Chisanbop (지산법, 指算法), Korean for "finger calculation method," turns two hands into a two rod abacus. On the right hand each finger is worth 1 and the thumb 5; on the left each finger is worth 10 and the thumb 50, so the hands hold any number from 0 to 99. Adding and subtracting use the same complement moves as the soroban.
This post shows the method the way its own manuals teach it, with a finger diagram for every state. Then we run the fixed problem set from our mathematics series through it, count every addition and every finger movement, and say plainly where the hands run out and paper takes over. Every number below was produced by a small Python simulator and checked against ordinary arithmetic.
Key takeaways
- Chisanbop stores a number on the fingers pressed against a table. The right hand holds the ones digit (thumb 5, fingers 1 each), the left hand the tens digit (thumb 50, fingers 10 each). Two hands reach 99, never 100.
- Every single digit addition or subtraction falls into one of four moves: direct, five exchange, ten exchange, or a mixed move that combines both. Of the 90 possible digit additions, 35 are direct, 10 need a five exchange, 35 a ten exchange and 10 the mixed move. The counts are the same as on a soroban rod, because each hand is a 1 plus 4 rod.
- The 1978 manuals teach multiplication first as repeated addition, and they carry anything past 99 to paper. Our 98 x 97 took 38 finger additions and 140 finger movements, plus six written digits for the partial products.
- Chisanbop has no square root, squaring or decimal expansion procedure of its own. We worked √7,744 and 1/19 with two paper aids of our own, which we label as adaptations, not as Chisanbop doctrine.
- The method was created in Korea by Sung Jin Pai and brought to the United States by his son Hang Young Pai in the mid 1970s. Sources disagree on both dates.
- The classroom evidence is thin and mixed. The most recent peer reviewed study we found (2014, 75 children) reported a better attitude to maths among at risk grade 2 pupils, but no significant skill gains over control classes.
The problem set for this series
The fast calculation series uses the same problems as our mathematics traditions series, so you can compare methods directly:
| Problem | Answer (checked in Python) |
|---|---|
| 98 x 97 | 9,506 |
| 47 x 53 | 2,491 |
| 386 x 524 | 202,264 |
| 85² | 7,225 |
| √7,744 | 88 |
| 7,429 ÷ 37 | 200 remainder 29 |
| 1/19 | 0.052631578947368421, repeating every 18 digits |
Chisanbop does the arithmetic inside these problems, the single digit products, the column sums and the subtractions, extremely well. It does not have its own procedure for long multiplication, roots or repeating decimals. Where the method needs help from paper, the worked examples say so at the step where it happens.
How to read the finger diagrams
Chisanbop is done with both hands resting palms down over a table, fingers spread. A finger that touches the table counts. A finger held up does not. The manuals call these two actions Press and Clear.
Every diagram in this post has the same layout, read left to right across both hands as they sit on the table:
LEFT HAND (tens) RIGHT HAND (ones)
little ring middle index thumb | thumb index middle ring little
10 10 10 10 50 | 5 1 1 1 1
X = pressed (touching the table) . = raised
In the compact form used in the worked examples, the left hand is written as four fingers then the thumb, and the right hand as the thumb then four fingers:
. . X X X | X X X X . = 50 + 20 + 5 + 3 = 78
l r m i T | T i m r l
The index finger is always the first finger pressed on each hand. On the right hand you count 1, 2, 3, 4 with index, middle, ring and little finger. On the left hand you count 10, 20, 30, 40 with index, middle, ring and little finger, so the pressed fingers on the left hand fill in from the thumb side outward. This matches the 1978 Home Study Book, which names the right hand fingers "First, Second, Third and Fourth" from index to little finger and calls the thumb the "Fifth Finger," and the 2014 study by Calder Stegemann and Grünke, which shows 78 as the left thumb, left index and middle, right thumb, and three right fingers.
Where Chisanbop comes from
The name joins the Korean words for finger (ji, 指) and calculation method (sanbeop, 算法). Contemporary English sources spelled it Chisanbop, sometimes Chisenbop, and the American publisher also sold it as Fingermath.
| Date | Event | Source |
|---|---|---|
| 1940s or 1950s | Sung Jin Pai creates the method in Korea | 1940s per Wikipedia (citing Hang Young Pai's 1981 book), the Computer History Museum and the 2014 study; the 1978 Parent's Guide says "about thirty years ago"; Lieberthal's 1978 Home Study Book says "some twenty years ago" |
| From age ten | Hang Young Pai learns the method and later refines it for children | Home Study Book (1978) |
| 1976 or 1977 | Hang Young Pai brings Chisanbop to the United States | 1976 per the Parent's Guide, the Home Study Book and Dougherty's ERIC bibliography; 1977 per Wikipedia citing Pai (1981) |
| 1978 | New York Times article "Fingers Make a Comeback in Math" describes Pai, then 31, as a Korean teacher living in New York | ERIC record EJ180666 |
| 1978 | Chisanbop Enterprises publishes Lieberthal's Home Study Book and Pai's Parent's Guide with audio records; Mount Vernon, New York schools are the first system to try it | Internet Archive scans; Christian Science Monitor (1982) |
| About 1978 | Lieberthal and children demonstrate it on the Today show and the Phil Donahue show | Internet Archive clip descriptions |
| 1979 | Arithmetic Teacher publishes two critical articles; a Shawnee Mission, Kansas pilot is dropped | ERIC EJ200177, EJ200178; Christian Science Monitor |
| 1979 | McGraw-Hill publishes Lieberthal's The Complete Book of Fingermath | Wikipedia bibliography; 2014 study references |
| 1981 | Pai's The Complete Book of Chisanbop (Van Nostrand Reinhold) | Wikipedia bibliography |
| 1982 | Christian Science Monitor survey: Mount Vernon phasing it out, Newark expanding it | Christian Science Monitor, 17 May 1982 |
| 2014 | First controlled study in many years, in British Columbia | Calder Stegemann and Grünke, Learning Disabilities: A Contemporary Journal 12(2) |
Two dates are disputed and we leave them disputed. The creation date ranges from the 1940s to the late 1950s depending on which 1978 booklet you read, and the arrival in the United States is given as both 1976 and 1977. Edwin Lieberthal, who wrote the first English manuals, says in the Home Study Book that he met Hang Young Pai through the Korean-American school his two adopted daughters attended, after Pai's arrival "early in 1976."
The Computer History Museum puts Chisanbop in its calculator history for a reason. Its exhibit text says Sung Jin Pai "applied the abacus principle to human hands." That is the right way to think about it: Chisanbop is an abacus whose beads are fingers.
How does Chisanbop represent numbers?
The ones digit on the right hand
Each finger of the right hand is worth 1 and the thumb is worth 5. The Home Study Book puts it in one line: when all fingers of the right hand are used, the total is nine units, five from the thumb and four from the fingers.
value right hand (T i m r l)
0 . . . . .
1 . X . . .
2 . X X . .
3 . X X X .
4 . X X X X
5 X . . . .
6 X X . . .
7 X X X . .
8 X X X X .
9 X X X X X
Look at the jump from 4 to 5. Four fingers are pressed, and then all four lift as the thumb goes down. The manuals call this out as the first hard moment for a child, and it is the same moment a soroban learner meets when four earth beads are exchanged for one heaven bead.
