Teacher Use of Writing in the Junior High Mathematics Classroom

Teacher Use of Writing in the JuniorHigh Mathematics ClassroomDaniel L. PearceDavid M. Davison

Division of Elementary/Secondary EducationEastern Montana CollegeBillings, Montana 59101-0298

t�. . . Writing is a mode of language that involves theactive manipulation of knowledge.^

In the last five years, a call has been issued for increased student writing inthe schools. One reason for this, as both Emig (1977) and Haley-James(1982) have noted, is that writing can lead to a deeper understanding andimproved mastery of a topic. That is because writing is a mode of languagethat involves the active manipulation of knowledge. Creating an original pieceof writing requires students to analyze and synthesize information, focus theirthoughts, and discover new relationships between bits of knowledge. Writingabout something involves many of the thought processes teachers would liketo foster in their students. Consequently, writing can be an instructional toolto promote learning in areas not usually associated with writing.For example, in the area of mathematics, writing can be used in a number

of instructional ways. Some of these ways are: 1) having students write theirown definitions, which gives students the chance to describe something intheir own words; 2) having students translate symbols, formulas, andproblems into words; 3) having students write the steps or processes involvedin solving a problem; 4) having students make up and write their own storyproblems; and 5) having students write reports on important people andevents in mathematics. In short, writing activities can be used to facilitatemost aspects of students’ mathematical development, from concept acquisi-tion through problem solving abilities (Davison and Pearce, in press; Evans,1984; Fennell and Ammon, 1985; Shaw, 1983).Writing in mathematics classes can run the gamut from relatively "low

level" and passive tasks, such as copying and transcribing information,through more original writing activities, such as writing story problems. Evenpassive writing tasks can be mathematically valuable, because students exertmore effort and the written information is available when their memories

School Science and MathematicsVolume 88 (1) January 1988

Teacher Use of Writing 7

lapse. However, "higher level" activities, which require students to composean original and coherent piece of writing, are an even more valuable way tofacilitate students’ learning because original writing requires active thought.For instance, asking students to find the sum of the first n positive integers,and requiring a written explanation for full credit, requires analysis,synthesis, reflection, and precise thought.

<(. . . a problem writing assignment is enhanced ifinstructional support is supplied.

Original writing, in turn, is more effective if students are involved indifferent aspects of the composition process. The composition process refersto the series of stages a person goes through while producing a writtenproduct. These stages are: 1) prewriting (where ideas are generated, anauthor identifies what he or she already knows about the topic, and where awriter establishes goals); 2) drafting (where an author actually writes); 3)revision (where an author rewrites what has been written). While these stagesare not always clearly separate nor linear, going through them makes writingmore of a learning experience.

Writing activities are enhanced by teachers supplying instructional supportthrough involving the students in the writing stages. For instance, whileassigning the writing of story problems is a valuable exercise, the writtenproblems may not be exactly what the teacher had expected. In contrast, aproblem writing assignment is enhanced if instructional support is supplied.One form of instructional support is prewriting assistance, which can takedifferent forms. Fennell and Ammon (1985) offer a variety of prewritingideas for story problems (i.e., presenting a stimulus such as a picture or anumerical table and having students ask questions before they begin writing aproblem based on the stimulus). Prewriting assistance can also be providedby the teacher writing a problem for the class and talking the studentsthrough the steps while he is writing the problem (a form of modeling). Thepoint is that prewriting assistance generates ideas, helps focus thought, andgives some idea of what is expected and how to go about it. Without someform of prewriting assistance, the students’ efforts may not be successful.Another form of instructional support is involving students in revising what

has been written. For instance, student produced story problems, even with


8 Teacher Use of Writing

prewriting assistance, may not be what was assigned or may not be solvablebecause of errors. In order for the writing of problems to be a valuableexercise, students should be allowed an opportunity to rewrite and correcterrors in their original problems (Fennell and Ammon, 1985). Revision effortscan be induced by having the teacher react to problems, having students solvetheir own problems (and if a problem cannot be solved then rewriting it), andresponding to another person’s problem (causing the problem to be rewrittenif it is inaccurate). Rewriting the content of something forces students toconsider and change what has been written, thereby promoting new learning.

Writing activities in mathematics are also more valuable if students writefor an audience other than just the teacher. This can take a variety of forms.The simplest is having students read and respond to each other’s work.Another way is having students write to an uninformed third party, whichforces the writer to be more specific than if writing for the teacher. Forinstance as part of a geometry unit, Evans (1984) had her fifth grade classwrite a letter to the class hamster on how to draw a 60 degree angle. Shaw(1983), in turn, recommends having a class write story problems for studentsin a lower grade. Writing to different audiences can make activities moreinteresting and foster precision.

