1. Effectiveness of Teaching and Learning in Technology-Supported Math Education - the Approach to Assessment of Students' Achievements Anna Rybak University of Białystok, Poland Institute of Computer Science

2. Student’s activities during technology-supported math lesson activities related to computing (technological activities), activities related to mathematical problem solving (mathematical activities), activities related to planning and undertaking - with using proper software - actions that lead to solution to various mathematical problems in creative way.

3. Research project "Assessment of students' achievements in technology- supported math education in secondary school" I decided to start with such research because: Using computers becomes more and more popular, students like lessons with using technology. Computers (with proper educational software) should become – and in many cases becomes - a didactical tool not only for individual work, but also for a common work in a classroom. All students – working in normal school circumstances - should profit from using computers in their learning, so research on results of using this tool in the whole math education, with all obstacles that school reality brings, should be done. During technology-supported math lesson students have opportunity to develop some special abilities, so the ways of assessment should take into consideration this change in students’ achievements.

4. Research project "Assessment of students' achievements in technology- supported math education in secondary school" Obstacles Small number of math lessons per week, Not easy access to computer laboratory, Teachers’ abilities to use technology in their work with students, There is a paradox in Polish educational reality: there is written in the national curriculum that “Teachers have to create for students suitable conditions for developing the following abilities: - applying their knowledge in practice, - solving problems in a creative way, - finding, selecting and using information from different sources, - using technology effectively”, but using all technological tools is forbidden during the exams (except of the simplest calculator during the exam after secondary school).

5. Research project "Assessment of students' achievements in technology- supported math education in secondary school" Aims introducing the elements of assessment of students’ work on the computers to technology-supported math education, introducing the elements of alternative assessment to the whole process of assessment of students’ achievements, making research on the influence that using technology and assessing students’ work on computers have on some aspects of effectiveness of teaching and learning process, recognition students’ and teachers’ opinions about new way of assessing in math education.

6. Research project "Assessment of students' achievements in technology- supported math education in secondary school" For many years effectiveness of educational performance in school was interpreted as improving results of teaching and learning, but now it has new meaning and is interpreted as the desired changes in students’ knowledge, skills, interests and attitudes that take place under the influence of the educational process. These changes indicate the progress in student’s development.

7. Research project "Assessment of students' achievements in technology- supported math education in secondary school" From among problems that are included into the idea of “effectiveness of educational process” I chose the following to investigation: taking up by students active and creative position in technology-supported learning, the range of students’ own work on problem solving with the use of technology (work at home and everywhere outside classroom is included), taking up by students position of responsibility for the results of their learning and development: their own planning and consistent accomplishment of their educational objectives, formation (structuring) knowledge by students based on the results of their work with computers. 

8. Research project "Assessment of students' achievements in technology- supported math education in secondary school" Research problems What kind of influence has introducing the alternative assessment into technology-supported math education on effectiveness of math teaching and learning? - the main problem 1. What is the influence of introducing assessing abilities to use technology in learning on students’ creative activity? 2. Does introducing assessing abilities to use technology in learning cause changes in students’ attitude toward their learning? 3. How does the constructing knowledge by students in technology-supported math education progress?

9. Research project "Assessment of students' achievements in technology- supported math education in secondary school" Research methods, techniques and tools I chose an action research and an exploratory probing as the methods of investigation. I chose a questionnaire and document analysis as research techniques. As investigation tools I created questionnaires for teachers or students and a number of special form of homework after the lessons in which computers were used. Also all students’ documents – in paper or electronic form - created during the lessons or outside classroom are collected in portfolios and used as documents for analysis.

10. Research project "Assessment of students' achievements in technology- supported math education in secondary school" Investigation started in two classes (totally 56 students) in second grade of secondary economical school in Białystok. There are two math lessons per week in each class, mathematics is taught on basic level. Students from selected classes did not work with computers on math lessons before the beginning of the project. Software: Polish version of program Graphic Calculus (authors: Piet van Blokland and Carel van de Giessen from Vusoft, Netherlands). During all school year it was possible to have THREE technology-supported math lessons in computer lab with each class.

11. Research project "Assessment of students' achievements in technology- supported math education in secondary school" First lesson: Graphs of polynomial functions Homework: Answer the following questions: 1. What was the lesson about? 2. What were you doing during the lesson? Describe your activities. 3. Was using computer during this lesson useful? Justify your answer. 4. What was good about the lesson? 5. What was bad about the lesson? Draft the graphs of following functions: 1. f(x) = -2x(x-3) 3 (x-5) 2, 2. f(x) = 4(x+5)(x+4)(x+3)(x+2)(x+1)

12. Graphs of polynomial functions What was good about the lesson? A graph has been made immediately after typing a formula. Cooperation Easy examples New experiences Learning computing It was possible to understand the topic faster and easier Mathematics with computers is more interesting Lesson was quite different from typical math lessons Fast pace and precision of work It was like a play We were mobilized to conclude from graphs It was possible to compare a few graphs in the same coordinates system Computer did work for us

13. Graphs of polynomial functions What was bad about the lesson? I could not learn too much because computer did all work for me. It was necessary to commit myself very much. Not enough number of computers in the lab. It was difficult to determine properties of function. It was difficult to conclude from graphs. We had to conclude from graphs by ourselves. Lack of skills in making conclusions. Computer did all work for us (we had only to type formulas).

