No One of Us Alone is as Smart as All of Us Together

“No one of us alone is as smart as all of us together.” This is a quote to live by in any collaborative environment; but it admittedly isn’t easy to implement and embody in a classroom, department meeting, or even a circle of friends. For this post, I’d like to focus on how this mantra could be woven into student collaboration. In essence, how do we go from the ‘divide and conquer’ mentality to a place where student groups genuinely work together to create shared knowledge? There are of course a few important things at play, but one striking current that can work against this ideal is the issue of status. Status, high or low, can stem from gender, race, socioeconomic status, social status, strength in other classes, prior math experiences, etc. And whether it is voiced or not, this sense of status affects daily work and interactions in a huge and meaningful way. By this I mean that when presented with a task or problem, students with high status are expected to do well and so, they often do. The opposite happens for low status students. And this is not just self-perception. The truly tragic part is that this status is propagated by self, other students, and occasionally (even if inadvertently) the teacher.


The good news:

There is something you can do about this inequity when working to have students create shared knowledge while working on a task. Task design is of course crucial; tasks must be complex enough to genuinely require all students and provide equitably entry points. Group work norms are also a vital piece; do all students have a role and equitable access to the work at hand? But to grapple with, tackle, and reduce status issues, this is where smartnesses come in! Yes, I said smartnesses, or if you prefer, competencies. In her book Designing Groupwork, Elizabeth Cohen describes how addressing competencies can address status, “The strength of the treatment lies in the way that it attacks expectations for competence held by the low status student for himself as well as those held by the high status student for the low status student’s performance.” We must challenge current beliefs to show that all students have individual math strengths to share and contribute to the newly found, shared knowledge. Critically, students must genuinely believe and internalize this, too.


Making this practical:

Assigning competence in the classroom is something that takes prep work and practice to be sure. To assign competence, you are pointing out to a student (and his/her group) why and how he/she is smart in math and how this is useful to the group. Assigning competence has three requirements to be successful. The competence assigned…

  • Must be public – privately telling a student why she is smart may help her begin to change her sense of self, but will do nothing to help change the way other students see her and engage with her in the work
  • Must be math-related and specific – we want to focus on the skills/abilities that make mathematicians great at what they do
  • Must be relevant – we want to state why this skill/ability is useful to the group, raising this student’s status in the group


When designing your task, think about the ways a student could be smart while investigating the problem. This is a task that takes some practice and would be great to with peers when co-planning. These do not have to be, and in fact probably shouldn’t all be, traditional math skills like computation. Cohen gives the example of teaching that I think is a great framing thought here. A shallow view of smartnesses of a teacher would be that to be a good teacher, you need only to have good content knowledge, but we all know this is a drastically minimized view. In reality, “teaching requires great interpersonal intelligence, organizational ability, conventional academic ability, verbal ability, as well as creative ability.” These are abilities that may not be in the forefront when many think about teachers, but man are they vital. So as you plan your problems/tasks and as you listen and watch your students work, try to formalize a few traits and abilities that are essential but not always highlighted. Here are three examples of things that I have said to students as I circulate in the classroom as starting points:


“That color-coding that you did to show the point on the graph and in the table is a really smart way to show that    connection to others.”

“It is such a smart idea to do what I just saw you do; rotating your paper can help get a different perspective on a diagram so you can all see what you’ve been given.”

“I’m so glad to hear you say, ‘Well, let’s try it again.’ That perseverance and re-starting that we talked about is such an important piece to help your group get to that final solution.”


In essence here I’m highlighting connection-making, perspective-taking, and perseverance, but in ways that are clear to students. These are not things I necessarily ever thought to be vital math abilities when I was in school, but they are so powerful as students investigate and grapple with tough problems in their groups. If we as teachers can all begin to build a vocabulary of smartnesses, I believe we could dramatically shrink the deficit-based thinking of students and teachers alike. Many days, I got to walk around my classroom all day telling students how they were authentically smart. To me, that’s a pretty great way to spend a day.


Some extensions for your consideration:

  • Multiple Ability Orientation (MAO): instead of only sharing the smartnesses as you see them, identify them ahead of time and state them to students. Here is an example of a MAO I used before starting a new problem on inverse trigonometry. I posted the list and clearly stated that not one students will have all of this knowledge nor all of these skills, but that as a group, all abilities were present. At times, I’ve even had students identify which ones they know they are good at (and share them with their group) and which ones they wanted to work on improving during the problem. In this way, I hope students gain awareness and accountability.
  • Smartness List for Underachieving Students: print off your list of underachieving students (either by grade earned or by some rubric you set personally) and write at least one smartness next to the name of each student on the list. Carry this list with you throughout the next week trying to identify these smartnesses and share them in the moment with students.


Note: In writing this post, I must thank the math department at Cleveland High School in Seattle, Washington as well as our former coaches, Lisa Jilk and Karen O’Connell, from the University of Washington. It was with the guidance of these coaches and the collaborative work with these teachers that I have gained an understanding of status issues, the importance of equity, and the tenants of Complex Instruction.