This is part of a series on mastery-based learning in Connecticut. See posts on New Haven Public Schools,Windsor Locks Public Schools, Naugatuck Public Schools, Superintendents Leading the Way in Connecticut, and New Haven Academy. Connecticut uses the term mastery-based learning, so that will be used instead of competency education within the series.
Scroll to the bottom to see an example of Naugatuck’s curriculum framework for math.
“As a teacher, I couldn’t get traction. If mastery-based learning isn’t the district’s vision, how much can a teacher accomplish?”
I like to stay in touch with competency education leaders as they move from one position to another, from one organization to another. One might think of a bumble bee pollinating ideas – each idea become a richer hue as it interacts with other ideas, other people, and new applications.
Thus, during my trip to Connecticut, I visited Caroline Messenger, Curriculum Director, Naugatuck Public Schools, who had previously been a teacher at the high school. (Messenger has also been a writer at CompetencyWorks. See Learning My Lesson and How Do You Measure Competency? Curriculum Can Help Guide the Way.) I was interested to find out how her perspective had changed from being a teacher to being part of the leadership team. The conversation was quickly focused on instructional strategies, proving to me once again that mastery-based learning can create the conditions for lifting up the teaching profession from the narrow role of delivering curriculum as structured in the factory model to the astoundingly challenging and meaningful role of teaching children to learn.
“Mastery-based learning operates on a different set of assumptions,” Messenger reflected. “Even if you have two or three colleagues working together, it is difficult to bring mastery-based learning to life in the classroom without a district vision. As a teacher, you can focus on standards and develop your units around them, but there is no way to create a greater understanding of how the standards fit together to create a sense of purpose for learning if you are working in isolation. Teachers can organize their classrooms around standards, but we want so much more for kids. It takes a much broader vision. The vision of the district and the philosophy of the school shape how people relate to each other, determine what is important and where attention is directed, and sets the values.”
In 2015, Superintendent Sharon Locke began to engage the community in creating a mission for the district. As the district began to explore what it would mean to prepare all students to be active, adaptive, self-directed learners, it was clear that they would need a strong curriculum structure, instructional strategies that engaged students in active learning at deeper levels of knowledge, and a strong collaborative orientation toward meeting the needs of all students. Locke set two priority areas to focus the efforts of the district: 1) Improve math instruction and 2) Improve the learning climate with a focus on growth mindset and building trust and respect.
Our Mission is to develop a community of learners who:
- Are responsible and engaged community members
- Demonstrate initiative, persistence, and adaptability
- Are curious and value risk-taking as part of the learning process
- Access and analyze information and formulate opinions
- Communicate effectively
- Work individually and on teams to solve real world problems
Enter Messenger as the new director of curriculum. “Our challenge was to take a vision for students that was not discipline-specific and integrate it throughout the curriculum. Our goal was to bring the mission alive.”
Beginning with Math
“We asked ourselves, what does math learning look like when our students graduate? When they are crossing the stage, what do we want kids to have?” Messenger reflected. “We challenged ourselves to have the competencies so they were rooted within the mission. As a district, we set high expectations through the graduation requirement competencies. This started the transition to mastery-based.”
Messenger went on to explain, “Before we dove in, we needed to create a common language for teachers to use to talk about knowledge, learning, and teaching and to think about what it means for students to understand.” They explored elements of Grant Wiggins’ framework Understanding by Design to help teachers talk about different types of knowledge, understand how they help students build meaning, and transfer that understanding to new contexts.
They focused on math first because it has been identified as a weakness in the district. As the teachers created the math graduation competencies, they were more cross-cutting than Messenger had expected. Messenger realized that the cross-curricular framework could be applied to different academic domains but would have different nuances. For example, research and inquiry has different contours within each academic domain. Thus, more than one rubric would be needed to review the cross-curricular standards.
They created a three-tiered system of competencies, performance indicators, and learning targets. Teachers may find that they need to break down learning targets into even smaller pieces to support scaffolding. Messenger raised an insight regarding learning targets I had not heard before. “Do we want a set of fixed learning targets, or can we think of them in a more personalized, developmental way? One way to think about learning targets is to consider ‘What does each student need to do today?’ This would make learning targets highly personalized.” There are large implications for designing information systems, organizing units and flexible grouping students, and monitoring progress and pace if we think about meeting students at the learning targets they need to master.
