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I live in Brazil and here we have some problems with teaching mathematics in High School. In some point of the students' life (I think it happens in the 5th grade), they start "hating mathematics" and, at least here, it's totally acceptable. So students start thinking they are not capable enough of learning mathematics and simply stop studying. It becomes dull and they think it's useless.

My colleagues and I discuss a lot about how we can motivate them to keep enthusiastic about learning.

This topic is for us to discuss some ideas!

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    $\begingroup$ Just a sympathetic comment: similarly, in the U.S. teenagers "rebel" against parents' culture, which includes math (even if the parents are essentially ignorant of it), and, more awfully, being outspoken about rejection of the previous generation's ideas can be a ticket to legitimacy among one's peers. It's the usual thing. The obstacle to getting kids to pay attention to mathematics has very little to do with mathematics, although, certainly, top-heavy, authoritarian versions have no traction whatsoever, and for reasonable reasons. "Can math help solve their problems?" That's the question. :) $\endgroup$ – paul garrett Feb 17 '17 at 0:56
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    $\begingroup$ In this mathematical difficulty post, my aim was to list the math difficulties to explore possible solutions. If as in your case students think "math is useless", I believe that this is a "math difficulty" and one possible solution is to show that this is wrong. $\endgroup$ – sapienz Feb 17 '17 at 10:07
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    $\begingroup$ There is a wonderful book from a Brazilian author that you might find inspiring. In English it's The Man Who Counted, by Malba Tahan. That's a psuedonym for Júlio César de Mello e Souza. Apparently the title in Portuguese is O Homem Que Calculava. I wonder if you could share some of the stories in it with your students. $\endgroup$ – Sue VanHattum Feb 22 '17 at 3:30
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    $\begingroup$ Also, have you heard of Math Circles. There are many in Brasil. $\endgroup$ – Sue VanHattum Feb 22 '17 at 3:31
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    $\begingroup$ Pardon the self-promotion, but... By 5th grade students can understand some of the geometry of pop-up book design and the mathematics of origami, which I have sketched (at the high-school level) in How To Fold It. I've had success engaging students with this material. The topic can serve as a vehicle to introduce many concepts in geometry. $\endgroup$ – Joseph O'Rourke Apr 3 '17 at 0:05
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I will try to give a research-related answer. There are several suggestions from the literature and you may have to take a deeper look at them.

First, a decrease in motivation is also observed in other countries, not just Brazil (Frenzel, Goetz, Pekrun, & Watt, 2010).

In recent psychological theories (Krapp, 2002), (Krapp, 2005), (Renninger, 2009), interest development is based on the satisfaction of psychological needs, especially the needs for perceived competence, autonomy and social relatedness from self-determination theory (Deci & Ryan, 1985), (Deci & Ryan, 2002). Students should have these needs satisfied in your teaching as often as possible. But how should this work?

Empirical studies on mathematics interest confirm factors like competence support (Rakoczy, Harks, Klieme, Blum, & Hochweber, 2013) and autonomy support (Valås & Søvik, 1994), but also work on different conceptual levels, e.g. teaching methods (Bikner-Ahsbahs & Halverscheid, 2014), (Lerkkanen u. a., 2012), (Prendergast & O’Donoghue, 2014), (Rowan-Kenyon, Swan, & Creager, 2012), (Schukajlow u. a., 2011), (Sonnert, Sadler, Sadler, & Bressoud, 2015), classroom management (Rowan-Kenyon u. a., 2012), task design (Schukajlow & Krug, 2014) or the big-fish-little-pond effect (Frenzel u. a., 2010), which all more or less explicitly relate to need satisfaction (see also (Carmichael, Callingham, Watson, & Hay, 2009)).

Note, however, that the motivation role of applications tends to be over-estimated by teachers since students may also have interest in pure aspects of mathematics (Rellensmann & Schukajlow, 2016).

The best framework for the design of classroom activities that support the psychological needs and foster students’ motivation is the one by Bikner-Ahsbahs and Halverscheid (2014). In brief, they plan student activities based on exploration and discovery, group work and valuing of (nearly) any student observation and comment. These activities cannot be found for each session (e.g., not for the fostering of calculation routines) but may really help for deep connections of the mathematical content and most of all they may substantially improve students’ motivation.

I am sorry I cannot give a short and simple answer. If we had such an answer, it would have been spread around the world already. Anyway I hope my post may help you.

