Abstract
The purpose of the study was to describe the experiences adult learners have while solving mathematical word problems. The focus of the study was on how these adult students used prior mathematical knowledge and how their past experiences with mathematics influenced their solving of mathematics word problems. The study found that the attitudes, feelings and beliefs that adult students in the study hold toward mathematics and problem solving are an integral part of their mathematics learning experience. This study also reports on the particular pattern observed within the participants' attitude toward mathematics education during their schooling years beginning from elementary school till college. The adult students participated in the study lacked the necessary knowledge of such concepts as motion and concentration. Finally, the study found that even after learning the topic during the college class, the participants had difficulties with applying algebraic approaches to word problem solving.
Because learning transforms who we are and what we can do, it is an experience of identity. It is not just an accumulation of skills and information, but a process of becoming. (Wenger, 2004, p. 215)
The single most important reason to teach mathematics is that it is an ideal discipline for training students how to think. (Schoenfeld, 1982, p. 32)
TopIntroduction
Difficulties Experienced by Adults Learning Mathematics
I would like to begin with providing some information on the studies in adult mathematics education. These studies found that the numeracy proficiency of 58.6% of U.S. adults was below level 3, the minimum level needed for managing today’s working and living requirements (Statistic Canada and OECD, 2005). Furthermore, the quantitative literacy skills of 55% of U.S. adults are at a Basic or Below Basic level (NCES, 2006). The economic impact of having low numeracy skills has been reported by the Adult Literacy and Lifeskills Survey (ALL). U. S. adults performing at numeracy levels 1 and 2 (the lowest of five levels) are about three times more likely to receive social assistance payments from the state than those who score in levels 3, 4, or 5 (Statistics Canada and OECD, 2005). The Adult Literacy and Lifeskills Survey (OECD, 2005), examined adults numeracy skills in the context of daily life and work across seven countries, including the United State, and showed that those with low numeracy skill levels are more likely to be unemployed for six months longer that those at higher levels and three times more likely to receive social assistance payments. In 2009, passing rates on the GED mathematics exam were the lowest among the five academic subjects tests (American Council on Education, 2010).
Additionally, about 60 percent of community college students in the United States are referred to take developmental courses since these students are deemed insufficiently prepared to start college-level work (Attewell, Lavin, Domina, & Levey, 2006; Bailey, Jeong, & Cho, 2010). Mathematics classes in particular are a common roadblock for a large proportion of the community college student population (Achieving the Dream, 2006c). Approximately two of three community college students referred to a remedial mathematics sequence do not complete it (Bailey et al., 2010). According to a U.S. Department of Education study (Adelman, 2004), the three courses with the highest rates of failure and withdrawal in postsecondary education are developmental mathematics courses. About 50% of the thousands of individuals interviewed for the National Adult Literacy Survey, including numerous persons holding high school and college credentials, have major difficulties with quantitative literacy (Nesbit, 1996). This data reveals that the adult numeracy issue in the United States is severe, and its negative effects fall far beyond the classroom.
Key Terms in this Chapter
A Coherent External Representation: Means a drawing, an equation, or a graph (Goldin, 1998 AU143: The in-text citation "Goldin, 1998" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ).
Internal Cognitive Representations: Include five kinds of mutually interacting systems which are (Goldin, 1987 AU147: The in-text citation "Goldin, 1987" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ): (a) a verbal/syntactic system (use of language), (b) imagistic systems (visual/spatial, auditory, kinesthetic encoding), (c) formal notational systems (use of mathematical notation), (d) planning, monitoring, and executive control (use of heuristic strategies), and (e) affective representation (changing moods and emotions during problem, solving).
Adult Learner: The definition revolves around the learner, not the level of mathematics being studied. Knowles (1990) AU145: The in-text citation "Knowles (1990)" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. argued that there four definitions of the term adult: biological, legal, social, and psychological. The last occurs at a point where self-direction comes into function and is the most central from the point of learning. In this study, adults are individuals of 18 years or older and continue their education intentionally. For some of them, it is a continuation of their school experience; for others there may be a break of a few years or more since their last formal mathematics course.
Problem Solving: In the study is defined as “…finding a way where no way is known off-hand, to find a way out of a difficulty, to find a way around an obstacle, to attain a desired end, that is not immediately attainable, by appropriate means” (Polya, 1980 AU151: The in-text citation "Polya, 1980" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. , p. 1). Problem solving is a process through which individuals utilize the knowledge they have gained previously and applied it to a new unique situation or condition.
A Complete and Coherent Verbal Reason: Means one based on a described pattern (Goldin, 1998 AU144: The in-text citation "Goldin, 1998" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ).
Mathematics Education: In the study is a field defined by a multiplicity of practices including: (1) The teaching and learning of mathematics at all levels in school and college (2) Out of school learning of mathematics (3) The design, writing and construction of texts and learning material (4) Research in mathematics education (Coben, D., O’Donoghue, J., & FitzSimons, G. E., 2000 AU149: The in-text citation "FitzSimons, G. E., 2000" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ).
Symbolic Language: Includes words, symbols, and notations used (Goldin, 1987 AU152: The in-text citation "Goldin, 1987" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ).
Word Problems (or Story Problems): Is the traditional format of application problems intended to develop in students the skills of knowing when and how to apply their mathematics effectively in diverse problem situations encountered in everyday life. Word problems are also defined as verbal descriptions of problem situations wherein one or more questions are raised, the answer to which can be obtained by the application of mathematical operations to numerical data available in the problem statement (Verschaffel, Greer, & De Corte, 2000).
Affect: Is a combination of three dimensions: beliefs, attitudes, and emotions (Evans, 2000 AU146: The in-text citation "Evans, 2000" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ).
Mathematics: Is a living subject which seeks to understand patterns that permeate both the world around us and the mind within us. Now much more than arithmetic and geometry, mathematics today is a diverse discipline that deals with data, measurements and observations from science; with inference, deduction and proof; and with mathematical models of natural phenomena, of human behavior, and of social systems. Although the language of mathematics is based on rules that must be learned, it is important for motivation that students move beyond rules to be able to express things in the language of mathematics (National Research Council, 1989 AU148: The in-text citation "National Research Council, 1989" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ; NCTM Standards, 1989).
Numeracy: Describes an accumulation of skills, knowledge, beliefs, dispositions, communication resources, and problem-solving skills that individuals need in order to separately engage and effectively manage numeracy situations that involve numbers, quantitative or quantifiable information, and visual or textual information, that are based on mathematical ideas or have embedded mathematical elements (Gal, 2000 AU150: The citation "Gal, 2000" matches multiple references. Please add letters (e.g. "Smith 2000a"), or additional authors to the citation, to uniquely match references and citations. ).
Mathematical Problems: Can be defined in many different ways. In the study, mathematical problems will consist of problems in which the individual would analyze the situation (s), draw diagrams, pose questions, search for patterns and solutions, use reasoning, and illustrate and interpret results.