Mathematics: What are the different learning styles?

Post Reply New Topic

I have heard many times of people who struggle with learning Maths with conventional pedagogy(ie rote)
I have also heard of people who, with the right teacher that matches their learning style, excel, where before they struggled.

So what are these learning styles in Maths?
What are the different ways of teaching Maths?

I was a straight A student in Maths but I never felt confident in my understanding. I never felt like I really 'got it'. I believe that Maths is more a way of thinking than rote memorization of equations and rules, and somehow I never achieved mastery despite my good grades.

I would appreciate any insight any of you have on this issue.

This is my math learning style. Get on Khan Academy. Obligate myself a few minutes on some topic. If it sucks for me, move on to some other math subject. Lather. Rinse. Repeat. I could spend hours jumping around math areas like this for months on end. I stopped because my wife was starting to worry and my therapist was getting annoyed.

I think this is an incredibly interesting question to pose!
I think that there are a number of different ways to learn mathematics.
I when I was in primary school (back to about Kindergarten I'm thinking here) absolutely hated with a fiery burning passion that consumed me, hated. mathematics. Absolutely hated it. Somehow this soured me to the idea of maths - combined with everyone telling me I sucked at it and was terrible at it- for about 13 years. When I got to college and tested into calculus classes (not sure how that happened), it was as if I had seen the light. Suddenly, with my new professor who taught in a way I could understand, made mathematics amazingly fun. I fell in love with the subject. However, for other reasons I ended up pursuing a different degree, to my infinite regret. Regardless, my love of the subject can't be turned off now. It amazes me how much there is to learn about it. I feel as if it might take my entire lifetime before I have even a rudimentary grasp of the field; honestly, it's so esoteric and niche at times... However, having a job doesn't allow for exploration of many things outside of that job so...
Oh, and here's a link that really opened my eyes! Lockhart's lament.
https://www.maa.org/external_archive/de ... 03_08.html

This might help you out. This is a list of different teaching styles.

http://education.cu-portland.edu/blog/t ... ng-styles/

For those too lazy to click the link:

No two teachers are alike, and any teacher with classroom teaching experience will agree that their style of teaching is uniquely their own. An effective teaching style engages students in the learning process and helps them develop critical thinking skills. Traditional teaching styles have evolved with the advent of differentiated instruction, prompting teachers to adjust their styles toward students’ learning needs.
What are the different styles of teaching?
The following list of teaching styles highlights the five main strategies teachers use in the classroom, as well as the benefits and potential pitfalls of each respective teaching method.

Authority, or lecture style
The authority model is teacher-centered and frequently entails lengthy lecture sessions or one-way presentations. Students are expected to take notes or absorb information.

Pros: This style is acceptable for certain higher-education disciplines and auditorium settings with large groups of students. The pure lecture style is most suitable for subjects like history that necessitate memorization of key facts, dates, names, etc.
Cons: It is a questionable model for teaching children because there is little or no interaction with the teacher.
Demonstrator, or coach style
The demonstrator retains the formal authority role while allowing teachers to demonstrate their expertise by showing students what they need to know.

Pros: This style gives teachers opportunities to incorporate a variety of formats including lectures, multimedia presentations and demonstrations.
Cons: Although it’s well-suited for teaching mathematics, music, physical education, arts and crafts, it is difficult to accommodate students’ individual needs in larger classrooms.
Facilitator, or activity style
Facilitators promote self-learning and help students develop critical thinking skills and retain knowledge that leads to self-actualization.

Pros: This style trains students to ask questions and helps develop skills to find answers and solutions through exploration; it is ideal for teaching science and similar subjects.
Cons: Challenges teacher to interact with students and prompt them toward discovery rather than lecturing facts and testing knowledge through memorization.
Delegator, or group style
The delegator style is best-suited for curriculum that requires lab activities, such as chemistry and biology, or subjects that warrant peer feedback, like debate and creative writing.

Pros: Guided discovery and inquiry-based learning places the teacher in an observer role that inspires students by working in tandem toward common goals.
Cons: Considered a modern style of teaching, it is sometimes criticized as newfangled and geared toward teacher as consultant rather than the traditional authority figure.
Hybrid, or blended style
Hybrid, or blended style, follows an integrated approach to teaching that blends the teachers’ personality and interests with students’ needs and curriculum-appropriate methods.

Pros: Achieves the inclusive approach of combining teaching style clusters and enables teachers to tailor their styles to student needs and appropriate subject matter.
Cons: Hybrid style runs the risk of trying to be too many things to all students, prompting teachers to spread themselves too thin and dilute learning.
Because teachers have styles that reflect their distinct personalities and curriculum — from math and science to English and history — it’s crucial that they remain focused on their teaching objectives and avoid trying to be all things to all students.

This paraphrased quote might be helpful as well:

"Average students answer the questions, good students question the answers."

I'm currently working my way through Lockhart's Lament, which is UNFVCKINGBELIEVABLY awesome!! !
10/10.
Many thanks for the recomm.

I'm sry to hear your story. It sounds like you missed your true passion. Is it too late? I'm drawn to Maths in a powerful way. It is a great regret of mine to have not studied it in a devoted way. The greatest language ever written, imo. Science would be an infant without it. Anyway, I share your attraction to it, to say the least.

I read the article.
Thanks for adding to the discussion, I appreciate that.

What I am trying to understand better is learning styles not teaching styles.

I find that the teachers that I have encountered in K-12 are average IQ, unmotivated, utterly devoid of passion, only interested in classroom control, obsessed with a top-down approach, and getting through their miserable excuse for a career to the big juicy pension/benefits at the end.

