The Read, Draw, Write Process

December 11, 2019

Excelling in problem solving requires students to stretch the boundaries of their understanding, using skills and concepts that they already know.  It challenges them to think and reason, assembling small understandings into a larger truth.  Although there are many ways to engage children in critical thinking, elementary school students most commonly experience it through story problems which provide authentic context to their learning.

To solve story problems students need to regularly read and analyze text, create visual representations, perform skill work, and communicate their answers.  This is abbreviated as a Read, Draw, Write (RDW) process (1):

Its effectiveness is directly proportional to the integrity with which teachers facilitate it.

Too often, teachers read problems aloud and sketch diagrams while their students passively listen and watch them draw.  They then provide the class with a different problem to work on independently.  This I do, You do approach is problematic for all math learning, but is especially damaging when building problem solving skills.

Unlike an algorithm, in which a set process can help students consistently arrive at correct answers, following a sequence of steps doesn’t lead children to become better problem solvers.  Insisting that students underline key words and numbers might help some individuals solve simple problems that teachers have handpicked for them, but it stunts the flexible thinking needed to solve more complex word problems that they can’t prepare for.  Teachers, therefore, play an integral role in making the RDW process qualitatively rich.

A few outliers aside, students only become great problem solvers when their teachers possess an academic and pedagogical RDW expertise.  Skilled instructors not only know the answers to the word problems they deliver, but also feel comfortable solving them using methods that make sense to the children they’re teaching.

Having spent hundreds of hours practicing model drawing, the teacher’s diagrams are logical and transparent to their students.  In the end, each diagram is a pictorial representation of the problem that they’ve presented, and the concepts and calculations needed to solve the problem never extend beyond the students’ mathematical understanding.  Vertical algorithms are off limits to first graders and Algebra is never used to solve third grade word problems (see examples below).

Although it’s essential to great teaching, content knowledge devoid of pedagogical expertise is useless to children. Concert pianists and professional golfers aren’t excellent (or even competent) teachers unless they can transfer their knowledge in terms that novices can understand. Likewise, a teacher can be a master problem solver, but if they’re unable to communicate their thought processes, students won’t collectively excel at solving word problems.

Expert teachers guide their students through the RDW process, prompting them with thinking/reasoning questions but never explaining.  This delivery method prepares students to become better critical thinkers, capable of solving word problems independently (see scripts below).

Deducing through questions is profoundly effective, but not intuitive.  During their apprenticeships, master math teachers often scripted out their questions, practicing what they would say, draw, and anticipated student responses.

When teachers direct students to solve word problems independently, they begin with a choral class reading to ensure everyone is on task.  They then say “Draw” and watch their children work, resisting the urge to talk their students through the problem (2).

This counterintuitive action is essential for two reasons.  First, children need to develop proactive work habits.  Becoming proficient independent problem solvers is nearly impossible if students don’t have the opportunity to regularly read, think, sketch, and solve without instructor interference.  This invariably leads to students making mistakes but in the long run, allowing productive struggle results in superior work.  Secondly, observing diagrams allows teachers insight into student thinking.  Seeing drawings – both accurate and inaccurate - helps them understand children’s thought processes and diagnose misunderstandings.

Too often, teachers see students on a wrong track and - not wanting them to get a wrong answer - immediately interfere.  Although well intentioned, this intuitive tendency is damaging to students’ long term problem solving development.  Instead of correcting children, they might ask them why they drew what they did.  Instead of telling them to underline key words, they might direct them to include a specific word in their diagram. When teachers don’t provide opportunities to craft graphic representations, they confine their students’ thinking and impede their intellectual growth.

The best math educators engage students in the RDW process daily for eight to 12 minutes, helping them become expert drawers and thinkers.  They do this through modeling but never procedural instructions.  The word problem content can vary, but it tends to be most valuable when it applies recently taught concepts, often from the previous day’s lesson.

(1) Teachers of students who can’t yet read, draw, or write are exceptions to this rule.  Instead of having their students read story problems, they deliver them orally.  Instead of directing students to draw, they have them use linker cubes as representations.  Instead of telling them to write number and word sentences, they invite students to express them orally. Back to Text.

(2) The prompt “Draw” initially leads many students to stare hypnotically at their paper or instructor, not knowing what to do.  This is because many children have become accustomed to teachers spoon-feeding them instruction, never allowing them to freely reason about problems.  But, like any habit, students adjust when they are consistently prompted to demonstrate their thinking through diagram/drawings. Back to Text.