# How to make math class interesting?

By Murray Bourne, 05 Oct 2011

I received this question recently from reader Maria in the Philippines:

Pls give some tips on how to make math interesting to college students.

Well, Maria, it's not only college students that find math boring, so this set of suggestions is for all math teachers (and I hope students benefit from it, too!).

[**Note about time needed:** Most of the following suggestions will take time away from your normal curriculum. You need to make a decision - do I plow through **all** of the topics but leave my students bored and unmotivated, or do I spend some time getting them excited about math (and hopefully, motivated enough to go and fill in any gaps by themselves)?

**Note about knowledge needed: **The following are basic suggestions. Of course, you are encouraged to find out a lot more about each one before trying them out.]

## 1. Make it meaningful

Many math courses suffer from the following issues:

- The teachers don't know why they are teaching particular math topics, and they often don't know what else the students are learning in other subjects.
- As a result, the students don't know why they learn those math topics, either. The common question, "Why do we have to learn this?", is a reasonable one. Do you have a good answer, beyond "It's in the exam" or worse, "Because it's good for you"?

See Dan Meyer: Math class needs a makeover

Some possible ways to fix this:

- Find out where the students will use each math topic you teach (it may be in their science class, or some engineering subject). It's great when you can use actual examples from those other subjects and let the students know that's where they'll use each math topic.
- Help students make connections between the math topic and the "real world". If you're not sure how it's used in the real world - do a search!

## 2. Start with concrete examples - leave the abstract concepts to later

Math is largely about abstraction. Mathematicians for centuries have thought about real problems and come up with practical ways to solve those problems. Later, they have generalized the process, usually presenting the solution using algebraic formulas.

When students have no idea what the original practical problems actually mean, how can they be expected to understand the abstractions of those problems (using the formulas)?

Use watermelons to teach calculus

Instead of starting each topic with a formula, start with concrete examples of the problems that were originally solved using that math. Then, help the students see how the math theory can help to solve such problems by showing them the thinking behind the solution.

One example of this approach is the watermelon volume problem at the bottom of this page: Volumes of Solid of Revolution.

Another thing to consider is these days students spend less time playing outdoors than they used to, so they have less experience to draw on when it comes to concepts like velocity, acceleration, gears on a bike, and generally how things work. So when we say "Imagine ...", students often find it hard to imagine what you are talking about due to lack of concrete experience with that concept.

This video about the FIRST program gives an idea of what's possible:

## 3. Start with an interesting, real-world problem (preferably localized)

Most math lectures start with "Here's the new formula for today, here's how you plug in values, here's the correct answer."

Problem is, there's no attempt to motivate the learners.

It is good to pique curiosity with a photograph, a short video, a diagram, a joke, or perhaps a graph. This trigger should outline an interesting problem in your local area (so students can relate to it better and feel more ownership).

Here's one: Engineered Drought? (China will continue to face severe water shortages, This will have serious implications for the millions of people living in Southeast Asia, since China will either have to buy (or take) water.

Twenty Global Problems and Twenty Years to Solve Them

Earth killer – composite trigonometry CO2 graph

Of course, refer back to your various real-world problems as the students learn more and eventually, give them a chance to propose a solution.

## 4. Where you can, use computers to do the drudge work

Many math courses seem to be more about calculation rather than concepts. These days, it doesn't make sense for humans to spend hours learning how to calculate using complicated algebra.

To quote John Allen Paulos:

Mathematics is no more computation than typing is literature.

And then this one, usually attributed to Albert Einstein:

Computers are incredibly fast, accurate, and stupid. Human beings are incredibly slow, inaccurate, and brilliant. Together they are powerful beyond imagination.

For the vast majority of your students (who will not eventually become mathematicians), it's more important they understand the concepts and which process to use when confronted with different real problems. They then should learn how to use computer algebra systems (or graphics calculators) to solve such problems.

Some examples:

- I observed a lesson recently where the math teacher got his students to calculate the standard deviation of a set of scores. He started with the formula then allowed the students to use Excel. He wanted them to apply the formula (rather than let Excel do it directly using STDEV, which is what many students actually did).
The problem was, the students didn't even know what "standard deviation" meant. They were just plugging in numbers with little idea of what it meant. Finally someone remembered the standard normal curve and could explain what they were all doing. (See Probability Distributions - Concepts)

The teacher should have made sure the students had the general idea first, including the general meaning of "distance from the mean".

