In this proposal we demonstrate the benefits of conducting a formative evaluation in order to investigate if and how the novel element, “Step In” supports differentiation. Based on results of such evaluations, modifications for improvements of textbooks can be derived.

Because textbooks are the core for instruction and lesson design it is extremely important that they are clear, useful and comprehensible to teachers. Therefore it is vital that the books are evaluated in a systematic way that incorporates feedback from students, teachers and subject experts and then modified prior to publishing.

The Zurich University of Teacher Education developed a new mathematic textbook for primary schools “Mathematik Primarstufe”. In addition to traditional testing as part of textbook development, we have introduced formative evaluation in the development process. According to Stuffelbeam and Shinkfield (2007) formative evaluation provides ongoing feedback to support the planning, development and introduction of a product. During textbook development, the formative evaluation is an assessment to provide the authors and developers with information for improvements before publication (McMillan, 1981).

A major concern for the development of the textbook “Mathematik Primarstufe” was how to support differentiation. Differentiation should provide students with different avenues to acquire content, to process or make sense of ideas, and to develop products in order to learn effectively (Saalfrank, 2008; C. A. Tomlinson, 2005). As part of the mathematic textbook, a novel element has been integrated. A specific form of open task was developed as an introduction for each new topic. This introduction was called “Step In”. The main idea of “Step In” was that all pupils have multiple options for taking in information, making sense of ideas, and expressing what they learned.

It was important for the textbook developers to have a better understanding of this novel approach before the textbook was introduced to the market. Therefore it was agreed to perform a formative evaluation in addition to the traditional testing of textbooks, where usually a group of teachers is asked to provide written feedback on difficulty, clarity, length of tasks and so on.

Within the formative evaluation the following questions have been investigated:

• How do students work with the “Step In” task, what kinds of products do students develop, and what forms of differentiation do these products emboy?
•  Do teachers notice the differences between how students solve these “Step In” open-ended problems?
•  What kinds of interaction processes happen between students and teachers during a “Step In” lecture?

Tomlinson (1999; 2005; 2003) and others (Gregory, 2003) identified key elements of differentiation: content, learning process and learning products. These addressed the different needs of students.

However in the German literature (Hirt & Wälti, 2008; Moser Opitz, 2010; Saalfrank, 2008; Scholz, 2010), one will find a slightly different categorization of differentiation. Scholz (2010) categorizes differentiation by:

• learning material,
• learning pace,
•  learning levels,
• content and interest,
• learning path and learning style,
•  forms of interaction (individual work, group work, pairs, whole class instruction).

In our study we used the latter categorization, called “inner differentiation” as our conceptual framework.

Gregory, G. H. (2003). Differentiated instructional strategies in practice. Thousand Oaks, CA: Corwin Press, Inc. Hirt, U., & Wälti, B. (2008). Lernumgebungen für den Mathematikunterricht, natürliche Differenzierung für Rechenschwache bis Hochbegabte (Vol. Band 2). Velber Kallmeyer. Kuhn, P. (2003). Thematische Zeichnung und fokussiertes, episodisches Interview am Bild. Retrieved 07.01.2012, from Forum Qualitative Sozialforschung http://www.qualitative-research.net/fqs-texte/1-03/1-03kuhn-d.htm Mayring, P. (2008). Qualitative Inhaltsanalyse. Grundlagen und Techniken. Weinheim: Beltz Verlag. McMillan. (1981). Formative Evaluation of Textbooks. American Journal of Evaluation, 2, 343-349. Moser Opitz, E. (2010). Innere Differenzierung durch Lehrmittel: (Entwicklungs-)Möglichkeiten und Grenzen am Beispiel von Mathematiklehrmitteln. Beiträge zur Lehrerbidlung, 28(1), 53-61. Saalfrank, W. T. (2008). Differenzierung. In E. Kiel (Ed.), Unterricht sehen, analysieren, gestalten. Bad Heilbrunn: Julius Klinkhardt, UTB. Scholz, I. (2010). Pädagogische Differenzierung. Göttingen: Vandenhoeck & Ruprecht GmbH & Co.KG. Seidel, T., Prenzel, M., & Kobarg, M. (Eds.). (2005). How to run a video study. Technical report of the IPN Video Study. Münster: Waxmann. Stufflebeam, D. L., & Shinkfield, A. J. (2007). Evaluation theory, models, and applications. San Francisco: John Wiley. Tomlinson, C. A. (1999). The differentiated classroom: Responding to the needs of all learners. Alexandria, VA: Association for Supervision and Curriculum Development. Tomlinson, C. A. (2005). How To Differentiate Instruction in Mixed-Ability Classrooms. Upper Saddle River: Pearson (Merrill Education/ASCD College Textbook Series). Tomlinson, C. A., Brighton, C., Hertberg, H., Callahan, C. M., Moon, T. R., Brimijoin, K., . . . Reynolds, T. (2003). Differentiating Instruction in Response to Student Readiness, Interest, and Learning Profile in Academically Diverse Classrooms: A Review of Literature. Journal for the Education of the Gifted 27(2/3). Yin, R. K. (2009). Case study research: design and methods. Los Angeles: Sage Publications.