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'Seifert,. Edward H.; Beck, John J., Jr.Time/Learning Relationships in Secondary Schools: A.Research Report.Mar 8345p.; Cherts may reproduce poorly due to marginal

A legibility of original document.Reports - Research/Technical (143)

MF01/PCO2 Plus Postage.*Algebra; Classroom Observation Techniques; HighSchools; *Mathematics Achievement; SchoolEffectiveness; Statistical Amalysis; *StUdent TeacherRelationship; -Tables (Data); *Teaching Methods; *TimeFactors (Learning); *Time on-Task

.ABSTRACT". Sixty students in 10 classrooms in 5 high schools

were extensively observed over a'10-week period during the fall:semester of 1982. Based on pre- and posttests to measure achievementgain on algebraic objectives and change in attitude, the stuayinvestigated the relationships between student achievement andvariables of student behavior, instructional strategy, and time ontask. In addition to the text, the data are illustrated in ninecharts. Significant positive relationships were found betweenachievement gain and the lecture/discussion method, the amount_oftime students spent on tasks related to the learning objective, andstudents' total engaged time. Significant negative relationships werefound between academic gain and directed study strategy, the amountof-time students spent on tasks not related to the learningobjective, and students' total unengaged time, including waiting forhelp. A significant positive relati nship was found between thelecture/discussion strategy and the a unt of time students spent ontask. Achievement gains for individual c Iss srooms were significantlyrelated to minutes of time on task per classroom. Implicatibns of .

these findings for teachers and adminiltrators are discussed..(MLF)

4.

I

f

****************************************************4;******************,Reproductions supplied by EDRS are the best that can be made *

from the original document. * °

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a.

1.

TIME/LEARNING RELATIONSHIPSIN SECONDARY SCHOOLS:A RESEARCH REPORT

US CIEPARTMENT OF EDUCATIONNATIONAL INSTRIIKOF EDUCATION

EDUCATIONAL RESO ES INFORN1ATION'' CENTER I ERIC)k Thts dOcurnent has been reproduced asreceryed from the person or organizationoriginating it

Melo, chanpes have been made to improvereproduction clualr4_Points of crew or opinions stated M this &Curnent do not necessarily represent otficralNIEposition or policy

BY -/

"PERMISSION TO REPRODUCE THISMATERIAL HAS BEEN GRANTED BY

Edward H. Seifert, Ed.D.

Assistant ProfessorSouthwest Texas State University

. John J. Beck, Jr., Ph.D.

Assistant ProfessorSouthwest Texas State University

fir

San 'Marcos , Texas 78666

Vs,

March, 1983

Tb THE EDUCATIONAL RESOU 'RCESINFORMATION CENTER (ERIC)

Abstract

TABLE.OF CONTENTS

Review of Related Research

Page

2

Methqd and Organization of the Study 4

11

Results 'of Data Analysis r 8

Implicatiotis 12

Bibliography 14

Chart I: Achievement With Teaching Strategy 15 ,

Chart II:Achievement With Time on Learning.Objective 16

Chart III:Achievement With Engaged Time 17

Chart IV: Achievemept With Urrengaged Time 18

Chart V: Achievement vs.- Attitude 19

Chaart VI: Achieveent On-Task With Setting- 20

Chaft VII:Achievement Off-Task With Setting 21

Ch'art VIII:Achievement OnnTask Time Per 554linute.Periodand Achievement Gain 22

Chart IX: Achievement On-TasK Time by Recording Cycle

Appendix A: Assessment of Algebraic Competencies

_Appendix B: Math Attitude Scale

pendix C: Student-Obtervation Form

1

23

24

31

32

TIME/LEARNING RELATIONSHIPS IN SECONDARY SCHOOLS: A RES RCH REPORT

X by

Edward H. SeifertJohn J. Beck, Jr.

ABSTRACT

Sixty students in ten classrobm's among five high schools wereextensively observed over a ten-week period during the fall semester,of 1982. The research question investigated was whether or not evidenceof certain task behaviors among students was related to student achieve-me'nt. Based on pre- and post-tests to measure achievement gain on,algebraic objectives and change in attitude, significant relationships(pm. 0.05) were found among these variables and various time-on-taskrelated variables. Significant positive relationships were found betweenachievement gain and time spent in the-lecture/discussibn teachingstrategY; between achievement gain and time spent in covert task tehaviors;between achievement gain and time spent in all on-task behaviors; betweenachievement gain and-attitude change: and between the amount of time spentinythe Jecture/discussion teaching strategy and the time spent on-task.Signtfi&nt neOtive relationships were found between achievement gainsandthe amount of time spent in seatwork; between achievement gain and theamount of time spent working off the objective; between achievement gain'and the ampunt of time spent waitin4 for help; between achievement gaili andtime spent in all off-task behaviors; end between achievement gain and theamount.of unengaged tjme.

