Using Jilk’s (2016) “It was smart when…” statement to name and notice students’ mathematical strengths

For a while now, you’ve read about the Rights of the Learner (RotL) (1 2 3 4) and how it can help push students’ ideas/voices/thinking to the forefront.  Students who exercise their rights to learn see that ALL of their ideas are valuable and can make a contribution to the classroom.  But other than encouraging students to exercise their rights as learners (and doers) of mathematics, how else can teachers redistribute the power in the classroom so that more students find success in mathematics?

For the past three years, I have been blessed to work on a project Sandra Crespo, Nicole Bannister, Diana Bowen and Lori Jacques. Without getting too much into the weeds about the specifics of the project, we use an online digital platform called LessonSketch to present a series of cartoon storyboards that shows children working on a mathematical task. The goal of our project is to help our pre-service teachers to use strength-based language to name and notice students’ mathematical strengths.

Strength-based language emphasizes what students KNOW instead of what they DON’T know (Jilk, 2016).

Mathematical strengths are more than just getting the right answer or being fast to solve a problem– those are strengths that are overvalued in our schools. Those students are always seen as smart. What about everyone else? What are their strengths? How are all kids smart in some way? By only focusing on a small subset of smartness, we are missing the subtle examples of students’ mathematical strengths. Maybe a story might help put this in more concrete terms:

Imagine that you are a student who is presented with the following division problem, “I have 24 cookies to share with some friends. Each friend can get 4 cookies each. How many friends can you share your cookies with?” What if you as the student said, “well I know that 24 – 4 – 4 – 4 – 4 – 4 – 4= 0 so because there are six 4s, that must mean I can share my cookies with 6 friends?” Let’s pause here and consider the following scenarios and tell me which one you would want to hear if you were the child:

  1. Your teacher interrupts you and says, “24/4=6, so the answer is 6. You need to memorize your division facts. What you did took too long to get to the answer.” 
  2.  Your teacher listens to your strategy and says, “Ohh… well, at least you got 6. Good job.”
  3. Your teacher listens to your strategy and then responds, “Ohh it was smart when you used repeated subtraction to solve that division problem. I see that you arrived at the answer of 6 friends. How you solved it actually represents the actions in the story and helped you to find an answer.”

What’s the difference between these scenarios? Did one feel different to you than the others? Scenario1 emphasizes the deficits in the child’s strategy. What did the child NOT do well or correct. The Scenario2 gives the child praise, but it isn’t really a neutral statement (something that our LessonSketch group is writing about now). The Scenario2 has a subtext that says “you didn’t solve it how I wanted you to solve it, but at least you got the right answer.” The Scenario3 should feel different because it has the three markers of a strength-based statement (Jilk, 2016):

  1. uses the phrase “it was SMART when”
  2. states the mathematical smartness (using repeated subtraction to solve a division problem)
  3. provides a justification for why this is something smart to notice (using repeated subtraction actually represented the actions in the story.)

Learning how to do this is hard because we’ve been trained to look for what’s wrong. Sound familiar? (if not, maybe you need to read my blog about the football Wonderlic test and how these assumptions about being smart can last for years…) Using strength-based language is challenging because as Jilk (2016) states:

…many of us experienced a very narrow and limited version of math as students, which can make it difficult to notice strengths in our classrooms. We teachers were often apprenticed into school mathematics communities with dominant cultural norms and practices that required us to memorize, practice, reproduce and solve problems quickly. (Hand, 2012; Secada, Fennema, & Adajian, 1995). Sadly, we might never have experienced the broad and beautiful practices that make up the field of mathematics, which makes it hard to know what counts as a strength. (p. 189)

If you want to hear Jilk talk more about this, you might listen to this great interview. For the past few years, I’ve been working with my LessonSketch colleagues on ways to help my pre-service teachers learn how to name and notice students’ mathematical strengths in everything that they do in my class. They learn about the three components to a strength-based sentence and use it when they examine students’ work or when they watch a video of a child solving a problem. 
As an adaptation to our elementary mathematics methods class, Emily Bonner and I asked our pre-service teachers to conduct a Mock Parent Teacher Conference at the end of the semester. During this 15 minute Mock Conference, they present evidence of a child’s thinking after conducting a series of problem solving interviews (as developed by TEACH Math). Over the years, I’ve had my students use the sentence stem…but not as consistently as this one student, who we’ll call Ms. R. With her permission, I’ve posted pictures from her notes that she used during the Conference.  In the three examples below, we’ll see how Ms. R. uses the strength-based sentence stem to name and notice Ariel’s (another pseudonym) mathematical strengths when working on problem solving tasks. 

Example 1: Ms. R. asked Ariel to group the green blocks in whatever way she wanted.  Ariel grouped them in a pattern mixed with light green and dark green blocks (2 groups of 3). Although Ms. R. expected Ariel to group them by the same color, Ms. R. made a strength-based statement about how children can group blocks by color that also shows different groups of items (3 groups of 2).
IMG_3922

Example 2: Ms. R. gave Ariel 20 guinea pigs to put into 2 cages (from their textbook). One cage was blue and the other was purple (based on Ariel’s favorite colors. Ariel said that 11 guinea pigs in the blue cage and 9 in the purple was DIFFERENT than 9 guinea pigs in the blue cage and 11 in the purple. Ms. R. then wrote a strength-based statement about Ariel’s ideas. During our Mock Parent Teacher Conference, Ms. R. and I also talked about the importance of providing a specific, mathematical justification. In Ariel’s work below, we could note evidence of the commutative property (11+9 = 9+11) to show Ariel’s smartness when solving the task. IMG_3923

Example 3: In this final example, Ms. R. gave Ariel cookies arranged in a pattern so that Ariel would quickly count the cookies by groups without counting them individually (Based on the task in Intentional Talk by Kazemi and Hintz). When Ariel posed an example of cookies arranged in a pattern, she arranged the cookies in two groups of 4.  Ms. R asked Ariel what she did to arrange the cookies. Ariel talked about how she knew that 4+4=8 and that her groups were even. During our Mock Parent Teacher Conference we talked about how it was important to also note that seeing even groups like 4+4 can lay the foundation for multiplication (2×4) which both equal 8! IMG_3924

Coupled with the Rights of the Learner, I am so excited to see what my students do in the future with these strength-based sentence stems. It truly shifts the tenor of the Mock Parent Teacher Conference to a place that publicly values children’s ideas as important and worthy to note! If you’re a parent at a conference, listen to for that language and see if you can work with the teacher to use it more. If you’re a teacher, test out the strength-based sentence stem the next time you listen to your students communicate their thinking. And don’t forget to make the statement public so more kids can hear the assigned competence! And if you’re a principal, I have some AMAZING new teachers who I think you should hire!

References

Cohen, E. G. (1994). Designing group work: Strategies for the heterogeneous classroom (2nd ed.). New York: Teachers College Press.

Cohen, E. G., & Lotan, R. A. (2014). Designing group work: Strategies for the heterogeneous classroom (3rd ed.). New York: Teachers College Press.

Cohen, E., & Lotan, R. A. (1997). Working for equity in heterogeneous classrooms. New York: Teachers College Press.

Hand, V. (2012). Seeing culture and power in mathematics learning: Toward a model of equitable instruction. Educational Studies of Mathematics, 80, 233–247.

Jilk, L. M. (2016). Supporting Teacher Noticing of Students’ Mathematical Strengths. Mathematics Teacher Educator, 4(2), 188-199.

Secada, W., Fennema, E., & Adajian, L. B. (Eds.). (1995). New directions for equity in mathematics education. New York: Cambridge University Press.

 

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