I want to take a minute and ask you to think about a non-math THING that you either have learned to do, or aspire to learn… To speak a new language?... Bake a complicated cake?... Play a musical instrument?…Knit an intricate sweater? 

I’m going to play with the musical instrument idea, but please adapt the metaphor for yourself. Imagine that you went to a concert and saw someone play the cello beautifully! 

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You are inspired!  You buy a cello, sit down to play, and become quickly frustrated because while you watched the cellist play, you didn’t have any insight into all the different components, sub-skills, and musical domain knowledge that make up playing the cello. At this moment, your vision of playing the cello is one big unit of information, rather than a collection of smaller attainable topics. You need help identifying the smaller components of “celloing,” recognizing what you are able to do, and figuring out how to improve in each component so you can make music. 

I want to explore how we can use Magma to help students see where they are and where they are going. In Building Thinking Classrooms (BTC), Dr. Peter Liljedahl writes that all assessment and evaluation should be formative, and some of it will also be summative. The distinction he makes between formative and summative assessment is that formative assessment is the gathering of information for the purposes of informing learning and teaching, and summative evaluation is the gathering of information for the purposes of grading and reporting. In this blog, we will explore how to use tools that Dr. Peter suggests in BTC with Magma to support assessment for learning.

In his research, Dr. Peter found that students who see the mathematics in a chapter as one big idea have a much more challenging time on assessments than the students who see the mathematics as a collection of smaller topics. To help students know where they are and what they need to learn, he suggests creating rubrics that he calls navigation instruments. He says these tools help students lift out of the maze of the mathematics they are learning to better see the path towards the mathematical goal. 

A navigation instrument is a rubric that lists the subtopics of a chapter, and then either two or three columns that describe what basic, intermediate and advanced level problems look like for each subtopic. One can then incorporate Magma into this rubric by alerting students as to which problems fall into which category. Here is an example navigation instrument, in which the problem numbers from a Check-Your-Understanding assignment are named in the rubric.

Example problems from a Magma Assignment aligned to the Navigation Instrument

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A few things to notice here. For the headings, or levels of conceptual complexity, you can use Mild, Medium & Spicy like we have here, or something completely different that makes sense to you and your students. Dr. Peter has found that the important thing about the three levels is that the names should have to do with the difficulty level of the content, NOT the skill level of the learner. Also, he talks about this instrument being “backwards compatible.” If a student can do spicy problems, then we know they are capable of solving the mild and medium ones. The navigation instrument can be passed out to students at the start of the unit of study, and extended as students have additional opportunities to self-assess their understanding. He suggests using a key that makes sense to students like this:

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Part of “studenting” is learning how to evaluate how we are progressing. I have a pretty painful memory from my freshman year in college around my first physics midterm. It was my first ever physics class, and to be honest, I didn’t really know what I was doing, even though I had done well in high school math and science. I remember sitting (with my feet up!) reading through my notes, thinking, “Yep, I’ve got that.” 

Well, not so much! I had not figured out how to self-assess, I don’t think I had a clear understanding of what to self-assess on. Thanks to a wonderful professor, who both gave me the opportunity to talk through what I did know and also helped me identify what I needed to learn and how to tackle it, I made it through the experience! 

Let us know how you are using Magma to help your students self-assess. We’d love to hear your experience!

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