SYSE.49:5.1 - Make a missed carry observable in human practice

The receiving engineering question is whether a proposed worksheet and sequence make carry recording and use recoverable. HCD.6 supplies a practice design for a person already able to perform the digit products: produce a correct stock total with intermediate working, first with an allowed demonstration, then correct the affected action. The arithmetic criteria are supplied. The engineer prepares the worksheet, task cards, independent answer basis and an available observer who can give the designed feedback.

Use 123 × 3 = 369 as a no-carry contrast and 127 × 3 = 381 as a carry case. The latter requires recording the 2 from 7 × 3 = 21 into the tens column and using it in 2 × 3 + 2 = 8. Capture the written relation and performed operation: an absent carry record, a recorded 2 ignored during calculation, and correct working copied into a wrong report are different observations.

If the person records 2 but writes tens 6, feedback preserves the correct units/hundreds, points to the unused carry and asks for correction of that operation. The corrected result is 381. This can be supported correction on the same case. A subsequent changed-value task is needed if the next question is whether the person recognizes and uses the carry without the answer-bearing cue. A partially worked demonstration must not be counted as that independent recognition.

Challenge the feedback itself: an answer key that approves 361 despite the visible unused carry fails the supplied arithmetic criterion. A sheet whose carry row is misplaced returns to SYSE.48/.52; a missed use despite a correct supplied layout returns to the procedure or the human learning diagnosis. The qualified material and observations can inform that repair. They do not establish that learning occurred; HCD.11–13 supplies the corresponding performance, transfer and retention questions.