Development of Formative Classroom Assessments: "Mathes 5-6"

Learning progress diagnostics is considered an essential element in assessing and enhancing the effectiveness of teaching and support measures (Hattie, Beywl & Zierer, 2018). While in the USA, research on curriculum-based measurements (CBM; including Deno, 1985, 2003; Fuchs, 2004) as a method of formative diagnostics has been conducted intensively since the 1970s, scientific interest in this topic has only recently emerged in German-speaking countries. Accordingly, in many areas there is currently a lack of assessments that are able to reliably and sensitively capture performance developments over time (an overview of available formative diagnostic instruments is provided by Blumenthal [2022]).

To achieve a good compromise between the goal of both precise and educationally relevant diagnostics, and the goal of efficient diagnostics, a combination of various progress diagnostic methods and procedures is recommended in literature: Curriculum-based measurements (CBM) and formative classroom assessments, as mentioned above, have already proven to be practical in the school setting. The former are more suitable for assessing development in relation to short-term learning goals, while the latter serve to measure the achievement of longer-term learning goals or performance standards.

Curriculum-Based Measurement (CBM)

CBM consists of sets of tasks, so-called probes, on curricular content, which are completed within a predetermined time frame of just a few minutes (Hosp, Hosp & Howell, 2016). To avoid memory effects, typically parallel tests are administered. This means that although different tasks are completed at each measurement point, they are equivalent in terms of the competences being assessed and their level of difficulty (they are parallel). The number of correctly solved tasks is tallied, documented, and potentially presented graphically. Depending on the research question, measurements are usually conducted monthly to weekly. This allows for an evaluation of current teaching and support measures, from which short-term adjustments can be derived.

In the past, members of the department have been involved in research projects where CBM for the areas of mathematics and spelling have been successfully developed (Sikora & Voß, 2017; Voß, Sikora & Mahlau, 2017; Blumenthal, Sikora & Mahlau, 2021). In the future, as part of the diagnostic and support concept "Mathe-Navi", further CBM for outlined learning objectives in mathematics, such as number decomposition, addition of tens, or structured quantity perception, are planned to be designed.

Formative Classroom Assessments

Formative classroom assessments should cover the spectrum of competencies as comprehensively as possible according to the respective educational standards of the subject, so that the development of competencies to be addressed over a longer period (e.g. a school year) can be tracked. The diagnostic statements particularly relate to long-term learning goals and indicate corresponding instructional adaptations. Formative classroom assessments are more extensive than CBM and are typically administered without time constraints. This results in a higher effort in administration and evaluation, which is why it is realistic to apply them much less frequently than CBM. A formative classroom assessment should be used for progress diagnostics at least twice in the school year (e.g. at the beginning and in the middle); ideally, it would be used three to four times in a school year (e.g. Diehl & Hartke, 2012).

Image of Mathes test series
Image of Mathes test series

Formative classroom assessments meet test-theoretical quality criteria and thereby serve various functions for teachers:

  1. Screening function: Selection of students who need additional support measures 
  2. Benchmarking function: Documentation of learning progress for individual students as well as entire classes
  3. Support planning: Targeted identification of knowledge gaps

With the Mathes tests (Sikora, 2017; Sikora & Hartke, 2020), a series of formative classroom assessments for the subject of mathematics was constructed and evaluated for the entire primary school period. Currently, this series is being expanded to include methods for grades five and six. The evaluation of psychometric quality will take place from February 2024 to February 2026 in all regional schools on the islands of Rügen and Hiddensee.

All diagnostic procedures developed so far are available for free under a Creative Commons license at www.lernlinie.de.

Here you can find the project's presentation in the research database of the Europa-Universität Flensburg.

Contacts
Phone
+49 461 805 2994
E-mail
simon.sikora-PleaseRemoveIncludingDashes-@uni-flensburg.de
Building
Gebäude Helsinki
Room
HEL 236
Street
Auf dem Campus 1a
Post code / City
24943 Flensburg
Phone
+49 461 805 2849
E-mail
pascal.kintscher-PleaseRemoveIncludingDashes-@uni-flensburg.de
Building
Gebäude Helsinki
Room
HEL 238
Street
Auf dem Campus 1a
Post code / City
24943 Flensburg
References
  • Blumenthal, S. (2022). Lernverlaufsdiagnostik. In M. Gebhardt, D. Scheer & M. Schurig (Hrsg.), Handbuch der sonderpädagogischen Diagnostik. Grundlagen und Konzepte der Statusdiagnostik, Prozessdiagnostik und Förderplanung (S. 633‐648). Regensburg: Universitätsbibliothek. https://doi.org/10.5283/epub.53149
  • Blumenthal, S., Sikora, S. & Mahlau, K. (2021). Lernverlaufsdiagnostik im Rechtschreibunterricht der Grundschule. Konstruktion und Güte eines curriculumbasierten Messverfahrens. Diagnosticahttps://doi.org/10.1026/0012-1924/a000261
  • Deno, S. L. (1985). Curriculum-based measurement: The emerging alternative. Exceptional Children, 52, 219-232.
  • Deno, S. L. (2003). Developments in Curriculum-based Measurement. Journal of Special Education, 37, 184-192.
  • Fuchs, L. S. (2004). The Past, Present, and Future of Curriculum-Based Measurement Research. School Psychology Review, 33, 188-192.
  • Diehl, K. & Hartke, B. (2012). Inventar zur Erfassung der Lesekompetenzen von Erstklässlern. IEL-1. Göttingen: Hogrefe.
  • Hattie, J., Beywl, W. & Zierer, K. (2018). Lernen sichtbar machen. 4., unveränderte Auflage. Baltmannsweiler: Schneider-Verlag Hohengehren.
  • Hosp, M.K., Hosp, J.L. & Howell, K.W. (2016). The ABCs of CBM. A practical guide to curriculum-based measurement (2nd ed.). New York: Guilford Press.
  • Sikora, S. (2017). Lernverlaufsdiagnostik im Mathematikunterricht. Theoretische Grundlagen, Konzeption und Güte eines formativen Schulleistungstests für dritte Klassen. Hamburg: Dr. Kovač.
  • Sikora, S. & Hartke, B. (2020). Zur Konstruktion und Güte eines formativen Schulleistungstests für das Fach Mathematik in dritten Klassen. Diagnosticahttps://doi.org/10.1026/0012-1924/a000254.
  • Sikora, S. & Voß, S. (2017). Konzeption und Güte curriculumbasierter Messverfahren zur Erfassung der arithmetischen Leistungsentwicklung in den Klassenstufen 3 und 4. Empirische Sonderpädagogik, 3, 236-257.
  • Voß, S., Sikora, S. & Mahlau, K. (2017). Vorschlag zur Konzeption eines curriculumbasierten Messverfahrens zur Erfassung der Rechtschreibleistungen im Grundschulbereich. Empirische Sonderpädagogik, 2, 184-194.