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9 Strategies for Motivating Students in Mathematics

Alfred Posamentier

Dean and professor of mathematics education at Mercy College, New York
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Motivating students to be (enthusiastically) receptive is one of the most important aspects of mathematics instruction and a critical aspect of the Common Core State Standards. Effective teachers should focus attention on the less interested students as well as the motivated ones. Presented in this blog post are nine techniques, based on intrinsic and extrinsic motivation, which can be used to motivate secondary school students in mathematics.

Extrinsic and Intrinsic Motivation

Extrinsic motivation involves rewards that occur outside the learner's control. These may include token economic rewards for good performance, peer acceptance of good performance, avoidance of "punishment" by performing well, praise for good work and so on.

However, many students demonstrate intrinsic goals in their desire to understand a topic or concept (task-related), to outperform others (ego-related), or to impress others (social-related). The last goal straddles the fence between intrinsic and extrinsic.

With these basic concepts in mind, there are specific techniques which might be expanded, embellished and adapted to the teacher's personality and, above all, made appropriate for the learner's level of ability and environment. The strategies are the important parts to remember -- examples are provided merely to help understand the techniques.

Strategies for Increasing Student Motivation in Math

1. Call Attention to a Void in Students' Knowledge

This motivational technique involves making students aware of a void in their knowledge and capitalizes on their desire to learn more. For instance, you may present a few simple exercises involving familiar situations, followed by exercises involving unfamiliar situations on the same topic. The more dramatically you do this, the more effective the motivation.

2. Show a Sequential Achievement

Closely related to the preceding technique is that of having students appreciate a logical sequence of concepts. This differs from the previous method in that it depends on students' desire to increase, but not complete, their knowledge. One example of a sequential process is how special quadrilaterals lead from one to another, from the point of view of their properties.

3. Discovering a Pattern

Setting up a contrived situation that leads students to "discovering" a pattern can often be quite motivating, as they take pleasure in finding and then "owning" an idea. An example could be adding the numbers from 1 to 100. Rather than adding in sequence, students add the first and last (1 + 100 = 101), and then the second and next-to-last (2 + 99 = 101), and so on. Then all one has to do to get the required sum is multiplying 50 X 101 = 5,050. The exercise will give students an enlightening experience.

4. Present a Challenge

When students are challenged intellectually, they react with enthusiasm. Great care must be taken in selecting the challenge. The problem (if that is the type of challenge) must definitely lead into the lesson and be within reach of the students' abilities.

5. Entice the Class with a “Gee-Whiz” Mathematical Result

To motivate basic belief in probability, a very effect motivation is a class discussion of the famous "Birthday Problem," which gives the unexpectedly high probability of birthday matches in relatively small groups. Its amazing -- even unbelievable -- result will leave the class in awe.

6. Indicate the Usefulness of a Topic

Introduce a practical application of genuine interest to the class at the beginning of a lesson. For example, in the high school geometry course, a student could be asked to find the diameter of a plate where all the information he or she has is a section smaller that a semicircle. The applications chosen should be brief and uncomplicated to motivate the lesson rather than detract from it.

7. Use Recreational Mathematics

Recreational motivation consists of puzzles, games, paradoxes or facilities. In addition to being selected for their specific motivational gain, these devices must be brief and simple. An effective execution of this technique will allow students to complete the "recreation" without much effort.

8. Tell a Pertinent Story

A story of a historical event (for example, math involved in building the Brooklyn Bridge) or contrived situation can motivate students. Teachers should not rush while telling the story. A hurried presentation minimizes the potential motivation of the strategy.

9. Get Students Actively Involved in Justifying Mathematical Curiosities

One of the more effective techniques for motivating students is asking them to justify one of many pertinent mathematical curiosities. The students should be familiar and comfortable with the mathematical curiosity before you "challenge" them to defend it.

Teachers of mathematics must understand the basic motives already present in their learners. The teacher can then play on these motivations to maximize engagement and enhance the effectiveness of the teaching process. Exploiting student motivations and affinities can lead to the development of artificial mathematical problems and situations. But if such methods generate genuine interest in a topic, the techniques are eminently fair and desirable.

