For several years, standards-based assessment (SBA) has been the focus of much of my work with Surrey teachers. Simply put, SBA connects evidence of student learning with learning standards (e.g., “use ratios and rates to make comparisons between quantities”) rather than events (“Quiz 2.3”). The change from gathering points to gathering data represents a paradigm shift.
In this traditional system, experience has trained students to play the game of school. Schools dangle the carrot (the academic grade) in front of their faces and encourage students to chase it. With these practices, schools have created a culture of compliance. Becoming standards based is about changing to a culture of learning. “Complete this assignment to get these points” changes to “Complete this assignment to improve your learning.” […] Educators have trained learners to focus on the academic grade; they can coach them out of this assumption.Schimmer et al., 2018, p. 12
- Writing Learning Standards
- Constructing Proficiency Scales
- Designing Assessment Items
- Determining Grades
Writing Learning Standards
In BC, content learning standards describe what students know and curricular competency learning standards describe what students can do. Describe is generous–more like list. In any mathematical experience a student might “bump into” both content and competency learning standards. Consider Nat Banting’s Quadratic Functions Menu Math task:
Think about the following ten “design specifications” of quadratic functions:
|A.||Two negative x-intercepts||B.||Vertex in quadrant II|
|C.||Never enters quadrant III||D.||Vertex on the y-axis|
|E.||Positive y-intercept||F.||No x-intercepts|
|G.||Never enters quadrant I||H.||Has a minimum value|
|I.||Horizontally stretched||J.||Line of symmetry enters quadrant IV|
You could build ten different quadratic functions to satisfy these ten different constraints.
Instead, build a set of as few quadratic functions as possible to satisfy each constraint at least once. Write your functions in the form y = a(x − p)2 + q.
Which constraints pair nicely? Which constraints cannot be paired?
Is it possible to satisfy all ten constraints using four, three, or two functions?
Describe how and why you built each function. Be sure to identify which functions satisfy which constraints.
Students activate their knowledge of quadratic functions. In addition, they engage in several curricular competencies: “analyze and apply mathematical ideas using reason” and “explain and justify mathematical ideas and decisions,” among others. Since the two are interwoven, combining competencies and content (i.e., “reason about characteristics of quadratic functions”) is natural when thinking about a task as a learning activity. However, from an assessment standpoint, it might be helpful to separate the two. In this series, I will focus on assessing content.
The content learning standard quadratic functions and equations is too broad to inform learning. Quadratic functions–nevermind functions and equations–is still too big. A student might demonstrate Extending knowledge of quadratic functions in the form y = a(x − p)2 + q but Emerging knowledge of completing the square, attain Proficient when graphing parabolas but Developing when writing equations.
Operations with fractions names an entire unit in Mathematics 8. Such standards need to be divided into subtopics, or outcomes. For example, operations with fractions might become:
- add and subtract fractions
- multiply and divide fractions
- evaluate expressions with two or more operations on fractions
- solve contextual problems involving fractions
Teachers can get carried away breaking down learning standards, differentiating proper from improper fractions, same from different denominators, and so on. These differences point to proficiency levels, not new outcomes. Having too many subtopics risks atomizing curriculum. Further, having as many standards as days in the course is incompatible with gathering data over time. I aim for two to four (content) outcomes per unit.
In Foundations of Mathematics and Pre-calculus 10, systems of linear equations can be delineated as:
- solve graphically
- solve algebraically
- model and solve contextual problems
My solve algebraically includes both substitution and elimination. Some of my colleagues object to this. No worries, separate them.
In my next post, I’ll describe constructing proficiency scales to differentiate complexity levels within these learning standards. Here’s a sneak peek:
What do you notice?