.

4

"TIME LEARNING RELATIONSHIPS IN SECONDARY SCHOOLS:A RESEARCH REPORT"

Improvement of schooling and the search for ways to iiprove school

effectiveness continue to be popular endeavors.among,educators as they

'strive to meet the modern demands of educating America's youth. These

endeavors have apparently yielded less sticcess at thedsecondary school

level than at the elementary leyel. In a recent Phi Delta KappAn-,

Eleanor Farrar, Vice-President of the Huron Institute said that, in

general, school.reformers have by-passed the moire complicated secondaryI

schools. She contihued by saying "consequently, there hasn'ebeen much

change in high schools, and there hasn't been much improvement."

(Newsktes, Phi Delta Kappan, 1983)

Recent attention to efforts to improve school effectiveness, brought

. to the forefront.in large mdsure by the new accountability movement, has'4

invariably led to a con,sideration of time as an influencing variable.

Researchers may disagree on'the best ways to evaluate the influence of

this vartable, but little disagreement exi5ts1 concerning the notion that

time is a crucial variable. (Salmon, 1982)

Concerns about the purported importance of time, coapled with the

relative lack of research in a secondary school setting, led to the .

following research questions:11,

. . .

1. Do relabonships exist'between student achievement gains andselected time-related variebles at the secondary level?

;

2. Do relationships exist between student attitude changes'andselected time-related variables.at the secondary level?

e )

Review of Related Research

Effective schools tend to characteristfcally demonstrate allegience

to several factors which make a difference in Sfective instruction'.

Edmonds (1982),.in an/overview of effective schooling research, listed

five characteristics of effective schoo)s:

1. Strong leadership and attentiom to the quality of instructionby the building principal.

2. A pervasive, and broadly understood yistructional focus.

3. An orderly and safe climate conducive to teaching and learn

4. Teacher 'expectations that all students can achieve minimum mastery.

5. Use of pupil achievement measures as a basis for program evaluation.

High staff expectations for studehts influence how time,is usSLIn the

classroom. The degree of influence is affected by school policies enforce:

,ment practices, and by classroom practices and behaviors which consistently

comMunicate to s,tudents that success'is expected and reachable (Murphy, et al.,

1982). Murphy reported that the classroom practices which make a difference

in academic,expectations are:

1. Establishing anejcademically demanding climate.

2. Conducting an orderly, well-mankged classroom.

3. Ensuring student academic success.

4. Implementing instructional practices that promote student achievement.

, 5. Providing opportunities for student responsibility and leadership.

The common variable in these effective practices is'time. :Each of the

five critical Practices is time dependent. This set of expected practices

must-be.expanded to include a systematiCally planned consideration of time

by the teacher.' Berliner includes three tiThe-related behaviors among the

six behaviors to look for When observing classrooms (Brandt, 1982):

4

1. Time.allocation

2. .Engagement rates

""\k.

3. Time management

4. Match of idlt6tional materials to the goals of the school.

5. Classroom management and dtscipline

6. Politeness and kiridness

Clauset (1982) reports that allocate'd time is in large measure a

function of school policies and may be outside the sphere of influence for

many teachers. -With respect to engaged time, however, Clauset shows that

this variable does influence the Tevel of achievement among students.

Perhaps the .landmark research on the issue of time and learning'was.

the Beginning Teacher Evaluation Study (BTES). ,This major enterprfse,

,funded by the National .Institute of Education through the California

Commission for Teacher preparation and licensing, sets benchmarks for

identifying the conditions and skills a teacher needs to teachef;ectively.

Conducted.among elementary school albjects, the BTES researchers (Fisher,

et al., 1980) developed a measure of student classroom 1/earning called

Academic Learning Time (ALT), deined as the amount of Vme a student spends,e

engaged in an academic task that can be performed with higii success by

the student. ALT is derived from engaged time which is that part of

allocated iime during which.the student iS paying atteniion. Allocated

time is the time available during school hours Mt a student to work

on instructional objectives. Using these three time measures as

references, the researchers delineated fourteen major findings:

1. The amount of time that teachers allotate to instruction in' a particular-content area is positively associated with student

learning in that content area.

