Math Games with Elfe and Mathis

For students, math is one of the moste controversial subjects: Some children easily grasp mathematical concepts, whereas others struggle and lose their motivation during elementary school. Until the age of 12, a negative and stable academic self concept in math is shaped and they gain the impression, nothing can improve their abilities.

In Germany, there are numerous diagnostic tests to identify math problems or dyscalculia in grade 1 to 5 and above, e. g. the tests of the DEMAT series, HRT 1-4, TeDDy-PC and RZD 2-6. To identify problems is only the first step, though. The diagnostic information should lead into appropriate educational and therapeutic activities.The math games try to go one step ahead: Results from standardized tests can be imported and the programm adjusts the level of difficulty to the according profile information. Moreover, the trainer is able to do a fine tuning. The content and scope of the programms are adapted to the German national educational standards. Moreover it includes well balanced motivational elements and a systematic reinforcement of success in order to prevent or to reduce motivational problems in students. The games within the trainings are embedded into a fairy tale adventure land. The background story as well as the reinforcement elements within the uer interface are faded out during the work, though, in order to reduce cognitive load.

There are two versions of the math games:


Rechenspiele I: Math Games for students from grade one to three

by Wolfgang Lenhard & Alexandra Lenhard

The first part of Rechenspiele mit Elfe und Mathis I aim at basic skills and focus on preliminary abilities like estimation of magnitudes and numerical skills. It contains 17 different games in the domains Magnitudes (4 games), Numbers (4 games), Word Problems (3 games), Pictures (i. e. mental roation; 2 games) and Arithemtics (4 games). The item pool contains 14.516 different items.

Rechenspiele II: Math Games for students from grade three to five

by Wolfgang Lenhard, Alexandra Lenhard & Klaus Lingel

The second part (Rechenspiele mit Elfe und Mathis II) deals with mathematical at the end of the elemtary school (grade 3, 4 and 5). The training consists of 15 different games from the domains Geometry (4 games), Arithmetics (7 games) and Word Problems (3 games). The item pool contains 9.161 items in total.


From April 2009 to July 2010, 385 children from grade one to four took part in the evaluation. Whereas the controll group participated in normal regular math instruction, the experimental group received one hour per week instead of math instruction over a time period of 10 weeks. The time, that was invested on math was kept constant in both groups. Prior and post the training, the mathematical competencies were assessed via standardized tests. The children from the experimental group developed significantly faster in all grades with effect sizes from d = .15 to .39. The math games helped to deepen and broaden the mathematical skills. Therefore this training is an ideal enhancement for the regular instruction in elementary schools. It supports the teacher in the mediation of mathematical concepts and motivates the children.

Results of the evaluation of Math Games with Elfe and Mathis (Rechenspiele mit Elfe und Mathis)