Math Trajectories


Math Trajectories Tool

The Math Trajectory Assessment Tool was created in conjunction with Oakland Schools in suburban Detroit, MI and is based upon the book by Douglas H. Clemens and Julie Sarama, Learning and Teaching Early Math: The Learning Trajectories Approach as well as the training courses by Dr. Chris Cain in the Teaching of Mathematics for Students with Severe and Moderate Cognitive Disabilities. This tool is intended to be a teacher ready assessment, standards, and instructional connector.

The tool can be used as a visual reference to show current student abilities, target next steps, and a way to demonstrate progress over time. The trajectories are grouped into two broad areas: numeracy/operations and geometry/measurement/data. This lends itself to the concept of having two math goals using overall growth in a number of trajectories that work together rather than viewing each column as a separate math concept to teach in isolation. Ideally, the teacher would individually assess the student and then color code each area to show if the skill is present, emerging, or not being addressed. For reference, the standards will be aligned to make goal writing for IEPs a natural crossover. Instructional activities, web references, trade book suggestions, and teacher created materials will be made available to align with each trajectory.

Math has not received the focus that has been given to reading in teacher education programs and too often students with disabilities are not given exciting mathematical concepts to learn or problems to solve. While we know what to do when a student cannot read, we are only beginning to have solid strategies and tools readily available in math education. The learning trajectories showed me the potential of early math concepts and this tool is meant to support teachers in creating math opportunities for all.

Table of Contents

The Math Trajectories Assessment Tool


1. Number Recognition and Subitizing
2. Counting
3. Comparing, Ordering & Estimating
4. Addition & Subtraction
5. Composition, Place Value & Multi-digit Arithmetic


6. Spatial Thinking: Orientation
7. Spatial Thinking: Visualization and Imagery
8. Shapes
9. Composition in 3D Shapes
10. Composition and Decomposition in 2D Shapes
11. Length, Area & Volume Measurement
12. Angles
13. Patterns