The tens digit on the left hand
The left hand works the same way at ten times the value. Each finger is worth 10 and the thumb 50, so the left hand shows 0, 10, 20 and so on up to 90.
value left hand (l r m i T)
0 . . . . .
10 . . . X .
20 . . X X .
30 . X X X .
40 X X X X .
50 . . . . X
60 . . . X X
70 . . X X X
80 . X X X X
90 X X X X X
Both hands together
Put the two hands side by side and you have every number from 0 to 99, with the tens digit on the left exactly where it sits in written numerals.
number left (l r m i T) | right (T i m r l)
11 . . . X . | . X . . .
36 . X X X . | X X . . .
50 . . . . X | . . . . .
78 . . X X X | X X X X .
85 . X X X X | X . . . .
99 X X X X X | X X X X X
The Home Study Book tells parents not to start calculating until the child can press any number called out "quickly and accurately," and warns that this alone can take weeks. That is a real cost, and it is the same cost a soroban learner pays to read beads at a glance.
Adding with Chisanbop: the four moves
Counting on
The simplest Chisanbop addition is counting on, one finger at a time. The 2014 study describes adding 65 and 23 this way: show 65, then press 20 more on the left hand and 3 more on the right.
start 65 . . . X X | X . . . .
press 20 . X X X X | X . . . . (left middle and ring go down)
press 3 . X X X X | X X X X . = 88
That is five finger movements and no thinking about carries, because 6 + 2 and 5 + 3 both fit on their hands. Most additions are not so kind.
Move 1: direct
A direct move just presses the fingers you need. Adding 3 to 1 presses three more fingers. Adding 6 to 2 presses the thumb and one more finger. Nothing needs to be cleared.
Move 2: five exchange (the five partners)
Add 3 to 4. The right hand shows four fingers, and there is no fifth finger to press. The Home Study Book's rule is that "the addition of 3 to any other number delivers the same result as the simultaneous addition of 5 and the Clearing of 2." Press the thumb and lift two fingers.
4 . X X X X
+3: press 5, clear 2
7 X X X . .
The pairs that make 5 are 1 and 4, and 2 and 3. A five exchange always adds a number by pressing the thumb and clearing its five partner.
Move 3: ten exchange (the ten partners)
Add 5 to 5. The thumb is already down, so you cannot press another 5. The manuals call the fix "Exchange 5": "Press 10 and Clear 5 Simultaneously."
5 . . . . . | X . . . .
+5: press 10 (left index), clear 5 (right thumb)
10 . . . X . | . . . . .
The general rule: to add d when the right hand cannot take it, press 10 on the left hand and clear d's ten partner (10 minus d) on the right. The ten partners are 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5.
Move 4: mixed (ten exchange inside, five exchange to finish)
Add 7 to 7. You need to press 10 and clear 3, but 7 is shown as the thumb plus two fingers, so there are not three fingers to clear. Clear the thumb instead (minus 5) and press two fingers back (plus 2): clearing 3 becomes clearing 5 and pressing 2.
7 . . . . . | X X X . .
+7: press 10, then clear 3 as (clear 5, press 2)
14 . . . X . | . X X X X
That is four finger movements for one digit. It is the hardest addition move in the system.
How often each move comes up
We ran every pairing of a starting digit (0 to 9) with an added digit (1 to 9) through the simulator. D is direct, F five exchange, T ten exchange, M mixed.
hand shows | add 1 2 3 4 5 6 7 8 9
0 | D D D D D D D D D
1 | D D D F D D D D T
2 | D D F F D D D T T
3 | D F F F D D T T T
4 | F F F F D T T T T
5 | D D D D T M M M M
6 | D D D T T M M M T
7 | D D T T T M M T T
8 | D T T T T M T T T
9 | T T T T T T T T T
Out of 90 cases, 35 are direct, 10 need a five exchange, 35 need a ten exchange and 10 need the mixed move. The mixed moves cluster where the thumb is down and you add 5 or more. If you have read our Japanese mathematics post, this table should look familiar: it is the soroban's direct, five complement, ten complement and mixed table, because a hand is a soroban rod.
A two digit addition with every kind of move: 38 + 47
The 2014 study's example goes tens first, then ones, and we follow that order.
start 38 . X X X . | X X X X .
+40 (tens) left hand shows 30, needs 40 more: press 50, clear 10 (five exchange)
. . X X X | X X X X . = 78
+7 (ones) right hand shows 8, needs 7 more: press 10, clear 3 (ten exchange)
the left hand takes the carry directly
. X X X X | X . . . . = 85
38 + 47 = 85, in four finger movements on the left hand and right hand combined after the start state. The carry happened inside the ten exchange, with no carry digit held in your head.
Running past 99
Try 47 + 53. Both hands fill and still need one more. There is no third hand.
start 47 X X X X . | X X X . .
+50 press 50: X X X X X | X X X . . = 97
+3 right hand 7 + 3 needs a ten exchange, left hand 90 + 10 has nowhere to go
The answer, 100, cannot be shown. The Home Study Book's solution for longer sums is column addition on paper. Add one column on the fingers, write the ones digit (always on the right hand) below the line, then "transfer the number of Left Hand Fingers to the Right Hand as a carry-over" and add the next column on top of it. Children first write the carry above the next column, then drop the written carry once they trust the transfer.
That rule is the whole secret of Chisanbop past 99. The hands are a 0 to 99 register; paper holds every column you are not working on.
Subtracting with Chisanbop
Subtraction is addition run backwards, with the same four moves.
Direct
38 minus 5: lift the right thumb. The 2014 study uses exactly this example.
38 . X X X . | X X X X .
-5: clear 5
33 . X X X . | . X X X .
Five exchange
6 minus 3: only one finger is down besides the thumb, so you cannot clear three fingers. Clear the thumb (minus 5) and press two fingers (plus 2).
6 . X . . .
-3: clear 5, press 2
3 . X X X .
Ten exchange
12 minus 5: the right hand shows 2, which is less than 5. Clear 10 on the left hand and press 5's ten partner, 5, on the right.
12 . . . X . | . X X . .
-5: clear 10, press 5
7 . . . . . | X X X . .
Mixed
13 minus 7: clear 10 and press 3 on the right, but the right hand shows three fingers and has only one free finger. Press 3 becomes press 5 and clear 2.
13 . . . X . | . X X X .
-7: clear 10, then press 3 as (press 5, clear 2)
6 . . . . . | X X . . .
The subtraction table is the addition table turned upside down, with the same totals: 35 direct, 10 five exchange, 35 ten exchange and 10 mixed.
A full two digit subtraction: 85 minus 29
start 85 . X X X X | X . . . .
-20 (tens) clear 20 directly (left ring and middle lift)
. . . X X | X . . . . = 65
-9 (ones) right hand shows 5, cannot clear 9: clear 10, press 1 (ten exchange)
. . . . X | X X . . . = 56
85 minus 29 = 56, in four finger movements.
