I’d rather drive standard

I can’t completely explain it – either it was channeled procrastination, or my top-down brain demanding more structure. Either way, I found I couldn’t get this first unit test written until I committed myself to a standards-based assessment strategy and wrote up a full rubric for that unit’s learning standards.

I’m glad I went through with it. I was kind of wussing out and just going to put together “the usual” – write tests, add up scores, call that a grade. Now I feel much more in control of how this is going to come together. I’m still unsure of whether I want to expose the system to the students; we’ll see. But at least when students come to me after bombing a test, I’ll have a framework for getting them to demonstrate future mastery of those skills. Even better, it means I can split apart the re-demonstrations into subparts, rather than having them rewrite an entire test at once (which, being a night school course, we don’t really have time for).

What was interesting about the write-up experience is that our provincial standards are *so close* to being directly usable for a solid standards-based (concept-based? whatever) system. They’re already written up in nice bite-sized chunks of understanding. The problem is, they’re totally imbalanced. One unit that takes about 1/7th of your class time over the year contains 1/4 of the total number of standards. Worse, in other grades there are individual “standards” that have subpoints that encompass an entire unit on their own.

Now that I type this up, I suppose arguably I’m making the same classic mistake – assuming that an accurate summative grade should come from simply adding up all of the individual standard marks. But with a nice manageable number of concepts listed, keeping them weighted equally makes the entire system more accessible for students as well as for yourself. Students can glance at their scorecard and know immediately how they’re doing and what to focus on mastering. (In theory.)

After the break I’ll c&p the provincial standards, and my own reworking I came up with including marking rubrics. I’d love to hear critique in the comments! (I pulled a sneaky trick with my third ‘concept’; I can’t decide yet if that was evil or not.)

Provincial “Prescribed Learning Outcomes”:
Transformations
B1 describe how vertical and horizontal translations of functions affect graphs and their related
equations:
− y = f(x − h)
− y − k = f(x)
B2 describe how compressions and expansions of functions affect graphs and their related equations:
− y = af(x)
− y = f(kx)
B3 describe how reflections of functions in both axes and in the line y = x affect graphs and their related
equations:
− y = f(−x)
− y = −f(x)
− y = f −1(x) 1
B4 using the graph and/or the equation of f(x), describe and sketch
f (x)
B5 using the graph and/or the equation of f(x), describe and sketch |f(x)|
B6 describe and perform single transformations and combinations of transformations on functions and
relations

My version:
1. Understand the relationship between horizontal and vertical
translations of a graph of a function and the corresponding
changes to the equation of a function.
_Rubric:_
1: No consistent understanding shown.
2: Shows general understanding but makes frequent errors in
conversion from graph to algebra and back.
3: Good understanding of translations when isolated (not
combined).
4: Consistent understanding of translations in isolation and
when combined with other transformations.

2. Understand the relationship between horiz. and vert. scalings
(compressions / expansions) of the graph of a function and the
corresponding changes to the equation. (Includes horizontal /
vertical reflections.)
_Rubric:_
1: No consistent understanding shown.
2: Shows general understanding but makes frequent errors in
conversion from graph to algebra and back. (eg. changes
compressions to expansions or vice versa)
3: Good understanding of compressions/expansions but has
trouble with reflections, or with combining in other
translations.
4: Consistent understanding of compressions / expansions /
reflections in all forms and when mixed with other
transformations.

3. Understand relationship between graphical and algebraic
representations of the following transformations: absolute
value, reciprocal, and reflection on the line y=x.
_Rubric:_
1: No consistent understanding shown for any of the above.
2: Shows good understanding of one of the three
transformations.
3: Demonstrates good understanding of two of the above.
4: Understands all three of the above, and can sketch the
reciprocal of a function.

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