How does an interactive learning environment affect the students’ learning? Marina Issakova...
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Transcript of How does an interactive learning environment affect the students’ learning? Marina Issakova...
How does an interactive learning environment affect the
students’ learning?
Marina Issakova
University of Tartu, Institute of Computer Science
Estonia
Outline
• Description of T-algebra interactive learning environment
• Description of experiment
• Results of experiment
• Conclusions
Introduction to T-algebra
• T-algebra is an interactive learning environment, enabling step-by-step (and line-by-line) problem solving in four areas– calculation of the values of numerical
expressions– operations with fractions– solving of linear equations, inequalities and
equation systems– simplification of polynomials
Design principle of T-algebra
• All the necessary decisions and calculations at each solution step should be made by the student
• The program should be able to understand the mistakes and offer feedback
Main properties of T-algebra
• Monitors, whether the student works according to the algorithm
• Supports it with the respective dialogue
• Diagnoses transformation errors
• Offers advice
Step dialogue in T-algebra• Each solution step in T-algebra consists of
three stages– selection of the transformation rule– marking the parts of expression– entering the result of the operation
Error diagnosis in T-algebra• In case of an error
– T-algebra immediately informs about the mistake– the student has to correct the error in order to proceed to
the next stage
• Possibility to make mistakes at all three stages of the step– Choosing the rule– Marking the parts of expression– Entering the result of the operation
• If a mistake can be made, then T-algebra can respond to it as well
Experiment to clarify how T-algebra affects the learning results
• In Estonia in the winter of 2007• 7 classes (126 students) of 7th grade
(13 years old) from 4 schools– 5 experimental classes– 2 control classes
• Linear equation theme– Right after the topic was explained and
practiced in the schools
Description of experiment
• Four 45-minute sessions1. Pre-test on paper
2. Practice of solving similar problems (linear equations)• Experimental classes – with T-algebra• Control classes – using paper and pencil
3. Practice in the same way
4. Post-test on paper
Pre-test• Using paper and pencil• The students could not use any
assistance materials• Test in two variants composed by one
of mathematics teachers• The other teacher advised assigning
points to each problem• 17 problems (6 types of problems) • 39 points in total
Rating scale
• 5: > 35 points (90% - 100 %)• 4: > 27 points and <= 35 points (70% - 90 %)• 3: > 19 points and <= 27 points (50% - 70%)• 2: > 11 points and <= 19 points (30% - 50%)• 1: <= 11 points (0% - 30%)
Practice – experimental group
• Using T-algebra in computer class
• The next mathematics lesson
• Linear equations were not taught in the ordinary class between pre- and post-tests
• The students had seen and tried T-algebra before in learning other topics
• Problem file contained 40 problems
Practice – control group• Using paper and pencil• Exactly the same problems• The students solved the problems in their
notebook– The teacher did not correct solutions in the
notebooks
• Somebody wrote solution to the blackboard– The teacher showed and corrected mistakes
in the solutions on the blackboard
Results of experiment
• All done – 115 students
• Result of pre-test > 11 points (supplementary learning, should have basis) – 106 students– 76 – experimental students– 30 – control students
Average number of points
Experimental Control
Pre-test 29.4 29.3
Post-test 31.3 29.9
• The groups can be considered as equal in pre-test– The difference is not statistically significant
(unpaired t-test t = 0.0368, p = 0.97)
Statistical analysis of results
• The knowledge of students from experimental group is statistically significantly improved (paired t-test t = 3.571 p < 0.01)
• No statistically significant difference (improvement) can be found in the points earned by the control group (paired t-test t = 1.2024 p > 0.05)
• Even short use (2 lessons) of T-algebra affects the results of learning
More resultsTest Correct
answerWrong answer
Half solution
Blank
Experimental pre-test
59.7% 32.3% 5.3% 2.7%
Controlpre-test
60.1% 35.6% 3.8% 0.5%
Experimental post-test
68.5% 27.7% 2.7% 1.1%
Controlpost-test
65.0% 28.8% 5.2% 1.0%
Division of students (from experimental group) between scores in pre- and post-tests
Students with scores 5
Students with scores 4
Students with scores 3
Students with scores 2
Pre-test 25% 38% 24% 13%
Post-test 39.5% 38% 14.5% 8%
Imitation of writing style of T-algebra
• In Estonian textbooks,using paper and pencil(2 rows)
• In T-algebra,one student in post-test(pre-test blank)(3 rows)
65
15|5
2
3
3|5|
x
x
655
2
3
15|5
2
33|5|
x
x
x
Mistakes in sign of second termNature of mistake
Example of mistake Experimental group
Control group
Minus sign before fraction is taken into account only at first term
52% 82%
In opening parentheses minus sign before parentheses is taken into account only at first term
47% 85%
5 3 14 2 3 4| 15
3 5 1520 6 9 4
y y
y y
yy
yy
23269
23)13(29
Mistakes in sign
Nature of mistake
Example of mistake Experimental group
Control group
Mistake in sign in dividing
31% 33%
Sign is not changed during moving to other side
50% 50%
2
)4(|:84
y
y
615458
641558
uuu
uuu
Mistake in treatment of objects
Nature of mistake
Example of mistake Experimental group
Control group
Whole number is not multiplied
18% 43%
732
10|10
73
5
1|2|
x
x
Mistakes in algorithm
Nature of mistake Experimental group
Control group
In problem Reverse sides all variable terms are moved to the left side and all constant terms to the right side
24% 43%
In problem Check if number is a solution the equation is solved
48% 33%
Arithmetic mistakes
Nature of mistake
Example of mistake Experimental group
Control group
Arithmetic mistake in combining and in evaluating
45% 67%
Arithmetic mistake in dividing
53% 50%
242
12297
s
ss
4.0
)3.0(|:2.13.0
y
y
Conclusions
• The students from the experimental group did better than the students from the control group
• Even short use (2 lessons) of T-algebra affects the results of learning
Conclusions (2)
• T-algebra affects some error types– the students from experimental group
made fewer mistakes of certain types (like mistakes in sign of second term)
• Strange results for some error types (arithmetic mistakes)
• Explanation and confirmation from the long-term experiment