14. Graphs of polynomial functions Some conclusions from homework: Many students wrote: “It was possible to understand the topic faster and easier”. In the same time about 80% students did not solve exercises (did not draft two graphs) correctly. Conclusion is: students’ knowledge after the lesson was very weak; they learnt almost nothing about the connection between zeros and graph of polynomial. The short-term effectiveness of this lesson was very low. Many students wrote: “Computer did all work for us”, and assessed this as the wrong part of the lesson. Conclusion is: Students consider math activities only as manual actions, like drawing graphs. Also they wrote: “We had to conclude from graphs by ourselves” and, mostly, assessed this as the wrong part of the lesson. Conclusion is: Students are not used to put hypotheses and make conclusions. They are not used to construct knowledge. They are a little bit lost when computer does all “manual work” and leaves them thinking. Some students copied their homework from each other.

15. Research project "Assessment of students' achievements in technology- supported math education in secondary school" Second lesson: Graphs and properties of functions y = sin x and y = cos x Some conclusions from homework: Only one student wrote that using computer on this lesson was not useful, many other students noticed two good things: possibility of observation the process of rising graphs and possibility of work with radians and degrees. Conclusion is: students want to understand the processes, not only the results. Two students wrote: “Computer did all work for me, it was bad in the lesson”. Conclusion: Still some students do not count thinking, reading from the graph, concluding, discussing etc. as the mathematical activities. All students made exercises, although some of them made mistakes. Conclusion: the effectiveness of the lesson was better than in case of first lesson with computer.

16. Research project "Assessment of students' achievements in technology- supported math education in secondary school" Third lesson: Transformations of graphs of trigonometric functions Procedure of the lesson: Students were working in pairs with program Graphic Calculus, option Draw Graphs. They had to create the proper graphs and fill in the given table. After work with computers students formulated the conclusion about the connection between the kind of transformation (the direction and distance of translation) of graph and the formula of obtained function. Conclusions from homework:  Students are used to work with the program. They do not complain that concluding is hard, but are happy that computer allows comparing graphs and helps – by visualization - to remember the mathematical rules.  Students solve exercises (sometimes with mistakes) by themselves.

17. Assessment During all lessons students had opportunity to be given good mark for active participation in the lesson. Homework was not assessed in marks. After third lesson eager students had opportunity to take additional tasks (related to the topics) for their own work - for good mark. Only 14 students from one class and nobody from the other class decided to do this additional work. All home works, sheets with tables completed during the lessons and additional works became a parts of students’ portfolios.

18. Questionnaires  Question: What results of using computers in math education do you observe in yourself? – Students could choose and mark items from the list. Item from the listNumber of students Percent of choices Bigger motivation for learning 13 34,2 Bigger activity 12 31,6 Easier understanding the topic 30 78,9 Bigger abilities to problem solving 24 63,2 Easier concluding, structuring knowledge 19 50,0 Better results of class tests 9 23,7 Other

19. Questionnaires  Question: Is it necessary to keep the results of students work with computers in any form (notes, printouts, files on hard disk)? Answers: Yes - 28 students, 73,7% No - 7 students, 18,4% No answer - 3 students, 7,9%  Question: Should students' work on computers during math lessons be assessed? Answers: Yes - 21 students, 55,3% No - 14 students, 36,8% No answer - 3 students, 7,9%

20. Conclusions Students accepted computer and software not only as a tool that can increase attractiveness of lesson, but also as a tool for learning. Progress in using computer for change of style of work during math lesson (from drawing graphs in exercise book to concluding and structuring knowledge) was visible and quite fast. Many students understand that the results of their work with computer should be saved somewhere in some form; they accepted the portfolio idea. About 50% of students agree that the results of their work with computer should be assessed in school mark and this mark should influence the final grade. But, in the same time, the opportunity to receive good mark used only several students.

21. Conclusions Some students noticed better results of their class tests after lessons with computer. Maybe it is result of better understanding topics or possibility of solving more exercises instead of drawing graphs by hand. That indicates in some way the change in effectiveness of learning in new circumstances. Connection between using computers in math education and results of class tests and exams will be investigated in the next stages of research. It is hard task; special tools should be constructed. Math teachers from selected classes’ notices that shy students became more self-confident after introducing computers into learning process. Possibility of work at home with computer on homework assignments and possibility of good, creative preparing homework was very encouraging for students, especially if students’ skill for computing were better that for math. One more result of introducing technology into math education appeared: cooperation between students and ICT teacher and cooperation between math teachers and other subjects’ teachers (statistics, economics, ICT). We did not expect this result and now we are very pleased.

22. Thank you for the attention