15.Witzel Fluency Part2

Aug 29, 2026

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Incremental Rehearsal (IR) instruction organizes flashcard learning by tracking each fact as known (K) or unknown (U), presenting unknown items with an immediate answer to build speed, momentum, and long-term recall through short sessions over multiple days. It outlines the IR steps, including a 9:1 practice ratio in ten-card stacks, and adds a drill-sandwich method using seven known and three unknown items following a fixed order. The document also describes Cover-Copy-Compare (CCC) and Detect, Practice, Repair (DPR) procedures for improving math-fact fluency using modeling, copying, comparison, metronome-paced detection, targeted practice, and corrective feedback.

LanguageEnglish

CategoryExam

FormatPDF

Pages6

Reading Time15 min

AccessFree to download

Incremental Rehearsal (IR)

IR steps and session scheduling

Drill Sandwich (Browder & Roberts, 1993)

Known/unknown stack pattern and updating

Cover-Copy-Compare (Skinner, McLaughlin, & Logan, 1997)

Preparation and step-by-step worksheet use

Detect, Practice, Repair (Parkhurst et al., 2010)

Detect, practice with CCC, and repair feedback

Incremental Rehearsal Organizational structure of flash cards Each unknown • unknown (given) • known, known, known, known, unknown (given) • known, known, known, known, known, unknown (not given) • known, known, known, known, known, known, unknown (not given) • known, known, known, known, known, known, known, unknown (not given) • known, known, known, known, known, known, known, known, unknown (not given) • known, known, known, known, known, known, known, known, known, unknown (not given) Fluency charts can be developed from this approach Incremental Rehearsal (IR) Steps 1. Print flash cards for visual and auditory practice 2. Assess the student to determine which facts are known (K) and which are still unknown (U) . 3. Present one unknown fact (U) 4. Practice known to unknown material at a ratio of 9:1 . In a ten-card stack, this means that 9 of the answers are known and only one is yet to be learned. 5. Immediately provide the answer when the unknown problem is presented 6. Build momentum and motivation by having the student answer several questions correctly in a row before an unknown problem is presented. Hold IR sessions over several days, so that not too many answers are learned per day (three to five) . Long-term recall is benefitted by short intervention sessions rather than long ones. Drill sandwich (Browder & Roberts, 1993) 1) Make or obtain a set of flashcards for the information to be learned. 2) Go through the complete stack of cards once, separating the list into two piles – knowns and unknowns. 3) Build a “sandwich” using seven knowns (K) and three unknowns (U) . Be sure to follow the pattern (K-K-K-U-K-K-U-K-K-U) 4) Have the child/children practice identifying all ten items in the order above. 5) As the unknown items are learned so that the response is immediate and automatic, move them into a known section of the sandwich by removing repeated accurate knowns. 6) Add new unknowns and repeat This approach adds 3 new facts daily for a total of 12 by a summative assessment on Friday Cover-Copy-Compare (Skinner, McLaughlin, & Logan, 1997) [https://www.youtube.com/watch?v=WjlkAi44qTY](https://www.youtube.com/watch?v=WjlkAi44qTY) Preparation: The teacher selects up to 10 math facts for the student to practice during the session and writes those facts (including number sentence and answer) as correct models into the left column of the Cover-CopyCompare Worksheet. The teacher then pre-folds the sheet using as a guide the vertical dashed line ('fold line') dividing the left side of the student worksheet. [ebi.Missouri.edu](ebi.Missouri.edu) Cover-Copy-Compare Steps 1) Study the correctly completed math fact (model) that appears in the left column of the sheet. 2) Fold the left side of the page over at the pre-folded vertical crease to hide the original math fact ('Cover') . 3) Copy from memory the math fact and answer, writing it in the first response blank under the 'Student Response' section of the Cover-Copy-Compare worksheet ('Copy') . Teacher uncovers the original correct model and compares it to the student response ('Compare') . If CORRECT, the student moves to the next item on the list and repeats these procedures. If INCORRECT, the student draws a line through the incorrect response, and repeats earlier steps and again checks the correctness of the copied item. Continue until all math facts on the sheet have been copied and checked against the correct models. Detect, Practice, Repair (Parkhurst et al., 2010) Detect, Practice, Repair (DPR) is a multi-component, class-wide procedure that focuses on enhancing fluency by allowing students to practice those math facts that they have not developed to the point of automaticity (Poncy et al. 2006) . Parkhurst et al (2010) improved multiplication facts with 5th grade students in 6-10 trials. Detect = During a detect phase, Poncy et al. used a metronome to pace a group of students thr

FAQs

What are the main steps of Incremental Rehearsal (IR)?

IR prints flashcards, assesses which facts are known (K) versus unknown (U), presents one unknown fact, then practices using a 9:1 ratio with immediate answers. It also builds momentum by getting students to answer several known questions correctly before returning to an unknown item.

How does the Drill Sandwich method structure known and unknown cards?

The method uses a fixed pattern of seven knowns and three unknowns, following the sequence K-K-K-U-K-K-U-K-K-U. As unknowns become automatic with immediate practice, they are moved into the known portion by removing repeated accurate known responses and adding new unknowns.

How do CCC and DPR improve math-fact fluency?

CCC uses a worksheet workflow where students study a correct model, cover it, copy from memory, and then compare for accuracy, repeating until all items are copied correctly. DPR uses a detection phase paced by a metronome, identifies problems not answered correctly, then applies CCC practice to those items and uses corrective feedback to repair errors.

Aug 29, 2026

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