## Opinions

Here are a few answers^{1} to the question. (I have highlighted aspects of the answer that I believe are what make mathematics difficult.)

- First, teachers. A lot of elementary school teachers hate math and almost none of them ever do any math. That is, they don’t try to prove theorems or solve puzzles or come up with conjectures.
*They don’t know 10 ways to solve each problem*and they don’t find math interesting. They communicate this to the kids, perhaps not directly, but indirectly. And when kids ask interesting questions, the teachers can’t answer.^{2} - Second,
*curriculum*. What we do in math education is amazingly awful.^{2} - Another “very short answer” to this question says: because it’s taught badly.
^{3} - A very short answer: because they were badly taught and had
*no sufficient support from the family*.^{4} - I have never really had a good math teacher in my school. I’m not saying they were not good at math, in fact, on the contrary, they were quite intelligent. However, the problem is,
*teaching is not all about intelligence*. It’s*an art*and a lot of people are not very good with it. But back then, I used to think that the problem was only with me and not with my teachers because my classmates were able to comprehend and calculate math problems in their head. I didn’t realise at that time that*everyone’s mental capacity is different and that your mental capacity is influenced by a lot of different factors*like your background, your environment, your health, etc.^{5} - There is not a single reason for this but it is a combination of reasons:
^{6}- Because it is difficult. It’s a simple fact that not every subject is as difficult as the others and mathematics is just one of most difficult ones so of course students will find it difficult.
*Learning something and understanding something is not the same.*For most subjects learning is enough but mathematics requires understanding. On the other side if you understand mathematics you hardly need to learn at all.- Mathematics is intimidating.
*This ties into the previous point, if people encounter things they don’t understand they get intimidated by it which makes them apprehensive engaging with it.*This is a point where a lot of students kinda give up unconsciously and they just want to get past this without having to deal with it. In the end they try to learn some recipes for specific problems and apply that without real understanding. *Mathematics requires abstract thinking*and a lot of people struggle with that as it seems too detached from the perceived reality. Getting to the level of abstract thinking that is necessary to understand more complex math is for many people like breaking through a wall and some just don’t make it.- Mathematics has a learning curve and this obscures the progress for the ones who try to learn it. In most subjects learning stuff is quite linear, e.g. (simplified) when learning a language you can learn say 20 new words in an hour, and you see the result after that hour of learning. In history you can learn X facts in an hour, and so on. On the other hand you can try to learn a mathematical concept for an hour and still not understand it and thus you see no progress. This makes some people think it is pointless for them to learn math and they give up.

- So, usually, the problem boils down to
*how the subject is taught*.^{7} - Public education began with the ideas that:
^{15}- Parents would be involved in their child’s education.
- Parents would be supportive of teachers and schools.
- Students would be respectful towards their teachers.
- Few students would end up going to college.
- Most students would finish school at age 18 and go straight into the workforce.
*Schools were primarily academic centers, with some sports thrown in after school.*- Schools would be primarily funded and run at the local level, thus making them more responsive to the wishes of the taxpayers who are actually paying for them and sending their children there.
- Students whose bad behaviors distracted from their classmates’ education would be removed from the classroom.
*Students who did not meet academic requirements for advancement to the next grade level wouldn’t be advanced to the next grade level.*

- Because it is! advanced pure mathematics requires
*a very high level of abstraction and precision*. it’s a two-sided game of intuition and rigor, and these skills need to be honed and developed.^{8} - The Department of Education is and always was unconstitutional, and since Jimmy Carter created it, the performance of American schools has constantly declined. The USA is now barely mediocre among OECD countries in reading, math, and science where once we were the best in the world.
^{13} - The idea is that if your emphasize collaboration, social-emotional learning and giving students a voice in how or what they learn they will be more engaged and not only learn more, but learn more deeply. In the child centered classroom,
*the adult doesn’t so much teach, but creates an environment where the students teach themselves and each other*. Ideally, the student’s learning is driven by their interests.^{14} - I have tutored students in math for nearly 25 years. There is a small set of things I recognize in students who have difficulty with math.
*Their problem is almost invariably at least one of these things*:^{9}- They had a “bad experience” with math at some point in their past which causes them to have an emotional mental block.
- They have, for some reason which may not have anything to do with a previous bad experience, decided that they simply don’t like math or will never be good at it.
- They fail to concentrate on understanding CONCEPTS. They prefer to look at math as a bunch of formulas or cookie cutter approaches to be applied in well-defined situations which closely resemble the situation in which they were “taught” the cookie-cutter approach.

- This answer is a bit more USA-centric, but compare these two curricular coherence charts. See the difference?
*In the USA, math is taught in an incredibly disorganized and slapdash manner that fails to respect the cumulative nature of math as a discipline.*Without mastery – not “passing,” but mastery – of arithmetic, more advanced topics such as algebra make no sense. Add that to the fact that math anxiety and poor arithmetic skills are pervasive in American society, including among grade school instructors, and it’s no surprise that students find math difficult.^{10}

## My Observations

Some of the additional reasons why I, based on being a student and a tutor, think students find mathematics difficult are as follows.

