Activity: Common errors in subtraction The diagnosis of errors in arithmetic is an essential part of evaluation in any mathematics program. Mathematics teachers have to be careful not just to score written work but to analyze it as well. A teacher needs to observe what a child does and does not do. Diagnosis should then be followed by corrective and remedial instruction (Ashlock, 1986, see References). Errors may sometimes be: the result of carelessness, as in writing down the wrong numbers or performing the wrong operation based on an error in recalling basic number facts a result of not knowing how to proceed and providing random responses caused by applying a defective algorithm. A child who has misunderstood an algorithm or invented a defective algorithm tends to systematically use the same procedure in all of his/her work. Sometimes it will yield correct answers. By analyzing the child's written work teaching strategies specific to the error the child makes can be employed. Teaching strategies may include: reinforcement of the concept of place value using concrete teaching aids (e.g. to see 346 as 3 hundreds, 4 tens and 6 ones) the use of place value material to give concrete experience of the need for borrowing and decomposition leading the child to see that their method is incorrect by demonstrating that their answer is not possible using a number expander to help child see number in expanded notation (e.g. to see 346 as 300 + 40 + 6) Given below are the written responses of various students to subtraction questions. Try to analyze the procedures used to develop an understanding of the common error patterns of students. | Beth | Don | Lynn | Meng | Pepu | Richard | Click here to go back to the previous page Beth Here are three subtractions which Beth has done. Which questions did Beth get correct? Explain the error in Beth's method. Complete these questions as Beth would. 7 7 4 - 2 8 5 ______ ______ 7 0 4 - 1 5 8 ______ ______ Click here to see Beth's response and possible teaching strategies. Don Here are three subtractions which Don has done. Which questions did Don get correct? Explain the error in Don's method. Complete these questions as Don would. 7 0 4 - 1 5 8 ______ ______ 2 0 6 - 4 9 ______ ______ Click here to see Don's response and possible teaching strategies. Lynn Here are three subtractions which Lynn has done. Which questions did Lynn get correct? Explain the error in Lynn's method. Complete these questions as Lynn would. 6 0 3 - 3 7 1 ______ ______ 1 2 4 - 1 0 3 ______ ______ Click here to see Lynn's response and possible teaching strategies. Meng Here are three subtractions which Meng has done. Which questions did Meng get correct? Explain the error in Meng's method. Complete these questions as Meng would. 7 0 4 - 1 5 8 ______ ______ 2 0 6 - 4 9 ______ ______ Click here to see Meng's response and possible teaching strategies. Pepu Here are three subtractions which Pepu has done. Which questions did Pepu get correct? Explain the error in Pepu's method. Complete these questions as Pepu would. 2 3 6 - 5 4 ______ ______ 7 0 4 - 1 5 8 ______ ______ Click here to see Pepu's response and possible teaching strategies. Richard Here are three subtractions which Richard has done. Which questions did Richard get correct? Explain the error in Richard's method. Complete these questions as Richard would. 8 2 - 4 6 ______ ______ 3 1 8 - 1 7 3 ______ ______ Click here to see Richard's response and possible teaching strategies.