Assessment at Long-View: To “Assess” is to“Sit Beside”

The word “assess” comes from a Latin word meaning “to sit beside.” While the concept of assessment has taken on a life of its own, especially in the world of education, the word’s etymology reminds us of the true intent. As a teacher, if you are not sitting beside a learner when you set out to assess, you are actually grading, not assessing. The difference matters. 

As discussed in our recent post on conferring, much of our culture at Long-View centers around talk. Across the day, learners are expected to say more about their thinking. It is not enough, for example, to say that you think that the midpoint between 8 and 46 is 27. There’s always the follow-up question: “How did you think about that?” Early on, learners may respond by saying, “I am not sure,” or “It just seems like it should be.” As teachers, we lean into these responses and support learners in developing their metacognitive processes so that they can articulate the thinking by which they arrive at understanding. 

Through this continuous dialogue, Long-View teachers are constantly assessing. We don’t wait until the end of the week and give a quiz to gain insight into a child’s thinking; instead, the feedback loop is much shorter and occurs many times across the day. 

In the previous example about finding the midpoint, a series of questions guided the learner to verbalize his thinking process. His teacher first asked, “How far do you need to jump to get to the midpoint?” (This question was predicated on the work the learner had already done developing a mental number line, and thus the teacher was referencing ‘jumping’ from 8 to 27 on a horizontal number line.) Next his teacher asked, “How does it compare to the range?” And followed up with, “Say more! Can I write that thinking for you?” Frequent individual experiences like this, as well as similar ones that are situated in whole-class conversations, are formative. With this type of talk happening across the day, learners develop important metacognitive and communicative skills. And teachers can assess the teaching/learning process.

Amid our daily work, assessment often looks like a teacher sitting one-on-one with a learner in the bustle of the classroom to ascertain where that child is in the learning process and to provide clear feedback that will allow the learner to move forward more productively. These interactions, and the feedback provided therein, will look different for each learner, as everyone is working at their own pace. 

During a recent independent Studio in Magenta Band’s Math Block, for example, Mrs. White provided learners with nine problems to work through. As they worked, she was able to meet individually with — or “sit beside” —  six different learners. Below are a few notes from the exchanges.

Interaction #1:

After seeing that one learner was pondering 87 ÷ 6, Mrs. White sat beside her and asked a series of questions to find out more.

Mrs. White (referencing the given problem, 87 ÷ 6): “Let’s start by reading the expression.”

Learner A: “Eighty-seven sixths.” (Mrs. White scribed this for the learner: 87 (⅙) ).

Mrs. White: “Okay, what do you know about sixths? Where could we begin?” 

Learner A: “Six-sixths is one whole.”

Mrs. White: “I am going to write that down.” (Mrs. White drew a vertical line and continued scribing off to the right so that the child could focus on her thinking — see image below in which Mrs. White writes 6/6 = 1, followed by 60/6 = 10, which the child calculated by considering the relationship between 1 whole and 10 wholes and applying that to the fractional count.)

Mrs. White: “Ok, how could you build from there? What about two wholes?” 

At this point, Mrs. White handed over the pencil and stepped back to observe what the learner would do with that information. When the child said that 30/6 = 5 wholes and that two wholes would be equal to twelve-sixths, Mrs. White pressed her to explain: “How did you think about that?” The child’s explanation of her thinking gave Mrs. White further insight into exactly how the young learner was processing the mathematics — the way she was thinking about the idea of division (i.e. that she was able to read the given expression and recognize the definition of division and its relationship to counting sixths), as well as how she leveraged relational thinking to find, for example, that 12/6 = 2, recognizing its relationship to 6/6 = 1.)

Interaction #2: 

As Mrs. White looked over the work of another learner who happened to be working through this same problem, she pointed at the learner’s paper (see below image) and probed this child’s thinking.

Mrs. White (pointing to the line of the algorithm that says 16 + ⅙): “Can you go back and explain to me your thinking here?” 

Learner B: “Well, I had fifteen wholes, because sixty-sixths and thirty-sixths together is fifteen wholes.”

Mrs. White: “I agree that sixty-sixths is ten and thirty-sixths is five, but I disagree that, together, that is equal to eighty-sixths. Can you see the misstep?” 

Learner B: “OH! I see…that would be ninety-sixths, so I have too many sixths.”

Mrs. White: “Excellent. May I notate for you as you rework your thinking here?” (Mrs. White picked up the pencil and began scribing as the child re-visited the line of the algorithm.) “How do you want to refine this line?” (See below image, the finished version of this child’s revisions.)

During exchanges such as the above interactions between Mrs. White and both Learner A and Learner B, the teacher was assessing: gathering holistic, complex, real-time information about how learners are thinking and what the understand. This knowledge of where learners are and what they are growing towards provides the teacher information on the child and the future instruction that might be most beneficial.

Had Mrs. White not assessed in this way — by sitting beside these young mathematicians and working to understand their thinking — she would have learned little. If, instead, she had followed the tradition of many math teachers and assigned the problems, picked up the papers, and graded them at a later date, she would have very little information to work with in understanding the teaching/learning process and in assessing each child’s true understanding. In sitting beside learners, insisting that explanations are provided, teachers know exactly where learners are and can provide the critical instruction and support that empowers children to drive their own learning — the ultimate goal.