Writing is a useful way to deal with abstract ideas, provide review andreinforcement, and break the routine of computation. For these reasons,writing activities would be useful at the junior high level as a way to helpstudents learn mathematics.

Various studies have examined the amount and kinds of writing indifferent content area subjects (Applebee, 1981; Bader and Pearce, 1983;Pearce and Bader, 1984). Unfortunately, these studies supply little informa-tion about junior high mathematics classrooms. Applebee (1981) investigatedwriting in different content areas at the high school level and found thatwriting in mathematics classes was mostly mechanical and informational(copying, short answers, and notetaking). Bader and Pearce (1983) investi-gated writing at the junior high level through teacher interviews. However,the number of mathematics teachers in their study was so small that thefindings for mathematics were not presented as a separate subject area.Consequently, actual data on the amount and kinds of writing activitiesfound in junior high mathematics classes are limited.Data on teachers’ use of writing in mathematics classrooms at the junior

high level are needed to provide information on current uses. Suchinformation would also supply a framework for future suggestions on wayswriting can be integrated into mathematics instruction. The purpose of thisstudy was to determine the amount, kinds, and uses of writing in junior highmathematics classrooms.



Method

Data on the classroom use of writing by junior high mathematics teacherswere collected through a series of structured interviews, examinations oflesson plans, follow-up interviews, and examinations of student work.Mathematics teachers (grades 7-9) were recruited for this study by supervisorsin eight junior high schools in the Billings, Montana area. The supervisorssurveyed all of their mathematics teachers to find out if they wouldparticipate in this study and 31 teachers volunteered. These 31 teachersconstituted 69 percent of the mathematics teachers in the eight junior highschools. The average teaching experience of these teachers was eight years.

Teachers were individually interviewed in their schools by both investiga-tors together. Each teacher’s interview followed the same format, includingthe same questions. An opening statement was read giving the purpose of thestudy. The teachers were encouraged to identify one class currently beingtaught and to limit discussion to that class, for instance third period, 7thgrade basic mathematics. It was felt that limiting discussion to one classwould lead to more precise information. Teachers were allowed to selectwhich of the mathematics classes they would talk about. Teachers were alsoencouraged to consult lesson plans and to produce examples of student work.Each teacher was asked to tell about the kinds of writing, exclusive ofcomputational notations, that the students did. Following the openingremarks on writing, each teacher was asked a specific series of questions.

These questions were related to: 1) kinds of writing tasks; 2) frequency ofeach writing task; 3) extent of class time allotted to do writing tasks; 4)opportunities for students to see and hear what other students had written; 5)nature of the writing prompts (workbooks, review questions, etc.); and 6)amount of rewriting requirements. Responses to many of these questions werefollowed by a discussion to clarify answers.The initial interviews lasted from 10 to 40 minutes, depending on the

teachers’ answers and the types of writing activities engaged in by theirstudents. The distribution of investigated classes by grade and ability level arepresented in Table 1.

GradeLevel

7th8th9th

Totals

Basic

32

5

TABLE 1Distribution of Classes byGrade and Ability Level

Regular

6810

24

Advanced

2

2

Totals

912

31

School Science and! MathematicsVolume 88 (I) January 1988


Following each interview, the investigators compared notes and discussedthe data. If any clarification was needed, a follow-up interview wasscheduled. Specific examples of students’ work were requested in follow-upinterviews. Following the gathering of information, the investigators analyzedthe data from each teacher for: 1) writing types, 2) writing frequency, 3)audience, and 4) instructional support.

Results

Writing Types

Because of the unique nature of mathematics, existing classifications ofwriting (Applebee, 1981; Britton, et al., 1975) were judged to be a less thansatisfactory way to classify and tabulate the data. These classifications arenot always sensitive to the interaction between symbolic thought and writtenlanguage activities which can occur in mathematics. For instance, underApplebee’s (1981) system for classifying writing, a wide variety of writingtasks, such as writing a story problem, describing an operational process, oranswering a question about a graph could be classified as informationalwriting. Consequently, a new system for classifying writing, in whichfunctional aspects of mathematics could be incorporated into differentcategories of writing, was devised by the authors.