(

44,

2. The proportion of allocated time that students are engaged ,ispositively associated with learn-Mb.

3. The proportion.of time that reading and mathematics"tasks areperformed with high success is positively,associated with .

'student learning%41 11

4. The proportion of time that rea'ding or maihem5tics tasks areperformed with low succels is negatively associated with

*student learning. ,

,5. Increases in AL-flare not associated with more negative attitudestoward mathematics, reading, or school.

6. The teacher's accuracy in diagnosing student skill levels isrelated to student achievement nd ALT.

7. The teacher's prescription of 'appropriate tasks is related to'stUdent achievement and tudent'success rate. .

8. More substantive interaction between the student and All instructoris "associated with higher levels of student engagemenl.

9. Academic feedback is positively associated with stu ent learning.,

10. Structuring the les,son and giving directions on task procedureswere positively associated with high student success.

11. Explanation specifically in response to student need is negativelyassociated with high student success.

12. More frequent reprimands far in appropriate behavior are-negatively associated with student learning.

13. The teacher's value syStem is related o AltT and to studentachievement. Teacher emphasis on a emic goals is positivelyassociated with student learning.

14. A learning environment characterized by student responsibilityfor academic work and by cooperation on academic tasks isassociated with higher achievement.

Method arid Organization oflthe.Study

Five hijh schools in central Texas wei-e selected as research sites.

The selections were Made based on accessibility and size. Ifi order to

imestigate the relationship of size of school to student achievement,

an attempt*was made 't,13 include as many different school sizes as was

possible.

1.-

4

WitiiWeacii high schodl, twO\Sections of first-year algebra students

were identified after,consultatiot Xth the building princip4l, the class-

room teachers, and the department chairpersons in each school. First-;

year algebra was the disCipline'Selected for the researcVunder the

assumption.that objectives for this discipline were more likely to show

greater similarities among schools than objectives from othex disctplines.

After the'schools and the classrooms were identified, each was

labeled in the following manner for bookkeeping pu'rposes and to avoid.--

'the possibilityof unfair comParisons being drawn according to school

'names:

School Period # Students Teacher

A 2 17_ Al

A 3 , , 24 A2

2 25 Bl

B 3 18 B1

C 2 21 Cl

C 3 12 . C2

D 5 30 D1A

D 6 33. D1

E 4. 5 25, El,

,

E 6 19 E2

A pre-test on first-year algebra objectives (See Append,ix A) and a

pre-test on attitude toward mathematics (See ApPendix B) were administered

to every studentln each of the ten sections. These pre-tests were

administered during.the same week in early October ,of 1982., Scores from

these pre-tests were used to identify the research subjects as well as

to provide baseline data forresearch analysis.

5 u, 9 -

4

4 .

I e

Six students,, three male and three female, were.identified ie4th,

Classroom as research subjects. The identiflcation was based on

nearness of the'pre-test scores to the classroom mean for each test.

That is, the six students. whose scores were nearest to the classroom

mean on both content and attitude were the subjects -selected for further'

research. Only the researchers knew the identity of the six subjects

during the researtn. Neither the sVents nor the teachers Were given'.

this information.

An observati

,

,. .

schedule was determined so that each subject in

each classroom woul,d be observed during ten complte class.periods

over a chrse often weeks. The schejule was given to the classroom

teachers. The teacher& alwaA knew when the researchers would be

present in Xhe clastroom, but the teachers were never aware of wirrch

students were being observed.

fs.

The Student-Observation Form(See APpendix C) was developecteafter

reviewing the instrumentation used in the Beginning Teacher Evaluation

Study. The Student Observation.Form (SOF) was 'designed to take advantage

'of the unique qualities o.t the secondary classroom. After the desi.gn

was coMpleted, the researchers tested it in classroom simulations to.

insure consistency among observers and to reach a,subjettive measure of

internal validity of the instrument.. .

The observations were designed on a timed, rotatinlg c.icle format in a

-

such a .manner that each subject was observed at ten equally spaced time

inteevals during each class period. Each observatioh of a particular

subject required observing for five variables. After observing the

,subjecefor approxiMately sixty Seconds, entries were made on the SOF

on-the following vatiables:

k,_----

k 6 :

SETTING: The genqral teaching strategy common to high school'mathematics classrooms.

L:Lecture/Discussion

S:Small Group

Directed Study (Self-Paced)

ECTIVE: 'Student behaviors .generally related to the daily learningobjectives.

