Explicit Teaching for Transfer in Problem Solving
Category: Mathematics
Grade level: Grades 3-6
1. What is the purpose of Explicit Teaching
for Transfer?
Transfer is the ability to apply previously
learned knowledge to newly encountered
problems. The purpose of explicit teaching for
transfer is to improve awareness of the
relationships between new and familiar
mathematical problems by expanding the
categories students use to group problems with
similar methods of solution (increasing abstract
understanding of a problem) and by
encouraging students to search for these
categories when they encounter new problems
(promoting metacognitive abilities).
2. With whom can it be used?
This technique is intended for primary-grade
students. Research has shown than young
children have trouble transferring skills to new
problems that differ slightly from familiar
problems (Larkin, 1989). However, in theory,
this technique can be used with students at all
levels in order to enhance their understanding
of how to apply a solution from a previously
encountered problem to unfamiliar problems
with the same underlying problem structure.
3. What is the format of this technique?
This approach is an instructional technique that
can be implemented by teachers to complement
the school’s mathematics curriculum.
4. What are the steps involved in Explicit
Teaching for Transfer?
Before teaching for transfer can occur, students
must first learn the basic skills for solving a
problem within a certain category. Categories
are based on the problem’s underlying problem
structure. Two problems belong to the same
category when they contain similar underlying
problem structures which require the same
solution approach. For example, if two
problems both require the use of addition in
order to solve them, the two problems can be
said to contain similar underlying problem
structures. While the two problems can appear
different on the surface, the differing superficial
features do not change the problem’s underlying
structure, or category (Ross, 1989). Once a
student has acquired the basic skills for solving a
problem in a particular category, three steps can
be taken to explicitly teach the student how to
apply those skills to new problems in the same
category. These steps include:
I. Teaching the concept of transfer and how
it is useful: Students are taught that the word
“transfer” means “to move”. Concrete
examples such as “Just like we transfer
[move] to a different school, we can transfer
[move] skills we learn to new situations”
(Fuchs et al., 2002; Fuchs et al., 2003).
Specific examples of how one transfers skills
in everyday life are presented. For example,
“We learn to add working two-digit
horizontal problems, then move this skill to
solve two-digit vertical problems, then move
this skill to solve three-digit problems, then
move this skill to the check-out counter of
the market where we add the cost of two
items to figure how much money we need”
(Fuchs et al., 2002; Fuchs et al., 2003).
Students are explicitly made aware of the
need for transfer in various situations.
Teachers can also encourage students to
present their own examples of transfer.
II. Teaching types of superficial features
that can change a problem without
altering its underlying structure or
solution: Students are taught that a familiar
problem can be made to look unfamiliar by
changing a problem’s superficial features.
This can include changing the familiar
problem’s format or key words, adding
questions to the familiar problem, or
placing the familiar problem within a
larger problem-solving context (see Figure
1 for examples of these changes). A poster
illustrating the ways in which problems can
change can be used to facilitate teaching.
Students should be given a familiar
problem along with variations of the
familiar problem which contain superficial
feature changes. Students are asked to
identify which superficial feature changes
are in each new problem and should
explain how each new problem appears
different, yet maintains the same
underlying structure as the familiar
problem. Students should be asked to apply
a solution method learned for a familiar
problem to the same problems with
differing superficial features. Students are
grouped into smaller groups or pairs when
practicing how to apply familiar solutions
to superficially changed problems. Practice
can begin with partially worked examples
and students should check their work using
answer keys. Stronger students can be
paired with weaker students in order to
facilitate learning. Eventually, students
should be encouraged to work on problems
independently.
III. Encouraging the search for familiar
problem structures in unfamiliarlooking problems: Teachers should
encourage students to search for
superficial changes in unfamiliar problems
in order to recognize familiar problem
structures and apply previously learned
solutions.
5. In what types of settings is Explicit
Teaching for Transfer useful?
Research has shown that explicit teaching for
transfer can be effective when conducted by
teachers with large groups in classroom
settings.
6. To what extent has research shown Explicit
Teaching for Transfer to be useful?
The effectiveness of this technique has been
demonstrated with third-grade students,
including some with learning disabilities (Fuchs
et al., 2003). Explicit teaching for transfer
improved the ability of these students to solve
both near-transfer problems (problems that differ
from the original problem in terms of cover
stories and one superficial feature) and fartransfer problems (problems embedded in a reallife problem-solving context that differ from the
original problem in terms of four superficial
features, as well as the addition of irrelevant
information) when compared to control groups.
The effects of explicit teaching for transfer are
enhanced when children are given longer initial
instructional sessions in rules for problem
solution. Similar findings have been suggested
with fourth-grade students (Fuchs et al., 2002).
More research with other age groups is required.
References
1. Cooper, G., & Sweller, J. (1987). Effects of
schema acquisition and rule automation on
mathematical problem-solving transfer. Journal
of Educational Psychology, 79, 347-362.
2. Fuchs, L.S., Fuchs, D., Hamlett, C.L., &
Appleton, A.C. (2002). Explicitly teaching for
transfer: Effects on mathematical problemsolving performance of students with
mathematics disabilities. Learning Disabilities
Research and Practice, 17, 90-106.
3. Fuchs, L.S., Fuchs, D., Prentice, K., Burch,
M., Hamlett, C.L., Owen, R., Hosp, M., &
Jancek, D. (2003). Explicitly Teaching for
Transfer: Effects on Third-Grade Students’
Mathematical Problem Solving. Journal of
Educational Psychology, 95(2), 293-305.
4. Larkin, J.H. (1989). What kind of knowledge
transfers? In L.B. Renick (Ed.), Knowing,
learning, and instruction (pp. 283-305).
Hillsdale, NJ: Erlbaum.
5. Ross, B.H. (1989). Distinguishing types of
superficial similarities: Different effects on the
access and use of earlier problems. Journal of
Experimental Psychology: Learning, Memory,
and Cognition, 15, 456-468.
6. Salomon, G., & Perkins, D.N. (1989). Rocky
roads to transfer: Rethinking mechanisms of a
neglected phenomenon. Educational
Psychologist, 24, 113-142.
Reviewed by: Carly Guberman
Figure 1.
EXAMPLES OF SUPERFICIAL PROBLEM FEATURE CHANGES MADE
TO AN ORIGINAL PROBLEM (Fuchs et al., 2002; Fuchs et al., 2003)
Original Problem
You want to buy some lemon drops. Lemon drops come in bags with 10 lemon drops in each bag. How
many bags should you buy to get 32 lemon drops?
1) Superficial Feature Change: Different Format
 You want to buy some lemon drops.
 The sign at the store looked like this:
How many bags should you buy to get 32 lemon drops?
○
○
○
○
3
4
2
5
2) Superficial Feature Change: Different Key Word
You want to buy some lemon drops. Lemon drops come in packages with 10 lemon drops in each
package. How many packages should you buy to get 32 lemon drops?
3) Superficial Feature Change: Additional Questions
You want to buy some lemon drops. Lemon drops come in bags with 10 lemon drops in each bag. How
many bags should you buy to get 32 lemon drops? If each bag costs $4, how much money will you
spend?
4) Superficial Feature Change: Placing Familiar Problem Within Larger
Problem-Solving Context
You saved $37. Your friend saved $12. You and your friend want to buy some lemon drops. Lemon
drops come in bags with 10 lemon drops in each bag. You want 32 lemon drops.
1. How much money do you and your friend have?
2. If each bag of lemon drops costs $4, how much money will you spend on lemon drops?
3. If you also buy a hat that costs $15, how much money will you have left?