# Not Goodbye, but See You Later

As you may know, our own Rosalyn Gaines, in taking steps toward reaching her own professional goals, has moved into a new position within BCPS and will be the paraeducator in the PSFALS program at CCBC Catonsville. While we will miss her in our day-to-day, we support her in achieving her goals and wish her the best in her new position! We look forward to Ms. Gaines’s continued support of our African American Organization and work with our students in hosting Black History Month Celebrations. See you soon, Ms. Gaines!

# Aiming for the Productive Struggle

As we welcome another week (and the close of the first quarter!), I want to thank each of you for your efforts in teaching GRIT, not just in GRIT lessons, but through the ways you establish the culture of your classroom and the expectations you have for students to persevere. Throughout the week, I’ve been in classrooms where students have set goals for themselves (build this bird box correctly, write my best essay yet, or create just the right texture in clay) and have integrity in what they do (pull these nails out, I didn’t do it right this time; revise and rewrite; smash the whole piece and start again). For a shining example of one such collaboration, check out the music video Ms. Smith’s students created: GRIT Mixed Tape

The learning process can be frustrating (like the one I went through to insert the link above) and it takes stamina and perseverance, GRIT, to keep going, start over, or work to get it right. As you aim for students to find the productive struggle in their work, consider the article below by Rachel Dale and Jimmy Sherrer:

**The “Goldilocks” Level of Scaffolding and Support for Students**

In this *Kappan* article, Rachel Dale (an elementary teacher in Wake County, North Carolina) and Jimmy Scherrer (formerly of North Carolina State University) describe how the following math problem was taught in three different classrooms:

*Tyler and Samantha ordered same-size pizzas. Tyler’s was cut into eighths, Samantha’s into tenths. Tyler ate four pieces of his pizza. How many pieces would Samantha have to eat to consume the same fraction of her pizza? Explain your work with words, pictures, or numbers.*

*Classroom #1*– The teacher reads the problem aloud, asks students to solve it with a partner, and circulates. In one group, a student quickly solves the problem by seeing that 5/10 is the same as 4/8, but his partner doesn’t get it. The teacher decides to let them wrestle with it on their own. Another pair is arguing about whether the pizzas are pepperoni or cheese. The teacher is happy they’re engaged and again, doesn’t intervene. She notices that a number of students are drawing circles for the pizzas and having trouble dividing them up appropriately. She decides to let them struggle with this interesting challenge. At the end of the class, she assigns 20 equivalent fractions problems for homework.*Classroom #2*– The teacher reads the problem to students and walks around the room observing groups working. One is drawing circles representing the pizzas but has divided both into eighths. The teacher draws two circles and shows how to divide them up correctly. The students thank him. Another group is stuck trying to figure out 4/8 = ?/10. The teacher suggests that they draw two circles to represent the pizzas, divide one into eight pieces, the other into ten, shade in four of the eight pieces, then look to see the equivalent proportion in the other. Assuming that the students are no longer confused, the teacher moves on. Another group is making the mistake of dividing both pizzas into eighths, and the teacher decides to call the class to order and demonstrates the correct procedure on the board. He adds that they can use number lines instead of drawings. Unsure about the level of understanding, he doesn’t assign math homework.*Classroom #3*– The teacher displays the problem, asks a student to read it aloud, and challenges students to solve it in several different ways. She circulates and notices one group of students who quickly realize that 4/8 is the same as 5/10. “How might you be able to convince me of that without using numbers?” she asks. The students ponder this and begin to draw the pizzas to illustrate the fractions. The teacher overhears another group talking about their favorite kinds of pizza and immediately redirects them to the task. A third group is having trouble partitioning their circles; they tell the teacher they’re trying to compare the circles. “Say more about that,” she says. “If we can get this circle into 10 equal pieces, we could see how many of these pieces would equal the four pieces that we shaded in that circle,” says a student. “I see,” says the teacher. “If you are having a difficult time dividing the circle into equal pieces, perhaps you can apply your method using a different shape.” As she walks away, the group is discussing using squares or rectangles. The teacher lets students work for five more minutes and then convenes a whole-class discussion.

These teachers’ ways of handling the same task demonstrate three possible points on the “Goldilocks” scale:

- Too little scaffolding, resulting in unsystematic exploration;
- Too much scaffolding, constraining opportunities to think through and persevere;
- Just the right amount of scaffolding, resulting in productive struggle.
- The third teacher’s interventions were appropriate, say Dale and Scherrer. The teacher didn’t hesitate to get involved to help students who were off task or stuck, but she didn’t reduce cognitive demands and asked questions that pushed students to think through possible solutions on their own.

“Goldilocks Discourse – Math Scaffolding That’s Just Right” by Rachel Dale and Jimmy Scherrer in *Phi Delta Kappan*, Oct. 2015 (Vol. 97, #2, p. 58-61), www.kappanmagazine.org;

Dale can be reached at rdale@wcpss.net.