Tools of Transfer: Rubrics

In Tools of Transfer: Quality, we began to discuss some of the tools educators regularly use in order to allow students the opportunity to leave the classroom with an implicit understanding of the factors that create quality work. Of the tools discussed, rubrics seem to be the most confounding; here, we’ll dive a bit deeper into some strategies and techniques that educators may want to consider when creating a rubric.

Remember that ultimately, rubrics cease to exist for students once they become, as we like to call them, ‘people’ in the ‘real-world.’ That fact, however, does not render them useless. The purpose of a rubric is the same as the purpose of a ‘no shots until there’s been ten passes’ drill during basketball practice – it would be ridiculous to see the Golden State Warriors following that rule during the NBA Finals, but each and every member of that team completed that drill enough times that it made the skill (of seeing the court as full of opportunities to pass the ball) into something subconscious. The members of the team no longer have to refer back to the ‘pass the ball ten times’ rule, they have expanded their conception of the basketball court to see the abstract passing opportunities without needing the concrete rule.

When designing rubrics, we are creating rules for drills that students will use to make implicit their understanding of quality, allowing them to perform at a professional level. In the pursuit of what, though, is anyone’s guess. Thus, it is important in my opinion to make the drills broadly applicable to a student’s future pursuits… I know, that’s a “no, duh” statement. However, the component of making these ‘drills’ broadly applicable that often gets missed is twofold, I believe. First, secondary teachers get too caught up in their particular subject matter to remember to make their rubrics include more components than the content itself; secondly, we forget that rubrics need to be a continuum from concrete to abstract as students move from elementary to secondary school.

As to the first point, I will be speaking from the perspective of a secondary mathematics teacher, specifically. The first reason is trite: I am a mathematics teacher. The second reason is that mathematics seems to me the subject most likely to get caught up in the nuances and specifics of the content and forget to include components like communication of mathematical processes through writing (mathematics is, after all, about creativity and sense-making – two pursuits which require that we communicate our findings effectively, whether we’ve discovered the mysteries of antimatter or created a financial solution to the woes of a struggling business).

To illustrate how firmly grounded in our culture is the view that mathematics is just about ‘getting the right answer,’ I’ll relay that just last week, I had a student write in the self-assessment section of a project “I know that I could have put more effort into my write-up on this project, but I procrastinated and didn’t have as much time. That doesn’t really matter though because I am certain I got the right answer on the project, and that is all that matters!” The reason this highlights just how deeply rooted this perspective has become is that this is my rubric:

PDF of the Math Project Rubric

You will notice that my rubric has four sections, none of which are directly related to ‘getting the right answer.’ In structuring the rubric this way, I am not saying that ‘getting the right answer’ is not important in life – there are many situations in which we must pay attention to details and get the answers right (taxes, for example). However, I feel that tests in my class serve to fill that niche, and projects, on the other hand, represent an area where we can focus on other things that also matter in life.

Craftsmanship is the first section listed on my rubric; I like to think of this category as being useful for teaching the ‘first impression’ effect. Whether we like it or not, when we give a report on, say the new quota-setting analytics we are using at our company, our boss is going to take the report, give it a quick glance-over and say ‘awesome, I am excited to read this!’ That quick glance-over is ‘the first impression effect,’ and you can bet that she has made a quick judgement on whether the quality of the report will be high or not just based on the professionalism of its ‘look.’ As an extreme example, can you imagine coming up to your boss after two weeks and saying ‘hey, I got that report you wanted,’ and proceeding to rip 4 pages out of a composition notebook and hand it to them? If the answer is ‘no,’ then you understand why I give an automatic ‘No Evidence,’ in the Craftsmanship section if my students turn in a project that has rip marks or frillies on the loose leaf sheets.

The Content Communication section also has nothing whatsoever to do with ‘getting the right answer,’ but instead has to do with the process of telling the story of solving this problem, often times an engineering problem of some sort. Without being able to communicate our abstract solution processes, we are limiting ourselves by eliminating the ability to either check our work with the help of other brilliant minds, or to have our work create an impact at all!

The Creativity section of the rubric is the one I feel most needs improvement. It’s designed to remind students that mathematics is a creative subject, but also that creativity counts in content communication also – adding a unique visual to a project can help to both expand your own conception of the problem, but also your communication of it to others. Just because the particular graph you choose to add has been seen before does not mean that it’s not creative! Secondly, that creativity comes with self-discipline and repeated attempts – we aren’t just struck by some muse and – ‘poof!’ – become creative. I often say these things to students when assigning a project, but haven’t figured out how to capture the essence of creativity in words while keeping the rubric to one page.

Finally, the Content Understanding is the section that comes closest to our cultural perceptions that math is about ‘getting the right answer.’ However, you will notice that I do not grade students so much on the final answer that they provide, but on their ‘use of the mathematical toolbelt.’ The ‘Toolbelt’ is a concept I use often to describe the skills that we have covered in math class. An important component of being successful in my class is to figure out what tool to use – a carpenter is not going to choose to drive a nail into wood using his tape measure! Similarly, we wouldn’t choose to complete the square to solve a linear system of equations; choosing what tool you are going to use is a way of learning to ‘think in the language that is mathematics’ and therefore garners points on my grading scale more so than does arriving at the right answer through guess and check.

And now for the idea of creating rubrics that represent a continuum from the concrete to abstract: in my perfect world, we in the high school world would be working with teachers in the lower and middle schools that feed to us to create this continuum and to make explicit (literally have learning targets about) the shift from concrete to abstract and why it is necessary. However, this is a bit of a tricky goal because the abstract concepts of which I speak don’t necessarily work for every kid the same way… I mean to say that the culture of the school is important here. Where I teach, we have created a culture that, I think, maintains a love of learning, and kids begin to feel confident that they have internalized an understanding of quality and can innovate from there. For example, during the last project I gave I created a scenario about two of the musically-inclined students in my class borrowing $150,000 from our principal to start a record company. The students had to create a sales strategy for the company based on a number of constraints I gave them, and one student had her project’s write-up placed inside a ‘record album’ – she had created an artistic design of a record cover and had made a playlist of fake songs in her ‘record’ on the back. The songs included tracks like ‘Spagetti Squared Anthem’ and ‘Do Math Not Meth’. Ha!

However, imagine taking a traditional AP-taking student that is used to getting rubrics that have clear directives and actionable steps to take to achieve them. My rubric may drive them crazy! Yet, I feel that the abstract nature of my rubric is valuable… but I could certainly be creating students that get out there into the ‘real world’ and get bored when they are tasked with just doing what is expected of them. Personally, I’d be very alright with that!

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