In engaging in this process, NPS developed a comprehensive philosophy of curriculum that includes the structure of what students should know and be able to do (competencies, performance indicators, and learning targets), the pedagogy of creating active learning through problem-based learning, and performance tasks. Messenger explained, “We expanded the idea of what curriculum means. It is everything involved in the learning cycle, including how we are going to motivate and engage students.”
Messenger said, “It helped us to work on one domain really deeply. We began to understand the purpose of the competencies and how we can do backward design to learning targets throughout all the grades. When teachers have the chance to create the graduation level competencies, organize the framework, and unpack the standards, they begin to own them. They see how they can be used creatively in instruction. My job was to help create the processes and structure to draw on the expertise of our teachers.”
“We didn’t get it right in the beginning,” she noted. “We got off track in how we developed the performance indicators.”
Reflection: This issue, of the granularity of performance indicators and learning targets, is one that is challenging the field as different perspectives ask for different levels of granularity. We could think of it as a Goldilocks problem – some are just too specific and others are too large. Different criteria or lenses such as student-friendliness (creating meaning), ability to assess, time spent on assessments, ability to identify and support students in mastering the skill, and ease in organizing into interdisciplinary, inquiry-based instruction all demand different levels of granularity. At this point in our development it is not clear that one model is better or necessary. There may be other aspects of the culture, values, structures, and practices that are much more important in terms of engaging students and influencing learning engagement.
The goal is to have curriculum frameworks and learning targets all developed by June so teachers can have time to get comfortable with them before the fall semester. As the teachers work with the frameworks and target, they are bound to have new insights on how to improve them. Messenger knows that this process of becoming mastery-based is ongoing and iterative, “As we learn and grow, we will see another type of curriculum develop.”
Improving Math Instruction
Based on data on student achievement, Locke had set improving math instruction as one of the two main goals for the district. At the time, about 27 percent of kids were proficient on SBAC (compared with 48.4 percent in ELA on SBAC). Messenger explained, “We were close to the state average but not nearly good enough. What do you do if you have nearly 70 percent of your students not where you want them to be?” The district already had a positive experience of creating a positive trajectory in improving reading through a combination of reading consultants at the elementary and secondary schools and a stronger literacy program in elementary schools. Thus, Messenger’s challenge was to create the systems and processes that would improve math instruction.
First, there was a problem of varied expectations. After visiting classrooms through instructional rounds, it was clear that teachers had different expectations for students in their classrooms. Second, the instructional round identified several aspects of instruction that needed attention: it was very focused on procedural approaches; students were expected to absorb lessons sitting quietly in rows; and curriculum was delivered in a time-based process with teachers moving on to the next topic, thus creating a highly fragmented approach that left many feeling lost (and not liking math). Messenger pointed out, “We discovered that if teachers had a strong understanding of conceptual knowledge in math, so did their students. And vice versa.” Third, teachers depended on a curriculum with limited resources but didn’t have a framework or agreements about what it was important for students to know and be able to do. This was compounded by the new mission that required integrating higher order skills across the curriculum.
Thus, as they clarified the graduation competencies for math, NPS also implemented several efforts to improve math instruction:
Teaching Procedural Fluency through Conceptual Understanding: Messenger pointed out, “If we want all students to master the competencies, we need to think about the question ‘Why do students not understand?’ as equally important as the question of ‘What do students not understand?’ We believe that students often don’t understand because of gaps in conceptual thinking. We want our students to be able to explore mathematics and see how numbers can help them make sense of the world.”
One of the ideas NPS would like to pursue is to create professional development opportunities around learning progressions in math. The goal would be to deepen the understanding of all teachers on teaching math through conceptual understanding that could be applied throughout the grade levels. Thus, if a teacher finds out that one of their students in algebra didn’t learn about what fractions mean, they would have the skillset to help them beyond having them doing procedures over and over. Messenger pointed out, “Concepts build on each other in math. Partitioning shapes in kindergarten is foundational for fractions, and fractions are important to be able to do slope intersect and rise over run in high school. And so on.”
