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 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 sessions 1.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% %) 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 ExperimentalControl Pre-test Post-test The groups can be considered as equal in pre-test –The difference is not statistically significant (unpaired t-test t = , p = 0.97)

Statistical analysis of results The knowledge of students from experimental group is statistically significantly improved (paired t-test t = p < 0.01) No statistically significant difference (improvement) can be found in the points earned by the control group (paired t-test t = p > 0.05) Even short use (2 lessons) of T-algebra affects the results of learning

More results TestCorrect answer Wrong answer Half solution Blank Experimental pre-test 59.7%32.3%5.3%2.7% Control pre-test 60.1%35.6%3.8%0.5% Experimental post-test 68.5%27.7%2.7%1.1% Control post-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-test25%38%24%13% Post-test39.5%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)

Mistakes in sign of second term Nature of mistake Example of mistakeExperimental 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%

Mistakes in sign Nature of mistake Example of mistakeExperimental group Control group Mistake in sign in dividing 31%33% Sign is not changed during moving to other side 50%

Mistake in treatment of objects Nature of mistake Example of mistakeExperimental group Control group Whole number is not multiplied 18%43%

Mistakes in algorithm Nature of mistakeExperimental 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 mistakeExperimental group Control group Arithmetic mistake in combining and in evaluating 45%67% Arithmetic mistake in dividing 53%50%

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

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