Second Grader's Consistent Regrouping Errors
Mr. Chen teaches second grade in a school using a 30-minute daily math intervention block and a multi-tiered system of supports. One student, Jordan, age 7, completes addition facts accurately and reads at grade level. On two-digit subtraction, he consistently subtracts the smaller digit from the larger in each column: 52 − 27 = 35 and 81 − 46 = 45. With base-ten blocks, he can solve 52 − 27 correctly when the teacher prompts him to exchange a ten for ten ones, but he reverts to the same errors the next day without materials. On a recent place-value unit test, he scored 42%, with most points lost on regrouping and problems involving zero, such as 304 − 128 = 224. He says, 'You can't take 8 from 4, so I just do 4 minus 8 and make it positive.' The grade-level team meets in two weeks to review intervention data. Mr. Chen has 24 students, one 20-minute small-group slot, and no additional paraprofessional.
1. Diagnose Jordan's error pattern and explain why it is not simply careless borrowing.
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Jordan's pattern is a consistent procedural misconception, not carelessness. He applies a rule that each column can be subtracted smaller-from-larger, which preserves the digits but destroys place value: in 52 − 27, he does 5 − 2 = 3 tens and 7 − 2 = 5 ones. His zero error shows he has no meaning for regrouping across a zero; he treats 0 as 10 without decomposing. His success with base-ten blocks only when prompted indicates he can perform the exchange but does not connect it to the written algorithm, so the knowledge is not fluent or generalized. The fact that addition and reading are intact and errors are stable across days makes attention or motivation less likely. Instruction should therefore target the concept of composing and decomposing tens, the language of exchange, and linking each block action to the written record. Practice should include error analysis and comparison of correct and incorrect examples, not just more worksheets.
2. Design a Tier 2 sequence using the available 20-minute slot and describe how the team should monitor and decide next steps.
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Use a concrete-representational-abstract sequence in the 20-minute slot three times weekly for six weeks. Begin with base-ten blocks and place-value mats: build 52, attempt to remove 27, exchange one ten for ten ones, and say 'I regrouped 1 ten as 10 ones.' Record each step beside the blocks. Move to drawings of tens and ones, then to the algorithm with a regrouping checklist. Include zero cases such as 304 − 128 using expanded form and place-value disks. Provide worked examples, then faded guidance, and intermix two addition problems for retention. Tier 1 number talks should continue with composing and decomposing. Monitor twice weekly with four problems, including one zero case, scoring both answer and regrouping step. Bring to the team: baseline, weekly probes, fidelity checklist, and work samples. After four weeks, if accuracy remains below 60% or the regrouping step is not generalized, intensify to five times weekly or consider further evaluation; if the trend is upward, continue and fade manipulatives.