11:01 -the' objective

N:Not on the objectivee-

LEARNER MOVES: SpecifiC-6bserved behaviors'of the student duringthe instructional sequence.

E:Engagel, written response'

S:Engaged, spoken response

C:Engaged, covert activity (listening, thinkjng)

D:Engaged,,receiving directions

I:Not.engaged, interim activity fsharpening pencils, turning inand passi.ng out papers, *tiing books, etc., that are a part ofmath. activity.

N,,J4:Not engaged waiting for help

0:Not engaged, off-task (periods where the stuident is inappropriatelydisengaged from a math task. Socializing, daydreaming, misbehaving,3

- etc.).

GENERAL:

44:Waiting for-lesson to start (or waiting after work is finished andno other activity is initiated).

T:Transition (periods of change from one activitj, to another).

M:Management (cqpduct of class busineis Unrelated to instructionalactivity, e.g.% roll-taking, bookkeeping, etc.)

B:Break (recreatidnal r free time).

N:Non-academic'Instruct On (flag pleages, etc.).

, )

10:Other academic .Instructions'

'Alibsene

INTERRUPTIONS: ',Observable'breaks.ir the iastructional 'sequence.

I:Inte'rruptions from outside the.classroom (Public addressannouncementS, people at the door, students leaving for trips,

4 ,

At the conclusion of the ten weeks of observations, a total of 100

cycles of data with five recording6 per cycle [lad been recorded for

each subject. This provided a total of 30,000 xlassroom behavior observe-,

tions for the sample total of 60 subjectS., y

Post-tests were administered during the thi,rd week in December of

1983 to every student in each of the ten classrooms. Even though analysis

was'done'orNnly the Six sublects per classroom the tests were'administered

to all students to insui-e anonymit3"; of subjects.'

The data were analyzed usng the Statistical Package.for the Social

Sciences (SPSS). Tbe subprograms Frequencies and Scatterdrams were ran to

determine trends:'Pearson product-moment correlations were.rün,to determine,Sr

relationships; and, 2-tailed t7tests were computed.asmeasdres of significaace

of relationships.4

Results of Data Pirllysis

Achievement gain'', as measured by the 'difference betWeen post-test-scores

and pre-test scores on the Assessment of.Algelaraic Competencfes tesl,

- 0

was treated as the independent variable. The dependent.vahbables selected

for coMparative analyses were those observed in the classroom. SCattergrams,

.

Pearson R's, and 2-tailed t-teSts of significance were'computed for the

various relati'onships. For the purposes of this, research, a probabflity

of 0.05 was chosen as'the level-of significance.

812 I.

,p0

41.

,

When achievement gdin was oompared to,the classroom strategy, the

results indicated a significant positive' relationship between gailind

the lecture/discussion method ,and 6 significant negative eelationship,

etween gain and the directed study strategy.

PLACE CHART I ABOUT HERE

' As might_appearintuitively obvious, achievement ,gain yielded a

significant positive refationship with the amount of time students spent -

dn asks related to the learning objective and a significant negative,4

relationship with amount of timestudents spent on tasks not related to

the learningzobjective.

PLACE CHART II ABOUT,HERE

When achievement-gain was compared to engaged time and unengaged

time,,significant positive relationships were found with total engaged

time and the. subset of- the tofal time called engaged tovert behavior.e-

Significant negative reAtionships were found between achievement gain

and total unengaged time, between gain and the subset of total unengaged

time caqled "waiting for'help," ,and between gain the subset of total,

un ngage time called "off-task."

PLACE4CHART III AND IV°ABOUT HERE

The r'emainder of the subsets'of total engaged time and total<

.,uningaged time failed,to yield significant results. As indicated on

Charts III and.IV, these were achievement gain with "receiving directions,

°Tigaged written," "engaged spoke'n," and "unengaged, interim activity."

9 13

Even though_acoOarison of achTevement gain arid attitude change

yieldetraTpositive correlation', the strengtp of the relationShip did

not meet thetdesired level 'of significance.7.

PLACE CHART V.ABOUT HERE

Because it was of speqial interest to the researchers:further

investigations were made of the relationships between the selectO

instructional strategy and on/off task behaviors.

PLACE CHARTS VI AND' VII ABOUT HERE

Note that when the percentage of time,spent on-task, wa i. compared to

the percentage of time spent in a particular instructional strategy, a

significant pogitive Notionship was found'between tiMe spent on-task

and the lecture/discussion strategy. While the other two observed

strategies revealed a negative correlation, the strength of the relation-

ship di'd lot meet the set standard of.0.05.