- Poor choice of books.
- Teachers using only the books, and the information therein, to instruct the student. (Some teachers bring in additional information and teaching methods to make the education fun and easier to understand. Hats off!)
- Too little time to really learn the subject, i.e., teach this point, move on to the next and complete the book (or syllabus) by the time schools ends for the year, quarter or semester. Rush, rush rush!)
- Using some consultants to establish what is the best way to teach. (Why do teachers, vice principals, principals and superintendents obtain so much schooling? Are the colleges and universities deficient in instructing them on how to teach the best way possible?)
- Focusing on a college education for all students. (One of the biggest lies that colleges and

universities make is that you will get a better paying job with a college education. For example, see Will More Education Earn You a Higher Salary? Not Necessarily, According to Experts.) - Political involvement at all levels. (For example, see Op-Ed: California’s math education needs an update, but not the one proposed)
- Many more criticisms, but I would like to stress that the problem is at all levels of education. Too much bureaucracy! I do not know what the solution is but I am happy to raise what problems exist so others with the ability to make the changes may take the necessary action.

## Mathematics Trench

I think this graphic has to be considered when discussing why students find mathematics difficult. I look at the **Mathematics Trench** as an illustration of a student’s progress to more advanced topics in mathematics, the better a foundation in basic mathematics is critical, and more abstract thinking is required. There are problems with the topics in the trench^{11}, but the trench is a cool illustration!

## 3 Things I Learned from the Country with Europe’s Best Schools

I recently discovered a *Medium* author named Eva Keiffenheim. An excellent author with many interesting articles. I am highlighting the one below where she presents the comparison between US and some European schools. I urge anyone interested in education to please read the entire article.

Let’s take a look at three powerful factors of high-performing education systems.^{12}

1) Data Transparency and Feedback Loops

“Missing feedback is one of the most

Donella Meadows

common causes of a system malfunction.”

2) Agency for Teachers and School Principals

“Agency is defined as the capacity to set a goal, reflect and act responsibly to effect change. It is about acting rather than being acted upon; shaping rather than being shaped; and making responsible decisions and choices rather than accepting those determined by others.”

OECD

3) Evidence-based Teaching and Learning

“When one looks at the scientific evidence about how the brain learns and at the design of our education system, one is forced to conclude that the system actively retards education”

Daisy Christodoulou

## References

^{1} “Why Do Students Find Mathematics Difficult?”. 2022. *Quora*. https://www.quora.com/Why-do-students-find-mathematics-difficult.

^{2} Peter. “What Are The Main Reasons Why Young Students Start To Hate Math?” 2022. *Quora*. https://qr.ae/pvYqdL.

^{3} Eustis, Alex. “Why Do Students Find Mathematics Difficult?” 2022. *Quora*. https://qr.ae/pvYqES.

^{4} Borovik, Alexandre. “Why Do Students Find Mathematics Difficult?” 2022. *Quora*. https://qr.ae/pvYq3P.

5 Sinha, Priyanka. “Why Do Students Find Mathematics Difficult?” 2022. *Quora*. https://qr.ae/pvYqEP.

^{6} Spallerina, Spalle. “Why Do Students Find Mathematics Difficult?” 2022. *Quora*. https://qr.ae/pvYqjq.

7 Wallewein, Ken. “Why Do Students Find Mathematics Difficult?” 2022. *Quora*. https://qr.ae/pvYqEE.

^{8} Narkin, Angela. “Why Do Students Find Mathematics Difficult?” 2022. *Quora*. https://qr.ae/pvYqjl.

^{9} Mann, Michael. “Why do I study math very hard, but I still can’t understand mathematical thinking? Geometry can be understood a little, but algebra and function I really can’t do well, is it related to people’s thinking?” 2022. *Quora*. https://qr.ae/pvYqdi.

^{10} Wang, Charles. “Why Do Students Find Mathematics Difficult?” 2022. *Quora*. https://qr.ae/pvYqED.

^{11} “What’s wrong with the mathematics trench?” 2022. *reddit.com*. https://www.reddit.com/r/math/comments/aemqcn/whats_wrong_with_the_mathematics_trench/.

^{12} Keiffenheim, Eva. “3 Things I Learned from the Country with Europe’s Best Schools”. 2022. *Medium*. https://medium.com/age-of-awareness/3-things-i-learned-from-the-country-with-europes-best-schools-6410a430638d.

^{13} Steward, Scott. ” The Austin American statesman reports that Abbott has said Texas could resurrect the SCOTUS case requiring the states to educate all kids. Would that possibly mean the removal of the education department?” 2022. *Quora*. https://qr.ae/pvAW5E.

^{14} Kord, Ted. ” What kind of education reform would be most beneficial to the U.S. right now?” 2022. *Quora*. https://qr.ae/pvAWbg.

^{15} Bates, Matthew. “What are some of the biggest problems with public education in America?” 2022. *Quora*. https://qr.ae/pvAWW9.

## Additional Reading

Rebeca T. “Why do so many American students struggle with math in the US compared to other nations around the world?” 2023. *Quora*. https://qr.ae/pr4Mj0.

The US does not perform as well as other countries because mathematics is not very highly valued in US culture.