MePEnER tToUTOrRiINnG:Gcircle.adventist.org/files/jae/en/jae201375043809.pdf · beneﬁt multigrade students. Then some designs will be suggested for questioning strategies that facilitate

Educators everywhere can re-count times when their stu-dents have been exemplaryteachers. In one of my multi-grade classes, while grade 2

students were exploring how multipli-cation works, it was a keen kinder-garten student who helped the 2ndgraders see that we were adding same-sized numbers over and over. As the2nd graders struggled to master theconcept, Breann1 observed what theywere doing and said, “All of the num-bers are the same, Mrs. Duffy.”

Years later, in another grade 2 mathclass, Lizzi’s cheery request opened thelesson: “Mrs. Duffy, may I show youwhat I learned about addition?” Lizzirandomly chose numerals and wrote

them in two 20-digit rows on thewhiteboard. Then, adding from left toright, she exclaimed, “See! You can useregrouping in any size of additionquestion.” As a result of Lizzi’s explana-tion, even the struggling students read-ily mastered regrouping in both addi-tion and subtraction. When studentscan make contributions of such caliber,a love of learning is kindled, which en-ables students to see past the classroomwalls to embrace the challenge of pre -paring “for the joy of service in thisworld and for the higher joy of widerservice in the world to come.”2

Memories of the effectiveness ofthese student-led teaching experiencesinspired me to investigate approachesthat multigrade teachers can use to nur-ture their students’�ability to teach andencourage one another. Peer tutoring,where one student acts as tutor and the

other as tutee, emerged as a most helpfuland positive instructional tool.

However, it soon became obviousthat training would be needed to en-sure that peers became effective tutors,and that developing question-askingskills would be the key to implement-ing an effective peer-tutoring program.

This article will first review the re-search on peer tutoring and how it canbenefit multigrade students. Thensome designs will be suggested forquestioning strategies that facilitate theuse of mathematical language duringboth whole-class and peer-tutoring ses-sions. After exploring ways to incorpo-rate peer-tutoring sessions into themultigrade class, some easy-to-applyguidelines for peer tutoring and math-ematical questioning techniques will

38 The Journal of Adventist Education • Apri l /May 2013 http:// jae.adventist.org

B Y C A T H L E E N M A R I E D U F F Y

Students to Become Master Teachers

P E E R T U TO R I N G :MentorinG

follow. The last three sections will in-clude examples of how to apply this in-formation in math lessons.

Research Reveals the Benefits ofPeer Tutoring

Research suggests that peer tutoringis a reliable and effective way to varyclass instruction.3 Researchers,4 review-ers5 and meta-analysts6 have shown thatpeers can be reliable teachers. Depend-ing on its design, peer tutoring can pro-duce both short-term and long-termgains for tutors and tutees in all subjectswith the greatest gains seen in mathe-matics.7 In algebra classes, peer tutoringhas been shown to be as effective as classinstruction.8 Analysts9 therefore encour-age the use of peer tutoring as a supple-ment for teaching, rather than solelyto add variety to drill-and-practice ac-tivities. Peer tutoring fits well in themultigrade class because it saves timeand makes it easier to organize and as-sign tutoring pairs, since varied combi-nations of students are available in a sin-gle classroom: Cross-age groups, withthe best age range of two to four years,10

are available for work that reviews con-cepts already introduced to older stu-dents. Same-age groups are also avail-able in the multigrade classroom. Theycan benefit from either reciprocal peertutoring11 or general tutoring tech-niques, which enable peers of any abilityto tutor.12

Relationship Building a BonusTutoring also has positive affective

benefits.13 Multigrade teachers canreadily organize same-gender pairs14

and student-chosen pairs, which in-creases students’ enjoyment of activi-ties because it enhances their sense ofbelonging and rapport as they relatewith friends and children similar tothemselves.

