In the 2017-2018 school year several teachers across the elementary schools in the three towns of Pentucket began to use some common math materials. It had been quite some time since the district had reviewed math curriculum and purchased a program for district wide use. In fact up to that point, teachers had broad discretion deciding which math materials and resources they used and the assumption was that they would be using the state standards to guide what concepts they taught, leveraging older materials and supplementing as they saw fit. While some teachers were able to develop engaging ways to teach math, inevitably such a disjointed approach led to gaps and overall declines in math performance. A decision was made that the K-6 teachers would all start using Eureka Math by Great Minds in the fall of 2018.
In 2017, when the work to make math curriculum and instruction consistent across the district began, the district only had 39% of its students in grades 3-8 scoring Meeting or Exceeding Expectations on the state assessment MCAS while the state average was 48%. Just a few years before in 2014, the district average was 64% and the state average was 57%. The change was obviously needed as the decline in performance was undeniable.
For six years since, even in the midst of COVID related school interruptions, the math performance of students has been climbing. There have been bumps along the way, the climb was not a straight line either, but overall the data is clear, students have done better when we used a consistent and coherent curriculum. Pentucket is no different than districts across the country just as numerous articles and research has proven. This fact is so well established that it has been widely shared from 2002 in this article about the TIMSS (Third International Math & Science Study) to as recently as March 2021 in a message from the President of the NCTM (National Council for Teachers of Mathematics). Bottom line, even with talented teachers and training - curriculum matters.
Eureka was designed to build student conceptual understanding of math, while also establishing mathematical operational fluency with applications for students. It is important for students to know how to do math equations efficiently and effectively but also important that they understand why and how math is used to solve problems.
Evaluations and Adjustments
For context, and in fairness to the data, the standards changed in 2015 and schools were expected to make the appropriate curriculum and instructional adjustments. Without a new curriculum or attention paid to the resources and instruction, previous programs and approaches were not likely enough to meet the new demands. The MCAS test also changed and in 2017 we had our first scores reflecting the new more rigorous expectations. To compare the percent of students meeting or exceeding expectations in 2017 to that of 2014 is not exactly great data analysis. However, the district had always been above the state average, just as was the case in 2014. 2014 was the last year of the original MCAS test and the district was 7 points above the state average in math. But in 2017, the district was below the state average; 9 points below and that data point can be used to evaluate effectiveness and need for change.
One of the major points of curriculum coherence is that the learning builds over years so it is also fair to say that major gains in student performance are not likely to be realized in just one or two years. As we look back and take stock of the starting point in 2017 when 39% of our students in grades 3-8 were Meeting or Exceeding expectations and considering the interruptions COVID contributed, it is pretty impressive to see the district in 2023 at 50% of students in grades 3-8 Meeting or Exceeding expectations. That is also 9 points above the state average which is essentially an 18 point swing in only 6 years when compared to the rest of the state.
Seemingly, this is all good news. However, as we continued to dive into the data and listen to the teachers implementing Eureka, a pattern emerged. Several teachers expressed concerns over the amount and density of the complex language used in the curriculum. They were observing this as a barrier for our students with disabilities who struggled with language and the executive functioning around language. General Education teachers and Special Education teachers worked to scaffold that aspect and provide accommodations.
As we examined data for these students, the students with disabilities were not improving at the same rate as our aggregate. We had moved past the state averages and continued to climb past the state average, even post COVID, but our students with disabilities, while improving, were not matching that same advancement rate beyond the state average for students with disabilities.
The team at Great Minds had already been at work to help address similar concerns. Enter - Eureka Sq. with revisions to the Eureka we had been using but without compromising the coherence that was so badly needed for our math curriculum. We piloted it specifically in some of our separate special education classrooms and then with general education classrooms. While some differences were subtleties, the obvious change with it being less language focused, more visually reliant and adding more focus on building fluency, made it seem like a great fit.
What does it look like in classrooms?
The district invested money in both the print and digital tools. Using money from a MA DESE State grant for high quality instructional materials, funds from the ESSER III federal grant and curriculum resources from the district.
While more visual representation of math concepts is something we can and should see in all grade levels, we have most certainly seen the use of models and visuals in the younger grades. Reflected in the images below, this Kindergarten teacher was able to use the digital platform to provide students with an interactive way to connect the language of math to concepts that are visually represented. From the lesson designed by Eureka Sq. the teacher can then move the class to a different spot in the classroom and be interactive with one another, having the students conduct a math talk about the concepts of shorter than and taller than as comparison of height. The use of the math term “endpoint” only further advances the student's use of math language and concepts through models and representations that they see but also ones they can create.