In this system, writing activities were classified into five types: 1) direct useof language (copying and transcribing information); 2) linguistic translation(translation of mathematical symbols into words); 3) summarizing/interpret-ing (summarizing, paraphrasing and making personal notations aboutmaterial from texts or other sources); 4) applied use of language (situationswhere a mathematical idea was applied to a problem context); and 5) creativeuse of language (using written language to explore and convey mathematicallyrelated information). Examples of the kinds of tasks for the five categoriesare given in Table 2. For more specific examples for each of the five typessee Davison and Pearce (in press).

Student writing activities were tabulated and categorized into the five kindsof writing tasks for each teacher. The percentage of teachers that had theirstudents engage in each type were: Direct use of language, 74 percent;linguistic translation, 29 percent; summarizing/interpreting, 45 percent;applied use of language, 45 percent; and creative use of language, 13 percent.Based on this data, more teachers used writing tasks that were mechanicaland passive in nature (direct use of language) than any other kinds of writingactivities.An additional analysis was conducted to determine whether different

teachers used a variety of writing activities. The data presented in Table 3show that individual teachers did not use a variety of writing activities intheir classes. In fact, 29 percent of the teachers used one or fewer kinds of


Teacher Use of Writing

TABLE 2Examples of Writing for Each of the Five Kinds of Tasks

Direct Use Copying information from the board, the text or aworksheet.

Linguistic Translation Writing in a complete sentence the meaning of theformula A = R2

Summarizing/ Explaining how to solve a problem in students* words.Interpreting Keeping a journal (learning log) about what students

learned in class.Applied Use Having students write their own story problems.

Having students write their own test questions.Creative Use Having students write a report on a mathematics

project.

Percentage of Teachers

Number of Kinds ofWriting ActivitiesUsed by Each Teacher

012345

TABLE 3Using Different

PercentageofTeachers

623362960

Kinds of Writing Tasks

Cumulative PercentageofTeachers

6296594100100

writing in their classes while 64 percent of the teachers used two or fewertypes of writing in their classes.

Writing Frequency

Student writing activities within each of the five writing types were analyzedand classified by frequency of occurrence for each teacher. Three measures offrequency were used: (1) "frequently occurring," meaning at least once aweek; (2) "moderately occurring," meaning between once every two weeksand monthly; and (3) "infrequently occurring," meaning less than once amonth. The results of this analysis are presented in Table 4.


12Teacher Use of Writing

TABLE 4Percentage of Teachers Using Each Kind of Writing Task

by Frequency of Occurrence

Direct Linguistic Applied CreativeOccurrence Use Translation Summarizing Use Use

Frequent45066 0Moderate29192926 0Infrequent0101013 13None26715555 87

The data in Table 4 show direct use activities were used weekly by 45percent of the teachers, summarizing activities by 6 percent of the teachers,and applied use activities by 6 percent of the teachers. In contrast, creativeuse activities, such as writing a report, were almost never used; only 13percent of the teachers used them infrequently (less than once a month).An additional analysis was conducted to determine frequency of occurrence

for student writing activities other than direct use tasks. Percentages wereobtained by compositing the extent of usage for each individual teacher.Excluding direct use tasks, the percentage of teachers for frequency ofoccurrence were: 10 percent had students engage in weekly writing activities;45 percent had students engage in writing activities once a month; 23 percenthad students engage in writing activities once or twice a year; and 23 percentnever had students engage in writing activities.

Audience

An analysis of audience was done for each of the reported writing activities.Of the 31 teachers sampled, 77 percent had their students write for theteachers some or all of the time (i.e., the teachers collected, read and gradedthe material). Only 26 percent of the teachers sampled involved students insome form of reading each other’s work. These efforts included: Peerresponse (i.e., students exchanging story problems), answering each other’stest questions (i.e., students writing test questions and other studentsanswering these test questions), and whole group activities (i.e., havingstudents write something and putting it on the chalk board or posting thework for subsequent reading by students). Finally, 23 percent of the teachershad their students engage in some writing solely for the student’s own use(i.e., taking class notes and journal writing). Of the 31 teachers, 39 percenthad their students engage in writing activities for an audience other than theteacher (writing read by others or writing solely for the student’s own use).

In terms of frequency of occurrence, 10 percent of the teachers hadstudents write for themselves or other students on a weekly basis. With the



exception of this 10 percent, none of the teachers had students write for anaudience other than the teacher more frequently than once every two months.

Instructional Support

Writing activities and assignments were examined to determine to what extent(if any) the teachers in this study were supplying instructional support fortheir students. The first aspect of instructional support examined wasprewriting activities. Twenty-three percent of the teachers involved theirstudents in some form of prewriting activities. These activities includedprewriting discussion (group discussion prior to beginning writing) andteacher modeling (teacher sharing a model before students began writing).Overall, student involvement in prewriting activities ranged from sporadic tonon-existent. Even those teachers who utilized some form of prewriting didso no more than once or twice a year.The second aspect of instructional structure examined was revision of

written efforts. No instances of student revision of written work wereidentified.

