How to teach math effectively: 8 tips for math professors to improve their student success rates


Math, an academic subject that is both fascinating yet frustrating at the same time. The world runs on math, everything humans have achieved in science and technology has at least some elements of math in it from basic math problems to the more sophisticated formulas. Which is why math is a key subject in academics that can’t be worked around in college and thus math can be a road block for many students as I’ve mentioned before here. No disrespect intended but one of the reasons for math being a roadblock for many students is that unfortunately many(not all) math professors don’t know how to properly teach math as indicated by the high fail and drop rates in higher math courses. So many changes to the system have been implemented from new laws removing remedial math requirements to alternative math courses designed specifically for students who struggle with math. There are also many people(myself included) who think higher level math courses should be replaced with more reasonable alternative courses for non stem majors. One of the problems is how many math professors teach in a way that only works for the few students who are exceptionally good at math. Here are ways math professors can teach that can help improve success rates of their students.

Note: While this is primarily for college math professors, K-12 math teachers can benefit from these tips as well.

How to teach math effectively: 8 tips for math professors to improve their student success rates

1.) Be detailed but simplified in explanation: Some professors are either too vague when explaining problems, very detailed but confusing or both. When explaining how to do a problem be sure to thoroughly explain the problem but simplify the explanation as much as possible because remember not every student is as passionate and knowledgeable about math as you are.

How to teach math effectively: 8 tips for math professors to improve their student success rates

2.) Only give homework for stuff that will be on quizzes and tests: One of the most frustrating things about many math courses is that the instructors will assign homework on items that weren’t even thought in class or aren’t even on quizzes or exams. This causes cramming which causes material retention to be much harder since students have to invest more time and energy in stuff they don’t even need on the quizzes or exams. In many cases the stuff they do retain isn’t even on the exam.

How to teach math effectively: 8 tips for math professors to improve their student success rates

3.) Work out at least one example for each problem in the class work: I’ve lost count of how many math professors do a few problems on the board/projector yet stop midway and say “okay for the next 5 minutes do the rest yourselves”. When this happens the instructor will pace back and forth through the isles while students act as if they are actually doing the problems since they don’t know how to do them. It’s even worse when the professor says, “alright moving on” without even going over the example problems. And then when the class work comes around, the students don’t know how to do many of the problems because the professor failed to go over the examples or didn’t teach how to do every type of problem within the section. Instead be sure to go over every example and also include at least one worked example for every problem in the section.

How to teach math effectively: 8 tips for math professors to improve their student success rates

4.) Study guides should be study guides: Math study guides are notorious for simply being packets of unsolved math problems. How is the student expected to study when the study guide is blank? For starters the study guides should only have material that will be on the exam. Study guides should already be completed with all the steps included so the students can use the study guide to help them review the material they are struggling on.

How to teach math effectively: 8 tips for math professors to improve their student success rates

5.) Give out practice tests at least 2 weeks prior to the exam: Quizzes are poor indicators of how much the students have learned thus far since they are relatively short and don’t include all the material they’ve learned so far. Instructors should also give practice tests to the students so they can practice for the exam and see how ready they are for the exam. Of course these practice tests should only have material that will be on the exam and the material should be arranged in the same order that the material will be arranged in the exam. That way students won’t get any unwanted surprises during the exam.

How to teach math effectively: 8 tips for math professors to improve their student success rates

6.) Use digital programs wisely: As digital technology continues to expand it’s influence over teaching by replacing written homework with online homework and paperback textbooks with digital copies. Be sure to use such technology wisely by selecting programs that are truly competent enough to help all students succeed. Because like all products, certain programs are completely useless while others are very good. When selecting a program for your students to do their homework on, be sure that the program gives a worked example for each problem, be sure that if the program isn’t free that it isn’t too pricey and be sure that the program is easily accessible outside of school.

When your online math program is useless
When your online math program is useless

7.) Give students breaks: In certain places professors who teach courses that two hours long or longer are legally required to give students at least a 10 minute break. Not giving your students breaks can cause students to become jittery, fidgety and lose focus. Students need breaks so they can go use the restroom, take care of emergency calls, have a snack or even get a few minutes of shut eye. Please be courteous and respect your students need for a break.

How to teach math effectively: 8 tips for math professors to improve their student success rates

8.) Be approachable: Due to the intensity of math, it’s only natural for students to have questions. Be patient and remember that your students are not experts like you and many probably wouldn’t take the class if they didn’t have to. Leave whatever personal matters you are dealing with aside and focus on helping your students get the highest grade they can get. Don’t be rude to your students and make it clear that you are glad to answer any questions they may have about the subject.

