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Improving Teachers’ and Students’ Conceptual Understanding of Mathematics: Case Study from Two Rivers Public Charter School

A case study excerpted from Learning That Lasts

Created By

EL Education

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Topic

  • Classroom Instruction

Type

Guidance Documents

At Two Rivers Public Charter School, the transformation of mathematical culture began with a full year of building staff culture and capacity in mathematics, with no direct focus on application of mathematics instruction in classrooms. Led by school cofounder and mathematics guru Jeff Heyck‐Williams, the faculty began the journey with surveys about their mathematical backgrounds, skills, and attitudes, which helped them create differentiated teacher groups. Over the course of the year, the staff was involved in a series of seven three‐hour workshops on mathematical content, working as a whole staff and in differentiated groups.


The series began with the faculty spending three hours creating, sharing, and critiquing their personal “math stories.” Although some teachers found only pleasure and success with mathematics in their youth, for most teachers this was not the case. In fact, mathematics educator Deborah Lowenberg Ball (2003) reminds us that “teachers—like all other adults in this country—are graduates of the system we seek to improve.” Math stories impelled the Two Rivers staff to be candid with each other and begin the journey of pushing and supporting each other. There were many “math scars” left on the psyches of teachers that left them less than confident, unwilling to take mathematical risks, and with a propensity to cover up areas of mathematical confusion. Some of them referred to this collaborative work as “math therapy.” As they worked together that year to gain deep understanding of content, they would have to step up and show mathematical courage: the ability to admit when they were confused, and the willingness to take risks, ask questions, and propose ideas.


As Heyck‐Williams taught the Two Rivers staff, he modeled the kind of mathematical instruction that he wanted teachers to use with students. The sessions modeled the types of problems and discourse that is the goal for all classrooms. The mathematics that teachers were learning was primarily mathematics that they had “learned” themselves years ago as students, except that, for the most part, they had never really understood it deeply back then, and they needed to refresh their understanding or, in many cases, build it solidly for the first time.
In addition, most teachers had never experienced learning mathematics in a way that required them to grapple with concepts. By reconnecting with their own experience as mathematics learners, they developed greater empathy and insight into the learning process. As they developed new and deeper understanding of mathematics concepts, they also were learning how to structure experiences for students to do the same thing. Heyck‐Williams used Suzanne Chapin and Art Johnson’s book Math Matters: Understanding the Math You Teach (2006) as an anchor text during this year.


In the second year, teachers and leaders at Two Rivers identified the elements of good mathematics instruction and reconceptualized how units of mathematics instruction were  organized and delivered. Through professional learning sessions as a whole group, and through ongoing cycles of trying out strategies in classrooms, observations, coaching, sharing, and critiquing progress as a whole staff, Two Rivers staff began organizing units of instruction around the big ideas of specific strands of mathematics and integrating those with a focus on the Common Core Standards for Mathematical Practice. With this shift, the faculty reviewed textbook series and switched their core textbook to one that was easier to customize.


In the third year, teachers focused sharply on teaching problem‐based tasks (PBT). The Two Rivers PBT framework is similar to the Math Workshop 2.0 framework, with some details that are distinct. Problem‐based tasks at Two Rivers are used in all grades, preK–8, and they range from single‐day tasks to full‐week challenges (with most lasting for a day or two). Teachers focused on many of the same topics covered in this chapter: how to find, customize, or create good problems; how to support students to solve them individually and in groups; how to build strong thinking and discourse catalyzed by those problems; and how to synthesize learning. The Two Rivers PBT sequence also has an added step not explicitly in Workshop 2.0: after the grapple problem is introduced, the teacher leads a discussion using a KWI chart (what do you KNOW, WHAT do you need to find out, and what IDEAS do you have for solving the problem?). The “Learn with Two Rivers” website offers further description and resources about their approach to problem‐based tasks.


When students at Two Rivers saw their teachers getting excited about mathematics, learning new things and taking risks as a faculty, the energy and mathematical courage was infectious across the school. Teacher Jes Ellis described her own mathematical journey at Two Rivers: “At first I felt that this was impossible. Crazy even. I wanted my textbook back. Now we are using multiple resources and texts to plan lessons. By the end of the year I felt that I could actually create these experiences for students. And the students’ perceptions of math are transformed...They make it work with challenging material; they have new thinking routines.”


Beyond the professional learning sequence, the school also embraced a celebratory schoolwide culture of taking on mathematics challenges. Whole‐school community meetings feature mathematical problems, shared by the “Mathemagical Wizard” (Jeff Heyck‐Williams in a wizard costume), that students, families, and teachers can work on individually or in groups. The Mathemagical Wizardry Prize, as the weekly problems are called, has galvanized the community at Two Rivers by getting everyone, from students to the crossing guard, engaged in challenging mathematics problems. Students and adults are thrilled to have their names called out to the community for solving these problems. In addition, Two Rivers has hosted Math Coffees for parents, at which teachers and leaders share with families how to support their children with mathematics, and an annual community‐wide Math Festival at which students and families engage in an evening of games and problem solving. Most significantly, students in the school, whether in kindergarten or middle school, consistently try to “grow their brains” by taking on difficult mathematics challenges.