This kindergarten teacher was certain to have all of the students engaged in discussion with partners about the endpoints of the pencils and how endpoints related to accurate measurement and comparisons of items that are shorter or taller than one another. To hear kindergarten students discussing the concept of endpoints and using the word in their explanations, demonstrated the effectiveness of the whole class instruction. Not long after the activity, these students moved onto their tables to practice what they had learned, or receive some additional scaffolding and instruction from the teacher, if they required it.
Visual models are used in upper grades as well. Standard algorithms are taught and students are provided with plenty of practice to learn their math facts by applying them efficiently with standard algorithms, but students are also given visual models for how numbers are composed and decomposed. The images below from a 3rd Grade classroom help students to see the various factorials of numbers and how those factors can be represented in area models. The direct instruction model of “I do - We do - You do” is built into each lesson with students learning alongside the teacher to unpack a problem as the teacher first shows the students the steps. Then they work together to learn more where students are often engaged in dialogue with one another, partners or even small groups. Each lesson also provides students with time to practice the concept and demonstrate their own understanding.
Building Procedural Fluency
Throughout each module and at each grade are fluency building activities and daily expectations for this skill. Eureka Sq. has established routines for this but the teachers in Pentucket also had an opportunity to participate in a summer book study on procedural fluency for math. With over 40 staff spending time this summer on the book Figuring Out Fluency by John SanGiovanni and Jennifer Bay-Williams the teachers were able to understand how best to use the fluency building components and help students to better understand the strategy around various ways to build procedural fluency. We have seen multiple examples of this work in action and the district will be bringing Mr. SanGiovanni to a Professional Development day in the fall of 2024 to further advance the professional knowledge and understanding of fluency and productive struggle for all students.
Algorithms Concepts and Math Language
The example above in the photo helps to show how teachers are connecting the language use, with sentence frames for students to the application of standard algorithms. Students are able to more effectively talk about their work and use math language while also building fluency.
The standard algorithm is an essential part of the math instruction and practice. The work related to Eureka Sq. has students routinely multiplying and dividing numbers with the standard algorithm but it also provides students with choices of using other models, such as the area model shown below, when the circumstances may be better suited. That is the strategy side of the instruction that gives flexibility for students to understand the math from a conceptual standpoint but also builds their tool box to procedurally solve problems in an accurate and efficient method and the language to then describe it.
How are we doing?
At the mid-year point our benchmark assessment through I-Ready is showing that our students are continuing to grow and meet annual and stretch growth. In the fall of 2023, only 32% of the students in grades 3-8 started the year with an on-grade level benchmark score but by mid-year, that has risen to 52% with the most recent benchmark assessment. While we are raising the percent of students meeting the grade level expectation, we are also decreasing the students who performed well below expectation and required more intensive instruction. In the fall of 2023 we had 21% of the students in grades 3-8 who were well below expectations and that has fallen to only 10% at mid year.
All grade levels, 2-8 across the district, are showing mid year assessment scores in the High Performance and High Growth quadrant which is exciting to see and provides a solid foundation for the remainder of the year.
Of particular note were the improvements in the domains on Numbers & Operations and Algebraic Thinking - where we saw the greatest gains for students moving to “on grade level” performance with 60% of students on grade level in those domains. In the fall it was just 35% on grade level. Considering the conceptual work and procedural fluency focus of this year, that can easily be tied to improvements with those two domains.
Staff are still adjusting to some of the digital components and how best to balance the use of the short engagement videos with their own instruction. However, they are working their way through and in general the pacing of math instruction has been going well. Obvious familiarity with the wording, structure and design of Eureka has helped teachers with this. More professional development is planned for next year, even beyond the Figuring Out Fluency work. There are many accessibility features and tools for teachers to consider on how best to prepare for the variability of students in their classes and this is expected to be a focal point for future professional development.
In the meantime, we will continue to monitor student performance, seeking to address the needs based on data and as we observe them. The use of the consistent and coherent curriculum is not much of a debate in the district any more and the student data is where that discussion started and has ended.
Brent Conway
Assistant Superintendent