Welcome to the

Online Course

This online course provides information on early mathematics learning and presents the MADITA app. The MADITA app was developed as part of the Erasmus+ project MADITA through a collaboration between the University of Cologne, University of Cyprus, and Örebro University, led by Prof. Dr. Maike Schindler (Cologne). The materials are intended for teachers, school psychologists, headmasters and school managements working in primary education.

Goals of the Online Course

This course focuses on early mathematical learning, with a strong emphasis on the early mathematical skills assessed and supported by the MADITA app. So it is closely aligned with the MADITA app’s content, providing a solid understanding of early mathematical development and effective ways to foster these skills.

In addition, the course offers insights into the benefits and practical use of the MADITA app. You will learn how the MADITA app can be integrated into educational settings, what diagnostic information it offers, and how it supports the individualized development of early mathematical competencies.

Early Mathematical Learning

Before children enter primary school, they have individual learning and educational experiences. They gain these experiences during early childhood education in the family and through informal, exploratory and playful forms of learning in the pre-school sector (MSB NRW, 2021).
Mathematics education in primary school builds on the children’s early mathematical experiences, deepening and expanding them. Children can successfully acquire subject-specific competencies in primary school mathematics education if they have acquired basic prerequisite skills. These prerequisite skills relate, for example, to perceiving differences or similarities, classifying, sorting, recognizing patterns, simultaneous grasping numbers up to 4, determining unstructured quantities by counting, comparing quantities (more, less, equal), quantity invariance, one-to-one correspondence, saying the number word series to 10 forward, and understanding the direction concept of counting backwards (e.g., Desoete et al., 2009; MSB NRW, 2021; NCTM, 2000). If children bring these prerequisite skills with them only partially or inadequately when they enter school, they must first build them up to ensure further successful learning (MSB NRW, 2021).
Over the course of primary school, basic mathematical content, tasks and forms of presentation are repeatedly addressed at different levels and thus continuously enriched, differentiated and interlinked.
Mathematics education at primary level follows a pedagogical understanding of mathematical achievement that combines performance requirements of the school with individual support for students. In this context, it is the teachers‘ task to provide individual support to all students based on the identified learning level and thus create the conditions for successful further learning (MSB NRW, 2021). This is where the MADITA app comes in…

MADITA App

With the help of the MADITA app, individual learning levels of the children can be assessed, and personalized feedback and support are provided. The MADITA app focuses on basic prerequisite skills and children’s understanding of numbers. Specifically, it covers the following content areas: Sorting, Patterns, Numbers, Comparison, and Operations. To explore these topics in greater depth, individual learning units were developed for each of the app’s content areas. The MADITA app will be described in more detail following the thematic learning units.

Learning Units

Final Quiz

After completing the learning units, you can take the final quiz below.

Congratulations, you have reached the end of the online course. We hope you have learned a lot about early mathematical learning and that you would like to try out the MADITA app and use it in your math lessons.
To check whether you have understood everything, you can take the final quiz here. It contains questions on the content explained in the learning units. Each question has four possible answers, only one of which is correct (single choice).

Have fun doing the quiz!

1. Where do children mainly gain their early mathematical experiences before starting primary school?

 
 
 
 

2. What distinguishes “sorting” from “classifying”?

 
 
 
 

3. What is one strategy to simplify classification tasks for students who struggle?

 
 
 
 

4. How are mathematical patterns defined?

 
 
 
 

5. The development of pattern awareness is based on understanding which concepts?

 
 
 
 

6. What characterizes a repeating pattern?

 
 
 
 

7. What is the minimal unit of repeat in the pattern ABBABBABB?

 
 
 
 

8. Growing patterns are defined as patterns in which…

 
 
 
 

9. What is number sense?

 
 
 
 

10. What does the principle of cardinality mean?

 
 
 
 

11. What is subitizing?

 
 
 
 

12. Research shows that students with mathematical difficulties tend to show which behavior on number line tasks?

 
 
 
 

13. Which reference point strategy can improve number line performance?

 
 
 
 

14. How do children first experience addition and subtraction?

 
 
 
 

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If you have any questions regarding organization or content of the online course, please contact us at: madita-project[at]uni-koeln.de. 

References

Desoete, A., Stock, P., Schepens, A., Baeyens, D., & Roeyers, H. (2009). Classification, Seriation, and Counting in Grades 1, 2, and 3 as Two-Year Longitudinal Predictors for Low Achieving in Numerical Facility and Arithmetical Achievement? Journal of Psychoeducational Assessment, 27(3), 252-264. https://doi.org/10.1177/0734282908330588

MSB NRW (Ministerium für Schule und Bildung des Landes Nordrhein-Westfalen) (2021). Lehrplan für die Primarstufe in Nordrhein-Westfalen. Fach Mathematik. In Sammelband: Lehrpläne Primarstufe (pp. 71-97).

NCTM (National Council of Teachers of Mathematics) (2000). Principles and Standards for School Mathematics. NCTM.