- When finding the length of a curve using calculus, it's actually not possible to find the answer using ordinary integration (because the integral does not exist). But using a computer algebra system, we can easily find the answer for such problems and spend more time understanding the problem and the solution given. (See Arc Length of a Curve.)

Use free tools like Wolfram|Alpha and Geogebra with your students. It's best to get the students to use these tools, but if there are a limited numbers of computers, at least demonstrate the tools.

See:

## 5. Creativity and ownership

Many math students feel very little ownership for what's going on.

They have little say in what the topics are (that's usual for most formal education) and the exact same assignments are given to everyone. It's not surprising there is little enthusiasm for such "one size fits all" approaches.

Computer-generated flower

We are all creative, and we all enjoy being creative, but in most school systems creativity is discouraged. (See the excellent TED talk, Sir Ken Robinson: Do schools kill creativity?)

There are many ways we can encourage creativity in math. Technology is one avenue - get students to use creative means to describe a mathematical concept (it could be a video, an animation, a diagram or perhaps a concept map).

Such individualized assignments get them thinking about the bigger picture, encourages creativity, and is more likely to generate feelings of ownership than the normal mass-produced assignment.

## 6. Engage your math students

Involve your students in the lessons! When we talk **at** them (especially in a 2- or 3-hour hour lecture), without encouraging any involvement from them, it's no wonder they switch off.

In your class, get the students to **do** meaningful activities. These could include:

- Role play the concept
- Do a revision activity, particularly one that helps them to remember the vocabulary and symbols
**Discuss**(in pairs) a higher-level question about comparison, analysis, etc.- Get their ideas and feelings about the topic (this is rare in most math classes. They will appreciate being asked - and getting a response to their concerns)

Use **clickers** (or the good old low-tech hands up) to get feedback from them on:

- Are we going too fast or too slow?
- Ask questions which are often done incorrectly and get students to discuss how it should be done

Here's a good description of how this can work: Teaching math with clickers.

## 7. Ask more interesting questions

Consider this statement. Which is correct?

A boat carrying a large boulder is floating on a lake. The boulder is thrown overboard and sinks. The water in the lake (with respect to the shore)

1. rises.

2. drops.

3. remains the same.

For many students, math questions always come out of a text book or a worksheet. The questions are usually along the lines of "here's a word problem - take the figures, plug them into the given formula, do some calculation and move on to the next one."

But it's great to trigger the students into asking their own questions. This is more likely if the question is conceptual and interesting, rather than calculation-based. The above example (from Asking good questions in the mathematics classroom) is more likely to illicit a lot of genuine discussion than the normal text book question.

Here's another one from that paper:

Imagine that you are sky-diving. The graph of your speed as a function of time, from the time you jumped out of the plane to the time you achieve terminal velocity is most likely

a) Increasing concave down.

b) Decreasing concave down.

c) A straight line with positive slope.

d) Increasing concave up.

There's quite a bit going on here. A lot of conceptual understanding can result - and no calculation is needed!

Once students get used to this level of conceptual question, it is more likely they will ask deeper, more meaningful questions about what is going on.

## 8. Get the students to pose their own questions

Students gain a lot of insight into math when they have to create their own questions.

One simple idea to get the students into this is to get them to write questions for the mid-semester test (say). You could assign sub-topics to small groups of students and get them to propose 2 or 3 questions. It's surprising how well this demonstrates whether students really do understand what they've been doing. It also lets them see math from a broader perspective.

Then, get them to share their questions around the room and solve them. Some of them may be impossible to solve - it can be transformational when they discuss what's wrong with the question and then feed back their conclusions to the question posers.

They could do this using Google Docs (or a wiki) so there is a record of the thinking and problem solving process.

## 9. Journal

This will seem a crazy idea to start with, since it's very unusual in math class. However, it can be very beneficial for learning. (Reflection is a key element in efficient learning.)

Students don't see the value of **writing** about their math thought processes at first, but once they see how it can help them clarify their doubts, they become more enthusiastic about it.

This short article includes some ideas on the kind of questions you can use to prompt reflection in math:

Math journal with suggested prompts

Here are some more good ideas:

How to encourage critical thinking in science and math

## 10. Projects

A very effective way to engage students is to get them to design and make something that involves math.

This can be creative and hands-on (yet another thing that's missing in many math classes).

It would be really powerful if the item they need to make is related to other subjects they are studying. This helps students work out the big picture and make connections between what they need to know.

Some ideas:

- Create Lego robots
- Create an object that demonstrates the slope of a curve at a point
- Create Geogebra widgets that explain some concept.