How Chisanbop relates to the soroban
The modern Japanese soroban (算盤) has one heaven bead worth 5 and four earth beads worth 1 on each rod. That is the "1 plus 4" layout, and the right hand in Chisanbop is exactly one such rod: the thumb is the heaven bead and the four fingers are the earth beads. The left hand is a second rod. The Computer History Museum describes Chisanbop as replacing "the abacus's moveable beads with moving fingers," and a 1980 Lutheran Education article indexed by ERIC says the method is based on the Korean abacus with its emphasis on fives.
| Soroban | Chisanbop | |
|---|---|---|
| Unit of storage | Rod with 1 heaven bead (5) and 4 earth beads (1) | Hand with 1 thumb (5 or 50) and 4 fingers (1 or 10) |
| Number of digits | One per rod, as many as the frame has | 2 (one per hand) |
| Largest value | Trillions and beyond | 99 |
| Moves | Direct, five complement, ten complement, mixed | Direct, five exchange, ten exchange, mixed |
| Carry past the last position | Next rod to the left | Paper |
| Equipment | A soroban | A table, or the air |
| Mental version | Anzan, calculating on an imagined soroban | The manuals' Stage 4, where fingers are "no longer needed" |
So Chisanbop is a soroban with two rods and no frame. It gives up almost all of the soroban's capacity in exchange for zero equipment. The Chinese mathematics post shows an older relative, counting rods, where the numerals 6 to 9 also use one crosswise rod for 5 instead of five strokes.
The two rods matter more than they seem. A soroban user can multiply 386 by 524 entirely on the frame, writing nothing down. A Chisanbop user cannot, because each of the three partial products and the final answer has more than two digits. Every multi-digit answer in the worked examples below leaves the hands and goes onto paper.
How Chisanbop multiplies and divides
The 1978 Parent's Guide sets out sixteen stages: four each for addition, subtraction, multiplication and division. It says the difference between stage one and stage four of each operation "is basically the time required," and that at stage four the fingers "are no longer needed."
Stage 1 multiplication is "an extension of addition," taught as counting by a number: "add 2 repeatedly until you reach" the product, with a counting aid chart showing how many times you have added. Stage 2 adds faster finger manipulations, introduced in the Parent's Guide for the 5, 9 and 4 times tables. The Guide says that at stage 4 "many children can calculate multiplication problems, multiplying 3 digit numbers by 3 digit numbers, calculating the answers in a single line instead of using partial products." The stage 3 and 4 manuals were "in development" when the Guide was printed and we could not find them, so we cannot show the single line method.
Division, in the same spirit, is repeated subtraction: hold the partial dividend on your fingers, subtract the divisor until you cannot, and count how many times you subtracted. The 2014 study says that above 99 "one has to use paper and pencil and apply a variation of the standard algorithm."
That is the method used below: the standard written layout for long multiplication and long division, with every single digit product, every column sum and every subtraction done on the fingers using Stage 1 repeated addition. It is slower than what the Guide promises for Stage 4, and it is the version we can document.
One structural fact makes this work. In long multiplication, each step multiplies one digit by one digit and adds a carry. The biggest possible value is 9 x 9 + 8 = 89. That always fits on two hands. Chisanbop's 99 ceiling is just high enough for every step of long multiplication.
Working the problem set with Chisanbop
Each diagram below came from the simulator. The "move" notes name the exchanges. A "carry" note means the press of 10 landed on a left hand that itself needed an exchange, for example when 48 + 8 pushes the left hand from 40 to 50.
98 x 97
The layout on paper is ordinary long multiplication. The fingers compute each digit product.
98
x 97
-----
686 98 x 7
882 98 x 9, shifted one place
-----
9506
Partial product 1: 98 x 7. Start with 8 x 7. With Stage 1 counting, press 8 seven times.
start 0 . . . . . | . . . . .
+8 = 8 . . . . . | X X X X . direct
+8 = 16 . . . X . | X X . . . ten exchange
+8 = 24 . . X X . | . X X X X mixed
+8 = 32 . X X X . | . X X . . ten exchange
+8 = 40 X X X X . | . . . . . ten exchange
+8 = 48 X X X X . | X X X X . direct
+8 = 56 . . . . X | X X . . . ten exchange; carry needs a five exchange (press 50, clear 40)
Read 56. Write 6 below the line. The left hand shows 5, so the carry is 5: press 5 on the right hand as the starting point for the next digit.
Now 9 x 7 plus the carry of 5. Start at 5 and press 9 seven times.
start 5 . . . . . | X . . . . carry 5
+9 = 14 . . . X . | . X X X X mixed
+9 = 23 . . X X . | . X X X . ten exchange
+9 = 32 . X X X . | . X X . . ten exchange
+9 = 41 X X X X . | . X . . . ten exchange
+9 = 50 . . . . X | . . . . . ten exchange; carry needs a five exchange
+9 = 59 . . . . X | X X X X X direct
+9 = 68 . . . X X | X X X X . ten exchange
Read 68. There are no more digits in 98, so write 68 in front of the 6. Partial product: 686.
Partial product 2: 98 x 9. 8 x 9 is nine presses of 8; the first seven repeat the sequence above and reach 56, then:
+8 = 64 . . . X X | . X X X X mixed
+8 = 72 . . X X X | . X X . . ten exchange
Write 2, carry 7. Then 9 x 9 + 7: start at 7, press 9 nine times.
start 7 . . . . . | X X X . . carry 7
+9 = 16 . . . X . | X X . . .
+9 = 25 . . X X . | X . . . .
+9 = 34 . X X X . | . X X X X mixed
+9 = 43 X X X X . | . X X X .
+9 = 52 . . . . X | . X X . . carry needs a five exchange
+9 = 61 . . . X X | . X . . .
+9 = 70 . . X X X | . . . . .
+9 = 79 . . X X X | X X X X X direct
+9 = 88 . X X X X | X X X X .
Write 88 in front of the 2: 882, shifted one place, is 8,820.
Column sums. Now add 686 and 8,820 column by column on the fingers, using the Home Study Book's transfer rule.
ones: 6 + 0 = 6 . . . . . | X X . . . write 6
tens: 8 + 2 = 10 . . . X . | . . . . . write 0, carry 1
hundreds: 1 + 6 + 8 = 15 . . . X . | X . . . . write 5, carry 1
thousands: 1 + 8 = 9 . . . . . | X X X X X write 9
Answer: 9,506.
The cost, counted by the simulator: 38 finger additions (32 for the digit products, 6 for the column sums), 140 single finger movements, 6 digits written for the partial products and 4 for the answer. The head holds very little: which digit you are on, how many presses you have made (up to 9), and the multiplier digit. The running value lives on the hands.
For comparison, the Vedic base method in our Indian and Vedic mathematics post does 98 x 97 as 98 minus 3 = 95 and 2 x 3 = 06, giving 9,506 in two tiny steps. Chisanbop has no rule for numbers near a base, but nothing stops a Chisanbop user from using that trick, and both of its steps fit on the hands.
47 x 53
47
x 53
-----
141 47 x 3
235 47 x 5, shifted
-----
2491
47 x 3. Press 7 three times, then 4 three times on top of the carry.
7 x 3:
+7 = 7 . . . . . | X X X . . direct
+7 = 14 . . . X . | . X X X X mixed
+7 = 21 . . X X . | . X . . . ten exchange
write 1, carry 2
4 x 3 + 2:
start 2 . . . . . | . X X . .
+4 = 6 . . . . . | X X . . . five exchange
+4 = 10 . . . X . | . . . . . ten exchange
+4 = 14 . . . X . | . X X X X direct
write 14
Partial product: 141.
