Mathematics and Motivation

An Annotated Bibliography

by Liza Ewen

The question of how to motivate students in the classroom has become a leading concern for teachers of all disciplines. Student motivation becomes especially relevant to mathematics education in light of recurring questions about how to get more students interested and involved in math. We offer a collection of articles, chapters and Forum discussions that begin to address how student motivation affects mathematics learning and instruction. These references provide information and implications for student motivation in general, and for its specific relation to the field of mathematics. The general references on motivation are as applicable to the classroom as are those that are math-specific. Summaries appearing in The Forum's Learning and Mathematics Discussions speak specifically to issues of student motivation and how to tailor instruction to increase student involvement in math; we also include a few relevant discussions taken from the Forum's newsgroups. General References Blumenfeld, P.C. et al. "Motivating Project-Based Learning: Sustaining the Doing, Supporting the Learning." Blumenfeld and her colleagues describe how incorporating long-term projects into classroom instruction helps to engage students in the solving of "authentic" problems and increases students' investment in classroom learning. The article offers a comprehensive overview of the components of learning, motivation and instruction which need to be taken into consideration by teachers when involving students in project-based learning. The authors also discuss the implications for teachers and how they can find support for incorporating project-based learning and how they can stay motivated when working on projects. The article offers teachers with a solid outline of the components of project-based instruction and the elements which are crucial to successful projects. In Educational Psychologist , v. 26, nos. 3 & 4, pp. 369-398, 1991. Brown, A. and A. Palincsar. "Guided, Cooperative Learning and Individual Knowledge Acquisition." Brown and Palincsar explain how group activity and collaborative work can help to motivate students by allowing them to share the thinking load and to act as models of planning and strategy use for each other. Their chapter provides teachers with an outline for how collaborative learning can help students persist on certain projects. In Knowing, Learning and Instruction . Lauren B. Resnick (Ed.). (Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1989, Chapter 13.) Maehr, M. and E. Anderson. "Reinventing Schools for Early Adolescents: Emphasizing Task Goals." This article describes how an emphasis on task goals, such as focusing on the problem- solving process and working well with other students, may help motivate student learning. The article offers suggestions for how to stress task goals in middle-school classrooms in order to increase students' intrinsic motivation. Maehr and Anderson provide a comprehensive table of areas to focus on, objectives for teachers, and strategies for motivating students with the intrinsic benefits of learning rather than with extrinsic rewards. In Elementary School Journal , v. 93, n. 5, pp. 563-610, May 1993. Nolen, S. "Reasons for studying: Motivational orientations and study strategies." Nolen describes how students' goals affect the strategies they choose to use during problem-solving. Students who want to learn for understanding's sake and students who want to learn to get good grades use different kinds of strategies in their problem-solving, and the strategies they use influence their understanding of a problem and their motivation to work on a problem. Teachers can begin by teaching students strategies which will help them to understand concepts rather than find a "quick" answer and encouraging students to concentrate on the learning process rather than the final outcome. In Cognition and Instruction , no.5, pp. 269-287, 1988. Pressley, M. et al. "Good Strategy Instruction is Motivating and Interesting." Pressley describes how students' interests and motivation can be fostered through the teaching of strategy use. This chapter explains that when students have a repertoire of strategies with which to work, they are empowered with "the will and skill" to successfully problem-solve. Teachers can begin strategy instruction by modeling how they use certain strategies to solve particular problems and demonstrating to students that using strategies really can help them to figure out problems they encounter. In The Role of Interest in Learning and Development , Renninger, Hidi and Krapp, eds.. (Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1992, Chapter 14). Sansone, C. and C. Morgan. "Intrinsic Motivation and Education: Competence in Context." This article explains possible ways of using students' interests to maintain motivation, especially for work students find uninteresting. The authors explain how students use their own interests in learning and problem-solving, and describe how interests can help students continue working on tasks they do enjoy. By becoming more aware of student interest and providing feedback that supports students in their individual learning goals, teachers can help to increase students' motivation. In Motivation and Emotion , v. 16, no. 3, pp. 249-270, 1992. Motivation and Mathematics Gelman, R. and J. Greeno. "On the Nature of Competence." This chapter describes how ordinary experiences in the world can become meaningful learning experiences. As a result of such ordinary experiences, children already know a lot about math before they come into a math class. Teachers can use this knowledge about math as a motivator and a means of supporting students' learning of new mathematical concepts. They can begin "constructing math in the course of everyday experience" and pointing out the large and important role math plays in common, ordinary places. In Knowing, Learning and Instruction . Lauren B. Resnick (Ed.). (Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1989, Chapter 5.) Ginsburg, H. "Helping Young Children." Ginsburg describes how young children come to learn informal math on their own and how their interests motivate them to explore math and practice what they learn. This chapter outlines how adults can help children to sustain this intrinsic motivation to learn math by providing children with an appealing and stimulating environment to play in and letting the children decide what it is they would like to do. In Children's Arithmetic: How they learn it and how you teach it . (Austin, TX: Litton Educational Pub. [Pro Ed.], 1977, Chapter 4.) Li, A. K. F. and G. Adamson. "Motivational Patterns Related to Gifted Students' Learning of Mathematics, Science and English: An Examination of Gender Differences." Li and Adamson explain how gender