Peers relate well to one another bet-ter because they have much in com-mon.15 Thus, peer tutoring can posi-

tively affect class dynamics and encour-age cooperation as students gain in-sights into the teaching process and en-gage in meaningful practice.16 Thishelps class members to become pro-ductive citizens17 who show concernfor others and use their time more pro-ductively.18 They develop the interper-sonal skills needed for Christian wit-ness, and their caring actions revealthat God is growing them in His king-dom.

Time Savings and Flexibility The activities used by peer tutors can

also be incorporated into unstructuredperiods, which provides further timesavings and flexibility for the multigradeteacher. The use of math games duringtutoring sessions19 can make the subjectmore meaningful and interesting to stu-dents. As students learn these games andfind the activities to be rewarding, they

will enjoy playing them at a learningcenter, which further reinforces mathconcepts and facilitates mastery of othercurriculum subjects.

Multigrade teachers need instruc-tional techniques that result in optimallearning within limited time frames be-cause their time is frequently inter-rupted or restructured. Peer tutoringhelps teachers and students make bet-ter use of time and allows teachers theflexibility to effectively implementshort on-task sessions20 (i.e., 15 three-minute sessions during a three-weekunit).21 Amazingly, peer tutoring actu-ally can make a multigrade class easierto manage. Class size is cut in half22

when the teacher uses a reciprocalpeer-tutoring model in which partnerstake turns tutoring each other.23

Children with special needs receivemore individualized instruction andcompanionship because of increased

39http:// jae.adventist.org The Journal of Adventist Education • Apri l /May 2013

Throughout this article, the author’s students model techniques for peer tutoring.

“engaged academic time”24 and becausethe teacher is able to deal promptlywith incorrect responses. Most impor-tant, as students’ needs are met, thepeer-tutoring sessions allow the teachermore time to assess and gain new per-spectives on students’ strengths and toanalyze how best to meet their needs.25

Throughout the tutoring sessions, theteacher can encourage the use of math-ematical terms, support tutors and tu-tees in their use of prompts, facilitateand reinforce positive interactionsamong peers, troubleshoot by findingskilled tutors and asking them tomodel a difficult step for their class-mates, and make adjustments for thenext tutoring sessions.


Getting StartedSo how do you get started? First, be

sure to plan the specific, mathemati-cally related objective(s) that you wantyour students to meet as you develop ascript, or series of prompts, for the peertutors to use. Research has shown thatstructuring the tutoring sessions isbeneficial26 because structure promoteshigh-level mathematical thinking.27

Scripts, also called prompts, scaffolds, ortemporary supports, have been used ef-fectively by tutors to teach their peersalgebra, rounding numbers, and bargraphs.28 Further, scripts help tutors fa-cilitate high-level thinking because thistool helps them model questions ap-propriately, independently scaffold, or

adapt a task to meet a peer’s needs.Scripts provide tutors with vocabularythat enables them to encourage theirpeers to give more accurate mathemat-ical explanations.29 Mathematics readilylends itself to structuring, as it has itsown vocabulary. Structuring lessonsalso establish meaningful goals, givingstudents a sense of purpose while al-lowing the strengths of individual stu-dents to blossom.30

zeroing in on the Language ofMathematics

Choose key questions to encouragethe use of appropriate terminology andto provide scaffolds for tutors to useduring their work with the tutee. If you

have students brainstorm relevantmathematical language in smallgroups, question starters from bothmathematics and language arts willprovide insights on how to craft lesson-specific scaffolds. First, consider thefive basic teaching scenarios that en-capsulate mathematics instruction:patterning, sorting, following exam-ples, correcting non-examples, andmodeling. Figure 1 provides examplesof questions developed from theseideas for a lesson on addition with re-grouping. Curriculum guides and ref-erence books provide additional sam-ple questions and vocabulary.31

Collaborative Reading Group de-signs32 also offer guidelines for teachersas they design scaffolds for their stu-dent tutors. A collaborative group de-sign can be especially valuable becausethe assigned roles allow students towork from perspectives that emphasizetheir individual learning strengths,33

and can make them better tutors aswell. Any type of collaborative role canbe emphasized during each tutoringsession or questions can be taken fromeach modality. Teachers also have theoption of assigning tutoring pairs toshare their work collaboratively withother partners. Math-related descrip-tions for prompts used from the per-spective of each role are shown in Fig-ure 2.

