Mia Buljan has taught mathematics at Glassbrook Elementary in Hayward, California, for many years. At the time of this recording, in 2015, the student population at Glassbrook was predominantly Latino (86%), African American (5%), and Asian (3%); the majority of students were documented as socioeconomically disadvantaged (92%) and English language learners (70%). This lesson was recorded as part of a year-long process to document Mia’s teaching and develop practitioner guides for building strong practices in teaching and learning mathematics.
In her teaching, Mia makes regular use of “mentor problems” to help her students identify and connect mathematical concepts within quantitative problem-solving situations. She then uses experiences from students’ lives to give these concepts working titles the students can relate to: in this case, a “put-together” problem is given the name “Diva’s Stickers,” named for one of Mia’s students and capitalizing on the interest of all her learners in collecting and sorting stickers.
Early in the year, Mia had introduced a situation in which “Diva has _____ stickers. She then goes to the store and gets _______ more. How many stickers does Diva have now?”
In her recorded lesson from later in the year, Mia goes on to use the students’ prior experience with this problem to help them identify and distinguish “put-together” problems from “take-apart” problems. She gives them the opportunity to defend their thinking to her and to classmates, engaging them in productive struggle, use of appropriate tools, and the opportunity to look for and identify mathematical structures. One of Mia’s main reasons for using mentor problems is to create a space where she pushes students to try more strategies and moves them along to more productive strategies. Mia notes that before she started using mentor problems, that “if a student was counting on their fingers in September, they were still counting on their fingers in May.” By sticking with one problem, Mia has given students the cognitive space to experiment with strategies, to compare strategies, to think about which numbers work best with which strategies, and to be ever more efficient in their mathematical problem solving.