Clasvoom Analyses

In order to have a baseline reference for practitioner implication,

a the data were analyzed from the point of ciiew of a typical classroom,

that is , one of 55-minutes length. Achievement gain data and time-on-,

task data were then normaliled to the 55-minute class length.

PLACE CHART VIII ABaUT HERE

The average number Cminutes on task for the total sample was 28,

which represented 54.2 per cent of the total class time. Individual

classrooms reflected a range from seventeen minutes of on-task time at

the low end to 34 minutes at.the hiph end.

4t-

10

k

`st

When achievement gains for individual clas4rooms were comPared to,

minutes of on-task time per clas room, a strong relationship Wes found

to eest. (P > 0.95) In general, then, a significant Positive 011ationship

was found to exist between minutes of time spent on task during a .clasS

period,and achieveMent gain.

The rotating time segdence method of data collection provided the

means for a detajled analysis of the uee of time du4ng a typical 55-'

minute class period. Summary data for the entire sample cs well as

summary data for each classroom were analyzed.

PLACE CHAAT IX ABOUT HERE

NOtice that tne mean data for 'the total,sample reflected a relatively

low on-task rate at the 'beginning of the period, a maximum rate during the,

third cycle (18-24 minutes after...the class period began), and a second

relatively Tow on-task rate at the end of the typical period.

40Subjective comparisons of the classrooms at the extremes of the

acnievement gain sp ctrum revealed that the low gain classroom followed

a pattern similar-to,the overall mean but at a much lower magnitude.

The.high gain classroom, while beginning the period with a pattern

:virtually the same'as the overall mean, began to differ afte r. the fourth

4cycle. While dther classrooms showed a continuing decline, or lack of

incline in dn-tesk rate, the high gain pattern reflected a continuing

inclid to the degree that on-task at the end of the period was higher

any other point in the period.

1 1

15

19

IMPLICATIONS

The value-of this research lfes in its finplications for use by

-practicing administrators and teachers.

Implications for the teachers.

A. Teachers should'not allow students to begin the class with aperio4 of off task time. The teacher should start the classon time using a format that will cause students to be activelyinvolved in learning from class initiali444on. This means theteachers Should plan actiAities for students while taking careof the class administrative dutiet (i.e. taking attenddnee,lunch counts-,-stc.).

B. Teachers need to plan their instructional strategies to fillthe entire class period. StUdent engaged time fluctuatesduring any class period. The most significant downturn in -

student engaged time is during the first and last 1Q-15 minutesof the class period. In order to help diminish significadtchanges ill student engaged time, teachers need to change theirinstructional activities. These activity changes cause studentsto be more interested, thus more real learning occurs.

C. Teachers must have contrql of the classroom for significantachievement to occur. Discipline problems in classrooms areinterruptions that have a great affect on student achievement.Each time the teacher stops the engaged learning process todiscipline a student the entire class-is placed in an off taskmode. Several minutes will be consumed from the time ofdiscipline until engaged learning is once again at peak levelsof efficiency. Each incident of discipline reduces the 28minutes of engaged learning time froM 2 to 4 minutes, this doesnot take into consideration serious confrontations.

IinplicatioWfor the principals

A. Principals need to reduce classroom interruptions sucifts:I. Use of intercom systems for extraneous messages to teachers

and students creates a loss of learning time to magnitudeof 5. This means for each minute of :interruption it takes5 minutes for the students to return to on task activities.

-2. Limit the number of 'personal interruptions by Office aides,secretaries, and students. This requires principals tomake sure that unnecessary classroom contacts are not made.

B. A great deal-of learning time is lost in assemblies of all types,including such activities as pep assemblies, various entertain-ment type programs; and programs promoting.special interests.For example, a thirty-minute pep rally for each of ten footballgames results in the effective:loss of five hours pf instruction.

C. Encourage and vigorously pursue students with less than desirableattendance. The obvious: students can't learn if they are absentfrom class. If student ledrning time is reduced by classroominterruptions, assemblies, and absences it is little wonder that'the results of basic skill testing and achievements scores havedeclined. The average student learning time is reduced from 175days to approximately 135 days because of the aforementioneditems. This amounts to a 33 per cent loss in allocged time.

ImAications for supervision

A. Teachers who use a block of time for_bomework or seatwork assign-ments during a class period are, in most cases,Adding to thelearners off task time. Teachers who feel they need to givespdents the opportunity to complete homework assignments needtechniques that Will cause students to stay on task.