Deciding How and Where to UsePeer Tutors

After developing your prompts, thenext step is to determine where andhow you want to use your peer tutors.Warm-up lessons, quick reviews, drills,and even peer-tutoring training ses-sions are three- to five-minute activitiesthat work well with peer tutors.34 Per-haps you wish to begin a new mathunit with a cross-age project or a coop-erative problem-solving activity—peertutoring can help you assess your stu-


Role Name Role Description Sample Mathematical-Based Prompts

Question Master Metacognitive analyzer “What do we know about this question?”“What is easy for you?”“What is challenging?”“What related math ideas have you used?”“Have you been consistent?”

Practice Master Analyzes the main idea “What is the most important math idea to of the lesson remember when you (add, subtract,

balance an equation)?”“What are you trying to find out?”“Please tell me where you started.” “Explain how you solved this problem step by step.”“First you…. Next…. Then…. Last.…”

Vocabulary Defines terms from “What does multiplication mean?”Enricher lesson “What words in the question tell you

that you are (multiplying)?”“Please, show me other ways to write the number 1.”

Connector Connects math ideas “When/where have we (added) before?”to self, to other “Why is __________ useful?”questions, to world “What math ideas did we see at the zoo?”

“What math would we see at a farm?”“Let’s design a math field trip.”“If I were blind, how would you explain this problem to me?”

Illustrator Creates graphic “How can we create our own question likeorganizers or visual this?”representations of math “How can we create a problem that is one

step more complex?”“Please show me this question with base 10 blocks.”“Let’s make a (game, cartoon, diagram, flow chart).”

Patterns: “What patterns do you see?” (Regrouping, adding 5’s)

Sorting: “How can we change this question so that we can solve it more easily?”(Student rewrites the question vertically.)“What do we need to remember as we rewrite this question?” (To line up the place values.)

Following “Is this question done correctly? How do we know?”Examples: “Can you show me your first step? Second? . . . Last?”

“Can you tell me exactly what to do so I can solve this question?”

Correcting “Is this question done correctly? How do we know?” Non-examples: “What math word was forgotten? How do we correct it?”

Modeling: “What can we use to model this? Can you show me?” (Picture or base 10 blocks) “How can we show that we are regrouping in our picture?”

Figure 1. Sample Scaffolds Related to the Five Mathematical Basic Teaching Scenarios

Figure 2. using Roles to Create Prompts for Peer Tutoring Groups

Figure 6. Ideas for Reinforcinga Classmate’s Correct Answer

dents’ current application of mathe-matical language.

Peer tutoring can also be incorpo-rated into daily teaching as an instruc-tional strategy for entire lessons as wellas for practice, reinforcement, and re-teaching. For example, you could use aspecific questioning series to teach oneto three students (same ability or cross-age), and then have these students usethe same questions to tutor partners,who then tutor others. When usingpeers as instructors in this way, teach-ers have the option to tier the level ofpractice exercises either within thesame grade or across grades. See Figure3.35 Or perhaps after a whole-class les-son with the teacher, grade 8 studentscould review multiplication of deci-mals and whole numbers. They couldthen teach grade 6 multiplication foronly decimals. grade 6 tutors couldteach 3-digit by 2-digit multiplicationto grade 5 students,36 who in turn re-view the concept of repeated additionwith students in grade 2.

Using Reciprocal Peer TutoringAnother idea for practice time, rein-

forcement, and re-teaching: Include re-ciprocal peer tutoring, where the stu-dent has a prompt card that shows eachstep for a problem. As Figure 5 shows,the tutee makes an initial attempt atcompleting the question. If the re-sponse is correct, he or she tries an-other question or switches roles withthe tutor. If the answer is incorrect, thetutor indicates the step from which thetutee should begin work and provides asecond chance. If the answer is still in-correct, the tutor models the solution,after which the tutee repeats it andthen goes onto another problem. Thetutor and tutee may switch roles after acertain number of questions or after astated time period.