47 x 5.
7 x 5:
+7 = 7 . . . . . | X X X . .
+7 = 14 . . . X . | . X X X X mixed
+7 = 21 . . X X . | . X . . .
+7 = 28 . . X X . | X X X X . direct
+7 = 35 . X X X . | X . . . . ten exchange
write 5, carry 3
4 x 5 + 3:
start 3 . . . . . | . X X X .
+4 = 7 . . . . . | X X X . . five exchange
+4 = 11 . . . X . | . X . . . ten exchange
+4 = 15 . . . X . | X . . . . five exchange
+4 = 19 . . . X . | X X X X X direct
+4 = 23 . . X X . | . X X X . ten exchange
write 23
Partial product: 235, shifted, is 2,350.
Column sums.
ones: 1 = 1 write 1
tens: 4 + 5 = 9 . . . . . | X X X X X write 9
hundreds: 1 + 3 = 4 . . . . . | . X X X X write 4
thousands: 2 = 2 write 2
Answer: 2,491. Cost: 22 finger additions and 64 finger movements, no carries at all in the final sum.
A faster route exists for this problem too. 47 x 53 is (50 minus 3)(50 plus 3) = 2,500 minus 9 = 2,491, the difference of squares used by mental calculators. Again, the fingers can do the one subtraction, but the method does not tell you to look for it.
386 x 524
Three partial products, each built from three digit products. In the compact form below, each line lists the running values the hands show after each press.
386 x 4:
6 x 4, carry 0: 6, 12, 18, 24 write 4, carry 2
8 x 4, carry 2: 10, 18, 26, 34 write 4, carry 3
3 x 4, carry 3: 6, 9, 12, 15 write 15
partial product 1,544
386 x 2 (shifted one place):
6 x 2, carry 0: 6, 12 write 2, carry 1
8 x 2, carry 1: 9, 17 write 7, carry 1
3 x 2, carry 1: 4, 7 write 7
partial product 772, shifted = 7,720
386 x 5 (shifted two places):
6 x 5, carry 0: 6, 12, 18, 24, 30 write 0, carry 3
8 x 5, carry 3: 11, 19, 27, 35, 43 write 3, carry 4
3 x 5, carry 4: 7, 10, 13, 16, 19 write 19
partial product 1,930, shifted = 193,000
Finger diagrams for the 8 x 5 row, the busiest one:
start 3 . . . . . | . X X X . carry 3
+8 = 11 . . . X . | . X . . . ten exchange
+8 = 19 . . . X . | X X X X X direct
+8 = 27 . . X X . | X X X . . ten exchange
+8 = 35 . X X X . | X . . . . ten exchange
+8 = 43 X X X X . | . X X X . ten exchange
Column sums over three rows:
1544
7720
+ 193000
--------
ones: 4 = 4 write 4
tens: 4 + 2 = 6 write 6
hundreds: 5 + 7 = 12 write 2, carry 1
thousands: 1 + 1 + 7 + 3 = 12 write 2, carry 1
ten thousands: 1 + 9 = 10 write 0, carry 1
hundred thousands: 1 + 1 = 2 write 2
Answer: 202,264. Cost: 43 finger additions and 133 finger movements, plus 11 written digits for the partial products and 6 for the answer.
It is worth noticing that 386 x 524 costs about the same as 98 x 97, even though the answer is twenty times bigger. Stage 1 cost depends on the size of the multiplier's digits, because a digit of 9 means nine presses and a digit of 2 means two. 524 has small digits. 97 has two large ones.
85²
Chisanbop has no squaring rule, so 85² is just 85 x 85.
85 x 5:
5 x 5, carry 0: 5, 10, 15, 20, 25 write 5, carry 2
8 x 5, carry 2: 10, 18, 26, 34, 42 write 42
partial product 425
85 x 8 (shifted):
5 x 8, carry 0: 5, 10, 15, 20, 25, 30, 35, 40 write 0, carry 4
8 x 8, carry 4: 12, 20, 28, 36, 44, 52, 60, 68 write 68
partial product 680, shifted = 6,800
The 8 x 8 row in full:
start 4 . . . . . | . X X X X carry 4
+8 = 12 . . . X . | . X X . . ten exchange
+8 = 20 . . X X . | . . . . . ten exchange
+8 = 28 . . X X . | X X X X . direct
+8 = 36 . X X X . | X X . . . ten exchange
+8 = 44 X X X X . | . X X X X mixed
+8 = 52 . . . . X | . X X . . ten exchange; carry needs a five exchange
+8 = 60 . . . X X | . . . . . ten exchange
+8 = 68 . . . X X | X X X X . direct
Column sums: 5, 2, then 4 + 8 = 12 (write 2, carry 1), then 1 + 6 = 7. Answer: 7,225. Cost: 31 finger additions and 81 finger movements.
The well known shortcut for squares ending in 5 is much faster: multiply the tens digit by the next number up, 8 x 9 = 72, and append 25. On the fingers, 8 x 9 is nine presses of 8 reaching 72, the same nine presses shown in the 98 x 97 section. So a Chisanbop user who knows the shortcut does 85² in 9 additions instead of 31.
7,429 ÷ 37
Division is where Chisanbop's 0 to 99 window fits surprisingly well. In long division by a two digit divisor, the working number is often under 100.
200
--------
37 ) 7429
74 first partial dividend
74 2 x 37
--
02 bring down 2: less than 37, quotient digit 0
029 bring down 9: 29, less than 37, quotient digit 0
remainder 29
On the fingers, 7 is less than 37, so take 74. Press 74 and subtract 37 until you cannot.
start 74 . . X X X | . X X X X
-37: tens 70 - 30 needs a five exchange (clear 50, press 20)
ones 4 - 7 needs a borrow: clear 10, then press 3 as (press 5, clear 2)
= 37 . X X X . | X X X . .
-37: direct on both hands
= 0 . . . . . | . . . . .
Two subtractions, so the first quotient digit is 2 and the remainder is 0. Bring down 2: the hands show 2, which is less than 37, so the quotient digit is 0. Bring down 9: the hands show 29.
29 . . X X . | X X X X X less than 37: quotient digit 0
Answer: 200 remainder 29. Check: 37 x 200 + 29 = 7,429. Cost: 2 subtractions and 11 finger movements, plus three numbers pressed (74, 2 and 29). This is the cheapest problem in the set for Chisanbop.
It would be less pleasant with a bigger quotient digit. A partial dividend of 369 with divisor 37 would need nine subtractions, and 369 does not fit on the hands, which leads to the same trick we use for 1/19 below.
√7,744
Chisanbop has no square root procedure. The manuals cover the four operations and nothing else. There are two honest ways to get a root with the fingers' help, and neither is part of Chisanbop as taught.
Estimate and check. 80² = 6,400 and 90² = 8,100, so the root is between 80 and 90. The last digit of 7,744 is 4, so the root ends in 2 or 8. 85² = 7,225 is below 7,744, so it must be 88. Check 88 x 88 on the fingers with the long multiplication layout above.
Subtracting odd numbers. The sum of the first n odd numbers is n², so you can find a square root by subtracting 1, 3, 5, 7 and so on and counting. Split 7,744 into pairs of digits: 77 and 44. The first pair, 77, fits on the hands.
start 77 . . X X X | X X X . .