This article has examples of summer projects that really should be happening in ordinary math class:

## Conclusion

I hope that gives you some ideas for how to math math class interesting, Maria. These are just "seed" ideas. There are many examples on the Web and your library will have even more.

If you still need some inspiration, (and more examples) you can always look at the 700 or so articles on math in SquareCirclez:

Do any readers have more to add? Please use the comments box below.

See the 40 Comments below.

5 Oct 2011 at 9:54 pm [Comment permalink]

As you note, some of the items you named, such as "ownership" and "students asking their own questions" may take time away from curriculum in a class where a teacher delivers information to students. However, this education model has never been efficient or sustainable in the first place! The same items shine in some of the more sustainable modern models of learning such as online peer-to-peer learning groups.

The Stanford AI class starting October 10th drew some 250,000 students by now. The tools you named are very significant, because they make such learning design not only interesting, but possible!

8 Oct 2011 at 1:37 am [Comment permalink]

I read the artecal carefully , it seems to me there is an experienced person behind it ,

The way I see it , we need not to presume that strong link between numbers and math in the first place,though most of my students think otherwise , I kept telling them " you may practice math without using numbers " , very few understood the point and many kind of refusing it , which is quite understandable to me considering the ways they have been tought math with, To make a long story short , I think math should not be looked at as a pure science rather a logical tool to handle certain type of problems , As much as math is useful to address some problem , it is not the appropriate way to express how much you love your mother for instance , writing a poem or kissing your mother cheek is much much better way to express your true feeling than telling your mother ,for example , "I have an exponential type of love to you " ,Mother would not appreciate your way at all ,she may even think of you as a jerck !!, So math should be tought as a logical tool to solve a certain type of problems . Thank you

8 Oct 2011 at 7:31 pm [Comment permalink]

Good article (above) - very insightful. Math is not a spectator sport. We teachers need to do everything we can to engage the students. It's amazing how even small things work: putting a student's name into a problem, calling a student up front to be the teacher's scribe or run a review session, changing a text book problem into something the kids relate to, challenging them to find out (google) the person who originated the math they are currently working with. This year I acquired an LCD projector and I've been making Power Point Lessons using lots of visuals (see some of my videos on YouTube - search "MrsCantey") ...what fun! Students are VERY engaged during those videos. The math songs I've created over the last five years have also been useful in livening up math classes. (Search "Susan Cantey" at CDBaby or Itunes if interested.)

8 Oct 2011 at 9:50 pm [Comment permalink]

The kids only remember a small amount of the standard curriculum when even dilegently taught by an experienced maths teacher .. so why not pique their curiousity and get them to think of questions outside of the standard and maybe they will desire to learn the answers and hence learn more of the standard curriculum.

9 Oct 2011 at 3:50 pm [Comment permalink]

I've read the article and found it very intresting.Also, I found that some suggestions can be applied directly which will help us (senior math teachers)to convince our students to accept (I can't dream and say like)learning math in higher grades. Students in some Arabic countries are forced indirectly to study higher level of math courses, as: Calculus or A-Level, although they are not planning to study engineering, or something related. They are forced according to the regulations of their Home-Countries or they think that studying these courses will give them better chances of acceptance in government universities. As a result we are suffering in some of these classes when considering different levels of students.

I had a chance to engage students in deciding the type of questions they will have in their exams (it worked with some of them and they've improved,but not for all). Also, our classes in my school are provided with datashow which enables us use different related videoes downloaded from You-Tube. I've liked the idea of the watermilon and I'm planning to use it when I will explain the related lesson, and trying to start with applied examples than just abstract formulas. Further more, software applications (especially graphical calculators) are used in the related lessons as: Functions, Transformations, ...etc. We are trying our best, but we are restricted by the time and preparation for formal exams. Nevertheless, I will be always very happy to benfit from my colleages' suggestions and experiences practically in classes and not only theorems far from reality.

9 Oct 2011 at 5:41 pm [Comment permalink]

@saad, I like your point about numbers. And yes, it is hard to convince people of this.

I would like to argue that the expression of love depends. I am a mother, and I would find "my love is exponential" to be much more endearing and fun than a kiss from my kid. That's because we are a family of mathematicians, and we do talk like this, and for us it is the language of love.

In "Here comes everybody" Clay Shirky had a phrase about open source developers: "Loving one another in the context of Perl."

It is one of my favorite ways to describe a productive, healthy community.