Level A: How can 2 people share 3 brownies? Strategy:How can 2 people share 5 brownies? Repeated halvingHow can 4 people share 3 brownies?How can 3 people share 4 brownies?

Level B: How can 4 people share 3 brownies? Strategy:How can 3 people share 4 brownies? Dividing into 1/4, 1/3, 1/6 How can 3 people share 5 brownies?How can 6 people share 4 brownies?

Level C: How can 3 people share 5 brownies? Strategy:How can 3 people share 2 brownies? Halving plus Level BHow can 6 people share 4 brownies? strategiesHow can 5 people share 4 brownies?

*Adapted from Lori Williams, Teaching Children Mathematics (February 2008), p. 326.

Figure 3. Example of Tiered Problems for a Fraction Unit*

Figure 4. Sample Reciprocal PeerTutoring Worksheet

First Try Second Try Model Third Try/Comments

Figure 5. Sample Prompt Card—

The Steps of an Effective Tutoring SessionGreeting: “Hi. How are you doing?”

Set the stage: “Let’s look at our assignment. What are we working on today?”

Work Time: “Please, show me…”

Closing: “Thank you for _______. Let’s record our work.”

“Good work. Thoughtful answer.”

“Good, you used regrouping [or any relevant mathematical term] in this question.”

“You put a lot of effort into__________________.”

Figure 7. Ideas for Helping aClassmate Correct an Answer

“That’s close. Try again from here.”

“What math fact do you need? How does that change things?”

“What math words would help us?”

“Your regrouping is clear to here.”

“How can you follow through from here?”

MotivationOnce you have chosen a tutoring

model, consider the option of incorpo-rating a rewards system. Rewards maybe contingent upon individual aca-demic performance or used to validategoals for cooperation within groups.For example, Hawkins et al.37 askedstudents to generate their own ideas forreinforcers. Then, during each session,the teacher randomly chose whetherthe rewards would be contingent uponappropriate tutoring behavior or per-fect test scores.

Previous to setting peer tutors towork, the teacher must incorporate

tablish the purpose for the session.Next comes the body of the session,then its conclusion. Within the mainsection of the tutoring session, tutorsneed to know how to respond to bothcorrect and incorrect answers. Theteacher can make specific suggestionsor take five minutes to brainstormideas with the class.

Teachers can scaffold communica-tion development for tutors and tuteesby making reference cards for “TheSteps of an Effective Tutoring Session”(Figure 5), “Ideas for Helping a Class-mate Correct an Answer” (Figure 7),“Today’s Math Words,” and “Ideas for


tutor training into everyday lessons.38

Coaching in both math language andinterpersonal support strategies helpstutors work more comfortably and suc-cessfully.39 When students are prepared,this helps them to take ownership oftheir tutoring sessions.40

Some simple, easily planned inter-personal support strategies can be im-plemented to make peer tutoring moremeaningful and to encourage account-ability and responsibility for all stu-dents. A tutoring session can be role-played.41 As Figure 6 shows, effectivetutoring sessions should begin with agreeting, followed by a question to es-

Reinforcing a Classmate’s Correct An-swer” (Figure 6).

Record-Keeping StrategiesThe teacher must plan a strategy for

pairs to record their work independ-ently. Charts that students can use totrack their progress give sessions asense of purpose, help students developa feeling of accomplishment, and pro-vide accountability.42 The teacher willalso want to create a record chart onwhich to record his or her observationsduring tutoring sessions. On the stu -dents’ record charts, there should be aplace for comments so that tutors canreflect on the lesson that they have tu-tored.