-1 = 76 . . X X X | X X . . . direct
-3 = 73 . . X X X | . X X X . five exchange
-5 = 68 . . . X X | X X X X . ten exchange
-7 = 61 . . . X X | . X . . . direct
-9 = 52 . . . . X | . X X . . ten exchange
-11 = 41 X X X X . | . X . . . tens need a five exchange
-13 = 28 . . X X . | X X X X . ten exchange
-15 = 13 . . . X . | . X X X . direct
Eight odd numbers fit before the next one, 17, is bigger than 13. So the first digit of the root is 8, and 77 minus 64 leaves 13.
For the second digit the method continues on paper. Bring down the next pair: 1,344. The odd numbers now start at 20 x 8 + 1 = 161 and step by 2: 161, 163, 165, 167, 169, 171, 173 and 175. Their sum is exactly 1,344, so eight subtractions empty the remainder. The second digit is 8, and the root is 88.
1344 - 161 - 163 - 165 - 167 - 169 - 171 - 173 - 175 = 0
Those eight are four digit subtractions, so they leave the hands and go column by column on paper, the same way the column sums did. Cost: 8 subtractions and 24 finger movements for the first digit, then 8 written multi-digit subtractions for the second.
Plainly put: Chisanbop can carry out the arithmetic inside a root, but it does not tell you how to find a root. That knowledge comes from somewhere else.
1/19 as a decimal
A decimal expansion is long division that never ends. Divide 1 by 19: multiply the remainder by 10, see how many 19s fit, write that digit, and keep the new remainder. The remainders run from 1 to 18, so the working number (10 times the remainder) can be as large as 180. That breaks the 99 ceiling on about half the steps.
We used a small paper aid, which is our adaptation and not something in the manuals. When the working number is 100 or more, write a "1" on paper as a hundred marker and press the rest on the fingers. Subtract 19 while the hands show 19 or more. When the hands drop below 19 and the hundred marker is still there, subtract 19 across the hundred by pressing 81 (100 minus 19) and crossing out the marker. It is the ten exchange idea one level up: subtracting 19 from a hundred is the same as adding its hundred partner, 81.
Here is step 2, where the working number is 100:
working number 100: write hundred marker, hands show 0
hands below 19, marker present: press 81, cross out marker
= 81 . X X X X | . X . . . (1 subtraction)
-19 = 62 . . . X X | . X X . . (2)
-19 = 43 X X X X . | . X X X . (3) the borrow needs a five exchange on the left
-19 = 24 . . X X . | . X X X X (4)
-19 = 5 . . . . . | X . . . . (5) mixed
digit 5, new remainder 5
And step 10, where the working number is 180, the largest it ever gets:
working number 180: write hundred marker, hands show 80
= 80 . X X X X | . . . . .
-19 = 61 . . . X X | . X . . . (1)
-19 = 42 X X X X . | . X X . . (2)
-19 = 23 . . X X . | . X X X . (3)
-19 = 4 . . . . . | . X X X X (4)
hands below 19, marker present: press 81, cross out marker
= 85 . X X X X | X . . . . (5)
-19 = 66 . . . X X | X X . . . (6)
-19 = 47 X X X X . | X X X . . (7)
-19 = 28 . . X X . | X X X X . (8)
-19 = 9 . . . . . | X X X X X (9)
digit 9, new remainder 9
The whole period, step by step:
| Step | Remainder in | Working number | Digit | Remainder out | Finger operations |
|---|---|---|---|---|---|
| 1 | 1 | 10 | 0 | 10 | 0 |
| 2 | 10 | 100 | 5 | 5 | 5 |
| 3 | 5 | 50 | 2 | 12 | 2 |
| 4 | 12 | 120 | 6 | 6 | 6 |
| 5 | 6 | 60 | 3 | 3 | 3 |
| 6 | 3 | 30 | 1 | 11 | 1 |
| 7 | 11 | 110 | 5 | 15 | 5 |
| 8 | 15 | 150 | 7 | 17 | 7 |
| 9 | 17 | 170 | 8 | 18 | 8 |
| 10 | 18 | 180 | 9 | 9 | 9 |
| 11 | 9 | 90 | 4 | 14 | 4 |
| 12 | 14 | 140 | 7 | 7 | 7 |
| 13 | 7 | 70 | 3 | 13 | 3 |
| 14 | 13 | 130 | 6 | 16 | 6 |
| 15 | 16 | 160 | 8 | 8 | 8 |
| 16 | 8 | 80 | 4 | 4 | 4 |
| 17 | 4 | 40 | 2 | 2 | 2 |
| 18 | 2 | 20 | 1 | 1 | 1 |
After step 18 the remainder is 1 again, which is where we started, so the digits repeat. Answer: 1/19 = 0.052631578947368421, repeating every 18 digits.
Cost: 81 subtractions (the digits of the period add up to 81) and 333 finger movements, with 18 digits written and 9 hundred markers written and crossed out. It is the most expensive problem in the set for Chisanbop, and the one where the method is least itself.
There is a much shorter route that also suits the fingers. The Vedic post shows 1/19 by doubling: write 1, then double repeatedly from right to left with carries (1, 2, 4, 8, 16 writes 6 carry 1, and so on). Every doubling plus carry is at most 9 + 9 + 1 = 19, which fits on the hands easily. Chisanbop does not teach it, but it is a good example of how the fingers can serve a better algorithm.
Checking answers: casting out nines on the fingers
None of the 1978 manuals we read teaches a check. Casting out nines works well on the fingers anyway, because it only needs digit sums under 99. Add the digits of each number, reduce until one digit is left, and compare.
| Problem | Check | Result |
|---|---|---|
| 98 x 97 = 9,506 | 98 gives 8, 97 gives 7, 8 x 7 = 56 gives 2; 9 + 5 + 0 + 6 = 20 gives 2 | passes |
| 47 x 53 = 2,491 | 2 x 8 = 16 gives 7; 2 + 4 + 9 + 1 = 16 gives 7 | passes |
| 386 x 524 = 202,264 | 8 x 2 = 16 gives 7; 2 + 0 + 2 + 2 + 6 + 4 = 16 gives 7 | passes |
| 85² = 7,225 | 4 x 4 = 16 gives 7; 7 + 2 + 2 + 5 = 16 gives 7 | passes |
| √7,744 = 88 | 88 gives 7, 7 x 7 = 49 gives 4; 7 + 7 + 4 + 4 = 22 gives 4 | passes |
| 7,429 = 37 x 200 + 29 | 1 x 2 + 2 = 4; 7 + 4 + 2 + 9 = 22 gives 4 | passes |
Casting out nines misses errors that leave the digit sum unchanged, such as swapping two digits, so it is a quick screen rather than a proof.
What it costs: steps, movements and memory
"Fast" has to be shown. Here is what the simulator counted for each problem, using Stage 1 Chisanbop with paper for anything over 99.
| Problem | Finger additions or subtractions | Single finger movements | Digits written (working) | Fits on the hands? |
|---|---|---|---|---|
| 98 x 97 | 38 | 140 | 6 partial product digits, 4 answer digits | Each step yes, answer no |
| 47 x 53 | 22 | 64 | 6 and 4 | Each step yes, answer no |
| 386 x 524 | 43 | 133 | 11 and 6 | Each step yes, answer no |
| 85² | 31 | 81 | 6 and 4 | Each step yes, answer no |
| 7,429 ÷ 37 | 2 | 11 | 3 quotient digits | Yes |
| √7,744 | 8 on the hands, then 8 on paper | 24 for the first digit | 2 root digits plus paper subtractions | First digit only |
| 1/19 | 81 | 333 | 18 digits, 9 hundred markers | Only with the paper marker |
Three things stand out.