How to teach math effectively: 8 tips for math professors to improve their student success rates

Conclusion: Overall you as the professor should be collaborating with the students not be at odds with the students. There should be good chemistry and understanding between you the professor and the students. Be organized, be thorough yet easy to understand, be specific with your subject material, only give students subject material they’ll need for the exam and be sure to give them enough time to study for the exams. Students should not have to over rely on tutoring just to pass the class, it should be both the lectures and the material given to them to study at home that allows the students to pass the class. While I’m sure there are great math professors out there, there are many math professors who need to work on their teaching skills.


How to teach math effectively: 8 tips for math professors to improve their student success rates
Add Opinion

Most Helpful Girl

  • Darcia
    Math can be difficult for some people. Some may suffer with dyscalculia where they have trouble with numbers, calculations, and even basic arithmetic. I by sure thought I was out of the woods with taking math. My last and only upper level math was suppose to be Elementary Statistics, but recently I’ve upgraded to taking College Algebra & now in Statistical Methods. Though, I’m at the end I know I’ll have to revisit the basic math that got me into the predicament where I am today. If only I can pass the entrance exam to go into a nursing program that would be a great start to a new beginning!
    Is this still revelant?

Most Helpful Guy

  • Snakeyes7
    I think I have another suggestion feel free to let me know if this works:

    9. Make the exam the same difficulty as the easiest question in the homework.

    I never understood why professors make the problems overly long and difficult on the exam. If the student didn’t know what to do on the problem they couldn’t do it anyway. What is the point in making it long and easy to mess up? Make it rewarding for those who remember how to do the problem.
    Is this still revelant?

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What Girls & Guys Said

  • Regmorus
    I totally disagree that teaching actual math at a highschool could function by using exam oriented study programm. Maybe that's a necessity, when you are teaching a course of students, who only need to learn how to apply math.

    But teaching actual math to mathematics students should happen followed by giving new types tasks in exam that can still be soved by teached methods, but that will require certain spontaneous thinking of new ideas. I would even be for the total change of the suggested paradigm: the tasks for an exam should be included in exam by only considering which skill and understanding of which matters students should have and not specifically which tasks they already had.

    With all due respect to suggested opinions, you have to teach mathematical thinking related to the subject by teaching maths and not just to teach how to solve some special problems. Otherwise the students would be able to solve only the types of problems you taught them in the future and some similar types would appear as terra incognita to them.

    Me as a student (who struggles with maths himself sometimes, - I'm not an ace yet - so that you don't have to think, that my opinion is such of a nerd or like that ) wouldn' t appreciate having had a course "just for exam" and neither I would appreciate being taught algorithms instead of understanding and general abilities to deal with stuff, that aren't restricted to some types listed somewhere. (Lucky for us, our professors do exactly the right job in this sense)

    About other things I agree with the starting posting, well pointed out!
    • ADFSDF1996

      The problem is mostly in regards to how only around 20% of the material in each section is on exams. It basically becomes a guessing game in having to guess the correct material to study. It’s also inconsiderate to students who suffer from learning disabilities such as Dyscalculia.

    • Regmorus

      But professors often have to cover larger areas by teaching just because students should be familiar with them. That is how it is meant, everyone has actually to learn all of the stuff. As you say that is really a guessing game, but it is not due to wrong didactic, I think, that's on purpose.

      I can also good follow you what concerns students suffering from learning diasabilities, so that the way it is it can be very difficult or impossible to them to complete courses. On the other side there is never a solution, that could be ideal for all of the students.
      I fear, that if math courses would look like you suggest, if only stuff, that is in exam will be taught, we'd have specialists (regardless in which branch, as long as we are talking about technical sciences) with a very restricted knowledge of mathematics. Therefore having problems to use maths to solve scientific real life problems in engineering or physics for example or even biology and so on, because you can't know beforehand, which maths will be needed for analyzing the models they'll have to create and analyze in their future.. In my opinion, you have to provide your students with certain flexibility on the matter of maths, when you teach it.