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Alfred Posamentier

Dean and professor of mathematics education at Mercy College, New York

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TODD SENTELL's picture
Author of the hilarious schoolhouse memoir, "Can't Wait to Get There. Can't Wait to Leave"

Savannah is in 7th grade and has freckles and brown hair with a pink ribbon in the back that helps keep her pretty hair out of her face. I think Savannah might be a little tall for her age. She has a high, sweet voice I don't think I'll ever get tired of hearing it's so cute. But when she starts whining in her other voice I want to gouge both of my eyes out with a dull spoon.

I was substituting in Savannah's math class and Kathy the math teacher left a pile of worksheets on fraction problems for them to complete. When I looked at the first page they were supposed to do and at those million fraction problems I started getting real woozy.

I understand that a lot of people in the world think math is important.

When Savannah started in on how hard these fraction problems were over and over and over and over I felt a deep and instant kinship with her ... until she started slapping the page on her desk over and over and over while she was saying real loud and whiney how hard it was over and over and over at the same time. Savannah also asked me real loud wasn't the numerator supposed to be greater than the denominator or did she ask me over and over and over was the denominator supposed to be greater than the numerator and that's when I started twitching and my body fluids started pouring out of all of my seven orifices like the Ogeechee River and I became a blob of quivering, useless, steaming biomatter in the real teacher's desk chair with two glazed-over eyeballs staring up at the ceiling and if there would have been a math poster on fractions stapled to the ceiling then that would have been an incredible comic and ironic touch but there wasn't a math poster stapled to the ceiling above Kathy's desk thank the Lord God almighty.

Gilligan finally said ... I"LL help her.

I said thank you, Jesus. I mean Gilligan.

A little while later after Gilligan had helped calm down Savannah and while she was rocking and rolling on those fraction problems with no problem at all, on her own, she asked me was I a math teacher.

I said no. Not even close.

She said then how come you're in here with us doing these math problems.

I said in a math class I'm definitely in a substitute supervisory role type situation.

Savannah said ... Well, I've seen you before around here.

Alan Bradley's picture
Alan Bradley
STEM Curriculum Specialist

Interesting article that lists some good ways to have students motivated in Math. I'm curious to know if any teachers have tried to introduce other kind of equipment or games into classroom to teach Algebra or Physics?

Katrica's picture
3rd grade teacher from Roselle, New Jersey

I must say after reading this blog that I have to agree with the things that motivate the students. I am exclusively teaching math and science to my 3rd graders this year which gives me the opportunity to try many different ways to get them motivated.

The one I would say that sticks out the most for me is number 7 (use recreational mathematics). It is a requirement at my school to involve workstations including games, computers, listening centers, real world word problems and small group hands on activities. I use these activities to reinforce the lesson that was taught and spiral back to skills that have been previously taught.

The students are actually excited to spend their 40 minutes per day working on the activities. It motivates them to critically think and work on areas that they may struggle with but in a more relaxed fun atmosphere without the pressure.

Jason Markey's picture
Jason Markey
Principal, East Leyden High School

[quote]Interesting article that lists some good ways to have students motivated in Math. I'm curious to know if any teachers have tried to introduce other kind of equipment or games into classroom to teach Algebra or Physics?[/quote]

Our Physics' teachers use all sorts of other "equipment" in the class. For example, I have witnessed lessons where they have used Nerf Guns and had students video record the activity and feed the video into the Logger Pro software from Vernier which allows them to chart the flight path of the nerf "bullet". They also take a field trip to a major amusement park and determine the "g" force on the different rides. These are just a few examples of how they bring in hands on activities to Physics.

Samer Rabadi's picture
Samer Rabadi
Online Community Engagement Manager

Jason, I'd like to take your school's physics class. :-)

Seriously though, those are some great, fun ideas for teaching how physics permeates everything we do.

Sam Mirs's picture
Sam Mirs
Director of Math Education: Amazing Math Tutor Inc.A

Based on my past experience, kids show more motivation when they realize the teacher is passionate about Math. Giving real life and relevant examples works very well when introducing new Math subjects in the classroom. When coaching Math teachers, I always remind them it is essential to combines the theory with as many practical examples as possible. This is very crucial, especially in the case of younger students.

