Aug 102017
 

The other day, Ann Arden posted about “Beyond tests in HS Math (part 1).” This was her very first ever blog post, and I am eagerly awaiting her second!

In Ann’s post, she set up a framework for understanding assessments which I had not seen before (someone please give me a citation if you have), and it really made me think about what I wanted to do with an assignment in the class I am teaching this semester. The image she posted and tweeted was this one:

She says she would change the top from feedback to assessment. I wanted to take it to another level, because I have both mathematics and science majors in my class. Because of that, want to address the actual standards of practice and content for both. In the ‘process’ and ‘product’ labels, I saw the conceptual and procedural ideals of mathematics learning in the CCSSM, which also has similar ideas (but uses completely different terms) in the NGSS. With that in mind, I updated the image to this, retaining the same positions of her quadrants.

What does that give me, however? Why?

Let me go back to Ann’s post. She said,

Quadrant 4: Assessment of a product /after the moment

In my experience, this is where most evaluation (and much formative assessment) occurs in high school math. The most common example of this is math tests. Students finish a section/unit of learning and write a test. This is usually done individually (more on this and group tests in an upcoming post). The teacher then marks these tests later in the school day or at home; away from the students. These hopefully get returned in a prompt manner, but can take a few days or longer sometimes as I can personally attest to. Most of the feedback is written and might involve short phrases, check marks and circles or other notations. Research has show that students have a difficult time interpreting this sort of feedback (e.g. Weimer, 2013’s review of Sadler, 2010). In addition, the delay between the “performance” and the feedback or judgment reduces the power of the assessment to serve LEARNING.

While tests are most common, formative quizzes and exit tickets are often also largely assessment of a product “after the moment” when the teacher responds the next class. For example, I routinely use “not-for-grade” quizzes. These quizzes are very short (usually 1-3 questions) and I give comment-only feedback. No grades, no levels, just written feedback. I also post solutions for these quizzes electronically so students can fully review solutions. Where multiple solutions are possible, I often post two interesting solutions and discuss in class. In addition to providing feedback to students, formative quizzes and exit tickets can also inform the teacher about next steps in instruction.

Notice something very important to the conversation (I put it in bold). In the first paragraph, is an example of a summative assessment, whereas in the second paragraph the assessment is formative. To give some grounding in how I will use those terms. Formative assessment is any assessment that is used to modify instruction either at the moment or in the future. Summative assessments are end of learning assessments that do not have an effect on instruction for this semester.

The question I had from this is, Can each quadrant have both summative and formative assessments?  What would that look like? What are examples that fit?

Quadrant 1, formative: Conversations about work being done (paper, VNPS, etc.), think, pair, share exercises, error analysis (teacher provides examples), My Favorite No, card sorts, etc.

Quadrant 1: summative:   <insert sound of crickets chirping here>  I am stuck.

Quadrant 2, formative: Journal writing, Reflect & Self-assess, correcting and re-evaluating turned in work, etc.

Quadrant 2, summative: Portfolio work that shows the process towards a learning goal, making a video which shows how to accomplish a learning goal, etc.

Quadrant 3, formative: In a presentation, keeping track of learning outcomes or goals through comments, question and answers or discussion during a presentation (thinking of a poster presentation here).

Quadrant 3, summative: <more crickets?> Again, I am stuck.

Quadrant 4, formative: A quiz, where the learners are encouraged to come in and relearn and retake or correct the quiz with grade replacement. <is this really formative? not sure> Exit tickets, collecting feedback on sticky notes, and other methods definitely are formative.

Quadrant 4, summative: An exam. This is a classic example of the end of chapter exam, or a quiz with no retakes.

I am not sure of all the types of assessments I put in the different quadrants. How would feedback being given in the moment on the process of factoring quadratics (for example) be summative? Is a quiz that is not fixed in the gradebook (as far as grade) really formative?

I find the structure of the quadrants helpful in thinking about when assessments are given and towards what end they are given to be helpful. However, the usual categories of formative and summative assessments don’t always fit here. Is this a problem of the terms formative and summative? Should we stop using them (fat chance, given the history and literature of assessment)?

Ann’s post really got me to think about assessment, and how I explain it to preservice teachers. I am not sure it is the last word, but I do know that I have had experience teachers explain to me that the only kind of assessment that is formative is “In the moment” assessment. Clearly that is false given the types of items listed in quadrant 4.

Any suggestions? Additions? Criticism?  I think this model of thinking about assessment has opportunity for understanding the different types, but it needs to be fleshed out more.

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