Using a Lifeline to Give Rational Number a

More documents

Recommendations

Info

$MATH 622 Selected Topics in Modern Algebra I$

$MATH 621 Selected Topics in Advanced Calculus II$

Fig. 5 Section of a student’s lifelineFig. 4 Students in conference about their lifelinesPHOTOGRAPH COURTESY OF DICK THORNTON, FORT KNOX COMMUNITY SCHOOLS; ALL RIGHTS RESERVEDThe next step was to create individual lifelines.To successfully accomplish this goal, the studentshad to make two important decisions. First, theyhad to decide what kinds of representations theywould use for the events that they had chosen.Some students chose magazine pictures, othersused photographs or drawings, and some usedcombinations of two or more of these types of illustrationsto represent events in their personal histories.Second, the students had to determine themanner in which they would represent time, especiallydivisions of time that were less than one year.Those decisions were based on the events that theyhad chosen. Hunt shared the scoring criteria in theform of a student critique sheet (see fig. 3).The students next constructed rough drafts oftheir lifelines. Using the personal-lifeline studentcritiqueform, the students met in pairs to providefeedback to each other. Some students were able topinpoint such difficulties as misplacement of numbers,inappropriate use of scale and labels, and lackof correspondence between labels and points onthe lifeline. After these conferences, the studentsrevised their personal lifelines (see fig. 4). Theycorrected errors, added detail, and designed theiredited copies on fanfold computer paper. The studentsthen submitted their final copies for grading(see fig. 5).The last step in the project was to write a summaryof the mathematics used in creating the personallifelines. The summary was to include a descriptionof what the students had learned aboutpositive and negative rational numbers. The studentswere to explain the representations that theychose for intervals on the lifeline. In addition, theywere to describe the things that they learned fromthe project and the areas that gave them particulardifficulty.To extend this project in conjunction with alanguage-arts class, students might be asked towrite family histories that include the events in theirpersonal lifelines. In preparation for the familyhistorywriting task, the language arts teachermight have students as a class rewrite Lu Lynne’sbiography in a more organized sequence. This extensionwould help students transfer the symboliclifeline representation to a narrative format andwould serve as an appropriate culminating activity.The teacher’s scoring guide for the personallifelineproject appears in figure 6. In addition, thestudents displayed their final projects on the classroomwalls (see fig. 7). Other students were allowedto place sticky notes on the finished projectsto make positive comments noting the differencesin the lifelines.VOL. 7, NO. 4 . DECEMBER 2001 213
CRITERIONLEVEL 4LEVEL 3LEVEL 2LEVEL 1MathematicalplacementAccurate scale withclear labeling;accurate placementof eventsAccurate scale;accurate placementof events with minorerrorsIntegers and somefractions correctlyplacedLittle attention toscale; limitedaccuracy in placementof eventsChoice ofeventsIncludes a varietyof significant eventsand meets criteriaoutlined in lifelinestudent critique;choice of events useswide varietyof fractionalrepresentationsIncludes eventsoutlined in lifelinestudent critique;several fractions areused but are limitedto those that areeasily represented(1/2, 1/3, 1/4)Includes a limitedvariety of events oruses mainly positiveand negative integers;only basic fractionsusedIncludes a limitedvariety of events;most events correspondto positiveintegersVisualpresentationCreative representationsof events;visually appealingChoice of symbolsaccurately representsevents; visuallyappealingChoice of symbols orwords accurately representsmost events;little attention toneatnessLittle attention tovisual detailWritingcomponentShows clear understandingof positiveand negative rationalnumbers, with clearrationale for choice ofintervals; insightfulself-assessmentShows clear understandingof positiveand negative rationalnumbers and goodrationale for choiceof intervals; lists (withexamples) someareas of learning ordifficultyShows basic progressin learning aboutpositive and negativeintegers and choiceof intervals; listssome areas oflearning or difficultyShows little understandingof positiveand negative integersand choice of intervals;gives littleattention to areas oflearning or difficultyFamily history(optional)Well sequenced andorganized; grammaticallycorrect; givesinteresting overviewof family lifeWell sequenced andorganized; only minorgrammatical errors;events accuratelydescribedSome attention toorganization andsequencing; somegrammatical errors;events accuratelydescribedLittle attention toorganization andsequencing; manygrammatical errors;little detail in descriptionof eventsFig. 6 Scoring guide for personal-lifeline taskConnectionsTHIS ACTIVITY CAN EASILY BE ADAPTED TO BEcomepart of an interdisciplinary unit on historical,community, or governmental events. For example,to connect the personal timeline with history, the 0coordinate might represent the signing of the Declarationof Independence. Events leading up to independencewould be represented by negativenumbers, whereas events that occurred after thesigning of the document would be represented bypositive numbers. Another project might use 0 torepresent 1900 and show pictures depicting inventionsthat affect the lives of students today in transportation,communications, and other fields.For community events, the coordinate for 0might represent the date that the school wasopened. Events before the building of the schoolmight include the charter of the town, the constructionof important historical buildings, and importantmilestones in the history of the town. Recent eventsmight include school awards, major athletic competitions,or community celebrations.Governmental connections could include the inaugurationof presidents, the granting of statehood,and the passing of important pieces of legislation.The choice of the event represented by 0 is not significant;the placement of the events on the numberline will reveal students’ understanding of the mathematicalpart of the interdisciplinary assignment.214 MATHEMATICS TEACHING IN THE MIDDLE SCHOOL
Page 1 and 2: Using a Lifeline toNumbers aPersona
Page 3: Hunt then placed a large number lin

Using a Lifeline to Give Rational Number a

Create successful ePaper yourself

Delete template?

Save as template?