Latin School of Chicago

W H A T I S S I N G A P O R E M A T H ? Singapore Math refers to the curriculum and teaching method that was developed by that country's Ministry of Education in the 1980s, based on the best education research and theories from around the world — including work from Jerome Bruner (U.S.), Jean Piaget (Switzerland) and Lev Vygotsky (Russia). After the country created textbooks and instituted the program for primary school students, Singaporean students have consistently dominated international rankings for math. One of the features of the teaching method is that students are taught in a three-step process: from concrete (where students use math manipulatives like blocks, paper clips or cards), to pictorial (where students look at and draw pictures such as bar models, that represent quantities and relationships), to abstract (what one thinks of as the typical math equation, for example 10+8+2=20). The other hallmark of the method is that it is student-led rather than teacher-directed — but more on that in a bit. The program was started at Latin in 2015, according to Julie Brooks, director of the lower school. Brooks said that the impetus for adopting Singapore Math was not so much about the students' skills at that time, but more about their critical thinking. In fact, the emphasis of the Singapore Math program is conceptual understanding before procedural fluency. Before its adoption, some students were not able to solve a math problem using more than one approach. "We want our students to be able to think flexibly and deeply," said Brooks. "Singapore Math benefits students because our kids are becoming adept problem solvers. It'll be exciting to see how this impacts them as they make their way into higher-level math." In the Classroom Students usually are given what is called an anchor task at the beginning of class with very minimal directions and no formal instruction. For Smith's first graders, the problem is usually picture-based, like "How many stepping stones are there altogether?" Students will work on this task, usually independently for a few minutes, then in small groups, working out the problem in their math journals. Students can use any method they want, including using their fingers or the manipulatives. Smith then will bring the class together as a whole and she will select three or four students to describe and demonstrate how they solved the task. Smith will write these on the whiteboard. With guiding questions from the teacher, students come up with what they learned based on the discussion of the strategies shared. The students then write a reflection in their math journals about how they felt about the lesson, such as "I made a mistake but I learned from Joey" or "This lesson was fun." The lesson usually concludes with some type of game that reinforces the concept. Anyone who has suffered through years of dull math lessons with the teacher droning on can see that this method of teaching is a radical departure. Math researcher Magdalene Lampert, author of "Teaching Problems and the Problems of Teaching," has likened it to a shift of the teacher role from "I/we/you" to "you/y'all/we." Smith likes the fact that Singapore Math puts the focus on the student. "The ownership is on the children with the teacher steering," she said. "Students really feel invested in the learning. It's a big shift from how we were taught." Smith also likes the fact that there are lots of entry points for students, which Jo Boaler, professor of mathematics education at Stanford and author of "Mathematical Mindsets," calls "low floor high ceiling," meaning everyone can begin to work on a problem at his or her own level, but the task also offers possibilities for students to be challenged. In Smith's class, this might mean that some students are using concrete materials to solve the anchor task or that she or an assistant teacher writes the student's solution method in the math journal for a student who cannot yet write. Of course, fourth grade students have more advanced anchor tasks, such as fraction problems ("Two people have six apples that they want to share with four friends. How many apples 24 24

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