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For years, schools typically had a generalized approach to math assessment and intervention. A teacher would give an exam that tracked student achievement based on course goals, often combining several skills into one exam. The students scoring in the lowest 20% might get interventions, and the other students would move on.

However, according to Amanda VanDerHeyden, Ph.D., Founder and Chief Product Officer of SpringMath Accelerate and a former district leader, this focus on the General Outcome Measurement (GOM) model doesn’t work for math. In fact, during the edLeader Panel “Using Math Curriculum-Based Measurement: From Screening to Instruction,” she explained that teachers should regularly measure student achievement based on mastery of discrete skills in order to provide effective instruction.

First, math is relentlessly hierarchical. Each baby skill a student learns (like adding one-digit numbers) becomes the foundation for a skill at the next level (adding two-digit numbers). Consequently, skipping a step or letting a student slide on mastery can fundamentally impede their math education.

Moreover, when an assessment is based on the GOM model, where the focus is on long-term measurements or goals across units, multiple skillsets are subsumed under the larger skills, and there isn’t specific insight into student learning.

Second, VanDerHeyden says many other assessments provide data that obfuscates a student’s understanding of—or lack thereof—a concept. For example, if a teacher gives students a test at the beginning of the year in second grade that includes complex addition, subtraction, and some multiplication, the teacher isn’t getting any real data if the students haven’t been taught that skill yet. Thus, the teacher will start most years with similar assessment results that don’t indicate where a student might be having difficulty.

In addition, even if the test focuses on a single skill, if the test isn’t timed, the results can create false equivalencies. If one student gets 10 answers correct, for instance, on an untimed test, and another gets 50 correct, they could both be marked as achieving 100% accuracy even though the first student completed fewer problems.

Instead, math assessments should use mastery measurement, grounded in the science of learning, with the ability to drop back a skill and drill down in order to understand where a student is on their journey. In order to accomplish this, assessments need to be situated in the phases of learning:

1. Acquisition: The student is building the new skillset and is learning to discriminate between the different elements of the skill.
2. Fluency: Here, the student is not only trying to achieve accuracy but also speed.
3. Generalization: Finally, the student is not only fluent in the skill, but they can also apply the skill in new situations

For example, if a student does not demonstrate mastery when converting improper fractions to mixed numbers, then the teacher needs to know whether the student is still in the fluency stage and has to build speed and accuracy, or if they don’t understand how to divide one-digit numbers into one-to-two-digit numbers with remainders. If the student doesn’t know how to divide with remainders, then the assessment might look at whether they can divide numbers without remainders.

In this way, the assessment is helping the teacher understand where the student is on the math skill tree and what intervention they need. Similarly, when an assessment shows that a student is at the generalization phase, the teacher knows the student is ready for the next skill.

Most important, this methodology can be applied to build proficiency in all students. There are no limits on what a student can learn, whether or not they have a learning disability. Different students will need different dosages of instruction to reach mastery, but teachers can use evidence-based assessments with all learners.

A significant component of this process is regular assessments throughout the school year rather than just one or two big exams. Teachers can’t adjust their instruction without frequent data on their students’ performances. In fact, VanDerHeyden made it clear that assessments are just a tool for teachers and that the teacher’s ability to act on the information and adapt to student needs is essential to effective math instruction.

Learn more about this edWeb broadcast, Using Math Curriculum-Based Measurement: From Screening to Instruction, sponsored by SpringMath Accelerate.

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Building Understanding in Mathematics is a free professional learning community that provides a platform, advice and support in helping educators learn methods that help students build understanding in mathematics.

SpringMath Accelerate is an MTSS solution designed to improve math achievement for all students through a comprehensive system of screening and progress-monitoring assessments, classwide and individual interventions, and data-driven decision-making tools. SpringMath Accelerate empowers teachers by automatically interpreting data, pinpointing specific skill gaps, and providing recommendations for instructional next steps, each and every week, so all students achieve grade-level foundational skills mastery.

Article by Stacey Pusey, based on this edLeader Panel