11 Oct 2011 at 1:51 am [Comment permalink]

The points made are quite practical. There are certain topic which when illustrated would lead the learners to the feeling they are being subjected to drudgery. It is more likely with the average and below average learners.

Besides the teacher is under numerous pulls and pressures to close the syllabus well before time. This is indeed the fact if it were a public funded school.

13 Oct 2011 at 10:40 pm [Comment permalink]

what is the importance of mathematics subject for our daily life?

14 Oct 2011 at 1:41 pm [Comment permalink]

Hello msee. You could do a search on real-life math on this blog and get plenty of answers!

14 Oct 2011 at 6:39 pm [Comment permalink]

this is a very helpfull information as specialy to young upcoming student teachers like me

16 Oct 2011 at 12:37 pm [Comment permalink]

I'm glad it was useful for you, Matheus!

3 Nov 2011 at 1:31 pm [Comment permalink]

I was very, very lucky to have, for 2nd-semester calculus, a teacher who FELT and, for me, conveyed the BEAUTY of mathematics. When he explained briefly the way Euler connected all math from all centuries, it was so beautiful that I almost cried. How can we convey, at all levels, the BEAUTY of mathematics?

Of more immediate practicality for some: I have found that I understand math concepts best when I first learn how the originators developed the concepts. It is as if I am with them; it makes me feel as if I had helped discover the concepts. Then I absorb the concepts, and often the procedural steps, much more readily.

15 Dec 2011 at 10:11 am [Comment permalink]

I found the material very good and certainly useful. Just a small comment on the quote by Einstein (justly admired as one of the giants in the history of science) about computers: at the time of his death (1955) computers were little known outside a small number of research labs, and were far from attaining the immense popularity they enjoy now. I don´t think the time was ripe for a dictum like the one by Einstein, since only a handful of people around the world were familiar with computers. Einstein is one of the more misquoted figures in history, I think...

15 Dec 2011 at 9:07 pm [Comment permalink]

@Tomas: Yes, that's why I wrote "usually attributed to Albert Einstein". I probably should have put "usually wrongly attributed to Albert Einstein".

1 Jan 2012 at 11:48 pm [Comment permalink]

Yes, we need to concrete mathematics more

but there is a point what we shouldn't forget that Mathematics has abstract nature so

if we try to relate all the concept with daily life

how we could teach abstraction ability to students. This is my point of view as a mathematician.

2 Jan 2012 at 8:36 pm [Comment permalink]

@Sevimli: You are right - the abstraction process is important. But we should let the students do that, rather than us do it for them! (The latter causes a lot of confusion if the students are not ready for it.)

18 Jan 2012 at 6:37 am [Comment permalink]

Between teaching them real mathematics at the expense of hindsight and telling them of the marvelous applications of it and risk raising spoiled brats who think everything's too easy because they're too good for it I'll have the first one. Truth is sometimes life comes down to doing extremely boring things to reap the rewards later..

13 Jun 2012 at 2:09 am [Comment permalink]

Very good ! It is so help full.

1 Sep 2012 at 2:28 am [Comment permalink]

I like the many views and pints raised on this blog. We seem to have a lot more in common about maths. Society has its effects also on the attitude of many learners.

I would appreciate many leads with more literature review

13 Sep 2012 at 7:18 am [Comment permalink]

I love your blog.

I would like to ask some tips in creating math tests. Basically the do's and dont's in math test writing. Thank you.

13 Sep 2012 at 2:39 pm [Comment permalink]

@Carylle: Thanks for your kind comment and for the good topic suggestion. I have a long list of requests already, but I will try to get to it as soon as I can!

15 Jan 2014 at 5:03 pm [Comment permalink]

Sir, I have created a puzzle based on the concepts of magic squares. I call it magic square puzzle. You can go to http://www.magicsquarepuzzles.com and play it. I have taken to several schools and find the interest level of the students to be high on this one. I request you to give your valuable feed back to me on this.

Mahesh

17 Jan 2014 at 11:53 am [Comment permalink]

Hello Mahesh. Thanks for sharing. I had a quick play of one of your magic squares and it looks good.

Since this is a good activity for children to learn mental addition and subtraction, it may be an idea to hide the sum of each row, and offer higher scores for those who choose not to look at them. Just an idea.