References:

  • Bikner-Ahsbahs, A., & Halverscheid, S. (2014). Introduction to the Theory of Interest-Dense Situations (IDS). In A. Bikner-Ahsbahs & S. Prediger (Eds.), Networking of Theories as a Research Practice in Mathematics Education (pp. 97–113). Cham: Springer International Publishing. Retrieved from http://link.springer.com/10.1007/978-3-319-05389-9_7
  • Carmichael, C., Callingham, R., Watson, J., & Hay, I. (2009). Factors influencing the development of middle school students’ interest in statistical literacy. SERJ - Statistics Education Research Journal, 8(1), 62–81.
  • Deci, E. L., & Ryan, R. M. (1985). Intrinsic Motivation and Self-Determination in Human Behavior. New York: Plenum Press.
  • Deci, E. L., & Ryan, R. M. (2002). Handbook of Self-Determination Research: Theoretical and Applied Issues. Rochester, NY: University of Rochester Press.
  • Frenzel, A. C., Goetz, T., Pekrun, R., & Watt, H. M. G. (2010). Development of Mathematics Interest in Adolescence: Influences of Gender, Family, and School Context. Journal of Research on Adolescence, 20(2), 507–537. https://doi.org/10.1111/j.1532-7795.2010.00645.x
  • Krapp, A. (2002). An Educational-Psychological Theory of Interest and Its Relation to SDT. In E. L. Deci & R. M. Ryan (Eds.), Handbook of self-determination research (pp. 405–427). Rochester, NY: University of Rochester Press.
  • Krapp, A. (2005). Basic needs and the development of interest and intrinsic motivational orientations. Learning and Instruction, 15(5), 381–395. https://doi.org/10.1016/j.learninstruc.2005.07.007
  • Lerkkanen, M.-K., Kiuru, N., Pakarinen, E., Viljaranta, J., Poikkeus, A.-M., Rasku-Puttonen, H., … Nurmi, J.-E. (2012). The role of teaching practices in the development of children’s interest in reading and mathematics in kindergarten. Contemporary Educational Psychology, 37(4), 266–279.
  • Prendergast, M., & O’Donoghue, J. (2014). “Students enjoyed and talked about the classes in the corridors”: pedagogical framework promoting interest in algebra. International Journal of Mathematical Education in Science and Technology, 45(6), 795–812. https://doi.org/10.1080/0020739X.2013.877603
  • Rakoczy, K., Harks, B., Klieme, E., Blum, W., & Hochweber, J. (2013). Written feedback in mathematics: Mediated by students’ perception, moderated by goal orientation. Learning and Instruction, 27, 63–73. https://doi.org/10.1016/j.learninstruc.2013.03.002
  • Rellensmann, J., & Schukajlow, S. (2016). Does students’ interest in a mathematical problem depend on the problem’s connection to reality? An analysis of students’ interest and pre-service teachers’ judgments of students’ interest in problems with and without a connection to reality. ZDM, 1–12. https://doi.org/10.1007/s11858-016-0819-3
  • Renninger, K. A. (2009). Interest and Identity Development in Instruction: An Inductive Model. Educational Psychologist, 44(2), 105–118. https://doi.org/10.1080/00461520902832392
  • Rowan-Kenyon, H. T., Swan, A. K., & Creager, M. F. (2012). Social Cognitive Factors, Support, and Engagement: Early Adolescents’ Math Interests as Precursors to Choice of Career. The Career Development Quarterly, 60(1), 2–15. https://doi.org/10.1002/j.2161-0045.2012.00001.x
  • Schukajlow, S., & Krug, A. (2014). Do Multiple Solutions Matter? Prompting Multiple Solutions, Interest, Competence, and Autonomy. Journal for Research in Mathematics Education, 45(4), 497–533. https://doi.org/10.5951/jresematheduc.45.4.0497
  • Schukajlow, S., Leiss, D., Pekrun, R., Blum, W., Müller, M., & Messner, R. (2011). Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations. Educational Studies in Mathematics, 79(2), 215–237. https://doi.org/10.1007/s10649-011-9341-2
  • Sonnert, G., Sadler, P. M., Sadler, S. M., & Bressoud, D. M. (2015). The impact of instructor pedagogy on college calculus students’ attitude toward mathematics. International Journal of Mathematical Education in Science and Technology, 46(3), 370–387. https://doi.org/10.1080/0020739X.2014.979898
  • Valås, H., & Søvik, N. (1994). Variables affecting students’ intrinsic motivation for school mathematics: Two empirical studies based on Deci and Ryan’s theory on motivation. Learning and Instruction, 3(4), 281–298. https://doi.org/10.1016/0959-4752(93)90020-Z
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I introduced a program for students in 2nd through 6th grade which made:

"math cool in my school".

There were two components:

Students who excelled in math had an opportunity to take enrichment at lunchtime. These students designed activities and assemblies for their peers. Assemblies included math fairs, original math games, math plays, treasure hunts etc. Additional activities included math newspapers, magic shows, and scavenger hunts. My enrichment students were proud to present, the attending students enjoyed the presentations, and many attending students worked harder at math to get into my program.