Discussion

Subject to the limitations of this study, student writing appeared to be aninfrequently used technique in junior high mathematics classrooms. Themajority of student writing seemed to involve some form of direct copyingand notetaking. Twenty-three percent of the teachers sampled never had theirstudents engage in writing activities beyond relatively low level copying tasks.Even those teachers who had students engage in writing tasks involving morethan direct transcription of material from lectures and books did soinfrequently. This finding was surprising since the authors had expected amore frequent occurrence of translation from symbols to written languageand of students writing story problems. However, both of these activitiesappeared to be seldom used.

Equally as noticeable as the limited use of student writing was the dearthof student response to each other’s writing. The writing that the students didwas almost always "one shot" writing for the teacher (the teacher was theonly reader).Not as surprising to the authors, but illuminating none the less, was the

way writing was assigned and developed by the teachers. Activities whichincorporated instructional support (i.e., prewriting and revision) were rare tonon-existent. Even those teachers who were utilizing original writing activitiesapplied them in a way which did not increase students’ chances of success.This is illustrated by the comments of one teacher who had students writestory problems. This teacher observed that the student generated problemswere frequently inaccurate and impossible to solve. However, this teacherutilized minimal prewriting activities with no revision efforts. Possibly,increased attention to aspects of the composition process would result in an



increase in teacher use of writing as a way to develop multi-facetedmathematics ability through improving the quality of students’ products.While it is impossible in this kind of study to assess the quality of writing

expected or the amount of student involvement with writing, some conclu-sions appear warranted. First, in junior high mathematics classes writing is aseldom encountered activity. This is especially true once one goes beyonddirect notetaking and copying tasks. Second, few of the junior highmathematics teachers in this study had their students engage in any form oforiginal writing as a vehicle for instruction in mathematics. Writing, when itoccurred, appeared to be almost incidental instead of a planned activity todevelop a deeper insight into mathematics. Because these conclusions arelimited by the sample and design of the study, the authors view these findingsas being tentative. However, classroom observations and subsequent follow-up investigations with mathematics teachers outside of this local area, suggestthat, at least for this region of the United States, the findings from this studyappear to be valid.

Reflections

Throughout the interviews, the authors kept in mind that the teachers wereteaching mathematics�not writing. However, it appears that the attainmentof instructional objectives would be enhanced through increased use ofwriting in mathematics classrooms. None of the teachers interviewedexpressed a lack of concern about student writing ability, but most saw noconnection between writing and mathematics. Two observations are relevantto this point. First, the majority of the teachers stated that they had littleidea of how they could implement additional writing activities. Second, whenwriting appeared it frequently seemed to be linked to plans in the teacher’seditions of the textbooks. These two observations suggest that junior highmathematics teachers would profit from inservice efforts in ways they couldincorporate writing into their classes and that the incidence of writingactivities in junior high mathematics textbooks could be increased. Implemen-tation of such writing efforts should promote a more reflective, analyticalattitude towards the study of mathematics by junior high students.

References

Applebee, A. N. (1981). Writing in the secondary school. Urbana, Illinois: NationalCouncil Teachers of English.

Bader, L. A., and D. L. Pearce. (1983). Writing across the curriculum, 7-12, EnglishEducation, 15, 97-106.

Britton, J., T. Burgess, N. Martin, A. McLeod, and H. Rosen. (1975). Thedevelopment of writing abilities (11-18). London: Macmillan Education Ltd. for theSchools Council.



Davison, D. M. and D. L. Pearce. (in press). Using writing activities to reinforcemathematics instruction. Arithmetic Teacher.

Emig, J. (1977). Writing as a mode of learning. College Composition and Communica-tion, 28, 122-128.

Evans, C. S. (1984). Writing to learn in math. Language Arts, 61, 828-835.Fennell, F., and R. Ammon. (1985). Writing techniques for problem solvers.

Arithmetic Teacher, 33, 24-32.Haley-James, S. (1982). Helping students learn through writing. Language Arts, 59,

726-731.Pearce, D. L., and L. A. Bader. (1984). Writing in content area classrooms. Reading

World, 24, 234-241.Shaw, J. G. (1983). Mathematics students have a right to write. Arithmetic Teacher,

30(9), 16-18.

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Teacher Use of Writing in the Junior High Mathematics Classroom