      Maybe a real alternative solution for people having specifical difficulties by studying maths would be really to offer generally three types of maths courses:

    • Regmorus

      one type for applied technical sciences (so yod'd learn mathematical thinking but not a whole lot of it),

      one type for mathematicians

      and, what's new then, one type for people who doesn't really need maths in their future educational or working life and for people, who only need to get the course done and for students, who suffer from any learning disabilities (maybe with the possbility to write their exam exam in special suitable conditions)

      Maybe that would be the only solution, which doesn't diminish the quality of specialists, that really need maths directly or indirectly and at the same time providing equal chances for all of us, who have special life situations like mentioned by you.
      Of course that would cost additional money and maybe would require some changes of the exsiting order at highschools, but maybe that's the only way to provide equal chances for anyone without havig a bad impact on the mathematical qualifications of specialists, who really need it.

      Would it be the solution we, people, should pursue (ideally) in your opinion too?

    • Show All
  • Avicenna
    Very good advice, but one thing I've also noticed at the high school level is that prior knowledge of lower level math can't be assumed, e. g., algebra and trig deficiencies causing problems in calculus.
    • zagor

      Yes, I was teaching an intermediate algebra class and the first day a student asked me what a negative number was.


  • SirRexington
    I think it's amazing @Darcia mentioned it but dyscalculia is a disorder which makes it extremely difficult to understand algebraic equations and calculations. I have dyscalculia.

    Math does need to be taught in a way that is reasonable for the average person.
    • Darcia

      Yes, I have it as well.

  • IlyaTheImpaler
    I dont think I have had any of these problems in my education thus far, but here's what I think:
    1. Agreed
    2. All professors I've known would say very clearly which topics will not be tested and are only needed for deeper understanding. However some students might expect more, they expect the homework problems to follow the same form as the test questions, as in, same routine. That would be unreasonable. The profs can only give you the information about which broad topics will be tested. The tests should be more than just applying formulas. Also I think this can be resolved by asking through emails.
    3. This depends on which class. In the classes I've taken, professors usually solve the significant problems. If you have difficulty with some problems that he deemed too trivial, I guess you need to go meet him directly after classes. To go over all problems would interrupt with the exposition of the theory. Theory is not problems, and there's not enough time for both.
    4. I've never seen a math study guide. I use either textbooks, or lecture notes from the professors, or notes I wrote.
    5. This is pretty cool idea. Some of my teachers make past year exams available since the beginning of the semesters. They are usually professors of applied math/engineering. Pure math profs don't usually do this.
    6. Agreed. Though all my homework are done by typing Latex then compile into pdfs, for programming everyone use Github for sharing and grading.
    7. Strongly agreed. Pee breaks are needed in cold lecture halls. We often have one 20 minutes break in 3 hours lecture
    8. Strongly agreed. All professors I've known actually want students to ask them any question they might have, they might actually look disappointed if nobody has any question (which is usually the case lol). We can ask questions during lectures, after class or during office hours. We are welcome to their office to discuss various topic related to the course, sometimes even unrelated topics about life, career, hobbies etc
    • ADFSDF1996

      2.) Not the same exact math problems but rather the same type of math problems as the homework. And the homework should only have the same type of math problems that will be on the exams, Nothing more nothing less. Including material on homework that’s not even on the exams is a waste of time. A lot times the instructor will be very secretive of what’s on the exam, they won’t even tell the students how many problems are on the exam.

  • _gigi18
    This is what my maths teacher is like. I'm currently working as a maths tutor to young kids and we use this exact method. This is really helpful for parents who want to help their kids with maths homework.
  • Tia_Maria
    I wish my maths teacher could have read this. I wouldn't be useless at maths if he had lol
    Maths is the only subject I struggled with at school. Even now I'm not very good at it.
  • simplelikeme
    In my opinion, it is 50% responsibility for the students and 50% responsibility for the teachers. Both need to take responsibility and their roles in this scenario. If a student is having problems they need to speak up and let that teacher know I need help I don't understand this. And teachers need to take more time and give that one-on-one experience for those who do need that help. With that being said not everybody can learn the same way. So we need to stop and evaluate and understand the individual students that need help and help them in the way that they can understand how math is and how it works. When I was growing up I had a learning disability, but once I got the right teacher to help me understand how math was, I became a master of it. I can actually come up with an answer quicker than anybody can come up with on a calculator. I know for a fact a lot of parents just push their kids off onto the teachers to raise their kids, teachers are not there to raise other people's kids. Teachers are there to educate our kids. I also find that it is most of the time the parents fault for not spending enough time in their children's lives to help them with these problems. And ultimately in the end teachers like you struggle. So I do feel for you teachers. I also feel for those children who have been neglected and not have that proper support from their parents.
  • BeingSingleBlows
    I'm good at math. Its all about repetition. The first thing you have to do is work through one problem following another similar one as an example. Do it more times and you eventually won't need the example. You will learn the process and at that point you learned it. I honestly found class a waste of time. The book was my teacher with examples in the beginning of the chapters and I've aced calculus already. They will see the overall patter in problems eventually no matter at what level.
  • es20490446e
    Here's my way:

    Do not explain, let the students figure out the way.

