Assessment for Learning in Mathematics Classrooms

1. Assessment for Learning inMathematics Classrooms Chris Suurtamm University of Ottawa

2. Drawing on data from • Curriculum Implementation in Intermediate Mathematics Research Project (Grade 7 – 10 teachers) (2006- 2010) • Professional Learning Communities: Enhancing Classroom Assessment (2008-2011) • Collaborative Inquiry: Enhancing Grade 9 Applied Mathematics (2014-2016)

3. Survey data from Grade 7 – 10 Ontario teachers Suurtamm, Koch, Arden, 2010

4. Dilemmas: A framework for consideration This example applies the framework to the dilemmas teachers face when implementing new assessment ideas in their classroom (Suurtamm & Koch, 2014).

5. Conceptual dilemmas • Pedagogical dilemmas • Cultural dilemmas • Political dilemmas Examination of dilemmas Use of Windschitl’s framework (2002) Created for dilemmas in constructivist teaching

6. Examples include discussions about: • different purposes of assessment • the role of formative assessment • the value of aligning instruction and assessment • what consistency really means • what it means to understand mathematics. Conceptual dilemmas in assessment arise as teachers attempt to understand the conceptual underpinnings of inquiry-oriented views of mathematics teaching and learning, and current views of assessment

7. Examples include: • Finding ways to record observations • Finding time for problem solving activities • Designing a meaningful rubric that provides students with information but not constraints • Developing students’ ability to peer- and self-asses • Creating time to conference with students and provide feedback Pedagogical dilemmas in assessment arise as teachers create and enact new assessment opportunities.

8. Examples include discussions about: • student expectations with respect to marks • grappling with colleagues’ concerns about new approaches to assessment • the role of consistency in assessment practices among department members • parents’ and administrator’s understanding of assessment Cultural dilemmas in assessment focus on changes in classroom and school culture with regard to assessment practice Cultural dilemmas often arose when new assessment practices threatened existing cultural practices

9. Examples include discussions about grading and reporting such as : • matching assessment levels used on rubrics with required report card percentage grades • being restricted to pre-made report card comments • having to organize marks into four categories of knowledge and skills (that seem to overlap) Political dilemmas in assessment arise when teachers try to align their thinking and practice with provincial, district and school policies around assessment, particularly with regard to accountability

10. Conversations included a variety of types of dilemmas which show the interconnectedness of the dilemmas Interconnectedness of dilemmas In a discussion on collaborative assessment, teachers who have students engage in collaborative problem solving tasks as part of instruction wonder whether and how they can assess students in such a collaborative setting. This led to a discussion of The value of aligning instruction and assessment Whether one is “allowed” to do this for a summative task What this might look like in practice Conceptual Political Pedagogical

11. Interplay of dilemmas Our adaptation of Windschitl’s framework provides a way of parsing out different sorts of concerns AND offers a way of recognizing and examining the interconnections between the categories. Different types of dilemmas may need different supports and in supporting teachers, the interconnections must be acknowledged. For instance, one can’t invoke policy without being aware of the implications conceptually, pedagogically, and culturally.

12. Current practices include: • Use of collaborative problem solving which incorporates observation and conversation • Use of mini-whiteboards and technology to see immediately what students are understanding • Use of ipads to capture students’ problem solving (educreations, explain everything) • Development of peer and self assessment through portfolio, reflections, journals, etc.