The NPS approach to teaching mathematics through conceptual learning will have implications for how districts would want to organize information systems to help track student learning, as it would need to include concepts, procedural knowledge, and content
Problem-Based Instruction: NPS has focused on introducing problem-based instruction in math courses. Naugatuck has embraced a problem-based approach to teaching math because it helps students build conceptual understanding as well as procedural fluency. Problems aren’t as big or open as project-based learning, which can require a lot of planning on part of teachers. Problem-based problems create the opportunity for students to have discourse about the problem and how they solved it. NPS is still drawing upon math programs (as compared to teachers creating their own units) but with a much clearer idea of their pedagogy and how it relates to the vision and graduation requirements. Messenger mentioned enVisions 2.0 and Big Ideas Math as some examples of programs aligned with their pedagogy of problem-based, conceptual understanding.
Instructional Rounds and Peer to-Peer Learning: The structure engages all the teachers in improving instruction, regardless of what they feel about the transition to mastery-based learning. Instructional rounds are an important part of the improvement process at Naugatuck. In its inaugural year, about 12 teachers, six math consultants and three instructional coaches were trained on instructional rounds along with administrators. They would visit one teacher in one school, drawing upon that experience to create a common understanding of what was effective instruction. As they visited more teachers and schools, they began to calibrate across the district their understanding of strengths and weaknesses of instruction.
NPS is expanding the professional development around problem-based learning and learning math concepts. They are also using video cameras with teachers filming each other so they can reflect on their instructional strategies using a set of guiding questions. They are building a video library to house the clips so teachers can draw on them as needed.
Other Domains, Other Opportunities
Naugautuck has partnered the Connecticut Center for Advanced Technology’s (CCAT) education division as they adopted the Next Generation Science Standards with hands-on workshops to help teachers understand how to create interactive units for studying phenomena. In one of the workshops, teachers began to analyze why the paper airplanes they built had different flight patterns.
Messenger explained, “It was helpful to get guidance on thinking through the NGSS, as you can go in many different directions. We are trying to marry knowledge and skills through a combination of science content and engineering practices with the cross-cutting concepts. Students will need to demonstrate their learning through performance-based tasks.” She was referring to the cross-cutting concepts in Appendix G. “You can look at the cross-cutting concepts in every grade and in every type of science. For example, you can be thinking about patterns in every grade whether you are looking at biology or chemistry.” Thus, the cross-cutting concepts are driving the development of the science competencies with the focus on research and inquiry, patterns, causality, scale and systems, stability, and change of energy and matter.
Messenger is already thinking about other domains besides math. “We need to make reading and writing just as intentional as math. Students need to know what the purpose is of what they are reading or being asked to write about. It makes sense to integrate reading and writing more deeply within social studies and science.”
She is also thinking about how Naugatuck might create more modular courses as well as more interdisciplinary, thematic courses that draw on all of the academic domains and beyond.
In addition to the CCAT, Messenger enthused about how helpful Great Schools Partnership has been, including responding to phone calls and allowing Naugatuck to adapt their materials. For example, the district’s Philosophy of Curriculum was created through design thinking, a process she experienced through Great Schools Partnership’s workshops/materials and Stanford University’s resources.
The district team received training on leading instructional rounds from the Connecticut Center for School Change so that it has become a consistent practice throughout the district.
Some of the books that have been helpful to Naugatuck in this process of creating a culture of learning, developing competency frameworks, and focusing deeply on math instruction include:
- Understanding by Design by Grant Wiggins
- Leading Instructional Rounds in Education by Thomas Fowler-Finn
- Rigorous Curriculum Design and Prioritizing the Common Core by Larry Ainsworth
- Mathematical Mindsets by Jo Boaler
- Number Talks by Sherry Parish has helped create common language about math discourse
- Principles to Action, NCTM
Messenger reflected on what she has been learning about leadership. “To bring about this type of change and to create a strong culture of learning, leaders have to be vulnerable and transparent,” she said. “We have to be willing to say ‘I don’t know’ or ‘We have to figure it out.’ The important thing to do is create an atmosphere of trying things with the confidence that eventually we will find something that works well.”
Looking at her wall filled with superheroes, you get the feeling that Messenger is inspired to leap over any walls and batter down any barriers that get in her way.
Below is the current version of the Naugatuck Public Schools Graduation Competencies for Math.
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