B. Teachers who planned several inkructional strategies appeared toproduce higher levels of engaged time among students than.didthoSe. who limited strategies to lecture alone. One way to increaseengaged time is to alternate lecture with aPpro-priate practice,supparted by the coaching technique. This methodology appears toyield the highest engaged learning time and greatest'situdentachievement.

('C. The teachershould establish academic achievement as an important

goal in the classroom. Those that do this appear to have higherrates of engaged learning time. The no nonsense, down-to-businesstone in the classroom indicates that academic achievement isexpected by the teacher. In addition, these students understandthat they are accountable for learning the material.

13 17

BIBLIOGRAPHY

Brandt, Ron, "On Improving Teacher Effextiveness: A Conversation withDavid Berliner," Educational Leadership, Vol. 40 (October, 1982),12-15.

Clauset, Karl H., Jr. and Alan K. Gaynor, "A Systems Perspective onEffective Schools," Educational Leadership, Vol. 40, (December,198?), 54-59.

Edmonds, Ronald R., "Programs of School Improvement: An Overview,'FEducational Leadership, Vol. 40 (December,.1982), 4-11.

Fisher, Charles W., et al., "Teaching Behaviors, Academic Learning Time,and Studedt Achievement: An Overview,' in Time to Learn. A Reviewof the Beginning Teacher.Evaluation Stud,y, Carolyn Denham and AnnLieberman (eds'.). Washington, D.C.,(National Institute of Educatio,1980).

Murphy, Joseph F., et al., "Academic.Press: Translatjng High-Expettations

-

into School Policies and Cl8sroom Practices," Edutational LeadershiVol. 40 (December, 1982), 22-26 .

, "Newsnotes.," Phi Delta Kappan, Vol. 64 (Febfpary, 1983),445.

,

Salmon, Paul B.-(ed.). Time on Task: Using Instructional Time M&reEffectively. Arlington, Virginifa (American Association of'Schoo)Admidistrators, 1982). ,

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APPENDIX-A<

ASSESSMENT OF ALGEBRAIC COMPETENCIES

Directions:

A

Read.each question carefully and decide which one of thg answers is best.Notice the letter opposite your choice. Then, on a.seplrate answer sheet,record the letter opposite the number ethe problem.

Do not write in thg'test booklet!

For ExamPl.el,

Test booklep Answer sheet

13. 4y 4. 9 1 eco aG,C,4111/100713

(A) 5

(8) 8

'(C) - 7

(D) - 2

(E) 2

Do not begin until you are told to do so.

You may use scratch paper if necessary.

t.,

24.

36

1. If 2x + 1 = 7, then x = (1)

A 4

B 1

3

C 3

D

E 11

FIRSTJEAR ALGEBRA-TEST

7, If n is an'even number, what is the next largereven number?

2, The tatement, "A certain number f

incr sed by twice another numbern equal to 30," can be wrttten

A f + 2n = 30B f + 2f = 30C 2f + n = 30D 2f + 2n =, 30E 2nf = 30

3. (-5) - (-9) = (?)A -14

.B -4

C 4

14E 45

4. If x = y = z = 1, then 2c,:.:aX "i

A -2

8

C 0

1/2

E 1

5. -2x + 5x - 9x = (?)

A -16x

B -14x

C -1Ix

D - 6xE - 2x

A n - 2

B n - 1

C n + 1

D n + 2E 2n

8. What is the coefficient of y in the expression2y5 6y4 4y2 5y .1. 1?

A -5 -

8 -1

C 1

D 2

.E 5

9. IfA*LWancj if A = 12 and L = 3, then W = (?)

A 3

8 3

'4

12

E 36

10. A7 (?)x3

A x3.5

8 x4

C x10

0, x21

E 3.5

.

11. Which of the following is equivalent to

x(x + a) - a(x - a)?

il ('x + e),(x - a)2h.B (x + a)4 (x - a)

C (x + a)3

6. The graph below shows that each change D. (x + al2

in x of 1 unit corresponds to a change E x2 + azi

in y of

A 1 unit

5 11/4 units

..... 4

32

V 12. Which of the following is on instance of the-77-71 distributive principle?

c 2 units3 units

/ .2C A (x - y)(x + y) = (x- Y)x + (x - y)yi-- 4%-.....-

i30'

. B °7 + x + 5 = 12 + x,

5 5.units 'CT 7.1 ....:7;_iC 8 + x = x + 8 ;

(x 4' Y)(x-Y) = (x Y) (x 4.

fk4t

13, EXpand as indicated:-: .

