Nationally, student K-12 math scores have been at an all-time low as measured by state accountability testing. Much of this started ten to twelve years ago, when state standards were updated to become more rigorous. Math was rightfully expanded to include not just basic numeracy (arithmetics) but also the application of mathematics in the areas of measurement, geometry, data/probability, and algebraic thinking. Of course, this change makes sense in our increasingly technological world.
The result of this expansion was that the pure number of skills and concepts that needed to be taught at each grade level grew. The growth really showed at the third grade level and maximized at the seventh and eight grade levels. But the problem with a rigorous curriculum is that if students fail to learn something along the way, there is not enough time to catch up. There isn’t even time for the teacher to reteach the materials.
Think of math instruction from grades three through eight as a train progressing at a moderate pace down the track. The teacher is at the front of the train, teaching all the kids who are sitting in the trailing cars. When kids miss class or fail to understand a concept when it was initially taught, it is as if they fell off the train. In early grades, they can jog, catch up, and jump back on. But when they get back on, they tend to be further back on the train. By the sixth grade, the kids are getting spaced out on the train’s many cars. The ones sitting farther away can’t really hear the teacher anymore. So even if they get back on the train, they are not learning much.
The key to solving this dilemma is understanding the nature of math. Math is like a foreign language. What you learn in earlier years is used later on as you advance in your oral and written skills and fluency. Early concepts must be fully understood in order to learn new concepts. There is a push to “not just teach skills.” Teachers or math specialists will say that it is best to focus on teaching grade-level concepts so that students can fully understand the grade-level materials. This sounds great, but the assumption that students have mastered the basics may be incorrect. Data clearly shows that students who are behind tend to be many years behind when given multiple-measure math diagnostics that can find exactly where they are within a range of K-8 instructional skills and concepts.
This misunderstanding manifests itself because everyone is used to looking at accountability tests or grade-level focused tests. For instance, let’s say we look at 7th-grade math results for a school. They are reported in terms of how many students met grade-level proficiency.
Example 7th-grade proficiency reporting for a school or district...
We may see that only 30% of the students passed. This makes everyone think that the other 70% of the students need to learn 7th-grade content. But this is not the case. That 70% of non-proficient students will have gaps in the range of 1 to 4 years. 45% of the students will be 3-4 years behind; 25% are 1-2 years behind.
The next step is to realize that grade-level math teachers cannot fill in these gaps with built-in review by core textbooks or other traditional math curricula. Students who are one to two years behind are not homogeneous. Likewise, students who are three or four years behind cannot be given an extra math class in which one teacher tries to support 20-30 students who are “behind.” Once students are behind in math, a personalized learning model is required. Remember, foundational math is essentially broken down into 44 content tracks that are taught linearly.
If we operate under this personalized learning model, we see that the solution is to adopt a model that isn’t based primarily on group instruction. The weight of group versus personalized learning needs to be flipped: maybe 30% group instruction to 70% personalized learning.
How do we do this? Well, the answer is in front of us! Differentiated learning through technology-based math instruction combined with structural changes to the traditional math classroom. But both of these concepts have to be implemented.
Possible Structural Changes
Flexible and small-group rotational teaching classroom integration
Additional math intervention period for a limited period of time
Addition of an extra period for personalized learning
At beginning of year, 2-4 weeks of personalized intervention
Summer school personalized math instruction catch-up
Math diagnostic that finds instructional points across grades K-9
Adoption of a special education model where students’ present levels are identified across all math sub-tests
The time for lamenting about poor math performance has passed. This isn’t rocket science or, in today’s science issues, EV battery development; we know what to do. Administrators have to stop being firefighters and instead demonstrate instructional leadership. Being an instructional leader isn’t just about setting a goal. It means operationalizing your team for success—adopting a diagnostic assessment and intervention model that is based on best practices and hard work.
Honestly, I am tired of administrators who are doubling down on screening assessments and summative assessments in lieu of real diagnostics. With the high numbers of students who are behind, we need true diagnostic tools to replace screeners. If the majority of a group has the disease, you start the tried and true treatment for everyone. This is certainly the case for any district that has a math proficiency of 40% or lower.
Learn more about Let’s Go Learn’s online math intervention platform
Richard Capone co-founded Let’s Go Learn in 2000. Let’s Go Learn is a pioneer in adaptive and diagnostic assessments. Capone is the chief technology officer and current CEO at Let’s Go Learn. He led the development teams in creating DORA and ADAM, assessments used by special education departments as well as general school administrators and teachers to support student achievement through powerful granular data. Today, Let’s Go Learn is used in all 50 states as well as internationally. Its solutions include assessment and online instruction that meet the needs of Generation Four educational assessments.