Assessment Alignment Curriculum , instruction, and assessment

1. Assessment Alignment Curriculum, instruction, and assessment

2. What does alignment look like? • Instructional tasks are connected to curriculum expectations • Formative assessment is embedded in instruction • Specific assessment tasks resemble instructional tasks and focus on achievement of curriculum expectations

3. Starting with curriculum Teachers use practices and procedures that are carefully planned to relate to the curriculum expectations and learning goals and, as much as possible, to the interests, learning styles and preferences, needs, and experiences of all students; (1 of 7 fundamental principles in Growing Success) “Assessment is the process of gathering information from a variety of sources (including assignments, demonstrations, projects, performances, and tests) that accurately reflects how well a student is achieving the curriculum expectations in a course.” (OME, 2005a, p. 17) Consider Content expectations Mathematical processes

4. NCTM Assessment Standards • Mathematics Standard • Assessment should reflect the mathematics that all students need to know and be able to do. • Inferences Standard • Assessment should promote valid inferences about mathematics learning.

5. What does alignment look like? • Instructional tasks are connected to curriculum expectations • Formative assessment is embedded in instruction • Specific assessment tasks resemble instructional tasks and focus on achievement of curriculum expectations

6. What does alignment look like? Content Processes • Instructional tasks are connected to curriculum expectations • Formative assessment is embedded in instruction • Specific assessment tasks resemble instructional tasks and focus on achievement of curriculum expectations

7. Mathematical Activity • Mathematical Processes • Problem solving • Reasoning and proving • Reflecting • Selecting Tools and Strategies • Connecting • Representing • Communicating Determining, through investigation Creating tables Investigating comparing describing representing modeling graphing Collecting data solving Drawing diagrams explaining

8. 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

9. Examining curriculum expectations Grade 1, measurement Students will: • estimate, measure, and describe length, area, mass, capacity, time, and temperature, using non-standard units of the same size(OME, 2005a, p. 35). What might instructional activity look like that addresses this expectation? How would we assess students with respect to this expectation?

10. Examining curriculum expectations Grade 4, geometry and spatial sense Students will: • construct three-dimensional figures, using two-dimensional shapes • construct a three-dimensional figure from a picture or model of the figure, using connecting cubes (e.g., use connecting cubes to construct a rectangular prism); • construct skeletons of three-dimensional figures, using a variety of tools (e.g., straws and modelling clay, toothpicks and marshmallows, Polydrons), and sketch theskeletons; What might instructional activity look like that addresses this expectation? How would we assess students with respect to this expectation?

11. 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? How would we assess students with respect to this expectation?

12. 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? How would we assess students with respect to this expectation?

13. Examining curriculum expectations Grade 11, Functions course Students will: • determine the formula for the sum of an arithmetic or geometric series, through investigation using a variety of tools (e.g., linking cubes, algebra tiles, diagrams, calculators)and strategies (e.g., patterning; connecting the steps in a numerical example to the steps in the algebraic development), and apply the formula to calculate the sum of a given number of consecutive terms (OME, 2007, p. 51) What might instructional activity look like that addresses this expectation? How would we assess students with respect to this expectation?

14. At your table Work with a partner(s) and decide on one of the grade expectations presented. Discuss What might instructional activity look like that addresses this expectation? How would we assess students with respect to this expectation?

15. Dilemmas • In my coaching role, I often hear the question, "This teaching through problem solving is fine and I can see the benefits to my students. How do I assess it? How do I keep track of everything?" This is a very good question because if teachers struggle with this aspect of teaching through PS, then they will be unlikely to persist with it because the assessment is too unwieldy. • I find that it is a real challenge for teachers to identify the types of questions in relation to the achievement chart in mathematics.

16. 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 What do you think? Conceptual Political Pedagogical

17. Alignment: A complex issue