The Side Table: Scaffolding Versus Watering Down in Co-Taught Math
In a co-taught seventh-grade math class, the unit is proportional reasoning: students use ratio tables, double number lines, and equations to solve multi-step problems. Three students have specific learning disabilities in math; one, Devon, has persistent difficulty with number sense and place value and still counts on fingers for basic facts. During the 50-minute block, the special education teacher takes these four students to a side table and gives them a worksheet of one-step problems with whole numbers, while the general education teacher teaches the grade-level lesson to everyone else. One paraprofessional is available. Devon's IEP goal targets solving two-step ratio problems with a calculator and a graphic organizer.
1. Evaluate the side-table arrangement. What is defensible about it and what is not?
Read the worked answer
Small-group instruction is not the problem; sustained separation from the grade-level content is.
Defensible: a quieter setting, more opportunities to respond, immediate corrective feedback, and a lower student-teacher ratio are all legitimate supports. Pulling a group for a focused, purposeful segment of the block can be good practice.
Not defensible:
- The content is not the grade-level content. One-step whole-number problems are a modification, not a scaffold. Devon's IEP goal is two-step ratio problems - the side table is not even aimed at his goal.
- It is the whole block, every day. Removal from the general curriculum is justified only when education in the general education classroom with supplementary aids and services cannot be achieved satisfactorily. Nothing in the setup establishes that.
- It is the same four students, always. A permanent, visible low group carries stigma and depresses expectations; peers figure it out quickly and so do the students.
- It widens the gap. Procedure-only practice on easier numbers does not build proportional reasoning, so Devon falls further behind on the standard he is accountable for.
The fix is not to abandon small-group work but to keep it tied to the same content and standards, for part of the block, with a stated purpose and a planned return.
2. Describe how to teach the same proportional reasoning content so Devon can access it, using explicit instruction and a concrete-to-abstract progression.
Read the worked answer
The difficulty gap is in number sense and working memory, not in the reasoning standard. Separate those so one does not block the other.
Sequence within the block:
- Concrete: two-color counters, tape diagrams, and real contexts (e.g., scaling a recipe, unit price) where students physically build both quantities.
- Representational: the same problem drawn as a ratio table and a double number line, with students explicitly connecting the two - 'the table column is the number line jump.'
- Abstract: the equation, and only then cross-multiplication as a shortcut for a relationship they already understand.
Explicit instruction structure: review prerequisite, model with a think-aloud, guided practice with a range of examples and non-examples, lots of student response and corrective feedback, then independent practice with a faded scaffold.
For Devon specifically:
- A graphic organizer with four fixed prompts: What two quantities am I comparing? → ratio table → double number line → equation. The structure carries the working memory load so the reasoning is visible.
- Calculator for computation, as his IEP specifies, so place-value and fact gaps do not consume the problem.
- Five minutes of daily targeted fact and place-value practice as a separate strand - not as a prerequisite he must clear before he is allowed to reason.
- Manipulatives kept available, not withdrawn once the unit 'moves on.'
3. How should the two teachers and the paraprofessional structure the block and their roles so this is sustainable?
Read the worked answer
The arrangement should change weekly by purpose, not by student identity.
Co-teaching structures that fit:
- Station teaching for part of the block: one station with the general educator on grade-level problem solving, one with the special educator using the CRA organizer on the same problems, one independent or technology station. Every student rotates; Devon is not permanently parked.
- Parallel teaching with both teachers teaching the same content to half the class, both using the organizer so scaffolds are normalized.
- One teach, one support during the whole-group launch, with the special educator circulating and pre-teaching vocabulary and the organizer before the lesson.
Avoid alternative teaching as the default, where one group gets a different, easier curriculum for the entire block - reserve it for short, targeted, content-aligned bursts.
Roles: both teachers plan together weekly; the general educator owns content accuracy and grade-level expectations; the special educator owns access, strategy instruction, and progress monitoring; the paraprofessional supports any student in the room, not only the four. Accommodations on Devon's IEP are delivered inside the lesson rather than in a separate track, and his progress data come from the same tasks the class is doing.