Diagnosing Error Patterns for Elementary Students

Session I – Computation

Addition Determine the error pattern in the following: 2+3=5 9+6=13 4+5=9 3+4=7 5+2=7 5+8=14 7+8=12 4+3=7 4+6=10 9+9=16

Addition Student is doing okay until they reach sums over ten – facts are not secure and the student has run out of fingers. Using a tens frame strategy with unit manipulatives is a good ideatens frame

Addition Determine the error in the following:

Addition If you correctly identified that the sums were off by one you were correct. Suggest at this point looking to see if this type of error is occurring due to finger counting. If so, replace fingers with counters or use a “counting on” strategy until facts are secure.counting on Once established drill with single digit facts is recommended to keep facts fluent. A tens frame strategy will also work here.tens frame

Addition Determine the error in the following:

Addition Student is correctly summing the addends but is recording them entirely at the bottom instead of regrouping. Recommend grid paper, partial sums practice, trading activities.grid paperpartial sums practice trading activities

Addition Determine the error pattern in the following:

Addition This type of error should be setting off alarms all over the place. It reflects a very incomplete sense of number sense/estimation (especially the last one) and place value. This student is still in the rational counting stage and needs to move to counting by place value with bundling or Base Ten Blocks. Some basic facts practice would help as well.

Addition Determine the error pattern in the following:

Addition The first two problems have the correct part of the sum recorded at the bottom but not the regrouping numbers at the top. The second two problems represent a partially correct response with part of the information left out. Note: hundreds/thousands is correct. The good news is that with this type of error the student realizes that regrouping must take place and partially understands and completes the process. More practice with the algorithm is recommended.

Addition Determine the error in the following:

Addition This type of error shows up at the beginning of the regrouping process. Notice that the student records the “tens” value in the ones column and the “ones” value above the tens place. This is a good example of a student who knows that regrouping must be done but doesn’t have a full understanding and tries to mimic the algorithmic process. This is why it essential to build the regrouping concept with trading models.

Subtraction Determine the error in the following:

Subtraction The student has simply subtracted the smaller number from the larger one regardless of direction instead of regrouping Suggest side-by side practice with trading models. Also focus on the directionality of subtraction in this type of algorithmic model.trading models

Subtraction Determine the error in the following:

Subtraction Student is regrouping when not necessary. Note the value of the differences. This represents a poor understanding of the regrouping process. It looks like the student is trying to approximate what a subtraction with regrouping problem looks like. Recommend estimation and place value concept building activities before attempt at this type of algorithm.

Subtraction Determine the error in the following:

Subtraction This type of error represents regrouping without converting the original digit in the process. In other words, where is the added value coming from? Again the student partially understands the regrouping process and practice with standard algorithm is suggested.

Subtraction Determine the error pattern in the following:

Subtraction This is typical of an incomplete understanding of subtracting across zeroes. It is a variation of the subtracting downward error pattern. Suggest trading activities using base ten blocks and alternate algorithms.

Subtraction Determine the error in the following:

Subtraction The student shows a more complete understanding than the previous example and has followed the rules for subtraction but has not regrouped for the zero and again subtracted down instead of up. Suggest side-by side practice with trading models.

Geometry/Measurement Determine the error in the following: What is the perimeter of these squares and rectangles (student responses in blue ):

Geometry/Measurement Student is correctly identifying the shape of a square having four equal sides and processing additively. For the rectangles, the student is possibly confusing the “double the sides and add” algorithm with multiplying the sides for area instead of perimeter (example: 2 x 6.5 = 13 instead of doubled) since the problems would look similar.areaperimeter This sometimes occurs when the” double the sides” algorithm is taught before the concept of perimeter is fully established. Best strategy is to physically measure the shapes going around and adding as you go.

Geometry/Measurement Determine the error in the following: What is the perimeter of these squares and rectangles (student responses in blue ):

Geometry/Measurement Student understands the concept of perimeter but is counting the dots instead of the linear units between them. This easy to spot because the linear measurement on any given side is always one over. This happens when perimeter is taught using grid boxes/counting from a textbook instead of physically measuring. Recommended strategy involves using a congruent unit measuring tool (ruler), starting in a fixed corner (upper left, for example), and following the figure around.

Resources Error Patterns in Computation Ashlock, Robert B. Special Thanks to the Teachers from the Pinellas County School District