Keith Heggart's picture
Keith Heggart
High School Teacher from Sydney, Australia

Some great suggestions here - I'd especially like to echo Sam Mirs' comment - students respond to teachers' passions, so if you, as a teacher, are excited about Maths, then students are far more likely to be excited. I also think that providing concrete manipulatives is essential too - for example, I'm about to start a course on probability, so you can guarantee that the big fluffy dice are going to get used, as are the playing cards.

notamathmom's picture
parent of a 9th grader

How do I get my 9th grader motivated. He has come from a charter learning environment small classes to a large high school. He has struggled with math since 6th grade. All his teachers have tried and we've had tutors since 6th grad to present. He thinks hes ok till he gets home and then everything seems to disappear. We have tried punishment reward, just saying pass and its ok. Now in highschool, he was given an iep but still in algebra 1 (a retake from last year, in 8th gr. with a c) Has tutoring 2 days a week and when he starts to do weel in math then the other subjects take a hit. I feel I am losing him. I go to the school conference and am told hes a good kid he'll be ok, But at home he melts down and cries ( at 14) that hes not good enough. What do we do now. I reached out to the counselor at school and she says she is only for personal probs. I should go directly to the teachers, which I have attempted with some satisfaction, to be told hes a good kid!!! In the meantime his confidence is in the toilet and I forsee some problems. I don't want to lose him now!

Laura Thomas's picture
Laura Thomas
Director, Antioch University New England Center for School Renewal, Author of Facilitating Authentic Learning, Director of the Antioch Critical Skills Program; Elementary Library Media Specialist

Hi notamathmom!

I think you're doing a good job. Your son knows that you're paying attention, that you're trying to support him, and that you get That this is hard. 9th grade transitions are really hard. And what often looks like disengagement, is actually fear. Stay in tough with the teachers, and try to stay positive.

You didn't mention if he has an IEP or a 504, So I'm assuming this is the case. Is there anyway you could lighten the load in his other classes? Can he drop something? Is he getting enough exercise and positive social interaction? You might also check with the doctor to find out if he's struggling with anxiety or depression.

Obviously I don't know your kid or all the details of the situation, but these are a few of the things that I've seen other moms do. Most importantly, take care of yourself. It's not easy being a mom to an adolescent, and you need something that renews you as well.

Let us know what happens, okay?

Whitney Hoffman's picture
Whitney Hoffman
Producer LD Podcast, Digital Media Consultant, Author

Hi notamathmom!

Algebra is interesting developmentally speaking. Sometimes kids aren't ready for the abstraction algebra takes, (Their brains are still developing) and making sure they have good, concrete examples of why algebra is important and associating the problem with real life makes it easier. There's also Khan Academy, where he can see lessons at his own speed (since sometimes I've found math teachers can go quickly and if you lose a step, you can be a goner!)

Another "alternative" suggestion is that there are a group of books by Paula Pondstone and a math teacher called "Math with a Laugh" that have great problems with a humor bent that just makes getting the math down a whole lot more fun.

I also have used some of the iPad apps available to help support and "study" for algebra with my kids. Algebra Touch is one.

My son was having issues balancing algebra with all his other classes in middle school, so we pulled him out and he then got all A's in the lower class, and has done better every since- he just wasn't ready. This of course, does not rule out that your son could have a math issue (dyscalculia, or maybe handwriting issues complicate keeping numbers lined up, underlying math fact weakness, ADHD so he may have a tendency to try to skip steps, etc.) associated with a learning disability, but often finding a way to scaffold the skills a bit more or find another way to get at them helps. Sometimes math can just seem so abstract, the closer you can get it to reality, the better for kids who are having a hard time grasping it.

(I know I was one of those kids who would say 'it seems dumb to have to reprove the Pythagorean theorem - he did it several thousand years ago, and I'm happy to take him at his word" not realizing the bigger point was to teach us logic as well as basic geometry principles that are helpful in everything from framing a picture to buying carpet, to name just a few- but once I got in my own way, the learning became more difficult.)

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