Debriefing can be helpful becausestudents, like teachers, need feedbackon their teaching skills,43 and studentsmay make helpful suggestions for fu-ture lessons.44 Tutor involvement in as-sessment and planning has been evalu-ated positively in the literature.45

As you consider how tutors can helpthe teacher structure subsequent ses-sions, the positive impact of peer-tu-toring techniques on the tutor needs to

be re-emphasized. Peer tutoring hasbeen used purposefully and effectivelyto both teach and tutor new mathskills. Student tutors especially advancein proficiency as they teach mathemat-ics to their peers.46

The reciprocal peer-tutoring systemuses prompt cards that enable tutors toevaluate their peers even though thetutors are still learning or consolidatingtheir own skills.47 Teachers may alsocompose mathematically focusedscripts that enable tutors to practicehigher-level mathematical thinkingskills.48 Tutoring helps students developboth interpersonal and intra-personalskills, which enhance their experiencein mathematics and make the subject afavorite class.49

ConclusionTo summarize, research and practice

show that peer tutoring works. Themultigrade classroom is an ideal fit forpeer-tutoring programs. Structuredlessons, flexibility of design, scaffoldssuch as prompt cards and role plays,

students’�use of mathematical lan-guage, and the development of positiveinterdependence all make peer tutoringin mathematics class practical anduser-friendly. As your tutoring pro-gram grows, you will find that lessondevelopment becomes a partnershipwith students. Positive interdependencegrows among students and betweenstudents and their teacher. This benefitfar outweighs any extra initial prepara-tion time.

Cathleen MarieDuffy lives inBritish Columbia,Canada, where shesubstitutes atHazelton Seventh-day AdventistSchool, home-

schools her son, Elijah; and tutors Eng-lish as a Second Language in the Lillooetarea. Mrs. Duffy has taught multigradeclasses in the British Columbia, Ontario,and Northern California conferences.She earned a B.Ed. at the University ofVictoria, British Columbia; and hascompleted Seventh-day AdventistTeacher Certification requirements.

NOTES AND REFERENCES1. Students’ names in this article have been

changed to protect their privacy.2. Ellen G. White, Education (Mountain View,

Calif.: Pacific Press Publ. Assn., 1903), p. 13. 3. R. Douglas Greer, et al., “Key Instructional

Components of Effective Peer Tutoring for Tu-tors, Tutees, and Peer Observers,” In Evidence-Based Educational Methods, Daniel J. Moran andRichard W. Malott, eds. (San Diego: Elsevier Aca-demic Press, 2004), p. 295.

4. Researchers agree across time and researchdesign. See Cristina Cardona and Afredo J. Ar-tiles, “Adapting Classwide Instruction for StudentDiversity in Math.” Paper presented at the 1998Annual Convention of the Council for Excep-tional Children, Minneapolis, Minn., 1998, p. 12;Lauren Rio Heller and John W. Fantuzzo, “Recip-rocal Peer Tutoring and Parent Partnership: DoesParent Involvement Make a Difference?” SchoolPsychology Review 22:3 (1993):517-534; Keri F.

�


Peer Tutoring—A quick How-to Review

• Define a specific goal for a lesson;

• List some math-specific scaffold questions;

• Decide on your design for the tutoring session;

• Determine how you will divide students into partners;

• Develop a record-keeping sheet for students and for yourself;

• Decide how you will incorporate feedback from students into future lessons;

• Design a reward system; and

• Communicate with your school family about peer tutoring—how you are using

it and what research has shown—that it enhances student and teacher interactions

in classromos.

Eight straightforward steps. Why not give it a try?


Menesses and Frank M. Gresham, “RelativeEfficacy of Reciprocal and Nonreciprocal PeerTutoring for Students At-Risk for Academic Fail-ure,” School Psychology Quarterly 24:4 (2009): 266-275; Leigh Mesler, “Making RetentionCount: The Power of Becoming a Peer Tutor,”Teachers College Record 111:8 (2009):1894-1915;Nathern S. A. Okilwa and Liz Shelby, “The Effectsof Peer Tutoring on Academic Performance ofStudents With Disabilities in Grade 6 through 12:A Synthesis of the Literature,” Remedial and Spe-cial Education 31:6 (November/December 2010): 450-463; Keith Topping and Judi Bamford, ThePaired Maths Handbook: Parental Involvementand Peer Tutoring in Mathematics (New York:David Fulton Publishers, 1998), pp. 15, 18; KeithJ. Topping, et al., “Cross-Age Peer Tutoring inMathematics With Seven- and 11-Year-Olds:Influence on Mathematical Vocabulary, StrategicDialogue and Self-Concept,” Educational Re-search 45:3 (Winter 2003):287-308.