(40 -*5k)2 =

A 4b2 - 5k2

8 161,2 - 40bk + 25k2

C 8b2 - 100

0 16b2 - 20bk + 25k2

E 4b2 + 5k2

14, If x Y 42, th en x - (?)

A 0

B 1

C 2

D 3

15.

E 6

.The .figure above show§ the graphs of twolinear equations. What is the solutionof these equations?

C (-2,1)

:1)"

17, What -is thesqUare, root of 1608?

AB

c 4b4

,D 8b28b4

S.

18. 22 (3x + 4xy) = (?)

A 6x2 + 8X2y

B 3x3 + 4x3y--/

C 6x3 + 4x3yo 6x3 +,8x.1f4

mak

,E 6x3 + 6x.3y

19. Solve R = i'S for d.1$1d,

A d =10 4

B d = KRnrr

C d =1°(

D d = K

E d 3B-t(KR

.1

20. 'Two of a student's test marks are 68 and84. A third mark is at least 40. Whatis his lowest possible average for thethree tests?

A_ 40a 58C 62

0 64E 76

21 : When factored, 4a2 + 12ab2 = (?)

A 4a (a + 302)

B 4a (a I+ 12b2)

C 4ab(a + 3b)

-D 4ab (a + 12b)

16. If 9x - 63 E 4a2_(1 + 3b2)18, X' = (?)

A 7944

BC 0

0 5

A

22. A boy who has q quarters and d diMes buysp pencils at 5 cents each. How many centsdoes he haiie left?

q+d-B q d - 5pC + 2(d - p)

38 o (-25q + 10d - p

E 25q + 10d - 5p

23. The statement x - 6 6 is 27.. Divide(Factor, etc.)equivalent toA x -36 x2 + 3x - 28 5x - 20

x 0x+6 3x + 15

E

24., An' automobile is moving at rmiles per hour, and an airplaneis moving three times as fast.How many ,hours will the planerequire for a 500-mile flight?A 1500

B 500

C

500 - 3r

E 1500r

25. If 4x + 5y = 13,and2x 4- 3y = 7, then x

A -2

-1

0 2

E 4

26; 'The

A

0

expression-1;7 equals

4a2-Nrg

2aVioT

2a-V-57-

10aa-V-27

4a-V 5a2 -

.27

A

0.

Which oi ihe following is thegraph of 2x + 3y '2=' 6?

3x + 217-1175(x,,+ 7)

3

5x + 357-17X + 7T"3(X°+ 7)

34 5 -5-4-3 1 2 34 5x

39BEST COPE

1

29. If x is a real nurrber, whatare all the values of oc forwhich x4 + 16 is a positivenumber?

A All x greaterthan -2B All x greater-than zeroC -All x greater than 2D All x betmeen -2 and 2E Al 1 val uellpfs x

30. Solve for x: 2(x .4- 3) = 15

A -92'

B

C

0

10

33. If 312 + b.x4 1 = A:l when x = 1,is b?

4

,A -4

13 -1

C 1

0 4

31. Simplify adlcais and corrbine:

\ .

+ 2-Nr-7-

A 18-trrB, 7 :\r'rC 4 -NTT

D 61/7E 8V-2-

-32. Factor the following e pressiori:49a2 - 91)2 \\ ,

(7a if- 3b)(7a - 39 \\

ba - 3b)2

A

B

c 9(7a2 - b2)

Dc 4pi a2-;_,P2)

E cannot be factored

4, \I

,E It--canncit be determined ftt.mthe information given.

34. Which of the following' expressionsis equal to (1 + x)(1 4- y)?

A'

B .1 + x + y

C 1 + ),z/

0 x -14- Y.+ xy

E 1 +xFy+XY

35. (-2)3 (.3)2 . (?)1

s.

A -72*

13( -54

C 36

0 54

E 72

.........

x x-5 - 1 = 3. + 2, them x = ,,(?)

A -15

B 2(T

C 3f0 15

E457

11.,

,

f

1

237. Factor 3x - 4x r- 4

A (3X - 2)(x + 2)

.13 (3x + 2)(x - 2)

. C '(3x + 1)(x - 4)

0' (3x - 4)(x + 1)

E (3x - 4)(x - 1)

41. 5a262 10b

2

41. 04

B

C.

; (?)3b4.1'

-8

3a4

8

i5b4

38. What is the result when

- x2 - 17x + 20 is divided

by x2 + 3x - 5?

