Research shows that through formative assessment teachers are able to improve their teaching, and this positively impacts on student learning (Black & Wiliam, 1998a, 1998b). In the field of Mathematics and Science Education, it is of great need to further research on new possibilities for formative assessment that are created through new learning environments and how these might relate to other forms of summative assessment. In this lecture, an assessment framework for generative learning environments will be presented.

Generative Activities (Stroup, Ares, & Hurford, 2005; Stroup, Hurford, Ares, & Lesh, 2007) are designed for knowledge and (mathematical and social) structures to emerge, or be generated by the responses and the interaction among students. They are designed for the participation of all students in which the diversity and agency in responses becomes the generator of the mathematical and social emerging structures. Generative activities embed a design of learning environments that embody formative assessment. The designing principles for generative activities are intimately related to formative assessment practices in the mathematics and science classroom, and with the use of network-based technologies, these activities allow teachers and students to get immediate feedback on their learning, allowing them to revise and refine their knowledge about powerful mathematical and science ideas.

According to the National Research Council (2001), one of the problems encountered in evaluation and assessment designs lies in the tensions among: how students learn mathematics, the tools used to elicit and document their knowledge, and the tools or instruments used to interpret this knowledge. In order to release this tension, the design of assessment and evaluation needs to be intertwined together with the design of the learning environment in order to form a coherent unit.

Formative assessment does not happen randomly in the classroom, and it is difficult to foster if it is thought of as separated from instruction (Wiliam, Lee, Harrison, & Black, 2004). Generative activities blur the distinction between instruction and assessment because they are useful in generating, eliciting and documenting students’ knowledge while making it visible; and because they allow for multiple sources of ongoing and opportunistic feedback for students and teachers (Stroup et al., 2005; Stroup, Ares & Hurford, 2005; Stroup, Carmona & Davis, 2005).

In this lecture, an assessment framework design for generative learning environments will be presented. This design allows for continuous assessment from a teacher perspective, because in this type of learning environment the teacher can focus on student responses at an individual and group levels. From a student perspective, these activities also allow for multiple types of feedback, including that from the teacher, other students, the emerging structure from the whole group, the individual solution with respect to the response space, and self-assessment. Summative assessment is also considered in this framework, focusing on those design aspects that are relevant in generative learning environments in a way that is valid, reliable and feasible to implement.

References
Black, P., & Wiliam, D. (1998a). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 8 (2), 139-144, 146-148.
Black, P., & Wiliam, D. (1998b). Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5(1), 7-74.
National Research Council. (2001). Knowing what students know: The science and design of educational assessments. Washington, D.C.: Author.
Stroup, W. M., Ares, N. M., & Hurford, A. C. (2005). A dialectic analysis of generativity: Issues of network-supported design in mathematics and science. Mathematical Thinking & Learning, 7(3), 181.
Stroup, W. M., Ares, N. M., Hurford, A. C., & Lesh, R. A. (2007). Diversity-by-design: The why, what, and how of generativity in next-generation classroom networks. In R. A. Lesh, E. Hamilton, & J. J. Kaput (Eds.), Foundations for the future in mathematics education. (p.367-393). Mahawah, NJ: Lawrence Erlbaum.
Stroup, W., Carmona, G., & Davis, S. (2005). Improving on expectations: Preliminary results from using network supported function based algebra. In G. M. Lloyd, M. Wilson., J. L. Wilkings, y S. L. Behm (Eds.). Proceedings of the twenty seventh annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Roanoke, VA: PME.
Wiliam, D., Lee, C., Harrison, C., & Black, P. (2004). Teachers developing assessment for learning: Impact on student achievement. Assessment in Education: Principles, Policy & Practice, 11(1), 49.