*Disclaimer: this post refers to “low kids” and “high kids” as ways students are often talked about in schools. I hope as you read it, it’s clear that I am using these terms to describe how students are consistently categorized in narrow and dehumanizing ways, and that we as educators need to stop doing this – not only because it’s damaging but because it’s inaccurate.*

I grew up thinking that intelligence, particularly in math, was both linear and elusive. On-demand fact recitation, no paper, fast and clever. Learn one thing first, and then the next. Your intelligence is reflected in above-average standardized test scores. That’s how you know you’re good at math. (By these standards, I was decidedly “mid”.)

Something about this fixed idea of smartness has never quite sat right with me, and I’ve always been drawn to ideas rather than performance – but truthfully, educators almost exclusively use these methods to categorize student achievement (the “whys” of that are complex and would take ages to unravel – but suffice it to say, this is how it goes). By now, I’m used to it, but it still makes my blood boil. Someone’s iReady score (sub in your standardized test) is the least interesting thing about them – even if the conversation is specifically about that student’s understanding of mathematics (or any subject).

Before school started, I did my customary go-around to my new students’ former teachers, excitedly sharing with them which kids from their class I get to work with this year.

“She’s sweet, but she’s *really* low,” said one student’s teacher from last year, without pause. (Blood boiling but biting my tongue – trying to tell myself it’s not this teacher’s fault, she’s part of a system that encourages this kind of categorization).

*But what do you see in this photograph? *

Three days into the school year, these two students (who were labeled as essentially unable to understand grade-level mathematics) were tasked with counting a collection of objects. Every other group started counting by ones. These two decided on a “big rectangle”. Their instinct was to organize, prior to counting. A sense of how structure and patterns can be utilized to help us understand mathematics seems vital. Their low iReady scores do not reveal their aptitude to think this way. (Surprise?)

This year, as a math intervention, my grade level was told to create ability groups to meet with during small group time. While this is not my ideal teaching strategy, I began to think how these groups could serve as a humanizing and empowering experience for these students – capitalizing on their strengths, and nudging them to explore new grade-level content. Getting to work explicitly with students who may struggle to feel successful in mathematics – and giving them new ways to engage with it and show what they know is actually *exciting*.

One thing I discovered was that using Illustrative Mathematics’ resources in small group was a way to engage these students in mathematical inquiry and problem-based learning (because the absolute *last* thing we should be doing is gatekeeping that sort of thing for the “high kids”).

These two “low kids”, using an IM card sort, immediately began making connections between representations, situations and expressions. They worked together, collaboratively, bouncing ideas off of each other and defending their thinking. They were able to show that they understood the multiplication ideas they’d only been working on for a week.

Another opportunity we’ve had in our classroom this year is to engage in mathematical modeling. In the below example, students used a consensus board to attempt to figure out how many days our box of Ritz crackers would last our class for snack. They had to use information they knew (6 stacks in a box, 32 crackers in a stack), make some decisions (how many crackers should students get per day? How many students will eat crackers each day?) to attempt to find a solution.

The student whose work is represented on the bottom is one who was labeled “low” by other teachers at the school. What do you see? What I see is that she diligently represented each cracker in each stack to show exactly how many crackers we were working with. I see she made a decision about how many crackers each student would get per day (4). I see she got stuck thinking about how to incorporate the number of people eating crackers each day (most students did) and would benefit from a nudge to consider how she might show the crackers eaten by the class in one day.

To be clear – I think her work is phenomenal – equally as fascinating as the others in her group, who had their unique strategies and models, and their own places they got stuck.

And let’s talk about math quizzes.

My feelings about quizzes are mixed. Long opposed to most traditional assessments, this year what I’ve found is when used strategically, they can be a really interesting tool to uncover students’ understanding of the mathematics they’ve been learning. Some students might choose to complete their quiz independently – while I might ask others if they can show me their thinking about a question in a different way (especially if they’re struggling to represent their ideas on paper, and are hesitant to grab manipulatives).

*What do you think this “low” student is doing?*

He correctly represented his thinking on paper – he counted his grapes by ones and slightly miscounted – but when prompted to show his thinking with cubes, immediately realized he could count by 10s, physically moving the cubes to show what had and hadn’t been counted.

He then used his cubes to immediately solve the next question (which was more complex, and involved ideas such as measurement division that we hadn’t explicitly talked about at this point).

Another “low” student, when working one on one with him building and counting equal groups, would join his cubes together to make his groups, and then join the groups into one long unifix cube tower and count each cube. He meticulously recorded his answers to multiplication equations as he worked through the questions with only slight nudges from me.

If these students understand the mathematical concepts being discussed in class just as much as anyone else, why are they even labeled the “low kids”?

When a computer assessment is your primary way of determining someone’s aptitude, you’re going to be left with the impression that some in your class “can” and some “can’t”. And what about when a significant amount of your students who are scoring low are designated as multilingual learners? They are literally processing language differently than students whose primary method of communication since birth has been English. (Similar for students with learning disabilities).

As a result, they may struggle with reading English at the level that grade-level assessments assume competency in – be it with decoding, comprehension, and/or vocabulary – and when the majority of math tasks students encounter have a high cognitive load up front (read it, understand it, solve it), the barriers are built right in.

Reading comprehension is connected to mathematics only insofar as word problems are the primary source of determining mathematical understanding. Without multiple ways for students to access mathematics content, and multiple ways for teachers to assess it, certain students will always seem “low” while others seem “high”.

Beyond reading, the pedagogical structures of many math curricula (and if we’re really getting into it, school in general) simply aren’t developmentally appropriate for some students. Kids need different things! School systems lacking the ability to give a student an accommodation they need to show they can understand a concept should not be taken to mean “the student cannot understand the concept”.

**Here are some questions I’m thinking and reflecting about:**

- Do we need to categorize students sometimes? It it even possible to categorize students in a humanizing way?
- If yes, under what circumstances does it make sense to categorize students? When doesn’t it make sense?

- What kind of categories are helpful? How do we know?
- I (and other teachers) have to teach a curriculum with fidelity. I have to give certain tests with fidelity. I have to show these tests to families, administrators, and coworkers, and decisions about these students are made as a result of these tests.
- Given all that, how do we push back on labeling “low kids” and “high kids” (or sub your favorite euphemisms – “struggling learners”, “high fliers”)?

- How much of the change that needs to happen is about what we say – i.e. the words we use – vs. what we do – i.e. the structures, routines, and learning opportunities in our mathematics classroom?

I think it’s encouraging that there are a lot more teachers questioning the old ideas of ‘ability’ – even if they are hard to shake off. Teachers in our school are all doing the Stanford course on how to learn math math for teachers, and there’s a lot in there about mindset, challenging the idea that we have a level of ability, and language that perpetuates this.

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I love how you mentioned computer based assessments with the kids who can or can’t. I abhor iReady for this reason. It doesn’t show a student’s thinking or allow for ideas. Thank you for this post.

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