differences affect the learning motivation of gifted students, including how they affect achievement motivation in mathematics. The article suggests that students are in general more likely to achieve success in subjects in which they are interested, and that girls in particular are more likely to attribute success and failure in mathematics to effort and strategy. Teachers can begin increasing math motivation, especially for girls, by striving to make mathematics interesting and attractive to students at a young age, giving students an interest in math to pursue across their school years. In Journal for Education of the Gifted , v. 18, no. 3, pp. 284-297, Spring 1995. Middleton, J. "A Study of Motivation in the Mathematics Classroom: A Personal Constructs Approach." Middleton explains how teachers can build student motivation into their math lessons. Teachers' own motivation often plays a large role in the activities they choose, and fostering motivation depends on the extent to which teachers' motivation matches that of students' for participating in class activities. Middleton describes how teachers can learn to understand their students' motivation and work those motivations into the goals of classroom work. Teachers can begin integrating motivation into their lessons by talking to individual students about their goals in math and considering how those relate to teachers' own teaching goals. In Journal for Research in Mathematics Education , v. 26, no. 3, pp. 254-279, May 1995. Schiefele, U. and M. Csikszentmihalyi. "Motivation and Ability as Factors in Mathematics Experience and Achievement." Schiefele explains that students' experiences in the math classroom are linked significantly to interest, and that interest often predicts student achievement in mathematics. The article suggests that standard mathematics instruction through lectures and seat work needs to be supplemented with more active and student-involved activity to increase student interest in math. Schiefele suggests that teachers can begin to increase their students' interest in math by incorporating activities such as small group work, projects, and the use of computers, and by placing problem-solving in real world contexts. In Journal for Research in Mathematics Education , v. 26, no. 2, pp. 163-181, March 1995. Learning and Mathematics Discussions Ball, R. "With an Eye on the Mathematics Horizon." March 1995 Ball explains how teachers can appropriately fit interest into the teaching of mathematics. The notion of placing math in a real-world context becomes a dilemma for teachers who want to create experiences that will connect to student interest and knowledge, but also want the concepts learned to be applied in many different situations. This article gives realistic suggestions about using everyday contexts and student interest to motivate math learning. Lampert, M. "Knowing, Learning and Doing Multiplication." February 1995. Lampert describes how posing students questions that encourage the discovery of problem- solving processes rather than just asking for correct answers works to motivate students to understand the concepts they use in math problem-solving. By making connections between school learning and what students care about outside of the classroom, both in the classroom and on assigned work, teachers can use student interest as a motivator to encourage and support learning. Lesh, R. "Mathematics in Everyday Situations." July 1994. Lesh explains how creating "mathematizable situations" in math problem-solving helps students to explore and use math concepts in useful and meaningful ways. By establishing everyday contexts for problem-solving, teachers will stimulate their students to ask questions, gather information, and evaluate their thoughts and answers. In helping students to use these planning and monitoring skills, teachers can play a role in sustaining students' motivation as they work on solving a particular problem, as well as motivate them in general problem-solving situations. Polya, G. "Common Sense Questions." August 1994. Polya describes a model of student problem-solving that includes planning, use of prior knowledge, and incorporating new ways of thinking about a problem into a student's repertoire. He suggests that this lens may help students to gain experience and confidence in problem-solving, both of which play a significant role in a student's personal motivation. Teachers can foster students' analytical skills, confidence, and motivation by asking "common sense" questions that encourage students to discover processes, not just give answers. Resnick, L. "Math as an Ill-Structured Discipline." September 1994. Resnick believes that students' motivation to learn math will increase and improve when teachers begin to build a math curriculum that focuses on conceptualizing and creating meaning in math problem-solving. She suggests that by inviting interpretations and encouraging students to talk about math, we can provide a classroom source of motivation. Teachers can begin to create classrooms that engage students in math by incorporating more question-asking and discussion into class time and by giving students math problems that place math in meaningful and realistic contexts. Tobias, S. "They're Not Dumb, They're Different." February 1996. Tobias describes the current learning environment in the sciences and how motivation can be deterred by the way educators approach teaching and learning. Her study offers insights into the kinds of learning experiences students find welcoming, and how those experiences help sustain student motivation in a particular discipline. She suggests that a key to a student's willingness to persist in the sciences is their constant and meaningful exposure to mathematics in their secondary school learning. Tobias' work offers teachers a look at math and science classes from a student perspective and may help teachers to think about how to make their classes interesting and appealing to the greatest number of students. geometry.pre-college Newsgroup Discussions "Math Teaching: Words, Symbols and Interests." January 1994. This discussion gives suggestions for how teachers can use interest in their classrooms as a motivator for teaching mathematical symbols and formulas. This thread offers discussions of both the research on interest in learning and the "real world" perspective on how that research fits into an actual math classroom. "Real Life Problems of Geometry." January 1996. This Forum discussion features educators talking about ways to incorporate such motivating factors as interest and real-world contexts into the teaching of mathematics. The discussion offers teachers a perspective on how they can really begin to apply the concepts offered by the authors featured in the Learning and Math Discussions.

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