PreK-2 Measurement Learning Trajectory

The expected measurement learning trajectory for students at grades PreK-2 is based on developmental research (see Measurement: Developmental Research and Theory at http://www.designedinstruction.com/learningleads/measurement-research.html), and is influenced by the measurement standard continuum of expectations described in the Principles and Standards for School Mathematics (NCTM, 2000), as well as the heuristics we've designed to accommodate various instructional aspects and philosophies that best promote student understandings and abilities to apply measurement skills with meaning and insight. The standards are grade-dependent; the heuristics are not. It should be noted that the expected measurement learning trajectory, as follows, is descriptive of the individual student.

Diagram of mathematical measurement learning trajectory.

To recast what we have asserted elsewhere regarding measurements (and to reassert this as truth that is not by any means restricted to measurement learning), no group ever learned. The trajectory therefore seeks to project the change necessary in a student's understanding and ability that should occur as the student moves toward meeting the intended learning goals and objectives. In a PreK-2 unit the trajectory is continually revisited and studied, while the cycle (see Measurement: Instructional Design and Approach at http://www.designedinstruction.com/learningleads/measurement-design.html) describes both the expected learning and the instructional actions of the teacher or facilitator as he/she works throughout to ensure that the individual growth of students and the taken-as-shared mathematical processes that evolve blend in a well-balanced and complimentary manner. The table below describes the cycle phases in terms of both teacher practices and the corresponding individual learning that takes place along the trajectory continuum. When related to the trajectory diagram above, one can see that the "modeling" phase of the cycle takes place when students are essentially in the transitional stage, the "application" phase when students are in the operational measurement stage, and "exploration and revision" at the interface of student development from transitional to operational.

- Corresponding Trajectory and Cycle -
Learning Cycle	Individual Learning Trajectory
Modeling: Teacher encourages structuring of linear distance by using "pace" as a model of distance measurement. Activities progress from the student's use of his/her own body to a derived common average, emphasis shifts from early to later transitive reasoning, and students emerge with an initial concept of distance that transcends counting.	- Body referents and distance (physical pacing, counting, and the concept of distance) - Third referents and taken-as-shared distances (the average distance of the pace, iterating paces as distances)
Exploration and revision: Teacher poses conditions that lead students to iterate measurements in groups of paces in order to simplify tasks and gain accuracy. Suggested use of ten (10) paces prepares students for revision of paced distance model to use of accepted tools for modeling distance measurements.	- Cumulative distance (grouping paces, base-ten counting, adding and subtracting by ones) - Quantified distance (tools, such as ruler and meter stick, as models for base-ten measurement)
Application: Teachers assist students in comparing and combining various distances, and in translating concept of distance measurement to length, height, and depth. Subsequent activities challenge students to solve problems that require numerical reasoning under increasingly complex spatial constraints.	- Quantified numerical relationships (ratios of individual measures to total distance, actual vs. scale size, comparison of heights and lengths of reference objects in a spatial context) - Reasoning in numerical and spatial contexts (problem solving applications involving numerical quantity and cumulative distance under varying spatial constraints)

If this is your first time to visit LearningLeads™, or if it has been awhile, be sure to take a look at the LearningLeads™ homepage at: http://www.designedinstruction.com/learningleads/index.html

For more on measurement, go to the Measurement, Geometry, and Spatial Sense curriculum and learning strand overview page at: http://www.designedinstruction.com/learningleads/measurement-geometry.html

If you teach or have colleagues who work with preschoolers, go to the PreKorner™ homepage to browse similar resources, at: http://www.designedinstruction.com/prekorner/index.html

You may be particularly interested in the early childhood numeracy resources, at: http://www.designedinstruction.com/prekorner/early-numeracy.html

PreK-2 Measurement Learning Trajectory

LearningLeads™ - PreK-2 Measurement Learning Trajectory (print-friendly html version)