What does alignment look like? CurriculumAssessmentInstruction  Instructional tasks are connected to curriculum expectations  Assessment tasks are similar to instructional tasks and assess student achievement of the curriculum expectations

Starting with curriculum  What are the messages in the curriculum?  Front matter of document(s)  What mathematical actions are encouraged?  (need more on this slide)

Starting with curriculum When developing their mathematics program and units of study from this document, teachers are expected to weave together related expectations from different strands, as well as the relevant mathematical process expectations, in order to create an overall program that integrates and balances concept development, skill acquisition, the use of processes, and applications. (OME, 2005a, p. 7) Assessment is the process of gathering information from a variety of sources (including assignments, day-to-day observations and conversations/conferences, demonstrations, projects, performances, and tests) that accurately reflects how well a student is achieving the curriculum expectations in a subject. (OME, 2005a, p. 18)

Starting with curriculum All curriculum expectations must be accounted for in instruction, but evaluation focuses on students’ achievement of the overall expectations. A student’s achievement of the overall expectations is evaluated on the basis of his or her achievement of related specific expectations (including the mathematical process expectations). The overall expectations are broad in nature, and the specific expectations define the particular content or scope of the knowledge and skills referred to in the overall expectations (OME, 2005a, p. 19)

Mathematical Activity Investigating solving graphing Collecting data describing Determining, through investigation comparing explaining representing modeling Drawing diagrams Creating tables

What does alignment look like? CurriculumAssessmentInstruction  Instructional tasks are connected to curriculum expectations  Assessment tasks are similar to instructional tasks and assess student achievement of the curriculum expectations

What does alignment look like? CurriculumAssessmentInstruction  Instructional tasks are connected to curriculum expectations  Assessment tasks are similar to instructional tasks and assess student achievement of the curriculum expectations Processes Content

Messages in Growing Success The curriculum standards describe the knowledge and skills students are expected to develop and demonstrate in their class work, on tests, and in various other activities on which their achievement is assessed and evaluated. (p. 16)

Messages from NCTM & PRIME Assessment Leadership (Indicator #1)  For PRIME, consider bullets under each stage; which to unpack within pre-plenary and which to explore in breakout and then debrief in plenary

Implications for assessment?  A test along will not do!!  The complexity of mathematical actions need to be assessed in a variety of ways  Observation  Performance tasks  Presentations  Journals  Investigations  Conferencing and dialogue

Grade 3

Examining curriculum expectations Grade 7, measurement Students will:  determine, through investigation using a variety of tools and strategies (e.g., decomposing right prisms; stacking congruent layers of concrete materials to form a right prism), the relationship between the height, the area of the base, and the volume of right prisms with simple polygonal bases (e.g. parallelograms, trapezoids), and generalize to develop the formula (i.e., Volume = area of base x height) (OME, 2005a, p. 101). What might instructional activity look like that addresses this expectation?

Examining curriculum expectations Grade 7, measurement Students will:  determine, through investigation using a variety of tools and strategies (e.g., decomposing right prisms; stacking congruent layers of concrete materials to form a right prism), the relationship between the height, the area of the base, and the volume of right prisms with simple polygonal bases (e.g. parallelograms, trapezoids), and generalize to develop the formula (i.e., Volume = area of base x height) (OME, 2005a, p. 101). What would we need to do to demonstrate that they have achieved this expectation?

Examining curriculum expectations Grade 9, geometry and measurement Students will:  verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems. What might instructional activity look like that addresses this expectation?

Examining curriculum expectations Grade 9, geometry and measurement Students will:  verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems. What would we need to do to demonstrate that they have achieved this expectation?

Breakout  Grade band vs cross-grade band?

Gallery Walk Discussion  Products posted from breakouts  Provide instructions, what to look for during gallery walk, what data to collect (e.g. looks for across grades?)

Dilemmas  (this may be a series of slides with some ideas drawn from my research – such as the next slide)  What are the implications for assessment?  What issues might arise?  Have you found a way to overcome any of these issues

Dilemmas in alignment 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 Conceptual Political Pedagogical