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

Problem solution window of T-algebra

Quick demonstration of T-algebra

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

The problems (with maximum points) of one variant

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

Post-test

• Using paper and pencil

• Arrangement of the post-test was the same as in pre-test

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

How does an interactive learning environment affect

the students’ learning?

Questions, Comments...