A x 4

B x - 2

C x - 1

x +

E x 4

39. 'If a = 3 and t = 2, then3 "

ab

(a - b)4.,(r)

Ae 5

B _2.24

C -18

D :24

E. 216,

40. What value of x, when substituted

in, 1, will make this fraction

;"-Z-r .

, meaningless'?

A

8

-2.

2

0 Any number between -2 and 0-

`E Any number between 0 and 2,

;

D 25a4. 6

E 3

. 8a2b

42. By factoring, find the rootsof the equati on :

2x2 9; + 4 =

,

A Solution set is 0,23

.13 Solution set is fi-,43

C. Solution set is 11,4)

0 Solution' set -Is (P3E Solution -set is is.2 ,4)

41, .5olve the equation

x2 '+ 10): - 24 = 0 for x.

A xy= 12 or :x =

B x 12 or x = 2

C x 6 or x =

x = 6 or _x 7 4

E x = -12 or x = 2

29

,

t..... i J

/f r,

44. On which of the following nimber 48. Solve the formula.E = ar for r.

lines does the heavy line represent a + r

rall numbers x such that A r , aE

-3 < x. 3? i7:7. - --vAti`ii t ----'.. 4 I ) B aE /

-4 -3 -2 -1 0 1 2 3 4 r = 177

-4 -3 -2 -1 0 1 2 3 4

-47r743 -2 4 o.. i .

r =' a-\ 177r

C r = aE-a.+ E

D r = aE - a - E

4 i 3°--21741-

E

-4 -3 -2 -1 0 1 2 3 449. If x is -.greater than 3, which. of the

1 fq3lowing is the smallest?45. If y = 7 and x is greater than 0,`

3which of. the fol 1 owing' statements A xis true?

3A As X increases, y increases B. ;--z-7ri-

B As x increases:, y decreases

C As x decreases, y decreases

0 When x is greater than 1, y isgreater than 1. .

E When x is less than 1, y isless than

46. What number must be added to

x2 - 6x + 4 in ordtr to make'ita. perfect square?

A -4

*E3 0

C 2

0 5

E* 32

47. For what values of xx 1 , x-g. a

s Catemen't?

A 0 onlyB 3 onlyC 0 and 3 onV0 Al 1 values

E ,No value

is

true

4

50. Add as indicated. Simplify answers:

9(x-7) 5(x+2),

4 3

A - 14x 53

a 14x - 532

47x - 149

47x - 149

E 49x - 53

30 4 2

NAME:

TEACHER: APPENDIX B

MATH ATTITUDE SCALE

.4..

Directions: Please write your name in the upper right hand corner. Each of thestatements on this opinionnaire expresses a feeling which a particular person hastoward mathematics. You are to express, on a fivepoint scale, the extent ofagreement between the feeling expressed in.each statement and younown personalfeeling. The five points are: Strongly Disagree(A), Disagree(B), Undecided(C),Agree(D), Strongly Agree(E). You are to darken the bubble 6r1 the answer sheetwhich best indicates how closely you agree or disagree with the feeling expressedin each statement AS IT CONCERNS YOU.

I am always under a terrible strain in a math slass.

2. I do not like mathematics, and it scares me to have to take it.

3. Mathematics is very interesting to me, and I enjoy math courses.

4.*_Mathematils is fascinating and fun.4

5. Mathematics makes me feel secure, and at...the same time it isstimulating.

6. My mind goes blank, and I am unable to think clearly when working math..

7. I feel a sense of insecurity when attempting mathematics.

8. Mathematics makes me feel uncomfortable, restless, irritable,and impatient.

9. The feeling that I have toward mathematics is a good feeling.

10. Mathematics makes me feel as though I'm lost in a jungle ofnumbers and can't find my, way out.

11. Mathematics is something which r enjoy a great deal.

12: When I bear the word math, have a feeling of dislike.

13. I approaCh math with a feeling of hesitatibn, resulting froma fear of not being able to do math.

14. I really like mathematics.

15. Mathematics is a course in schooliwhich I have always. enjoyed'studying.

41101*

16. It makes me nervous to even think about having to do a mathproblem.

17. have never like math, anCi it is my most dreaded subject.

18. 'I am happier in a math class than in any other class.

Itfeel at ease in mathematics, and I'like it very much. 43.20. I feel a definite positive eaction o mathematics: it's enjoyable.

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APPENDIX CSTUDENT OBSERVATION FORM

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45