MOTIVATION THEORIES FOR DEVELOPMENTAL MATHEMATICS

Nancy C. Miller <nmiller@austin.cc.tx.us>

Austin Community College

 Introduction

We want to understand how to influence achievement motivation positively. Some educators want to inspire students who want to learn mathematics to exert the effort and time required for them to learn developmental mathematics without repeating courses. I am investigating perceptions of what motivates students to learn in developmental mathematics courses. The focus of this study is to describe motivation in developmental mathematics students. I asked students in student learning journals to write about their motivations, goals, emotions, beliefs, attitudes, and study habits related to learning mathematics. The instructions in the student learning journals indicated that students should feel free to add to any of their explanations during the semester. The questions were primarily open ended statements for completion. I asked students who were referred to me by the non-course based remediation coordinators to tell me about their understanding of motivation to learn developmental mathematics based on their experiences. I asked faculty members to tell about their perceptions of what motivates developmental mathematics students based on their experiences.

Graham and Weiner (1996) describe the study of motivation as "the study of why people think and behave as they do" (p. 63). They continue by explaining,

These aspects of motivation may seem especially perplexing to developmental mathematics instructors, because we see such huge differences in motivation among students. The diversity of motivations among developmental mathematics students seems much greater than among college-level mathematics students. We sometimes see big differences in motivation in a student within one semester.

What teachers do and the curriculum choices they make have a very important impact on many students’ desire to make initial and persistent efforts in classes (Sass, 1989; Stipek, 1988; Stipek, 1996). Wolters and Pintrich (1998) agree, "activities students participate in can have an important impact on students' motivation and level of self-regulated learning in the classroom" (p.29). Teachers’ motivating or non-motivating behavior is partially responsible for differences in initiation and persistence of goal-directed behaviors in students.

 Enthusiasm

Sass (1989) found in his study of 700 college students, eight teacher characteristics associated with high motivation. Enthusiasm and communicating relevance tied for first place with these students. Enthusiasm concerning lesson content is strongly influenced by teachers (Rinne, 1998). Ralph (1998) consistently found that acting friendly, enthusiastic, and encouraging was highly valued by college students from freshmen through graduate students.

 Motivational Embellishments

Concerning motivational embellishments, Stipek believes that "students are more intrinsically motivated to complete tasks that are moderately challenging, novel, and relevant to their own lives than they are to complete tasks that are...perceived to be irrelevant" (Stipek, 1988, p. 73).

Pentrich and Schunk (1996) suggest that teachers focus on encouraging expectancy and self-competence beliefs that may improve students’ achievement rather than worry about increasing students’ value of and interest in course material. Ponticell and Beckett (1997) found that at-risk high school students sometimes were convinced to believe in themselves by teachers. These teachers were perceived by the students as believing in the students’ abilities and these teachers designed learning activities aligned with this belief in students’ abilities. Ponticell and Beckett (1997) found that these "teachers showed the students that they confidently expected them to do well" (p. 136).

Ames (1992) states that "establishing linkages between the environment, goals, and student motivational outcomes has been very important" (p. 261). She goes on to explain differences between contrasting achievement goal constructs of mastery goals and performance goals. She proposes attempting to establish classroom structures to enhance motivation by valuing effort-based strategies. Ames (1992) explains that classroom structures can influence students adopting particular goals. She recommends that entire programs be designed to focus students’ attention to effort rather than social comparison or competition with others. She suggests that educators choose learning tasks that include variety and diversity to promote interest, that students perceive meaningful reasons for doing tasks, and that tasks include challenge, interest, and student perceived control. She recommends a variety of motivational embellishments. Ames recommends focus on effort.

Ames (1992) advised that evaluation should focus on individual improvement and be privately communicated. Mistakes need to be recognized as a part of learning. She concludes that enhancing motivation does not mean enhancing self-concept of ability. Enhancing motivation does mean enhancing the value placed on effort and related strategies.

Higbee (1996) suggested that developmental educators convince students that past failures may have resulted from lack of background knowledge or lack of effective strategies if effort was exerted. Higbee (1996) also recommended teaching needed strategies and demonstrating methods of expanding background knowledge. She explained the value of developmental educators offering opportunities for success to enhance expectancy. She suggested encouraging students’ investigation of their own attitudes, values, and beliefs concerning their motivation to learn, as well as their own goals related to higher education. She believed urging students to take control and assume responsibility for their futures was valuable.