5. Two reviews stood out in the literature:Sinclair Goodlad and Beverley Hirst, Peer Tutor-ing: A Guide to Learning by Teaching (New York:Nichols Publishing, 1989), pp. 56-58; and DebbieR. Robinson, et al., “Peer and Cross-Age Tutoringin Math: Outcomes and Their Design Implica-tions,” Educational Psychology Review 17:4 (De-cember 2005):327-362.

6. Edward E. Gordon, et al., The TutoringRevolu tion: Applying Research for Best Practices,Policy Implications, and Student Achievement(Lanham, Md.: Rowman & Littlefield Education,2007), pp. 153-156, 161; Okilwa and Shelby, “TheEffects of Peer Tutoring on Academic Perform-ance of Students With Disabilities in Grades 6Through 12,” op. cit.

7. Gordon et al., ibid., p. 157; Michael Parkin-son, “The Effect of Peer Assisted Learning Support(PALS) on Performance In Mathematics andChem istry,” Innovations in Education and TeachingInternational 46:4 (2009):381-392; Sarah D.Sparks, “Researchers Find That Students Learn byTutoring Virtual Peers,” Education Week 30:10(2010):10.

8. David H. Allsopp, “Using Classwide PeerTutoring to Teach Beginning Algebra Problem-Solving Skills in Heterogeneous Classrooms,” Re-medial & Special Education 18:6 (November/De-cember 1997): 367-379.

9. Gordon, et al., The Tutoring Revolution, op.cit., pp. 166, 167.

10. Goodlad and Hirst, Peer Tutoring, op. cit.,page 84, agree with Robinson, et al., “Peer andCross-Age Tutoring in Math,” page 355.

11. Heller and Fantuzzo, “Reciprocal Peer Tu-toring and Parent Partnership,” op. cit.

12. Patrick J. Schloss and Sibyl A. Kobza, “TheUse of Peer Tutoring for the Acquisition of Func-tional Math Skills Among Students With Moder-ate Retardation,” Education and Treatment ofChildren 20:2 (May 1997):189-208; Menesses andGresham, “Relative Efficacy of Reciprocal andNonreciprocal Peer Tutoring for Students at Riskfor Academic Failure,” op. cit.

13. Gordon, et al., The Tutoring Revolution,op. cit., p. 153; Goodlad and Hirst, Peer Tutoring,op. cit., pp. 56, 58, 66; Menesses and Gresham,“Relative Efficacy of Reciprocal and Nonrecipro-cal Peer Tutoring for Students at Risk for Aca-demic Failure,” op. cit.; Schloss and Kobza, “TheUse of Peer Tutoring for the Acquisition of Func-tional Math Skills Among Students With MildRetardation,” op. cit.

14. Cross-gender pairs sometimes show lim-ited results, but appropriate peer training couldreadily overcome these challenges.

15. Cindy Meyers Gnadinger, “Peer-MediatedInstruction: Assisted Performance in the PrimaryClassroom,” Teachers and Teaching: Theory andPractice 14:2 (April 2008):129-142.

16. Goodlad and Hirst, Peer Tutoring, op. cit.,p. 66.

17. Ibid., p. 62.18. Ibid., p. 24; Messler, “Making Retention

Count,” op. cit.; Robinson, et al., “Peer and Cross-Age Tutoring in Math,” op. cit.

19. Topping and Bamford, “The Paired MathsHandbook,” op. cit.; and Topping, et al., “Cross-Age Peer Tutoring in Mathematics With Seven-and 11-Year-Olds: Influence on Mathematical Vo-cabulary, Strategic Dialogue and Self-Concept,”have developed some math games. As I reviewedthe games and the information accompanyingthem, I saw the need to be sure that activitiesmatch the curriculum and the abilities of students.