First, the hands are memory, not speed. The biggest benefit of Chisanbop is that the running value sits on your fingers, so the head only tracks a count (how many presses so far, never more than 9) and a position. That is a small load. The 2014 study's authors make the same argument for why finger methods may help anxious learners: an external, permanent representation reduces working memory load.
Second, Stage 1 multiplication is slow by design. A digit of 9 in the multiplier means nine additions for every digit of the multiplicand. The times table exists precisely so that 8 x 7 is one recall rather than seven additions. The Parent's Guide's Stage 2 and Stage 4 are meant to close that gap, and we could not measure them.
Third, paper does most of the long work. Every answer above with more than two digits passed through written partial products or written columns. A soroban keeps all of that on the frame; Chisanbop cannot.
How fast is Chisanbop, really?
The 1978 Parent's Guide claims that after Stage 4 of addition children "can add three to five single-digit numbers per second with remarkable accuracy and without any finger manipulation." The Home Study Book's introduction says the method has "already demonstrated superiority to calculators." Both are claims by the company that sold the method. We found no independent timing study that tested either claim.
We also found no Chisanbop event in any mental calculation competition and no measured Chisanbop speed record. The Korean children who demonstrated it at a National Council of Teachers of Mathematics conference and on television talk shows impressed audiences with their speed, according to the Christian Science Monitor, but a demonstration is not a measurement. So the honest answer is that Chisanbop's speed is unmeasured. What we can measure is the work per problem, in the table above.
What we can say by comparison is structural. For single and two digit addition and subtraction, a practised Chisanbop user needs no more than four finger movements per digit, and no recall of number facts. That is the narrow area where the method is quick. For long multiplication and division it is the standard algorithm with a slower inner step until the times tables are learned.
Where does Chisanbop stop scaling?
- At 100. Two hands are two decimal places. Anything bigger goes to paper, column by column.
- At multiplication. Repeated addition costs as many additions as the multiplier digit. The times table, or the soroban's built in multiplication, beats it once learned.
- At roots and powers. There is no procedure. You need an outside algorithm, as in the √7,744 example.
- At fractions and decimals. There is no fraction or decimal procedure beyond long division, and repeating decimals push the working number past 99, as in the 1/19 example.
- At negative numbers and algebra. The Parent's Guide uses "algebra" to mean missing addends (3 plus what makes 7), which is subtraction. Nothing more.
- At speed without practice. The Home Study Book warns that just learning to show numbers can take weeks.
None of these limits is a flaw in the design. Chisanbop was built to make the first years of arithmetic concrete, and that is where it stays.
Chisanbop in American classrooms
The story in the United States is short and well documented, because it happened fast and education journals noticed.
Hang Young Pai arrived in New York in the mid 1970s and met Edwin Lieberthal. Chisanbop Enterprises, based in Mount Vernon, New York, published the Home Study Book and the Parent's Guide in 1978, the Parent's Guide with two vinyl records of audio instruction. The New York Times covered it in 1978. Lieberthal brought children, including his two daughters, onto the Today show and the Phil Donahue show around 1978. The Parent's Guide claimed the method was being taught in "hundreds of schools across the United States" and in Canada, Mexico and Japan; we found no independent count to confirm that.
The Christian Science Monitor took stock in May 1982 and found a mixed picture:
| District | What happened | According to |
|---|---|---|
| Mount Vernon, New York | The first system to try it; being phased out by 1982 | Christian Science Monitor |
| Newark, New Jersey | About 25 percent of pupils taught it, about 10 minutes a day from kindergarten to grade 3; plans to expand | Christian Science Monitor |
| Woodridge, Illinois | Enrichment for gifted pupils in grades 1 to 6, in its fourth year, called very successful by local educators | Christian Science Monitor |
| Shawnee Mission, Kansas | A 1979 pilot in one school: first graders could add large numbers easily but did not know basic number facts or add mentally; dropped | Christian Science Monitor |
| Durant, Oklahoma | A university course training Chisanbop teachers; the instructor called her results "phenomenal" | Christian Science Monitor |
The criticism came from mathematics educators. Grace Burton of the University of North Carolina at Wilmington told the Monitor that the method "doesn't teach the basic number facts, only to count faster." Dan Knifong of the University of Maryland compared it to touch typing: it builds speed through drill without deeper understanding, and multiplication and division take even more drill. Knifong and Burton had already asked in Arithmetic Teacher in 1979 whether it was "just another kind of finger reckoning." In the same journal, Jay Greenwood's critique after a two week workshop concluded, in ERIC's summary, that Chisanbop "has presented a misleading picture and is highly overrated."
Supporters argued the opposite. Teachers quoted by the Monitor said the method gave children a solid grasp of place value and the decimal system, and one second grade teacher said "No one's afraid of math anymore." Lieberthal's materials stressed that the method was a supplement, not a replacement, and a 1981 ERIC report on finger mathematics by Ogletree and Chavez made the same point.
Interest faded through the 1980s as the evaluations came in mixed. Chisanbop did not vanish: a 1979 article explored it for blind pupils, Calder and Burchby wrote a Chisanbop manual for Foothills Academy in Calgary in 1992 (it is the format the 2014 study followed), and an Indonesian finger method called Jarimatika, which ERIC's abstract equates with Chisanbop, shows up in a 2010 study of Indonesian first graders.
What does the research say about Chisanbop?
| Study | Design | What it found | Limits |
|---|---|---|---|
| Benson, School Science and Mathematics, 1981 (peer reviewed) | First grade classes, half taught Chisanbop | ERIC abstract: the Chisanbop group scored significantly higher on the computation part of the Iowa basic skills test | We could read only the abstract; sample size, assignment and duration unknown to us |
| Struve and others, Education of the Visually Handicapped, 1979 | Discussion of uses for blind pupils | Proposes Chisanbop as a tool for visually impaired elementary pupils | Not an outcome study |
| Dougherty, ERIC bibliography, 1980 | Annotated bibliography | Collects history, materials and early research | Not peer reviewed; a guide to the literature |
| Rumiati and Wright, MERGA conference, 2010 | Assessment of 20 first and 20 second graders in an Indonesian school | Five first graders used Jarimatika (Chisanbop) | Descriptive, not an evaluation of the method |
| Calder Stegemann and Grünke, Learning Disabilities: A Contemporary Journal 12(2), 2014 (peer reviewed) | Quasi-experimental, one school year, 75 pupils in grades 2 and 5 in British Columbia (the stated total; the class sizes listed add to 79), about 20 minutes a day | Significant gain in attitude to maths for at risk grade 2 pupils; no significant differences in skill gains between Chisanbop and control classes in grade 2; in grade 5 the control class gained more on calculations | No random assignment, small sample, non-equivalent grade 5 groups, no follow-up, many comparisons |
The 2014 study is the most useful because its authors report its limits so clearly. They found real within group gains in the Chisanbop classes, but the control classes gained too, and comparisons between them mostly showed no difference. They describe their own study as "the first in many years that evaluated the effects of Chisanbop" and call for a larger randomised trial. That trial has not, as far as we could find, been run.
