Finding ways to have the students show problem solving so it can be assessed can be done, but I’m a little leery of it become a dog and pony show. What I strive for now is having problematic situations on which students can show content understanding. Then the grade isn’t based on right answer, it’s based on demonstrated understanding. Which for me is shown by explanation of thinking. Of course, good understanding leads to a lot of right answers, so they’re not uncorrelated. I think stepping away from points is another way to make this case.

]]>“intrinsic motivation is a medium to strong predictor of performance… The importance of intrinsic motivation to performance remained in place whether incentives were presented. In addition, incentive salience influenced the predictive validity of intrinsic motivation for performance.”

In other words, whether or not the undermining effect exists, performance is positively correlated with the presence of both intrinsic and salient extrinsic rewards. Additionally, the authors noted that “intrinsic motivation predicted more unique variance in quality of performance, whereas incentives were a better predictor of quantity of performance.” This is not much of a surprise.

So, why all this academic discussion? Because, quite simply, the evidence says that extrinsic rewards (such as grades, the gold standard of extrinsic motivation) correlate to higher performance, albeit strong quantity of performance rather than quality. Still, quantity has its place in educational work. Indeed, repeated exposure to a certain way of thinking or processing gives us an opportunity to reconsider hastily formed judgments and to develop intuitions that would otherwise have been unavailable.

In all of the above, there is one word that really stands out, salience. If it is salience that correlates to enhanced task performance, then salience is what we should be questing after when we grade, and this brings us back to the topic at hand. If we grade the acts of collaboration and participation in a community of learners, will the students perceive it as salient? My sense is that this depends a whole lot on the classroom culture in which you are operating, something which you do not exercise total authority over. Still, if you work (as mrdardy clearly does) to make these acts a regular avenue for classroom discourse and to make it explicit how you will grade this engagement (Bean and Peterson have a nice 6-point rubric – https://fresnostate.edu/academics/documents/participation/grading_class_participation.pdf … no paywall), I see no strong argument against assessing collaboration in a traditional classroom setting.

If you would like to read the cited article, it is not behind a paywall at the University of Hartford: http://unotes.hartford.edu/announcements/images/2014_03_04_Cerasoli_and_Nicklin_publish_in_Psychological_Bulletin_.pdf

]]>Thanks for jumping in the conversation and my apologies for being so slow to respond.

I like your idea of starting in one place but encouraging the conversion to a more familiar, or more ‘complete’ form of the equation. Another thought I had, probably way too picky for my Geometry students, is converting y – h = m(x – g) simply into y = m(x – g) + h as this form matches with vertex form and other forms they will encounter in Precalculus. I don’t think that the possible gains outweigh the additional confusion that this is likely to cause.

]]>Another issue I run into is the fact that standard form for a linear function is not the same as standard form for any other polynomial function. My algebra students have a hard time wrapping their heads around this. This year I began by teaching the linear function y=x as the parent function and then used transformations. This way I can follow the same format for quadratic functions, and in Algebra II for cubics, etc. I was trying to find a way to show them that linear functions follow the same rules and are not inherently unique.

]]>Thanks for the idea.

]]>The table I was referring to was more like this:

Style of equation: slope-intercept, point-slope, general form, two-intercept

Slope appears directly in equation: yes, yes, no, no

Y-intercept appears directly in equation: no, yes, no, yes

X-intercept appears directly in equation: no, no, no, yes

Lines missing: vertical lines missing , vertical lines missing, no lines missing, vertical and horizontal lines missing

Finding from two points: …

Finding from point and slope: …

]]>Thanks for dropping by to join the conversation!

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