Only when I got to a graduate level did I encounter cases of true passion. I was lucky to have the odd Undergrad. Prof. that was reasonably good. Some were truly pathetic however...just sayin'

Aside: I had this Physiology Prof. and that #%@#% useless %&#@ stood there and READ her notes and would not even take questions...just stood there and f*****g READ to us as though we were 5 years old!! !!

I suffered through the first lecture, walked up and said "Are you going to do this for every single lecture?" She said" Yes, I am." I never returned. Photocopied the entire year of notes and read it on my own. Pathetic, hey?
shakes head grimly*

At any rate, we learn optimally in different ways. I want to understand those ways, in order to find a way of learning Maths that works best for me. Rote sucks...f**k it I want to deeply understand Maths, and I don't.

Powerfully true, in all ways!

and you will find, Rudin, that very few students question anything EVER. There cGPA may be Summa Cum Laude, BUT that does not mean they are critical thinkers.

Indeed. Creative thinking is notches above simply reading and memorizing notes and completely questions based on those notes. There should be a little bit of intuition.

I do not understand this sort of mode of living. That is to say: I do not understand NOT questioning things.
Another thing, why do people get so angry about things being questioned? It isn't an attack on their personhood or value as an individual or sentient being.
I really don't get it sometimes.
Not sure if that's me being naive or idealistic or a hopeless romantic or... idk.
I've quite literally (and I don't mean this in a sort of braggart way because I don't attach VALUE JUDGEMENTS to such statements...) never met IRL someone that has had the stamina for questioning or ideation that I seem to be cursed with. The incessant need for discovery and rumination. I quite dislike it, but it is quite like a paroxysm of my own mind that will not let me breathe until I have heeded it- answered whatever question. I have had no other need or compulsion stronger than the one to answer questions, fundamental in nature, about my reality or the universe. In its tighest vicegrip it rivals the need to eat and sleep. I do not mean this in a sort of bragging sort of manner, but simply that without probing and thinking I simply start to die. I experience this sort of insufferable sort of listlessness and simply languish when not allowed to pursue whatever intellectual trail I happen to be upon at the moment. And it never seems to end... depression certainly dampens the impulse, but it never dies.
All this to reiterate that I don't understand how people can NOT be like that. What does it MEAN to not question?????
I may never know haha!
Sorry for the tangent...

It's okay as long as you tell me what means.

I'm primarily a visual thinker and learner, and this is especially true when it comes to math. One of the biggest complaints my teachers always gave to my mom was that I got the rights answers, but they needed me to show my work. Problem was my mental process nearly always had to tackle the problem in a different way from the one explained. When I was a kid, a few times I took literally the teacher's demands that I show my work on my tests and homework. And so I drew little pictures and diagrams all over the place attempting to show how I got my answers. Of course that didn't fly.

I'm also not a very good listener, especially in a crowded classroom setting, so more of my learning happened at home when I could quietly read and look at the examples and make sense of them on my own.

I guess the best advise I can give based on my own learning style is that the teachers I've had that had the most success at teaching their students had alot of variety in their teaching methods. Printouts of the material for the readers, if you don't want to spend too much time writing things out in class. At least one hands on activity for the kinesthetic learners. For the auditory lingustic learners, have disscussions, not just lectures. For the visual learners, pictures are always helpful. Just writing words on the board doesn't always help. They will inevitably make models in their head, anyway. But actively engaging visual learners with visual stimuli will help them get it more quickly, because they don't have as much to translate. I think teachers need to learn to tolerate different learning strategies that students develop, too. Not every method a student uses to understand something needs to be corrected.

The was just my reaction in surprise to how much I typed; I didn't expect to type all that

I like to digest the information more throughly by looking for more exact ways to explain it. It's kind of a struggle to do this at the schools pace but the dividends are reference material for later.

I wish I could upload some of the stuff I've done. I color code a lot, sometimes it can help you see a pattern in things, it definitely helps keep track of trig properties. There's definitely a higher level I want to take things to, but for now I'm happy mapping out all the ground rules I come across.

I also started this thing called the how-to section. I follow the format of GIVEN-FIND-STEPS-SOLUTION. After linear algebra, math got to the point to me where knowing the formula or theorem wasn't good enough because now we were being given information and asked to find things for more and more questions.

I'm a stickler for keeping it neat in case I need to reuse the information (which has happened). If you'd like some reference material, I can send what I've made as a PDF, that's my open offer with everyone anyway.

Kewl!
can u PM the file to my acct., I'd love to take a look!

I have always been a strong visual learner, including mathematics. When I was in high school, I had a very dry teacher who just wanted to solve equations and do proofs without showing how this could be useful in life. That meant that I really retained only a portion of what I learned from those classes. When I got into college, I had some very good professors who wanted to use real world examples in their problems. My uptake in those classes increase greatly because I could "see" what I was using the methods for instead of just honing my equation solving skills over and over again.

For example, linear algebra can be used to describe symmetry operations in crystal lattice systems, which is important in my field of chemistry. (Symmetry forms can play into certain chemical properties.) Without using matrices, we would likely not be able to solve crystal structures of materials using x-ray diffraction techniques. My hat goes off to the scientists who could figure them out by hand sixty years ago. It would take them months to years to solve just one (and they had to be careful that a mistake did not occur). Using different computer matrices programs, a good crystallographer can solve small molecules in 10-20 minutes, larger molecules taking more time to do. I am glad I never had to solve a complex protein structure, as some of them take weeks to months (to even years) to do with the aid of computers. I would hate to see how long it would take to do those by hand.