Created By

EL Education

Resource Downloads

Topic

  • Classroom Instruction

Type

Guidance Documents

At Two Rivers Public Charter School, the transformation of mathematical culture began with a full year of building staff culture and capacity in mathematics, with no direct focus on application of mathematics instruction in classrooms. Led by school cofounder and mathematics guru Jeff Heyck‐Williams, the faculty began the journey with surveys about their mathematical backgrounds, skills, and attitudes, which helped them create differentiated teacher groups. Over the course of the year, the staff was involved in a series of seven three‐hour workshops on mathematical content, working as a whole staff and in differentiated groups.


The series began with the faculty spending three hours creating, sharing, and critiquing their personal “math stories.” Although some teachers found only pleasure and success with mathematics in their youth, for most teachers this was not the case. In fact, mathematics educator Deborah Lowenberg Ball (2003) reminds us that “teachers—like all other adults in this country—are graduates of the system we seek to improve.” Math stories impelled the Two Rivers staff to be candid with each other and begin the journey of pushing and supporting each other. There were many “math scars” left on the psyches of teachers that left them less than confident, unwilling to take mathematical risks, and with a propensity to cover up areas of mathematical confusion. Some of them referred to this collaborative work as “math therapy.” As they worked together that year to gain deep understanding of content, they would have to step up and show mathematical courage: the ability to admit when they were confused, and the willingness to take risks, ask questions, and propose ideas.


As Heyck‐Williams taught the Two Rivers staff, he modeled the kind of mathematical instruction that he wanted teachers to use with students. The sessions modeled the types of problems and discourse that is the goal for all classrooms. The mathematics that teachers were learning was primarily mathematics that they had “learned” themselves years ago as students, except that, for the most part, they had never really understood it deeply back then, and they needed to refresh their understanding or, in many cases, build it solidly for the first time.
In addition, most teachers had never experienced learning mathematics in a way that required them to grapple with concepts. By reconnecting with their own experience as mathematics learners, they developed greater empathy and insight into the learning process. As they developed new and deeper understanding of mathematics concepts, they also were learning how to structure experiences for students to do the same thing. Heyck‐Williams used Suzanne Chapin and Art Johnson’s book Math Matters: Understanding the Math You Teach (2006) as an anchor text during this year.


In the second year, teachers and leaders at Two Rivers identified the elements of good mathematics instruction and reconceptualized how units of mathematics instruction were  organized and delivered. Through professional learning sessions as a whole group, and through ongoing cycles of trying out strategies in classrooms, observations, coaching, sharing, and critiquing progress as a whole staff, Two Rivers staff began organizing units of instruction around the big ideas of specific strands of mathematics and integrating those with a focus on the Common Core Standards for Mathematical Practice. With this shift, the faculty reviewed textbook series and switched their core textbook to one that was easier to customize.


In the third year, teachers focused sharply on teaching problem‐based tasks (PBT). The Two Rivers PBT framework is similar to the Math Workshop 2.0 framework, with some details that are distinct. Problem‐based tasks at Two Rivers are used in all grades, preK–8, and they range from single‐day tasks to full‐week challenges (with most lasting for a day or two). Teachers focused on many of the same topics covered in this chapter: how to find, customize, or create good problems; how to support students to solve them individually and in groups; how to build strong thinking and discourse catalyzed by those problems; and how to synthesize learning. The Two Rivers PBT sequence also has an added step not explicitly in Workshop 2.0: after the grapple problem is introduced, the teacher leads a discussion using a KWI chart (what do you KNOW, WHAT do you need to find out, and what IDEAS do you have for solving the problem?). The “Learn with Two Rivers” website offers further description and resources about their approach to problem‐based tasks.


When students at Two Rivers saw their teachers getting excited about mathematics, learning new things and taking risks as a faculty, the energy and mathematical courage was infectious across the school. Teacher Jes Ellis described her own mathematical journey at Two Rivers: “At first I felt that this was impossible. Crazy even. I wanted my textbook back. Now we are using multiple resources and texts to plan lessons. By the end of the year I felt that I could actually create these experiences for students. And the students’ perceptions of math are transformed...They make it work with challenging material; they have new thinking routines.”


Beyond the professional learning sequence, the school also embraced a celebratory schoolwide culture of taking on mathematics challenges. Whole‐school community meetings feature mathematical problems, shared by the “Mathemagical Wizard” (Jeff Heyck‐Williams in a wizard costume), that students, families, and teachers can work on individually or in groups. The Mathemagical Wizardry Prize, as the weekly problems are called, has galvanized the community at Two Rivers by getting everyone, from students to the crossing guard, engaged in challenging mathematics problems. Students and adults are thrilled to have their names called out to the community for solving these problems. In addition, Two Rivers has hosted Math Coffees for parents, at which teachers and leaders share with families how to support their children with mathematics, and an annual community‐wide Math Festival at which students and families engage in an evening of games and problem solving. Most significantly, students in the school, whether in kindergarten or middle school, consistently try to “grow their brains” by taking on difficult mathematics challenges.

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