The second component was given at Friday lunchtime. Anyone who was invited (usually about 40 students), could come and eat lunch with us and play math games. I had puzzles from think fun, math books, and a variety of math games. This was very successful in piquing additional interest in math. Students who were in enrichment were invited and were allowed to bring a friend. This made the enrichment program even more appealing (and more students worked harder at math). Additionally students who worked hard in math but weren't strong might be invited by me - giving additional motivation to students to work at math.

Any program which gives the successful math students special privileges (related to math) will increase motivation and give the students the feeling that math is cool!

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Thanks for bringing up a valid issue.

Myself have come across many situations when students doesn't take math seriously just because they think "they can't learn it" But sooner I have made a serious change to my "way of teaching". The change did not show a direct change but it did it, gradually.

The change was to make the class interactive, and also relating it will real time example.

Let's take Primary - 5 math problem: So the group of you are going for movie(Iron Man) this weekend, but the cashier asked only once person can pay the money to get 10% discount upon purchase of 10 tickets. If the ticket cost $10, what is the amount need to give to the cashier? (Multiplication, Understanding Percentage) what is the price each one has to contribute after discount? (Division, rounding off)

This way, going about with real-time example, they will know how important math is and how easy it could be!

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Just one example, that frustratingly to me, is rarely broached in algebra (in U.S. secondary schools) when covering polynomials.

When you print to a printer, or look at rendered text on a screen (say, PDF), you are likely using either Postscript fonts, which are drawn by cubic (Bézier) polynomials, or TrueType fonts, which are drawn by quadratic polynomials. So polynomials are used literally daily by the very students learning polynomials, without them ever realizing that the dry topic they may be avoiding by browsing is actually being used to support their browsing.


            Q
            The letter Q drawn with Bézier cubics. Image from this link.


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    $\begingroup$ This is a difficulty that I see with a lot of things that are presented as applications of math. We have to distinguish between situations that could be described using a mathematical concept and situations where a student actually used a mathematical concept. In this case, for example, the students benefited from polynomials but they didn't personally use one to achieve a goal. The font designer did it for them. $\endgroup$ – G. Allen Mar 2 '17 at 0:32
  • $\begingroup$ @G.Allen: Fortunately one can design e.g. Bezier curves in a variety of interactive tools, including Adobe Illustrator. So they can see polynomials in action, learn that they are incredibly useful, without getting into the details of smooth joins at knots points etc. $\endgroup$ – Joseph O'Rourke Mar 2 '17 at 1:00
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A short time ago I read the following article about motivation:

Ambrose, S. A., Bridges, M. W., DiPietro, M., Lovett, M. C., & Norman, M. K. (2010). What factors motivate students to learn. How learning works: Seven research-based principles for smart teaching, 66-90. Available under https://sites.temple.edu/bett/files/2014/01/Ambrose-Chapter-3-What-motivates-students1.pdf

It generally discuss the factors of students' motivation and how a teacher can enhance it. Thereby Ambrose et al. (2010) mention three dimensions which influence students' motivation:

  • students’ goal value
  • students’ efficacy expectancies
  • environment: supportive or unsupportive

Ambrose et al. argued that only in the case, when all three dimensions are fulfilled, the students are motivated. In total they see the following reaction of a student to the three dimensions:

image

So you can ask yourself which of the above dimensions are not met and how you can enhance them. Ambrose et al. also give a couple of concrete strategies which you find in their article. I also summarized the article in a blog post.

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  • $\begingroup$ I think in the linked chapter, it is the students' efficacy expentancies, rather than efficiency expectancies. $\endgroup$ – pjs36 Feb 18 '17 at 21:29
  • $\begingroup$ @pjs36: yes, you are right... :-) $\endgroup$ – Stephan Kulla Feb 20 '17 at 8:23
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Well... I really want to answer this question. Maybe two days earlier, I was watching a Numberphile video by Edward Frenkel. He discussed the question Why So many people hate mathematics??

The video start with an interesting example:

Edward said: Suppose you are gonna take an art class and you are given work of painting fence (This thing is quite boring if you don't like it initially) but were never shown the paintings of great artists. When you will grew older, you will say Man! I was really bad at art,I hated it but what you would really be saying is that I was bad at painting the fence and that's what actually happens in Mathematics.

I remember that once professor Walter Lewin said that if you are bad at physics, you didn't had a good physics teacher. I would say that this applies on Maths too. This is certainly fault of Maths teachers. Actually teachers are paid to make students love their subject because if they will love it, they will become good at it themselves.

So, Imho the only thing you should do is to relate Mathematics to daily life of students. If they will see it around them, they will try to explore it and hence they will love it.

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