Using Web-Based Assignments in Secondary School Mathematics Marja-Leena Viljanen Johanna Ojalainen Matti Pauna University of Helsinki

Introduction We all work in the WebALT group and Marja- Leena Viljanen teaches mathematics at the Helsinki School of Natural Sciences We describe new material developments and its uses in upper secondary level Finally we present further study topics

Background From 2005 the WebALT group has developed interactive web-based exercises with the MapleTA system for mathematics education Now over 2000 algorithmic questions in Finnish (over 1000 in English) Classified according to the standard MathTax (Living Taxonomy)

Classification: Living Taxonomy, aka MathTax

Difficulty 1: Lower secondary 2: Upper secondary, short math 3: Upper secondary, long math 4: Upper secondary, advanced questions 5: College, technical engineering school 6: University Example: _3_Differentiation

Recent development of question design Feedback from users: – simple question – ask basic concepts – standard answering formats New version makes it easier to write stepwise questions

Find from the graph questions Easy to author and make algorithmic Help to understand concepts, perceptional approach

Essay questions For expressing mathematical thinking verbally For self evaluation Implemented as essay questions or essay parts in exercises and they cannot be graded automatically

Answers “It cannot be true. The emission decrease 100% only if all the Baltic countries decrease their emission to the Baltic Sea 100%. ” “Everything is clear.” “It cannot be true. The emission decrease 100% only if all the Baltic countries decrease their emission to the Baltic Sea 100%. ” “Everything is clear.” “It cannot be true because every country decreases from its own emission. For instance Finland would decrease 15% of its own emission, not of the emission of the whole world. ” “I learned to work out better normal problems with percents. The coefficients I did not understand very well.” “It cannot be true because every country decreases from its own emission. For instance Finland would decrease 15% of its own emission, not of the emission of the whole world. ” “I learned to work out better normal problems with percents. The coefficients I did not understand very well.” “If the emissions would decrease 100%, there should not be any emission left.” “I learned some old concepts. Equations I did not get clear.” “If the emissions would decrease 100%, there should not be any emission left.” “I learned some old concepts. Equations I did not get clear.”

Practices of using assignments Students of short math have weekly revision sessions in computer lab Students of long math are introduced to the system a couple of times and they have possibility to use at home Adult high school: self study students practice until they have 80 % right before going to course examinations

Nursing schools Teachers see drilling to be important for drug calculations It is challenging to include in normal teaching

Research plans School has applied to get mini laptops for a group students for using at school and at home Further study of languaging How the results of WebALT tests correlate with final matriculation exam grade

How to make assignments more interesting: stories

Research: Johanna Ojalainen Lower secondary arithmetic. Blue group n = 15 practiced weekly with online exercises. Red group n = 19 did not. Johanna is continuing these studies. Lower secondary arithmetic. Blue group n = 15 practiced weekly with online exercises. Red group n = 19 did not. Johanna is continuing these studies.

Research: Kari Lehtonen Diagnostic tests and practicing in technical engineering school. Results in the test before and after practicing. Purple (four groups) n = 80, not using online assignments. Blue group n = 40, using online assignments. Diagnostic tests and practicing in technical engineering school. Results in the test before and after practicing. Purple (four groups) n = 80, not using online assignments. Blue group n = 40, using online assignments.