TECHNOLOGY MAKES A DIFFERENCE IN COMMUNITY COLLEGE MATHEMATICS TEACHING

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  • This article was downloaded by: [Kungliga Tekniska Hogskola]On: 10 October 2014, At: 20:49Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number:1072954 Registered office: Mortimer House, 37-41 Mortimer Street,London W1T 3JH, UK

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    TECHNOLOGY MAKES ADIFFERENCE IN COMMUNITYCOLLEGE MATHEMATICSTEACHINGThomasenia Lott Adams aa College of Education , University of Florida ,Gainesville, Florida, USAPublished online: 09 Jul 2006.

    To cite this article: Thomasenia Lott Adams (1997) TECHNOLOGYMAKES A DIFFERENCE IN COMMUNITY COLLEGE MATHEMATICS TEACHING,Community College Journal of Research and Practice, 21:5, 481-491, DOI:10.1080/1066892970210502

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  • TECHNOLOGY MAKES A DIFFERENCE IN COMMUNITYCOLLEGE MATHEMATICS TEACHING

    Thomasenia Lott AdamsCollege of Education, University of Florida, Gainesville, Florida, USA

    This study examines the influence of graphing calculators on a teacher's assessmentpractices in a college algebra course. The researcher focused on three techniques ofalternative assessment: oral discourse, teacher observations, and problem-solvinginvestigations. The teacher's assessment practices were revealed during 6 weeks ofclassroom observations. The researcher examined the teacher's assessment practicesbefore and after the teacher used graphing calculators as tools for teaching andlearning mathematics. The use of the graphing calculators enhanced the teacher'sassessment practices as related to oral discourse, classroom observations, andproblem-solving investigations. The results of the study indicate the potential fortechnological tools to influence teachers' practices of alternative assessment in themathematics classroom.

    Assessment is viewed by many mathematics educators as a means ofreforming the teaching and learning of mathematics. This view isencouraged by the development of and emphasis on techniques ofclassroom assessment that allow educators to increase and improveinformation obtained about instruction and learning. In addition, thesenew, authentic techniques of assessment are purported to be replace-ments for or supplements to traditional methods of assessment. Tech-niques of authentic assessment are characterized by assessmentmethods that are implemented to obtain multiple facets of informationabout teaching and learning in order to improve teaching and learning.These techniques are alternatives to traditional forms of assessment,which often provide only a one-dimensional view of learning and verylittle information about teaching.

    Many techniques of alternative assessment are applicable in themathematics classroom: constructed-response items, essays, oral dis-course, exhibitions, experiments, portfolios (Feuer & Fulton, 1992),

    Address correspondence to Thomasenia Lott Adams, University of Florida, College ofEducation, Gainesville, FL 32611-7048, USA

    Community College Journal of Research and Practice, 21:481-491, 1997Copyright 1997 Taylor & Francis

    1066-8928/97 $12.00 + .00 481

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  • 482 T. L. ADAMS

    journals (Bagley & Gallenberger, 1992), projects, group work (Mathe-matical Sciences Education Board & National Research Council, 1993),observations, diagnostic interviews, problem-solving investigations(Sammons, Kobett, Heiss, Fennell, 1992), and self-reports (Ginsburg,Jacobs, & Lopez, 1993).

    Various tools for teaching and learning (e.g., manipulatives) are usedin the mathematics classroom. It is important that educators viewassessment techniques in light of the tools used in the classroom.Mathematics educators heavily promote the use of computers andcalculators in mathematics classrooms at all grade levels (NationalCouncil of Teachers of Mathematics, 1980, 1989,1991). As a means ofassessing students' learning of mathematics while using computers,calculators, or both, many researchers have examined the impact oftechnology on students' achievement in mathematics (e.g., Koop, 1982;Palmiter, 1991; Rich, 1990). In most instances, students in these studieswere assigned a score on an instrument before and after participationin an experimental use of computers or calculators. Like many tradi-tional methods of assessment, these scores provided only partial in-formation about students' mathematical strengths and weaknesses(Association of State Supervisors of Mathematics, 1992) and almost noinformation about the teaching that occurred. In the wake of assessmentreform in mathematics education, mathematics educators have rarelyaddressed the question of how the use of technology, particularly theuse of graphing tools, affects assessment practices in the mathematicsclassroom (Senk, 1992).

    The framework of this study was built on three premises. First,among other things, assessment is a procedure for ascertaining whatstudents know (Webb & Briars, 1990; Mathematical Sciences EducationBoard, 1990). When teachers are able to determine what students know,they are more informed about the pace and effectiveness of the instruc-tion (Stiggins, 1988), and they are better equipped to inform studentsand other interested parties who are concerned about students' learning(Clarke, Clarke, & Lovitt, 1990). The idea that teachers should beinterested in what students know does not negate the idea that teachersshould not attend to students' mathematical weaknesses. However, bydirecting focus on students' mathematical knowledge and strengths,teachers can make more informed decisions about the appropriatenessof the curriculum and instruction.

    Second, mathematical assessment in particular is "the comprehens-ive accounting of an individual's or group's functioning within mathe-matics or in the application of mathematics" (Webb, 1992, p. 663). Ifassessment is to be aligned with the curriculum, as suggested by Cainand Kenney (1992), then one must design assessment that reflects the

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  • COMMUNITY COLLEGE MATHEMATICS TEACHING 483

    content of the curriculum and that provides some insight on the qualityof the interaction between the learner and the curriculum presented bythe teacher and between the learner and the instruction facilitated bythe teacher.