 Perceived Relevance

Most teachers want to meet the needs of all of their students in the best way they can. It is helpful for these teachers to be aware that students’ perceptions of the usefulness of mathematics are highly correlated with their plans to take more mathematics courses (Pedro, Wolleat, Fennema & Becker, 1981; Thorndike-Christ, 1991; Edkard, 1995). Female students often do not perceive mathematics as being useful. Information can be presented to them in general form as well as in female-specific form. Students’ perceptions of relevance or relatedness include seeing the connections between the course material and the students’ experiences and career goals. According to the students in Sass’s 1989 study, teachers sometimes make this explicit through explanations and examples.

Wolters and Pintrich (1998) found that knowing task value was a predictor of cognitive and regulatory strategy use, but not a predictor of performance. Wolters and Pintrich (1998) found that self-efficacy beliefs were predictors of achievement in mathematics. They suggest that task value may enable students to begin tasks, but that efficacy beliefs help students persist and overcome obstacles. Wolters and Pintrich (1998) also found that students with high test anxiety tended to use fewer regulatory strategies and received lower grades.

Frymier and Shulman (1995) found that college students, who reported instructors who used explicit relevance behaviors, perceived the content applied to themselves. These relevance or relevancy behaviors in professors help students connect content with the their values or goals.

Weaver and Cottrell (1988) suggest that instructors tell students how the course will increase their skills, add to their knowledge, and be useful to them. Students are more likely to listen and respond if they believe there is some personal gain in the experience for them. The content needs to relate to the students’ values, goals, behaviors, and relationships with others. Expectancy-value motivation theorists would classify this aspect as part of the perceived value necessary for motivation. Expecting to succeed is the other aspect of the expectancy-value model for motivation.

Pintrich and Schunk (1996) recommend that teachers discuss the importance and utility value of schoolwork with students. One of the reasons that teachers do not discuss this value extensively with their students may be that they did not receive direct instruction in the utility value of learning themselves. Schunk (1997) also recommends that learning strategies be integrated with regular instruction

According to Klinger (1977), "affect is the human’s ultimate artiber of value" and although "part of the human’s value system is innate...many of the adult human’s values are learned" (p.308). Students can learn that mathematics is relevant to their lives and that it adds important value to their futures. Teachers can teach that mathematics is connected to life outside of the mathematics classroom and useful in many areas of life.

Sanbormatsu, Shavitt, and Sherman (1991) believe that personal relevance increases the likelihood that incoming information will be integrated and organized. This integration and organization is something that teachers want to happen for their students. Unfortunately teachers cannot see what will be needed by each student during her/his life-time. An example of this need for knowledge was explained by one of my acquaintances. She mentioned that she might have been able to have kept her business if she had learned enough mathematics to have studied business calculus. Then the acquaintance might have noticed the importance of rates of change in revenue, costs, and profit.

 Student Interests

Schunk (1997) recommends personalizing learning by connecting to students’ interests to inspire perceived relevance of mathematics among developmental mathematics students. Noddings (1997) suggests working with students’ interests to involve the students and effectively influence motivation of students. Wolters and Pintrich (1998) study also indicated that interest and task value may help the students begin to engage in the learning tasks, but after they are engaged, efficacy beliefs may become more important for controlling performance.

Ma (1997) found that among Dominican Republic high school seniors there was a reciprocal relationship between measures of attitudes and achievement in mathematics. Ma (1997) concluded that ensuring "that difficult mathematical content is presented in an interesting, attractive, and enjoyable way" (p. 228) is very important for achievement.

 A Dedicated Human Relationship

Visser and Keller (1990) comment that a dedicated human relationship is a necessary, though not sufficient prerequisite, to being able to influence the motivation of another person. This may parallel Frymier and Shulman’s (1995) conclusions that teacher immediacy behaviors may be necessary before the student can perceive relevancy behavior of their instructors. Teacher immediacy concerns the perception of closeness that the student feels with the teacher.

Brown (1995) named teacher characteristics having to do with relationships, instructor concern. She included caring if the student passed or failed, encouraging students to stay in school, encouraging students that they are doing a good job, helping outside of class, and valuing conversations with students outside of class. Brown (1995) found these characteristics to be important to developmental students. Ralph (1998) also names this important characteristic relationship in his discussion of college students. He explains that the positive teacher-student relationship includes respect, support and warmth. He includes the students’ need for affiliation and belonging as being connected to the importance of the student-teacher relationship. Ralph (1998) even goes so far as to say, "the socio-emotional domain is as equally important as the cognitive and academic components" (p.37).

The teacher immediacy (perceived psychological closeness) may be used to gain the students’ attention. Certainly, teacher immediacy influences motivation and learning in college students (Christensen & Menzel, 1998; Christophel, 1990; Frymier & Shulman, 1995; Frymier & Houser, 1997). Christensen & Menzel (1998) found that teacher immediacy is related to perceived cognitive learning, perceived affective learning, and perceived motivation in positive linear relationships in their study of college students in a small liberal arts university. Noddings (1997) discusses the value of a caring, trusting relationship between student and teacher. Glasser (1990) indicates that students will do things for teachers that they like that they will not do for teachers that they do not care for.