13 May 2014 at 12:55 am [Comment permalink]

I believe your suggestions are spot on. Years ago a veteran teacher told me that the key to holding students' interest is making certain they experience a sense of accomplishment. For many students understanding math concepts and procedures and doing well on a quiz or test, just don't give them a sense of accomplishment. These are not positive motivators for them. They need something more tangible/something that is more meaningful from their perspective. I think that's what's really behind the question, "When will I ever use this?" I believe your 10 suggestions, as well as the caveat that these will take time from the curriculum, address the issue head on. For that reason I'd like to post a link on my blog. Note: I have just started my blog. The subject is the need to make math fun for both teachers and students.

13 May 2014 at 8:14 am [Comment permalink]

Thanks, Jim, and all the best with your blog!

3 Oct 2014 at 7:51 pm [Comment permalink]

Thanks ! Mostly the Students of the Collage got Bored as they want interesting facts in the Lecture and it could be happens when the teacher give the Students some perfect real time examples this will induce the student's interaction at the moment.

Thanks again for this Post and hope for many others from your side.

4 Nov 2014 at 6:29 pm [Comment permalink]

These are some of the best suggestions I ever read about maths learning. I have been a maths scholar since school days and I love to read and teach maths a lot. Nowadays, I take part time maths class in one or two schools and I am sure that my students are going to love these new ways of maths learning. Thanks for the wonderful post

8 Dec 2014 at 11:34 am [Comment permalink]

These are very good suggestions in terms of approach to math. Thank you for this post, it is so relevant to school students nowadays.

18 Dec 2014 at 12:31 am [Comment permalink]

thnx mann it made my presentation really welll.... thanx

3 Jan 2015 at 11:14 pm [Comment permalink]

This is an awesome articles.I really enjoyed and have fun in reading it.

Thank You very much for sharing.

I am just wondering, Effective teaching Mathematics has been a concern years ago but still a problem nowadays?

8 Jan 2015 at 3:23 pm [Comment permalink]

@Manuel: Yes, how to teach mathematics effectively is still very much a concern!

22 Jul 2015 at 1:16 am [Comment permalink]

Will be passing this over to my friend who has just started teaching, thanks for such a super post. What would you say your biggest fear is when engaging with a new class to teach maths

26 Jul 2015 at 2:19 pm [Comment permalink]

@Mary: It's a good question, to ask about fears when meeting a new class. To this day, I feel some excitement when approaching the start of a new semester. The new students don't know me and don't know what to expect (and don't know what I expect of them). But once those things are sorted out, it's usually good!

So the recommendation is to be very clear about what you are doing, and what you expect the students to achieve. Then it's easier for both sides!

4 Aug 2015 at 11:08 pm [Comment permalink]

I found the article(answer) interesting and useful. Its a great idea to use watermelon for calculus. In that way (too) the elaboration is great. I thnk , for the first time I am seeing a useful material free. As everybody is 'selling', no one seemed honest in this regard. I must thank him/her for this article. No more words.

25 Mar 2016 at 6:09 pm [Comment permalink]

I'm a maths teacher.The points given are extremly good. I'll try them in my classes. I like the article and say many thanks for the person who has given such a beautiful ideas.

20 Apr 2016 at 9:17 pm [Comment permalink]

Loved the video you have integrated

18 Jan 2017 at 1:39 am [Comment permalink]

I agree with your ideas. But above all, as teachers we should make sure that all students are psychologically prepared to attend through the lesson. To me, psychology, academic environment and real life approach make much more contributions to understanding math than both technical and tactical approaches. I will try to embrace your models immediately and I hope i will be able to squeeze results.

26 Apr 2017 at 2:18 am [Comment permalink]

I notice that the problem we have in mathematics often times is that we have teachers without foundation in mathematics and they make the foundation of the learners bad. These learners there after meets up with another teacher who will incorporate his own idea and method....there is no single generalization in mathematics. Even with different methods veing applied I feel there is need for teachers to be taught on what or how to teach

6 Sep 2017 at 2:00 am [Comment permalink]

Thanks for going over some different tactics that could be used to make math class more interesting. I appreciate that you mentioned to show examples of the problems that can be solved using a particular type of math. Definitely seems like a great way to help them understand the benefits of this and how it's applied in the real world.

11 Oct 2017 at 3:00 pm [Comment permalink]

Moving from concrete to abstract is a great tip. Being a Montessori teacher myself, I have included everything is my class. When it comes to elementary math, curriculum moves relatively slowly, so kids have months to master concepts before moving on to the next topic. I include whatever I get, from props to culture, from activities to worksheets, from stories to games. Like I love worksheets on Halloween themes and my kids enjoyed the stories with math. Through Pinterest, I seek activities of math with craft and art. I realized, making such effort really helped my kids/students.