One reason schools have been slow to apply a response-to-intervention (RTI) approach to math is because so far there’s little research identifying effective secondary prevention programs for children who do not respond well to primary instruction.

A recent study in *Exceptional Children* reports that a 15-hour preventative tutoring program researchers tested with low-achieving 3rd graders provides an effective secondary prevention program in an RTI model. The tutoring program trains students to recognize 3 types of math problems and teaches them to solve those three types of problems (total, difference or change problems); it also introduces algebraic equations to support math problem solving.

“Results show that this schema-broadening protocol, when used as a secondary preventative tutoring program and when implemented with fidelity, should be effective in improving word problem performance,” the researchers write.

In this small study (35 students), low-achieving 3rd-graders in both reading and math were randomly assigned to continue their general education math program or to receive secondary preventative tutoring 3 times per week for 30-minute sessions for 12 weeks. The authors said they screened a large number of students to identify a subset with documented math and reading difficulties but kept the study small so that statistically significant results would indicate large effect sizes.

Students in the tutoring program spent 2 weeks learning foundational skills for successful problem solving. Next were 3 three-week units covering each of the 3 problem types and then a final week review unit.

### Classifying word problems

Total problems combine two or more quantities. Difference problems compare a bigger and smaller quantity to find the difference. Change problems involve increasing or decreasing a starting quantity to end up with a new quantity. (Example: Tom baked 48 cookies. Then, he gave 23 of them to his friends. How many cookies does he still have?)

For the first activity in the regular 30 minute-sessions, students were shown flash cards on addition and subtraction for 2 minutes and responded to as many cards as possible. The child’s responses were sorted into 2 stacks of cards–correct and incorrect answers. The student counted and graphed the number of correct responses in addition and subtraction. The tutor gave corrective feedback on up to 5 errors.

For the second activity, which lasted 12-17 minutes, students were coached in the RUN strategy, namely to “run through” the problem by first reading it, then underlining the question, and finally naming the problem type. Students received a schema-broadening instruction lesson and were taught to recognize the underlying mathematical structure. Then they were shown how to label the numbers in the problem to make it easier for them to solve it. For example, in difference problems, they were taught to find the bigger number and label it B, to find the smaller number and label it S and find the difference and label that number D.

Throughout the sessions, students were taught to transfer in 4 ways:

- to look for irrelevant information and cross it out;
- to look for missing information and address it using solution strategies they learned;
- to set up problems involving addition and subtraction using algebraic equations
- to translate those problems to vertical formats for solution; and
- to be aware of and to use charts, graphs, and pictures.

Another activity in the sessions was to sort word problems. Students were presented with an assortment of problems representing the three problem types on flash cards. The problems used the same characters but varied actions and numbers. For two minutes, the tutor read problems and the student responded by identifying whether the problem belonged to the total, difference or change problem types. The student counted and graphed the number of correct responses and provided corrective feedback on up to five errors. During all activities, students earned tokens for correct responses which they could trade in weekly for prizes. All sessions were scripted to ensure consistency of information. However, to allow for natural teaching styles tutors studied rather than read the scripts.

The researchers measured performance with the following tests:

- Addition Fact Fluency
- Double-Digit Addition Test
- Algebraic Equations
- WRAT-Reading
- Story Problems
- Peabody Word Problem Test
- KeyMath-Revised Problem Solving
- Test of Basic Skills: Problem Solving and Data Interpretation

Students in the 15-hour program improved significantly more than comparable peers who remained in the general education program. There were significant effects on measures of word problem skills, the researchers report.

“The possibility that schema-broadening instruction may be useful for students with substantial math and reading deficits is notable given that students with learning disabilities, who typically have similarly low reading and math skills, are at particular risk for difficulty with word problems,” they conclude. The largest effects were seen on the Peabody Word Problems test and on Story Problems (Jordan & Hanich), which tested students for performance on novel problems.

Effect size on performance on the Iowa Test of Basic Skills subtest was disappointingly low although it meets the criterion for efficacy used in the What Works Clearinghouse, the researchers write.

“It is disappointingly low given that some version of the Iowa test is used in many high-stakes state assessment programs (and is similar to some other widely used state assessments),” they note.

The tutoring program also had a moderate effect on students’ skill with algebraic equations, which was a major strategy used to teach word problem skills.

“Given the strong focus on algebra in high schools and the requirement in many states that students pass an algebra course or an algebra test prior to graduation, introducing algebra this early in the curriculum may represent an important and productive innovation.”

*“Effects of Preventative Tutoring on the Mathematical Problem Solving of **Third-Grade Students With Math and Reading Difficulties,” by Lynn Fuchs, Pamela **Seethaler, et. al, Exceptional Children, Volume 72, Number 2, pp. 155-173.*