urff.app

Dezimat

The Decimal is an interactive visualization tool to deepen and explore the understanding of decimal fractions.

App-Icon Dezimat
Christian Urff, Axel Schulz, Daniel Walter · iPad
Download from the App Store
functions

The Dezimat This is a visualization option for decimal numbers and their place values. The following visualizations are also available, which can be shown or hidden:

  • number line: Displays a number line to visualize the range of decimal numbers between 0 and 1. The number line can be moved and you can also zoom in and out of the number line using two fingers.
  • fractions: Display the display of fractions for a better understanding of the decimal place values.
  • place value tableVisualizes the place values of numbers for a better understanding of decimal numbers. This representation can also display non-canonical representations. This means that places can be filled with numbers greater than 9.
  • decimal numbers: Displays decimal numbers up to ten thousandths.

In addition to a experimental environment With synchronized displays for trying out and independent discovery, there are also some exercises and games in the practice area.

Notes on didactic embedding

The app can be used effectively after an initial introduction with paper and pens for further in-depth exploration and practice. Materials suitable for this introduction include those based on... AMSI Calculate are available in English.

Example tasks

for the experimental environment

  • Represent the number 0.2456.
  • Convert the decimal number 0.75 into a fraction. Then check if you have converted correctly by displaying the fraction representation.
  • Order the following decimal numbers according to their size and explain using the decimal point: 0.0256 0.2560 0.5602 0.2056
  • You have 7 tenths, 12 hundredths, and 2 ten-thousandths. What decimal number is that?
  • Bundle 125 ten-thousandths at the decimat to obtain the largest possible number of hundredths.
  • Use the decimal point to form the largest / smallest decimal number possible from the numbers 5, 8, 1 and 6.
  • Describe the meaning of a number in different places, for example: 0.5 with 0.05 with 0.005. What do you notice?
Subject didactic background

The representation of decimal numbers as a decimat is a learning tool to promote the understanding of decimals and their place values, and is based on the idea by Roche (2010). The visualization serves to reduce common misconceptions about decimals by visually representing the concept of „tenness“ of our decimal place-value system. For example, a study by Steinle and Stacey (2003) found that many students have difficulty understanding the magnitude of decimals such as 0.97, which subsequently leads to fundamental errors in mathematical operations based on decimals. The representation as a decimat is intended to address this comprehension problem by offering a proportionally scaled model that makes decimals illustrative.

The Dezimat can not only help students intuitively grasp the magnitude of decimals, such as „almost one“ for 0.97, but also encourages the use of fractional terminology to describe decimal numbers. The use of the tool in playful activities, such as a partner game, enables children and adolescents to gain a deeper understanding of the relationships between tenths, hundredths, thousandths, and ten-thousandths.

The app is recommended as a supplement to other visual aids to introduce basic concepts of decimal notation and decimal fractions in grades 4 to 7. The app can also be easily adapted (for example, by only considering tenths or hundredths) to be used with younger students. It is important to use the app regularly and with appropriate introduction and support as part of well-structured subject-didactic lessons. learning environments to use.

conception and development

This app was developed by Christian Urff in collaboration with Dr. Axel Schulz (University of Bielefeld) and Jun.-Prof. Dr. Daniel Walter (University of Dortmund).

Sources