    Last, the power of technology and its application in mathematics canbe realized when computers and calculators are used as tools for teach-ing and learning. Computers and calculators can play a significant rolein the teaching and learning of every mathematical topic. These toolscan have a great impact in the mathematics classroom (Leitzel, 1989).

    I conducted the study reported here to examine a mathematicsteacher's classroom assessment practices before and after use of atechnological tool used for teaching and learning mathematics. Thepurpose of the study was to describe the effect of using graphingcalculators on three areas of the teacher's assessment of students: oraldiscourse, observation, and problem-solving investigations.

    Oral discourse is characterized by conversations in the instructionalsetting that take meaning from the curriculum and instructional prac-tices. The oral discourse can be teacher directed or student directed andinvolves the exchange of information that takes its context from themathematics and the processes of teaching and learning mathematicsthat occur in the classroom environment. My focus was on the influenceof using graphing calculators on oral discourse as related to teachingand learning mathematics.

    Teachers' observations of students' work and of students at work is avery important component of authentic, alternative assessment. I wasparticularly interested in the changes the teacher would make in re-gards to her observations of students' work and students at work duringthe use of technology.

    The National Council of Teachers of Mathematics (1989, 1991) sug-gested that mathematics is problem solving and that the learningenvironment should reflect this position. I was interested in whetherthe teacher's assessment of the students' mathematical learning wouldbe founded in problem-solving investigations.

    METHOD

    SubjectsThe subjects consisted of a community college mathematics teacher andthe students enrolled in the teacher's college algebra course. The teacherhad a master's degree in mathematics. Of her 19 years of mathematicsteaching experience, 16 years were in community college teaching. Shehad taught college algebra on 25 occasions. Although she had used

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  • 484 T. L. ADAMS

    computers as a tool for teaching and learning, she had never usedgraphing calculators to facilitate classroom instruction.

    There were 56 students in the two intact college algebra classes. Eachstudent completed a demographic questionnaire. On analyzing theinformation provided by the students (e.g., age, sex, high school history,grade point average, etc.), I determined that there were no indicationsthat the students in the classes were significantly different from stu-dents enrolled in other sections of college algebra at the communitycollege. In addition, there were no indications that these students weresignificantly different from the national profile of community collegestudents.

    Procedure

    I provided the teacher with a Casio 7000G graphing calculator beforethe study and met with the teacher on a weekly basis to provideinstruction on the operation and capabilities of the graphing calculator.Because of the teacher's mathematical background and mathematicsteaching experience and to preserve her natural teaching style, I did notprovide her with specific guidelines for incorporating the tool intoinstruction. In addition, at no time did I discuss the issue of assessmentin the mathematics classroom with the teacher. We met as often as theteacher desired to discuss issues regarding the operation of thegraphing calculator and to answer questions regarding the graphingtool's capabilities.

    At the beginning of the school term, I supplied the teacher with 35Casio 7000G graphing calculators. The teacher instructed the studentson use of the graphing calculators. As I directed, the teacher allowed allstudents to use the graphing calculators for class activities and assign-ments. Students were encouraged by the teacher to use the graphingcalculators freely, with and without prompting. The goal was to makethe graphing calculator a normal part of the learning environment.

    All students enrolled in college algebra at the institution were re-quired to use the same text, and all teachers of college algebra wererequired to follow the topical outline provided by the mathematicsdepartment. During the course of the study, the teacher presented thefollowing topics: linear functions, algebra of functions, quadratic func-tions, and application of parabolic functions. I chose to conduct the studyduring the time when function was being presented because the graph-ing calculator has proven to be most beneficial for graphing and analyz-ing functions (Barrett & Goebel, 1991; Hector, 1992) and for providingstudents the opportunity to enhance their understanding and intuitionregarding the concept of function (Demana & Waits, 1991).

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  • COMMUNITY COLLEGE MATHEMATICS TEACHING 485

    I observed the teacher and the two classes for 6 weeks. As a non-participant observer, I recorded data by means of field notes and a videocamera set up in the back of the classroom. The camera was in a verydiscrete location and remained stationary at all times. I received per-mission from the teacher to visit the classes on a random basis, and Irequested a course agenda from the teacher at the beginning of the termand thus was able to avoid days when the teacher was not facilitatinginstruction (e.g., holidays, intern visits, etc.). Three weeks of datacollection were conducted before the teacher introduced and began touse the graphing calculators in the classroom. During the remaining3 weeks, I observed the teacher and the students while they used thegraphing calculators during the designated unit on functions.

    RESULTS

    Oral Discourse

    During the first 3 weeks of data collection, I observed that there weretwo distinctive categories for oral discourse: review of homework andpresentation of new content in the next section of the textbook. Thesetwo activities were completely teacher led. In both cases, teacher-student and student-student verbal interactions were limited in qualityand quantity. The teacher's style of instruction in both cases wasdominated purely by the lecture mode. Even as she wrote on thechalkboard, she verbalized the words as she wrote them.

    The teacher began each class by reviewing the homework assignmentthat students should have completed for the designated class period.The oral discourse during this time consisted entirely of teacher ques-tions, student short-answer responses, and student questions, whichmost often were not academically motivated. As the teacher respondedto students' requests to present solutions to problems, she would askmany questions for which she did not receive resp...

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