20. Robinson, et al., “Peer and Cross-Age Tu-toring in Math,” op. cit.; Schloss and Kobza, “TheUse of Peer Tutoring for the Acquisition of Func-tional Math Skills Among Students With MildRetardation,” op. cit.

21. Menesses and Gresham, “Relative Efficacyof Reciprocal and Nonreciprocal Peer Tutoring forStudents at Risk for Academic Failure,” op. cit.



24. Greer, et al., “Key Components of Effec-tive Math Tutoring,” op. cit., p. 297.

25. Gordon, et al., The Tutoring Revolution,op. cit., p. 173.

26. Allsopp, “Using Classwide Peer Turoringto Teach Beginning Algebra Problem-SolvingSkills in Heterogeneous Classrooms,” op. cit.;Gordon, et al., The Tutoring Revolution, op. cit.,

p. 173; Goodlad and Hirst, Peer Tutoring, op. cit.,pp. 86, 87; Heller and Fantuzzo, “Reciprocal PeerTutoring and Parent Partnership,” op. cit.; Men -esses and Gresham, “Relative Efficacy of Recipro-cal and Nonreciprocal Peer Tutoring for Studentsat Risk for Academic Failure,” op. cit.; and Top-ping, et al., “Cross-Age Tutoring in MathematicsWith Seven- and 11-Year-Olds,” op. cit.

27. Marjorie Henningsen and Mary KayStein, “Mathematical Tasks and Student Cogni-tion: Classroom-Based Factors That Support andInhibit High-Level Mathematical Thinking andReasoning,” Journal for Research in MathematicsEducation 28:5 (November 1997):524-549; AlisonKing, “Structuring Peer Interaction to PromoteHigh-Level Cognitive Processing,” Theory IntoPractice 41:1 (Winter 2002):33-39.

28. Greer, et al., “Key Components of Effec-tive Math Tutoring,” op. cit.

29. Henningsen and Stein, “MathematicalTasks and Student Cognition: Classroom-BasedFactors That Support and Inhibit High-LevelMathematical Thinking and Reasoning,” op. cit.;Natalie McCosker and Carmel Diezmann, “Scaf-folding Students’ Thinking in Mathematical In-vestigations,” Australian Primary MathematicsClassroom 14:3 (2009):27-32.

30. Kate Ferguson-Patrick, “Writers DevelopSkills Through Collaboration: An Action Re-search Approach,” Educational Action Research15:2 (June 2007):159-180; Gordon, et al., The Tu-toring Revolution, op. cit., p. 173; Mesler, “MakingRetention Count: The Power of Becoming a PeerTutor,” op. cit.; Topping, et al., “Cross-Age Tutor-ing in Mathematics With Seven- and 11-Year-Olds,” op. cit.; Lori Williams, “Tiering and Scaf-folding: Two Strategies for Providing Access toImportant Mathematics,” Teaching ChildrenMathematics (February 2008):324-330.

31. Juanita V. Copley, “Questions Specific toPatterns, Functions, and Algebra,” in Spotlight onYoung Children and Math, Derry Korlek, ed.(National Association for the Education of YoungChildren, 2003), p. 24. This is algebra for Pre-Kto grade 1, but the general questioning strategyapplies to older children.

32. Chris O’Brien, “Using CollaborativeReading Groups to Accommodate Diverse Behav-iour Needs in the General Education Classroom,”Beyond Behavior (Spring 2007):7-15.

33. Ferguson-Patrick, “Writers Develop SkillsThrough Collaboration: An Action Research Ap-proach,” op. cit.



35. Williams, “Tiering and Scaffolding,” op. cit.36. The teacher will need to watch the progress

of the lessons because by this point, grade 5 stu-dents may need a short group lesson to review andsupport their understanding of the idea of how re-peated addition is related to multiplication.

37. Renee O. Hawkins, et al., “Applying a Ran-domized Interdependent Group ContingencyComponent to Classwide Peer Tutoring for Mul-tiplication Fact Fluency,” Journal of BehavioralEducation 18:4 (December 2009):300-318.

