How To: Improve Proficiency in Math-Facts Through a Self-Administered Folding-In Technique

Students should develop automatic recall of basic math-facts in the elementary grades. Math-fact mastery permits students to shift valuable cognitive capacity away from simple calculations toward higher-level problem-solving (Gersten, Jordan, & Flojo, 2005; National Mathematics Advisory Panel, 2008). An important goal for schools, then, is to ensure that students are proficient in math-facts by the end of grade 5 (Kroesbergen & Van Luit, 2003) to better prepare them for the demanding middle-school math curriculum. Teachers, however, may have difficulty finding instructional time and adult support to deliver math-fact interventions to students.

One solution to this intervention-resource problem  is the math-fact self-administered folding-in intervention (math-fact SAFI: Hulac, Dejong, & Benson, 2012). This approach trains students to take charge of their own intervention to acquire and develop fluency in math-facts. Using flash cards, the student reviews math-facts with immediate performance feedback, engages in repeated practice to correct errors, and records on a running log those math-facts that have been mastered. An additional advantage of this intervention is that it has been shown to be effective with middle-school students. 

Preparation.

In preparation for this intervention, the teacher creates or obtains the following materials:

• Math-fact flash cards. The entire collection of math-facts to be mastered are written onto flash-cards. One fact is written on each card, with the math-fact appearing on the front and the correct answer appearing on the back. For example, multiplication math-facts for 0 through 10 would require 121 flash cards to cover all possible number combinations for this fact-set. Tip: Students can be given a master set of math-facts with answers (e.g., on the blackboard or on a handout) and directed to create their own math-fact cards.
  

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• Math-Facts SAFI: Student Checklist. The student receives a copy of this checklist containing the essential steps of the self-administered intervention. The teacher can use this same checklist to observe the student and evaluate the integrity of the math-fact SAFI.
  

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• Dry-erase board, markers, and eraser. The student uses the dry-erase board to record all answers in the session.
  

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• Student Log: Mastered Math-facts. This recording-form is used by the student to log any math-facts mastered during the intervention.

In preparation for this intervention, the teacher also meets with the student to:

• nventory those math-facts the student already knows. The teacher reviews all math-fact cards with the student. The teacher shows each card to the student for 3 seconds. If the student responds correctly to the math-fact, the teacher sorts that card into the "known" stack. If the student answers incorrectly or hesitates for 3 seconds or longer, the teacher sorts the card into the "unknown" stack. The teacher then puts rubber bands around the "known" and "unknown" stacks for student use as outlined below.
  

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• train the student in the steps of the math-fact SAFI. Using the intervention materials and Math-Facts SAFI: Student Checklist, the teacher trains the student to implement the intervention.

Procedure. Below are the steps the student follows in each session to implement the math-fact self-administered folding-in technique. (NOTE: Because the student is the interventionist, the steps are written as student directions):

1. Start with the daily stack of cards from the last session. Or create a new "daily stack" by taking 7 cards from your weekly "known" stack and 3 cards from your weekly "unknown" stack and shuffling them.
   

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2. Take the first card from the top of the daily stack and place it flat on the table.
   

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3. Read the math-fact on the card and write the answer on the dry-erase board within 3 seconds.
   

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4. Turn the card over and compare the answer that you wrote to the answer on the card.
   

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5. If your answer is correct, sort that card into a "daily known" pile. If your answer is incorrect, sort that card into a "daily unknown" pile--then practice by writing the math-fact and correct answer on your dry-erase board three times in a row.
   

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6. Continue until you have answered all 10 daily cards. Then look at the daily "known" and "unknown" card stacks. If all daily cards are in the "known" stack, draw a star in the bottom left corner of your dry-erase board.
   

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7. Shuffle the 10 cards in the daily card deck.
   

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8. Continue reviewing all 10 cards in the daily deck as explained in steps 2-7 until you have drawn three stars in the bottom left corner of the dry-erase board. (In other words, continue until you have answered all 10 cards without error in a single run-through and have accomplished this feat a total of three times in the session.)
   

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9. When you have earned 3 stars, consider the entire daily stack to be "known" cards. So it's now time to update the daily deck.
   

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10. Take any 3 cards from your current daily 10-card deck and transfer them to the weekly "known" deck. Then, on the Student Log: Mastered Math-facts form, record the math-facts and current date for the 3 cards that you transfer. Congratulations! These now count as mastered math-facts!
    

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11. Next, take 3 cards from the weekly "unknown" stack and add them to your current daily deck to bring it back up to 10 cards. 
    

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12. Begin reviewing the daily stack again (as outlined in steps 2-7) until your time runs out.
    

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13. Before ending the session, place rubber-bands around the weekly "known" and "unknown" decks and the daily stack that you are currently working on. Also, be sure that your Student Log: Mastered Math-facts form is up-to-date.