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Table 4.3
Worksheet on uncovering alternative conceptions
Worksheet—uncovering alternative conceptions
High school students were asked to solve the same problem you just solved Write an
algorithm that returns true if all array A items are identical and false if they are not
identical
1. In what follows, six students' solutions are presented. For each solution
Determine whether it is correct or incorrect
If it is incorrect
Describe the mistake
Hypothesize the source of the mistake and write it down
Suggest how you would help a student understand the mistake
2. Present additional incorrect solutions based on a misconception you assume that
novice learners may have
Solution 1
Solution 2
are-equals (A, N)
are-equals (A, N)
ok ← true
ok ← true
for i from 1 to N do
for i from 1 to N-1 do
if (A[i]≠ A [i + 1]) then
if (A[i]≠ A[i + 1]) then
ok ← false
ok ← false
return ok
Else
ok ← true
return ok
Solution 3
Solution 4
are-equals (A, N)
are-equals (A, N)
ok ← true
ok ← true
for i from 1 to N-1 by 2 do
for i from 1 to N-1 by 2 do
if (A[i]≠ A[i + 1]) then
if (A[i]≠ A[i + 1]) then
ok ← false
ok ← false
return ok
for i from 2 to N-1 by 2 do
if (A[i]≠ A[i + 1]) then
ok ← false
return ok
Solution 5
Solution 6
are-equals (A, N)
are-equals (A, N)
ok ← true
count ← 0
for i from 1 to N-1 do
for i from 2 to n do
if (A[i]≠ A[i + 1]) then
if (A[i] = A[i + 1]) then
ok ← false
count ← count + 1
return ok
if (count = N) then
return true
Else
return false
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