Quantitative argument is fundamental to the construction of a healthy democracy. Quantitative argument is the presentation of an argument and claims that are supported by quantitative evidence and analysis and are important in science, policy, and engineering. As an educator, I work to cultivate these skills in students and demonstrate their importance in a functioning society.

Generating quantitative arguments requires a broad set of skills that range from computation to abstract thinking. Authors of these arguments must create an argument that supports a policy position or strategy as well as claims that support that argument. Within this framework, the author will create quantitative claims that must be sourced and calculated accurately. These claims should be presented with enough clarity and transparency to create confidence in the reader. This tasks range in complexity from rote mathematical calculations to abstract thinking about claims and evidence and are a challenge to teach. One tool that has helped me teach more effectively is Bloom's Taxonomy.

Bloom's taxonomy is the dominant categorization for cognitive processes that students acquire in education. The taxonomy divides cognitive processes into six categories and ranks them from simple to complex and concrete to abstract. These categories are remember, understand, apply, analyze, evaluate, and create. I don't take these to be a definitive categorization but rather a tool and guide for how I construct lessons and activities for students. By placing my teaching materials, activities, and objectives against this framing, I was able to identify gaps in my teaching.

Using Bloom's taxonomy, it was evident that my teaching was limited to lower-order cognitive processes around mathematical computation. Tightly-scripted story problems are a dominant teaching tool in technical classes and my early teaching used these extensively. Students call this combination of remembering, understanding, and applying of formulas to problems 'plug-and-chug'. When students who were proficient with plug-and-chug displayed difficulty analyzing new situations and deciding which models and formulas to apply I was surprised. This is a serious deficiency in my teaching since without the development of analysis and evaluation skills, these plug-and-chug skills could be easily replaced by automation. After reflection it was clear to me that I wasn't providing students with enough practice on analyzing new situations and creating their own models and that I had assumed that mastery of the lower skills automatically led to mastery of the higher-order skills.

I've addressed this overemphasis on remembering, understanding, and applying mathematical procedures by giving students more opportunities to analyze situations, evaluate the best models to apply, and create their own solution strategies. I now assign more open-ended assignments where students have to ask their own questions and apply models to new situations. These open-ended assignments different kinds of feedback that are more nuanced. Making room for this in the curriculum is challenging because mastering rote but necessary plug-and-chug skills is time-consuming. My approach has been to create assignments where I and the students can provide feedback on both the mechanics of computation as well as the arguments and explanation. To support this, I've been using computational notebooks created by the Jupyter team that allow students to narrate their work and provide the calculations in the same document. An area of development for me is the creation of manageable ways for students to create and receive feedback on their work to support their skill development. Since the notebooks can be easily be published online, we can use the web to facilitate sharing and commenting.

In a future post, I'll talk about work flows I have experimented with to facilitate the feedback on these higher-order skills.