So the evidence supports a modest claim. Chisanbop may help some young or struggling learners feel better about arithmetic and see place value. There is no good evidence that it makes children faster or better at mathematics in general than ordinary teaching, and we make no claim about its effect on the brain, IQ or exam results.
Chisanbop compared with other methods
This table compares the methods on the problems above. The soroban and Vedic columns summarise the traditions series; the comparison post works them in full.
| Chisanbop | Soroban and anzan | Vedic shortcuts | Standard written method | |
|---|---|---|---|---|
| Equipment | Hands and a table | A soroban, or a trained imagination | Paper or head | Paper |
| Capacity | 0 to 99 | As many digits as rods | Unlimited on paper | Unlimited |
| Multiplication | Repeated addition per digit, paper for partial products | On the frame, no writing | Very fast near bases and for special forms | Times table plus partial products |
| Roots and decimals | No procedure | Procedures exist on the frame | Special forms (for example 1/19 by doubling) | Long division, digit by digit roots |
| Error check | None taught; casting out nines works | Casting out nines | Digit sums | Estimation, casting out nines |
| Writing needed on this problem set | Partial products, columns and every answer over 99 | None on the frame | Usually only the answer | Every step |
| Best at | Single and two digit addition and subtraction for young learners | General calculation at speed | Specific number patterns | Everything, slowly |
The honest ranking for raw speed on this problem set, with a tool, is the soroban. Without a tool, trained mental methods win. Chisanbop's niche is narrower: the first years of addition and subtraction, and learners who benefit from something they can touch.
A practice plan
If you want to learn Chisanbop for yourself or teach it to a child, the manuals' own order works:
- Show numbers (one to three weeks). Have someone call numbers from 0 to 99 and press them. Do not calculate until this is instant. Watch the 4 to 5 and 9 to 10 transitions in particular.
- Count on, one at a time. Count 0 to 99 pressing one unit at a time. The exchanges (4 to 5, 9 to 10, 49 to 50) are where most errors happen.
- Learn the five partners. Practise adding and subtracting 1 to 4 with the thumb exchange until "add 3 is press 5, clear 2" is automatic.
- Learn the ten partners. Practise "add 5 is press 10, clear 5" and the other four pairs.
- Drill the mixed moves. Use the table above: start with a hand showing 5 to 8 and add 6 to 9.
- Two digit sums, tens first. Then column addition on paper with the carry transferred to the right hand.
- Counting by. Count by 2s, 3s and so on to 9s as Stage 1 multiplication. Then learn the times table anyway: one recall beats nine presses.
- Check with casting out nines. It costs a few digit sums and catches most slips.
Common mistakes
- Pressing the wrong finger first on the left hand. The left hand counts from the index finger outward, mirroring the right. Starting from the little finger makes 20 look like 40 at a glance.
- Forgetting the thumb is 5 or 50, not 1 or 10. Reading a hand with thumb and two fingers down as 3 is the most common misreading.
- Trying to show 100. The hands stop at 99. Write the hundred on paper before you need it.
- Losing the press count in repeated addition. In Stage 1 multiplication, the hands hold the total but not how many times you have pressed. Count aloud, or tick marks on paper.
- Dropping the carry when moving to the next column. The Home Study Book's rule is to transfer the left hand's fingers to the right hand before starting the next column. Skipping that loses the carry.
- Treating Chisanbop as a replacement for number facts. Educators in the 1979 Kansas pilot found first graders who could add quickly on their fingers but not in their heads. Use it alongside the facts, not instead of them.
- Claiming it is ancient or traditional. The method is a 20th century invention by Sung Jin Pai, built on the 1 plus 4 abacus idea. Finger reckoning is old; Chisanbop is not.
FAQ
What is Chisanbop?
Chisanbop is a Korean finger calculation method. The right hand's fingers are worth 1 each and its thumb 5; the left hand's fingers are worth 10 each and its thumb 50. Fingers pressed on a table count, so two hands show any number from 0 to 99 and can add and subtract with complement moves.
Who invented Chisanbop?
Sung Jin Pai created it in Korea, and his son Hang Young Pai refined it and brought it to the United States. Sources place the creation in the 1940s, though one 1978 manual suggests the late 1950s, and give the arrival in the United States as 1976 or 1977.
How do you count to 99 on your fingers?
Use the right hand for ones and the left for tens. Index, middle, ring and little fingers are 1 each on the right and 10 each on the left; the thumbs are 5 and 50. So 78 is the left thumb and two left fingers (70) plus the right thumb and three right fingers (8).
How do you add with Chisanbop?
Press the fingers for the number you are adding. If they are not free, use a complement: adding 3 to 4 is "press 5, clear 2," and adding 5 to 5 is "press 10, clear 5." Larger sums go tens first, then ones.
Can Chisanbop multiply and divide?
Yes, at a basic level. The 1978 manuals teach multiplication first as repeated addition and division as repeated subtraction. Anything past 99 needs paper, so long multiplication and long division still use the standard written layout.
Is Chisanbop the same as the soroban?
Not quite, but each hand works like one soroban rod: the thumb is the heaven bead worth 5 and the four fingers are the earth beads worth 1. A soroban has many rods; Chisanbop has two, so it stops at 99.
Is Chisanbop faster than a calculator?
The original publisher claimed it was, but we found no independent timed study or competition record. On our problem set the work ranged from 2 subtractions (7,429 ÷ 37) to 81 subtractions (1/19).
Does Chisanbop help children learn maths?
The evidence is thin. A 2014 peer reviewed study of 75 pupils found a better attitude to maths among at risk grade 2 pupils but no clear skill advantage over ordinary teaching. 1979 critics said it taught counting speed rather than number facts.
Why did Chisanbop fade in schools?
Early evaluations were mixed, critics in mathematics education journals called it overrated, and some districts, such as Shawnee Mission in 1979 and Mount Vernon by 1982, found children could finger add without knowing basic facts or adding mentally.
Can adults learn Chisanbop?
Yes. The manuals say older learners usually progress faster than young children. Expect to spend the first weeks just showing numbers quickly before calculating.
Where Safeguard fits
Safeguard does not do mathematics, and no Safeguard model computed anything in this post; the finger diagrams and every number came from a short Python script checked against ordinary arithmetic. The parallel we can draw honestly is about checkable steps. A Chisanbop answer is trusted because each move can be replayed and the result can be checked cheaply with casting out nines, and software you ship deserves the same treatment: know exactly which components and versions went into a build, check them against known vulnerability data, and keep a record you can replay, the way an SBOM supports incident response. Even a small simulator like ours runs on an interpreter and could pull in third party libraries, and keeping those dependencies on patched versions is the part of the job Safeguard is built for.
More in this series
Other posts in our fast calculation methods series:
- Babylonian Mathematics Explained: Base 60, YBC 7289 and Plimpton 322
- Egyptian and Russian Peasant Multiplication: Doubling and Binary
- Fastest Mental Math Methods Compared: 14 Systems, Same 7 Problems
- Lattice Multiplication, Napier's Bones and the Slide Rule Explained
- Line Multiplication: The Stick Method, Japanese, Chinese or Neither?