Ferrari and Mahalingam (1998) agree that caring pedagogy helps orient students’ actions by treating them as developing persons who are constructing cognitive tools to reach what they value. This caring pedagogy may be particularly important to the developmental mathematics students who have not yet made learning mathematics part of how they see themselves as individuals.

Brown (1995) reports from her two-year descriptive study that developmental students report valuing instructor helpfulness, caring, and accessibility. Her study also found that students believed it was valuable to have a sense of "belongingness" to their college community.

College developmental students reported to Smith and Price (1996) that more students believed they had not been made to work hard enough in high school rather than too hard. Of comments written by college students 83.8% of the comments were judged to indicate external locus of control. The students tended to blame external factors for their limited success in high school in the comments. Smith and Price (1996) suggest that attributional retraining by instructors’ encouraging students to attribute success to effort may impact student motivation to learn in developmental courses.

Higbee (1996) reported that her developmental students listed grades, future goals, parents’ expectations, sense of accomplishment, and friends, teachers or significant others most frequently as factors that influence their motivation to do their homework and study.

Ralph (1998) found that college students from freshmen through graduate students describe effective teachers as keeping order; explaining clearly; invoking their interest; treating students fairly; and acting friendly, enthusiastic, and encouraging.

 The ARCS Model for Motivation

Small and Gluck (1994) found that the ARCS model of motivational design provided a useful framework for finding methods to increase motivation and enhance learning. Their study concerns student perceptions of the relationships of the four ARCS factors to 35 instructional attributes. The ARCS model consists of attention, relevance, confidence, and satisfaction (Visser & Keller, 1990). Relevance strategies that Keller (1987) recommends include:

Keller (1987) suggests that in defining the motivational challenge, low expectancy of success may be a problem in an algebra class for non-college bound students. These students may need confidence strategies before they will be able to perceive the relevance of mathematics. Keller (1987) recommends defining the motivation problem, designing strategies, integrating strategies into instruction, and assessing motivational outcomes. Ralph (1998) includes the same four factors as Keller’s ARCS motivation model of attracting attention to the subject matter, enhancing subject matter relevance, building confidence, and promoting student satisfaction; but he adds building positive teacher-student relationship to his synthesis.

Small and Gluck (1994) describe motivation as a measure of the degree to which a person will expend effort to perform or learn. Therefore, Small and Gluck (1994) believe that motivation may be as important a factor as ability in predicting achievement

 Achievement Goal Theories of Motivation

Stipek (1988) explains that "students are more likely to be motivated to engage in a task if they understand the goals of the task, the skills it will help them develop, and the potential uses of those skills outside of school" (p. 61). Recent studies in achievement motivation focus on achievement goals (Ames, 1992; Middleton & Midgley, 1997; Middleton & Spanias, 1999; Stipek, 1996). These achievement goals, according to Ryan and Pintrich (1997), may be classified as task-focused goals, extrinsic goals, and relative ability goals. Other researchers classify goals in similar ways.

The task-focused goals are goals of developing understanding and competence. Task-focused goals are also called mastery or learning goals (Ames, 1992; Dweck & Leggett, 1988; Middleton & Midgley, 1997; Middleton & Spanias, 1999; Ryan & Pintrich, 1997; Stipek, 1996).

The extrinsic goals are goals of receiving rewards, grades, or other external consequences (Ryan & Pintrich, 1997). For some developmental mathematics students an important extrinsic goal is passing a state mandated test in order to continue taking college courses. Some students may see passing the state test as their only goal related to mathematics learning. Others see passing the state test and passing one required college level mathematics course for their program as their primary mathematics goal.

Relative ability goals are goals of receiving good judgments of ability from others and looking better or smarter than others (Ryan & Pintrich, 1997). Students with primarily relative ability goals may want to please or impress parents or teachers. These students may seek praise or public recognition. Evaluation by others is very important to these students. The self is most important rather than the task being particularly important (Middleton & Midgley, 1997). Relative ability goals are also called performance or ego goals (Ames, 1992; Dweck & Leggett, 1988; Middleton & Spanias, 1999; Ryan & Pintrich, 1997; Stipek, 1996).

Middleton & Midgley (1997) considered not only performance goals that involved impressing others, but also performance avoidance goals that involved the desire to avoid showing lack of ability. Their research indicated that both types of performance goals related to preoccupation with self rather than with the task. The study did not find a connection between either type of performance goal and successful achievement perceptions among middle school students. The performance avoidance goals are different from the work avoidant goals that some students have. Work avoidant goals involve avoiding doing work.