38. Gordon, et al., The Tutoring Revolution,op. cit., pp. 173, 163; Edward E. Gordon, “5 Waysto Improve Tutoring Programs,” Phi Delta Kap-pan (February 2009):440-445.

39. Goodlad and Hirst, Peer Tutoring, op. cit.,pp. 86, 87; Gordon, et al., The Tutoring Revolu-tion, op. cit., p. 173; Topping, et al., “Cross-AgeTutoring in Mathematics With Seven- and 11-Year-Olds,” op. cit.

40. Mesler, “Making Retention Count: ThePower of Becoming a Peer Tutor,” op. cit.

41. Goodlad and Hirst, Peer Tutoring, op. cit.,pp. 139, 140; Topping, et al., “Cross-Age Peer Tu-toring in Mathematics With Seven- and 11-Year-Olds: Influence on Mathematical Vocabulary,Strategic Dialogue and Self-Concept,” op. cit.

42. Gordon, et al., The Tutoring Revolution,op. cit., pp. 176-178.


44. Mesler, “Making Retention Count: ThePower of Becoming a Peer Tutor,” op. cit.

45. Goodlad and Hirst, Peer Tutoring, op. cit.,p. 140; Mesler, “Making Retention Count: ThePower of Becoming a Peer Tutor,” op. cit.

46. Sparks, “Researchers Find That StudentsLearn by Tutoring Virtual Peers,” op. cit.

47. Heller and Fantuzzo, “Reciprocal Peer Tu-toring and Parent Partnership,” op. cit.

48. Henningsen and Stein, “MathematicalTasks and Student Cognition: Classroom-Based

Factors That Support and Inhibit High-LevelMathematical Thinking and Reasoning,” op. cit.;King, “Structuring Peer Interaction to PromoteHigh-level Cognitive Processing,” op. cit.; Mc-Cosker and Diezmann, “Scaffolding Students’�Thinking in Mathematical Investigations,” op. cit.

49. Goodlad and Hirst, Peer Tutoring, op. cit.,pp. 24, 56, 58, 61, 66, 140; Gordon, et al., The Tu-toring Revolution, op. cit., pp. 153, 157; Mesler,“Making Retention Count: The Power of Becom-ing a Peer Tutor,” op. cit.; Menesses and Gresham,“Relative Efficacy of Reciprocal and Nonreci p -rocal Peer Tutoring for Students at Risk for Aca-demic Failure,” op. cit.; Robinson, et al., “Peerand Cross-Age Tutoring in Math,” op. cit.;Schloss and Kobza, “The Use of Peer Tutoring forthe Acquisition of Functional Math Skills AmongStudents With Mild Retardation,” op. cit.

Each of these articles in this issue ismeant to inspire and encourage you asyou lead students into the adventure ofmathematics.

The Coordinator for the special section onmathematics in this issue, Wil Clarke,Ph.D., is Professor of Mathematics at LaSierra University in Riverside, California.The editorial staff of the JOURNAL expressheartfelt appreciation for his assistancethroughout every phase of the productionof the issue from the selection of topics andauthors through the peer review process, re-visions, and preparing the final manu-scripts.

NOTES AND REFERENCES1. 1 Peter 3:15 (NKJV), italics supplied. Texts

credited to NKJV are from the New King James Ver-sion. Copyright © 1979, 1980, 1982, by ThomasNelson, Inc. Used by permission. All rights re-served.

2. Ellen G. White, True Education (Nampa,Idaho: Pacific Press Publ. Assn., 2000), p. 12. Italicssupplied.

3. See http://www-history.mcs.st-and.ac.uk/Biographies/ Thales.html. Accessed March 21, 2013.

4. Ibid.

Guest Editorial Continued from page 3

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MePEnER tToUTOrRiINnG:Gcircle.adventist.org/files/jae/en/jae201375043809.pdf · beneﬁt multigrade students. Then some designs will be suggested for questioning strategies that facilitate