Brows furrow in concentration as second graders at the University Laboratory School work in groups to come up with equations based on diagrams of 8 and two of its addends (e.g., 7 + 1 = 8, 2 + 6 = 8). They are then asked to draw a line segment representing the relationship of the addends and 8. After a specified amount of time, the teacher/researcher calls each group to come up and explain their answers to their classmates. Another researcher observes and takes notes on the lesson, including how the groups, with varying degrees of confidence, go through their explanations of how parts relate to a whole.
These second graders are helping the researchers at CRDG create a unique elementary mathematics program called Measure Up. The curriculum for grades 1–5 is based on preliminary work done by a group of psychologists, mathematicians, and educators at the Institute for Developmental Psychology and Pedagogy in Krasnoyarsk, Russia. For many years, it has been understood that the transition from arithmetic taught in elementary school to the algebraic thinking required for higher mathematics is a difficult one for students. This is a critical point in a student’s mathematics learning, since it is also recognized that successful completion of algebra is a gate-keeper for higher-level mathematics. The Measure Up program is addressing this critical issue in education by restructuring the way mathematical understanding is developed, thereby allowing an algebraic focus to be introduced in elementary school.
The research team uses its daily observation notes to chart the development of mathematical understandings and to identify instructional techniques that enhance the learning of mathematics. The team regularly conducts student interviews to validate or clarify what it observes in the class. These data are then used to assess students’ progress in understanding mathematics and identify revisions needed in the materials to optimize student learning.
Ultimately, the Measure Up team aims to improve the teaching of elementary mathematics by restructuring the way mathematical understanding is developed in order to lay the groundwork for all students to succeed in higher mathematics.
Measure Up “Family Night”
Measure Up “Family Night” at the University Laboratory School saw curious parents engaged in measurement tasks while their student “experts” eagerly provided guidance and explanations of the mathematics encountered.
First grade parents compared and equalized masses, areas, and lengths. Second grade parents solved addition and subtraction problems in different bases. Afterwards, parents and project staff sat down to talk about the foundation of the Measure Up program and to share insights about helping children with their homework.