Task-focused goals or learning goals are instrinsic motivations that concern learning "for its own sake" or as learning as its own reward (Middleton & Spanias, 1999). Relative ability goals and extrinsic goals are extrinsic motivations.

Task-focused goals are associated with attitudes, beliefs, and behaviors that are more likely to be connected to successful learning (Ames, 1992; Dweck & Leggett, 1988; Middleton & Midgley, 1997; Middleton & Spanias, 1999; Ryan & Pintrich, 1997; Stipek, 1996). Students who primarily have task-focused goals are more likely to connect effort with successful learning outcomes. Middleton and Midgley (1997) remind us that students are not limited to one goal orientation, but that they may have several levels of different goal orientations.

 Intrinsic and Extrinsic Motivation Theories

Deci , Vallerand, Pelletier, and Ryan (1991) divide motivation into intrinsic and four types of extrinsic motivations. The extrinsic motivation types are external, introjected, identified, and integrated. Intrinsically motivated behavior is for pleasure, curiosity, or personal interest. Intrinsic motivation involves activity for its own sake or self-determined activity according to Pintrich and Schunk (1996).

The types of extrinsic motivation range from external control of behavior toward integrated motivation that includes personally valuing the outcome. Pintrich and Schunk (1996) describe external extrinsic motivation using the example of the students who do not want to learn math, but they do because they want the teachers’ rewards and they want to avoid punishment. According to Deci et al., (1991) performing mathematics "because of its usefulness or instrumentality for the goal of improving math performance and succeeding in future endeavors, rather than because it is interesting" (p.330) may be an example of identified extrinsic motivation.

Attribution Theories

Many kinds of attribution theories have developed from social psychology since the 1970’s (Moghaddam, 1998; Weiner, 1992). The theories that are applicable to achievement motivation contend that students attribute causes for successes and failures in achievement (Graham & Weiner, 1996; Smith & Price, 1996; Weiner, 1992). The causes for success or failure are the reasons that the student believes are responsible for the success or failure. Weiner’s attributional model categorizes perceived causes into three categories for students. The attributions fall into categories of locus, stability, and controllability (Graham & Weiner, 1996; Smith & Price, 1996; Weiner, 1992).

The locus property concerns placing responsibility for success or failure on external, environmental causes, like difficulty or luck; or internal, personal causes, like ability or effort (Fanelli, 1977; Graham & Weiner, 1996; Smith & Price, 1996; Weiner, 1992). The stability property concerns attributing causes for success or failure on stable or unstable factors over time (Graham & Weiner, 1996; Moghaddam, 1998; Weiner, 1992). The stability dimension or property may be particularly important to expecting improvement in success rates in the future for students (Weiner, 1992). The student who attributes failure to lack of effort that is an unstable property may be likely to exert more effort in the future. The controllability concerns placing cause for success or failure on factors within the control of the student or not within the control of the student (Graham & Weiner, 1996; Moghaddam, 1998; Weiner, 1992). If a student did not study for a course, the student could perceive that failure in that course was caused by internal, unstable, controllable factors. The student could also have perceived that she believed she had to work 50 hours each week and help out with family responsibilities so that the not studying and failure were caused by factors that were external, stable, and uncontrollable, that is working and necessary family responsibilities. The attribution theorists believe that students behave like scientists looking for causes for success or failure (Graham & Weiner, 1996; Weiner, 1992).

Moghaddam (1998) indicated that causal schemata were strongly influenced by socio-cultural norms. Our ideas about what causes success or failure might be strongly influenced by our social group. Hashway, Hammond, & Rogers (1990) found different patterns for perceived controllability among the Asian students in their sample than the other ethnic groups.

Some researchers believe that one of the interesting areas for applications for attribution theories is in the research of a student characteristic of learned helplessness. The student described as learned helpless feels like she does not control her academic success (Stipek, 1996; Weiner, 1992). Students displaying some learned helplessness are not unusual in the developmental mathematics classroom. These students may generalize from past experience of not believing that they can control academic success to believing that they may not control academic success in the current course.

Middleton and Spanias (1999) suggested that students learn motivational patterns and that most students learn to dislike mathematics. These patterns and dislike for learning mathematics in the United States are in opposition to society’s need for more mathematics literacy.

I believe the opportunity for education that we enjoy currently in the United States is rare and precious in the world. Most societies do not offer second and third opportunities to learn formally like we have in the U.S. This opportunity for formal education is not something that we can count on as a right that we will always have access to use. While we have the opportunity we must grasp it, if we want it, and many of us want to encourage our students to do the same.

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