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Cross-Age Peer Tutoring and Fluency-Based Instruction to Achieve Fluency with Mathematics Computation Skills: A Randomized Controlled Trial

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Abstract

The current study employed a randomized controlled trial to evaluate the use of peer tutoring and fluency-based instruction to increase mathematics fluency with addition and subtraction computation skills. Forty-one elementary school students between the ages of eight and 12 years participated in the 8-week study using cross-age peer tutoring, Say All Fast Minute Every Day Shuffled, frequency building, and the morningside math facts curriculum (Johnson in Morningside mathematics fluency: math facts (vol 1–6; curriculum program), Morningside Press, Seattle, 2008). Pre- and post-test measures of mathematics fluency and calculation were conducted with all participants. A measure of social skills and competing problem behaviors was also conducted at pre- and post-testing to evaluate any additional effects of the peer tutoring model. The results demonstrated a statistically significant difference between groups on measures of mathematics fluency, with the experimental group demonstrating significantly higher scores than the control group at post-testing. There were no significant differences between groups on measures of social skills and competing problem behaviors or calculation. The findings indicate that cross-age peer tutoring and fluency-based instruction resulted in positive outcomes for tutees in the mathematics domain, specifically mathematics fluency.

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Author information

Authors and Affiliations

  1. School of Psychology, National University of Ireland, Galway, Ireland

    Irene Greene & Jennifer Holloway

  2. School of Psychology, University of South Wales, Pontypridd, United Kingdom

    Aoife Mc Tiernan

Authors
  1. Irene Greene
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  2. Aoife Mc Tiernan
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  3. Jennifer Holloway
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Corresponding author

Correspondence to Aoife Mc Tiernan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical Approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.

Informed Consent

Informed consent was obtained from all individual participants included in the study.

Appendices

Appendix: Training Script

  1. 1.

    Introduction to Tutoring

  1. I.

    Introduction of the term “Tutoring”

    1. A.

      “Today I’m going to show you how you can be a teacher and learn how to teach your partner math facts.”

    2. B.

      “I’ve divided you into pairs: you will all be tutors, and your partners will be the students.”

      [Key points: you can teach your partner]

  1. II.

    Folder Presentation

    1. A.

      “Each tutor and partner will get a folder like this one. It will have your name on it. The inside will look like this. It will have a graph on this side. It will have a ‘GO’ pocket that will have cards with math facts on them. It will have a recording sheet, and it will have a reward chart.” [Key points: show folder]

    2. B.

      “So when it’s time to tutor we’ll do the following:

      1. 1.

        Take out your reward chart and place it next to where you sit.

      2. 2.

        Take out your recording sheet and place it on the table.

      3. 3.

        Take cards from the GO pocket.”

        [Key points: Review the 3 steps—take out the reward chart and the recording sheet, take cards from the GO pocket]

        “Let’s practice”:

        Model: Teacher models the three steps with a single student (Teacher pretends to be a partner). Others watch and receive reinforcement.

        Lead: Each pair practices the three steps once with the teacher under teacher supervision, and the teacher and the other students provide reinforcement for correct steps.

        Test: All pairs practice the three steps simultaneously. [Key points: Model, lead, test steps executed in that order]

Tutoring Procedure

  1. I.

    Explain Tutoring Procedure

    1. A.

      Say “Here’s what you’ll do. Turn your folder over to the side with the smiley face and the X.”

    2. B.

      “Set the timer at one minute. When your partner is ready to start, press start on the timer.”

    3. C.

      “Show as many cards from the GO pocket as you can in one minute.”

    4. D.

      “If your partner says the answer correctly, place the card on the happy face. If your partner happens to say the answer incorrectly or doesn’t know it and doesn’t say anything, put it on the X sign.”

    5. E.

      “Tutors, remember to be really quiet during the testing. Do not say anything, just show the cards to your partner, and put the cards down on the happy face if it’s correct or X if it’s not.”

      [Key point: Demonstrate that cards are placed on the ☺ and X, depending on whether the math fact was said correctly. Remember to say to the students that we do not provide feedback during testing.]

  1. II.

    Correction Procedure (“Try Again”)

    1. A.

      “When the timer goes off, pick up the cards from the ‘X’ pile.”

    2. B.

      “Say ‘Let’s try these ones again. Show your partner these cards one by one. If they answer correctly, say ‘Well done’ and move on.”

    3. C.

      “If they answer incorrectly or don’t know the answer, tell her. For example, when you say ‘Try Again’, and your student still does not know the math fact, tell them the answer by reading the card, and have them repeat what you read.”

    4. D.

      “Make sure your partner looks at the card when she says it.”

      [Key points: Try again plus say math fact correctly.]

      “Let’s practice”:

      Model: Teacher models the tutoring procedure with a single student (Teacher pretends to be a partner).

      Lead: Each pair practices the procedure once with the teacher, and the teacher and the other students provide reinforcement for correct steps.

      Test: All pairs practice the procedure simultaneously. [Key points: Model, Lead, Test procedure]

  2. III.

    Treatment Fidelity

    1. A.

      “When we’re practicing the steps, we have a checklist of each step to complete. Everyone needs to get 70% of the steps right on the checklist before we can start tutoring”

Recording

  1. I.

    How to record the number of cards answered

    1. A.

      Say “Now I’m going to show you how to use the recording sheet in your folder.”

    2. B.

      “Count up the number of cards on the smiley face. Write this number into the ‘correct’ column.”

    3. C.

      “Now count up the number of cards on the ‘X’. Write this number into the ‘incorrect’ column.”

    4. D.

      “Do this for each one minute timing.”

      [Key points: Write in the number of corrects and incorrects]

      “Let’s practice”:

      Model: Teacher models how to record with a single student (Teacher pretends to be a partner).

      Lead: Each pair practices the procedure once with the teacher, and the teacher and the other students provide reinforcement for correct steps.

      Test: All pairs practice procedure simultaneously. [Key points: Model, Lead, Test procedure]

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Greene, I., Tiernan, A.M. & Holloway, J. Cross-Age Peer Tutoring and Fluency-Based Instruction to Achieve Fluency with Mathematics Computation Skills: A Randomized Controlled Trial. J Behav Educ 27, 145–171 (2018). https://doi.org/10.1007/s10864-018-9291-1

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