Word Problem Schemata Identification
Why Is This Strategy Useful?
Recent research in special education indicates the importance of explicit instruction and practice in
problem solving with an increased emphasis on graphically representing word problems. In the
context of solving story problems, models and diagrams can be used to represent the information
in a problem and to figure out what operation is needed to solve the problem. One effective
strategy is using schemata-based word-problem-solving instruction that emphasizes conceptual
understanding. Problem schemata identification involves recognizing the problem pattern
(e.g., “change” or “group”) and the semantic structure of the problem. This strategy, with its focus
on representation, is a viable approach for teaching students with learning disabilities to solve
addition, subtraction, division, and multiplication word problems. This strategy benefits elementary,
middle, and high school students, both with learning disabilities those at risk for math failure.
Description of Strategy
Problem schemata identification training is a prerequisite to understanding and organizing
information for problem solution. In this phase, students are provided with worksheets that
include story situations with problem schemata diagrams. These diagrams are used for
instruction and student work. The teacher demonstrates the problem schemata analysis, using
several examples. Examples of story situations help students recognize and understand the key
features and relations of the problem schemata. For example, the problem analysis for the story
situation "A car travels 25 miles on 1 gallon of gas; it can travel 75 miles on 3 gallons of gas"
has students identify several key features. They include
• a constant per unit (e.g., 1 gallon of gas) or unit ratio value that is explicitly stated or
implied by the story wording;
• four quantities (i.e., 25, 1, 75, and 3), two of which were subject units and two of which
are object units;
• the association (e.g., goes) that pairs each subject-object (e.g., gallon of gas and miles)
unit; and
• an if-then relationship ("If a car on 1 gallon of gas goes 25 miles, then a car on 3 gallons
of gas goes 75 miles").
In general, the problem schemata instruction employs teacher-led demonstration and modeling,
along with frequent student exchanges, to identify critical elements of problem schemata and
map them onto the relevant schemata diagrams. Before mapping the information, students are
taught to underline sentences in story situations that indicate the unit set and relational
statement in varied and multiplicative comparison story situations, respectively. The underlining
serves as a memory aid to help students identify and retrieve the essential elements in the
problem. At the end of the training session, students can work independently.
Research Evidence
At least one quasi-experimental study supports the use of this strategy. Its purpose was to
examine the effectiveness of the schemata strategy in solving multiplication and division
problems. The participants were four middle school students with learning disabilities. They took
a series of tests that consisted of six one-step multiplication and division word problems. After
schemata-based strategy instruction that lasted 18 sessions, the participants were tested again.
The participants also took a strategy questionnaire, intended to assess their use of the
schemata strategy. The four participants’ performance on word problems substantially improved
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Study abstract reprinted in compliance with copyright laws and publisher guidelines
after they received instruction. Results of the study indicated that middle school students with
learning disabilities or students who are low performing in mathematics can be taught to
effectively apply schemata-based instruction to solve multiplication and division word problems.
Sample Studies Supporting This Strategy
Jitendra, A., DiPipi, C., & Perron-Jones, N. (2002). An exploratory study of schemabased word-problem-solving instruction for middle school students with learning
disabilities: An emphasis on conceptual and procedural understanding. Journal of
Special Education, 36, 23–37.
Available at: http://sed.sagepub.com/cgi/content/abstract/36/1/23 and
http://www.ldonline.org/article/5678
This exploratory study extends the research on schema-based strategy instruction by
investigating its effects on the mathematical problem solving of four middle school students with
learning disabilities who were low-performing in mathematics. A multiple-probe-acrossparticipants design included baseline, treatment, generalization, and maintenance. During
treatment, students received schema strategy training in problem schemata (conceptual
understanding) and problem solution (procedural understanding). Results indicated that the
schema-based strategy was effective in substantially increasing the number of correctly solved
multiplication and division word problems for all four participants. Maintenance of strategy
effects was evident for 10, 5½, and 2½ weeks following the termination of instruction for Sara,
Tony, and Percy, respectively. In addition, the effects of instruction generalized to novel word
problems for all four participants.
Sample Activity
(Source: Jitendra, DiPipi, & Perron-Jones, 2002.)
Teacher-led demonstrations and a facilitative questioning procedure allow students to identify and map
critical elements of the specific problem onto the schemata diagrams. Instruction in word problem
schemata identification leads students to represent the given information in the diagram as a
mathematical sentence prior to solving it. For example, look at this math problem.
In Mrs. Jones's class, there are 9 computers for 27 students to share. How many students will share each
computer? Using the completed vary schema diagram, the student sets up the math sentence as follows:
9 computers
------------------1 computer
27 students
=
-----------------? students
Next, students are taught to use the equivalent fraction rule (i.e., multiply or divide the top and bottom
numbers by the same nonzero number to get an equivalent fraction) to solve the problem. In some
instances, instruction has to be broken down into more steps to apply the equivalent fraction rule.
For example, following scaffolded instruction using a simple problem (6 × ? = 12), students were
questioned as follows: 9 × ? = 27; therefore, 1 × 3 = ?
Finally, instruction requires the students to reason whether the answer made sense and to check their
answers using cross multiplication.
To assist students in remembering the key features of each problem type, provide a note sheet with the
essential elements by problem type. The note sheet is used as a scaffold while the students completed
problems during practice trials, until students could independently verbalize them.
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Study abstract reprinted in compliance with copyright laws and publisher guidelines
Additional Resources
Jitendra, A. K., Hoff, K.,& Beck, M. M. (1999). Teaching middle school students with learning
disabilities to solve word problems using a schemabased approach. Remedial and Special
Education, 20, 50-64.
Teaching students math problem-solving through graphic representations.
http://www.teachingld.org/pdf/teaching_how-tos/journal_articles/Article_5.pdf
Marshall, S. P., Barthuli, K. E., Brewer, M. A.,& Rose, F. E. (1989). Story problem solver: A
schema-based system of instruction (CRMSE Tech. Rep. No. 89-01). San Diego, CA:
Center for Research in Mathematics and Science Education.
Montague, M. Math problem-solving for primary elementary students with disabilities. Available
at: http://www.k8accesscenter.org/training_resources/mathprimaryproblemsolving.asp
Xin, Y. P.,& Jitendra, A. K. (1999). The effects of instruction in solving mathematical word
problems for students with learning problems: A meta-analysis. The Journal of Special
Education, 32, 207-225.
INQUIRE summaries available at schools.nyc.gov/inquire
Study abstract reprinted in compliance with copyright laws and publisher guidelines