    Start with the easiest exercises, give an example already written in paper, and let the students figure out the way to solve the exercises.
    • Sounds like a great idea to me 📚🗒️✍️✏️

    • QueenTanya

      that's too frustrating to make us try and figure it out ourselves. that isn't encouraging independence, that's just negligence. what are you good for if you aren't here to teach? i'd easily give up if a teacher refused to explain a topic, at least once. just my opinion

    • @QueenTanya yeah I just take back what I said I agree with you Queen I had a math tutor once. He wanted me to figure it out myself. With out actually should me how to get to the answers really... He just sat there.. smh

    • Show All
  • pocketman
    You also need to be interested in math. I had so many teachers that were not interested in their subject and couldnt get the class to pay attention
  • lookin64
    Those are some great guidelines and wish those that taught me had followed them.
  • Flamesofcinder
    Okay so before I read it I got a U in math at GCSE level and I have autism and have always struggled with this, in collage I had too resit primary school level maths (which is children from the ages 6-10) and I was one of two and it felt really embarrassing and has put me off wanting too learn unfortunately I want too be a sex therapist which from what am told am good at but need maths as I will be looking at data and statics a lot ><. Will this simplify maths for me or should I just give up we’ll am ahead?
  • Deathraider
    I think teaching maths and learning maths become much easier once you show proof of something. Because it then no longer appears like magic, but students can have a understanding of why it is true.
  • JimmyQ
    You want to cut to the quick. Pay money for correct answers. The smartest students are even paying attention.
  • DWornock
    I think the problem is that especially in high school, teachers teach rules rather than understanding. And, memorizing rules such as transpose and change signs rather than teaching an understanding of what that actually is (subtracting or adding the same amount to both sided of the equal sign). Memorizing rules without understanding prior to very advanced college math courses, makes learning math very difficult. In fact, most female high school math teachers have learned the rules without understanding.
  • Robertcw
    Actually the best way to be a great math teacher is to show all the students exactly why everything that is true in mathematics is true.

    That means highlighting the common sense theory when it is not explained in the curriculum. For example, when teaching limits countability should be explained clearly and logically. That there is no smallest positive rational ir irrational number should be explained clearly and logically. The relationship between these things and countability should be highlighted, and used to explain why limits require the epsilon-delta definition in order to make actual sense.
    • Robertcw

      Irrational numbers also need to be defined as the sequences of rational numbers that they are in order to be very clear as a math teacher.

    • Robertcw

      We need a more no nonsense approach to instruction.

    • Countability is a property of sets, limit is a property of functions/sequences, whoever told you that the relationship between these two things must be highlighted in order to explain limit just sounds deeply confused about Calculus to me, it's easy to connect the two ideas, but that connection isn't central, kinda missed the point of limit. Similarly, that there is no smallest positive rational or irrational is a consequence of density, who tf use density to explain limit lol, density is a relative property between two sets... e. g rationals are dense in reals -> no smallest positive rational, integers are not dense in reals -> there is a smallest positive integer.

      Showing the students why true things in mathematics are true is something every professor already does, it's called writing a proof. It might seem like magic to people who never took a serious math courses, but all serious math courses are about writing proofs, and not about applying formulas/algorithms. If someone doesn't understand a theorem, professors could give bazillion of proofs of that theorem and while the student could follow the logic, they might still not understand it. In fact this is the most typical situation for people who dont like math. The important thing missing is not why things in math are true, but why things in math are defined the way they are. There are deep reasons behind every definition of math, that's where the magic is.

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  • Chase7777
    You need to be somewhat intelligent to be a good teacher, specifically with abstract subjects like math. Those people are very rare though.
    The curriculum should be way more about solving actual interdisciplinary problems then just learning the basics without any way of applying them interestingly.

    I noticed that people simply found math way to boring to pay attention while attention is needed to learn the basics, math builds upon itself. That's what makes it seemingly hard when it really isn't if people would know the basics.
    The current way of teaching is inherently flawed, teachers should act more as inspirational figures than fact outputs which are rendered obsolete through the internet nowadays.
  • SecretGardenBlood65
    Good take
  • kim45456
    Great take