learning standards – Chris Hunter

In this series:

Determining Grades

It’s time to report out. How would you translate the following into a proficiency level, letter grade, or percentage? What would you assign to Aaron, Blake, and Denise?

Gradebook at time of first Learning Update

If your reporting policy requires a proficiency level (e.g., Grades K-9 in BC), analyze the data and make a judgement. To me, Aaron has demonstrated Extending, Denise Developing. Blake has also demonstrated Developing. Or Partial. I’m waffling.

What if this was your gradebook for Math 10? In BC, you may use proficiency scales but must provide letter grades and percentages. In this post, I’ll propose a solution–admittedly flawed–to this problem. But first, a bit about why this is a problematic practice…

Percentage Problems

Think of a student who has achieved 80% in Math 10. Describe their level of performance.

Got it? Great! Now do 79% and 81%.

Don’t stop! Finish the Bs.

A letter grade and percentage mandate suggests a difference between 73% and 85%–both Bs in BC. Quantitatively? Sure. In the point-gathering paradigm, 73% leaves almost twice as many points on the table as 85% (i.e., the “Lo-B, Hi-B” refrain).

But qualitatively? Not really. See the Ministry of Education’s letter grade definitions:

F; 0 – 49; The student has not demonstrated, or is not demonstrating, minimally acceptable performance in relation to the learning outcomes for the course or subject and grade.
Policy Development Background & Rationale Document (PDF)

There are not thirteen (85 − 73 + 1) variations on very good. Three is a stretch:

Extend the table. Write distinctly different descriptors of all levels, from 86% up to 100%, 72% down to 0%.

You can’t. Whereas letter grades differentiate six levels of performance, percentages differentiate one hundred one. No teacher can be that precise (or accurate). Like objectivity and consistency, precision is a myth.

Standards-based assessment is not designed to produce percentages. Proficiency scales are not numbers! Still, teachers–of Grades 10-12 only–are required to report out a number. So, holding my nose…

Imperfect Solutions

🔴 1-2-3-4

To turn the data into a number, values need to be assigned to proficiency levels (e.g., Emerging = 1, Developing = 2, Proficient = 3, Extending = 4). Students receive a value on each outcome. The numerator takes together these values from all of the outcomes; the denominator is the greatest sum that is possible. Aaron, Blake, and Denise receive 83% (B), 63% (C), and 48% (F), respectively.

This feels… off. Denise demonstrated partial (Developing) or complete (Proficient) understanding of seven of ten learning outcomes. Nevertheless, she is failing. This is because a 1-2-3-4 scale is harsh. One-out-of-four (i.e., 25%) for Emerging isn’t just a failing grade; it’s an unforgiving one. Also, two-out-of-four (i.e., 50%) for Developing leaves no wiggle room. Developing is more than a minimal pass.

🟡 2-3-4-5

A 2-3-4-5 scale feels more accurate. Aaron, Blake, and Denise now receive 86% (A), 70% (C+), and 58% (C-), respectively.

Note that Denise is now passing. I really like the example of Aaron since it illustrates that Extending is not “the new A.” To achieve an A, Aaron demonstrated Proficient in all, Extending in (just) a few. Further, Blake’s C+ feels fair. To “award” Blake a B, I’d want to see additional evidence of their proficiency (i.e., new data points at Developing in outcomes 2 or 6 or Proficient in outcomes 1, 7, or 10).

If 2-3-4-5 doesn’t work, play with 3-4-5-6. Or 46-64-85-100. And if you want to give some outcomes more weight than others, do so. For example, you can double values from solve systems algebraically.

Averaging

Conversations about averaging do not always offer nuance. The takeaway can be that averaging is just… wait for it… mean. Averaging across different outcomes–see above–is more than okay. It’s averaging within the same outcome that can be punitive. Let’s revisit the gradebook:

For the sake of simplicity, I skipped a crucial step. These letters are not single data points. For example, prior to “it’s time to report out,” Denise’s “P” on the third learning outcome might have been “Em, Em, D, P, P.” Averaging would drag Denise down to Developing; she’d be stuck to her initial struggles. In the end, Denise demonstrated–successively–a Proficient level of understanding in relation to this learning outcome. That’s what matters, that’s what counts.

The fact that she didn’t know how to do something in the beginning is expected–she is learning, not learned, and she shouldn’t be punished for her early-not-knowing.
Peter Liljedahl, 2020, p. 258

* * ** *** ***** ******** *************

Marc has extended my understanding of assessment and this blog series reflects our collective thinking. Check out his assessment video from BCAMT!

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

In this series, I’ll describe four practices of a standards-based approach:

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?

Tag: learning standards

[SBA] Determining Grades