- Maya Mathematics Explained: Base 20, Bar and Dot Numerals and Zero
- Mental Calculation Techniques of World Champions: Left to Right, Criss-Cross, Squares and Calendars
- Trachtenberg Speed System Explained: Rules for 11, 12 and Any Number
Fix it without waiting for upstream
Whatever the vulnerability, most of the risk sits in two gaps. The first is the time between a fix being published and that fix actually running in your production builds. The second, and worse, is the time before any fix exists at all, while a maintainer works out a patch and a release schedule. Waiting through both gaps is a habit, not a requirement. Safeguard gives teams three ways to close them.
1. Autonomous remediation: pull requests, not tickets
When a fixed version exists, Safeguard's Griffin models open a tested, policy gated pull request that moves the affected dependency to the safe version. You can run it on one repository or in bulk across every project that carries the vulnerable version. Remediation covers eight categories, including dependencies, licenses, security posture and findings. Reachability analysis ranks the vulnerable code paths your application actually calls first, so the first pull requests you merge are the ones that matter most. Autonomous remediation ships switched off, with every category set to Manual, so your team decides how much runs on its own and what still needs a human approval.
2. Gold Open Source: the safe version in seconds, free
gold.safeguard.sh is free and needs no login. Search any CVE or package to see affected and fixed versions, CVSS, EPSS, CISA KEV status and a recommended safe version, or use the "Am I affected?" checker. The same data is available through a free read API, README status badges and RSS threat feeds. The safeguard-sh/gold-scan-action GitHub Action can fail a build on a known exploited vulnerability, on any known vulnerability, or never, so a version you have just removed cannot quietly come back in next week's merge.
3. Gold Registry: start from components that are already fixed
registry.safeguard.sh provides hardened, drop in replacements for upstream packages and container images. Every Gold artifact is held continuously to zero exploitable critical or high CVEs, zero malware and a completed license check, with SLSA L3 or higher provenance, a Sigstore signature and a public evidence page you can hand to an auditor. An artifact loses its Gold badge if it regresses. Teams can point their own package directory at the registry so hardened equivalents resolve without changing how developers install anything.
When upstream has no fix yet, or will not ship one, Safeguard first works to get the fix accepted upstream. If the issue is severe or upstream will not move, Safeguard builds a fork, fixes the vulnerability there and publishes a hardened Gold build, so you are not stuck on a maintainer's release schedule. You can also request a hardened, compatibility tested build of a specific package. This fork and patch flow is in early access today, so ask which packages it covers before you plan around it.
| Your situation | What to use |
|---|---|
| A fixed version exists | Autonomous remediation opens the upgrade pull request; Gold Open Source confirms the safe version |
| You need to know today whether you are affected | Gold Open Source lookup and "Am I affected?" checker, free and without login |
| You want vulnerable versions to stop shipping | The Gold scan GitHub Action in CI, plus Safeguard policies and gates |
| Upstream has no fix yet, or will not ship one | A custom Gold request; fork and patch (early access) |
| You want to start clean on new projects | Pull hardened components and images from Gold Registry |
One honest limit: when the vulnerable code lives in a vendor appliance, a hosted service or an operating system runtime you do not build yourself, the fix still has to come from that vendor or distribution. The steps above apply to the open source dependencies and container images you build and ship, which is where most teams carry the largest and least tracked share of their exposure.
See how Safeguard would help
These demos show dependency scanning and remediation workflows, not mathematics. You can download Safeguard and follow the CLI docs to try them on your own projects.
This demo is a real CLI session. After installing, safeguard opens the interactive terminal; asked to "fix the lodash CVE in this repo," it reads the finding and the advisory, asks before any command that changes something, edits package.json to lodash 4.17.21, runs npm install and npm test with approval, prints a summary and pushes nothing. The same flow applies to the JavaScript behind a finger math practice app or a classroom quiz site.
Click through it at your own pace, or open it full screen.
This demo sets up the Safeguard runner on your own machine, approves it with its device code and scans from the terminal. Pointed at a project folder, such as a Python script like the simulator behind this post, the scan lists the packages and versions the project depends on and their known vulnerabilities, so you know what to update before you share it.
Click through it at your own pace, or open it full screen.
This demo is a real Android session. You send work from the phone to a computer running the CLI, and approve the command on the phone with Allow once, Allow for turn or Deny. It suits a teacher or developer who wants to start a dependency check on a lesson project while away from the desk.
Click through it at your own pace, or open it full screen.
Quick check
Your hands show 7 (right thumb and two fingers). You need to add 7. Which move do you use, and what do your hands show afterwards?
The mixed move. Press 10 with the left index finger and clear 3 on the right hand, but with only two fingers down you must clear 3 as "clear 5, press 2." The right hand ends with four fingers down and no thumb, the left hand with one finger: 14.
Why does every single digit product in long multiplication fit on Chisanbop hands?
The largest step is 9 x 9 plus a carry of 8, which is 89. Two hands hold up to 99, so every digit product with its carry fits, even though the partial products and the final answer do not.
Sources
- Wikipedia: Chisanbop
- Computer History Museum, Revolution exhibit: Chisanbop
- Edwin M. Lieberthal, Home Study Book: Chisanbop Finger Calculation Method (Chisanbop Enterprises, 1978), Internet Archive scan
- Hang Young Pai, Parent's Guide to Chisanbop (Chisanbop Enterprises, 1978), Internet Archive scan
- Internet Archive: Chisanbop on the Today Show (clip, about 1978)
- Internet Archive: Chisanbop on Phil Donahue (clip, about 1978)
- David B. Purcell, "What about Chisanbop: who's using it?", Christian Science Monitor, 17 May 1982
- Kim Calder Stegemann and Matthias Grünke, "Revisiting an Old Methodology for Teaching Counting, Computation, and Place Value," Learning Disabilities: A Contemporary Journal 12(2), 191 to 213, 2014 (ERIC full text)
- ERIC EJ1047461: record for the 2014 study
- ERIC EJ244533: Benson, "Chisanbop: Can Students Benefit from It?", School Science and Mathematics, 1981
- ERIC EJ200177: Knifong and Burton, "Chisanbop: Just Another Kind of Finger Reckoning?", Arithmetic Teacher, 1979
- ERIC EJ200178: Greenwood, "Critique on the Chisanbop Finger Calculating Method," Arithmetic Teacher, 1979
- ERIC EJ180666: Brooks, "Fingers Make a Comeback in Math," New York Times, 1978
- ERIC EJ230192: Struve and others, "Chisanbop for Blind Math Students," Education of the Visually Handicapped, 1979
- ERIC ED188906: Dougherty, An Annotated Bibliography of the Chisanbop Method of Finger Calculation, 1980
- ERIC EJ244796: Moser, "Chisanbop: Worth Trying?", Lutheran Education, 1980
- ERIC ED200422: Ogletree and Chavez, Finger Mathematics: A Method for All Children, 1981
- ERIC ED520965: Rumiati and Wright, Assessing the Number Knowledge of Children in the First and Second Grade of an Indonesian School, MERGA 2010
- ERIC API search results for "chisanbop"
Last reviewed: 25 October 2026. Dates for the method's creation and its arrival in the United States differ between sources; the table near the top lists each version with its source.
