem, you reach a point where a proven result will help you prove the theorem you want to prove. You have to understand how to apply that known theorem to your proof. Studying Logic can help you accomplish this application.

Logic can help with proof strategies, generally. For example, to prove that two sets are identical, you have to show that if every element of one set belongs to the other set. You accomplish this objective by showing that x belongs to S if and only if x belongs to T. To accomplish this objective, you show, first that if x belongs to S, then x belongs to T; then, you show that if x belongs to T, then x belongs to S. From these statements, you can infer that x belongs to S if and only if x belongs to T. Then, you can infer that S = T. In studying logic, you would prove the theorem, “(S → T) & (T → S) → (S ⟷ T),” in propositional logic.

Knowing some first-order logic can help you overcome some early challenges that you are likely to meet in your Maths courses. But, nothing will help you more than just attacking the proofs of theorems directly and seeking collaborators along the way.

Yes, they are two different areas of the brain. I would say that math and logic are complementary opposites.

Simply put, Math quantifies while Logic clarifies.

Math provides accurate numericle results, but little intuitive understanding of cause and effect.

Logic provides a greater understanding of cause and effect, but usually only first order estimates of quantitative results.

Math is only useful for matters dealing with numbers, logic is useful for all matters and is basically the creative thought process.

Logic is prone to errors due to intuitive false premise, while math is prone to errors of

Yes, they are two different areas of the brain. I would say that math and logic are complementary opposites.

Simply put, Math quantifies while Logic clarifies.

Math provides accurate numericle results, but little intuitive understanding of cause and effect.

Logic provides a greater understanding of cause and effect, but usually only first order estimates of quantitative results.

Math is only useful for matters dealing with numbers, logic is useful for all matters and is basically the creative thought process.

Logic is prone to errors due to intuitive false premise, while math is prone to errors of intuitive false conclusions.

Mathematical formalism is a rigorous step by step process that can only progress forwards.

Logic includes deduction (forward) and induction (backwards) process. Therefore it can solve problems in hindsite such as criminal investigations or trouble shooting problems. It can also solve hidden domains such as reverse engineering an Integrated Circuit.

Math is accumulative where methods can be further developed into more advanced methods and often requires a list of prerequisites, making it more suitable to learn through education and less suitable for learning in a piecmeal fashion. e.g. arithmatic, algebra, calculous, differential equations,…

Logic is less connected to academics and more connected to experience. Since it’s a creative proces and dependant on a wider base of circumstances it must be more flexible. It answers more than how much or how long, but it answers any question, such as why or how it does what it does.

The more math that you need to apply to solve a problem, the more complex the solution will become.

The more logic that you apply towards solving a problem, the more simple the solution will become.

Many problems can be solved by both logic and math. quite often logic may create a shortcut to a very difficult mathematical problem.

example:

Assuming all records are available, what is the average win rate for all poker players that play at a certain stakes in a certain card club when excluding any rake or time charge.

A mathematician will probably not even attempt such a difficult problem even with all available records citing problems with variance and sample size

A logician will tell you it’s 0, any money lost is also money won.

Read the question. Read it again. Think about previous, similar questions. Underline the bits you think are important. Read the question again, to make sure you understand what they want to know, and what you have to start off with.

Almost every text book has examples. Do Not Read them! WORK through them, step by step, and if you don't understand a step, ASK. Maths is really simple, unlike every other subject there is a right answer, so if you can get each step correct you should get the larger problem correct! Now, once you have worked through the problem, following each step, try again, check

Read the question. Read it again. Think about previous, similar questions. Underline the bits you think are important. Read the question again, to make sure you understand what they want to know, and what you have to start off with.

Almost every text book has examples. Do Not Read them! WORK through them, step by step, and if you don't understand a step, ASK. Maths is really simple, unlike every other subject there is a right answer, so if you can get each step correct you should get the larger problem correct! Now, once you have worked through the problem, following each step, try again, checking the steps against the book after each one. THEN do it again, only checking if you get stuck, then finally do it one last time, without the book. If you think that this is much too laborious, don't worry, because, as time passes, it will get easier. You will recognise problems as being similar to ones you met earlier, and, eventually, your confidence will increase and you will be able to work on more complicated mathematical problems without having to go through all the steps. Very few people are born mathematicians, most people have to put in some work, and the earlier you start the easier it is!
Just take it one step at a time!

No. I am a retired professor of mathematics with several degrees. When asked to divide up a check for several people in a restaurant, I always demur. “I taught calculus,” I always say, “not arithmetic.” In fact, I’m terrible at arithmetic.

No, that does not particularly mean that you lack in logical understanding, being not very good at math can have multiple reasons. One of the bigger reasons for people being bad at math, is the way society discourages from learning math. People say stuff like ‘I was never good at math/I hate math’, or it’s either the fact that a particular student is not prepared for what is taught in the class. So he/she should look back and try to understand the fundamental concepts, which are rather easy, behind the seemingly complex mathematical ideas being taught.