## ~ Oceanside Unified School District ~

**Summer Institute Mathematics Professional Development**

- Dates: June 20-23, 2023
- Number of teachers: 8
- Teachers’ home schools: Oceanside High School, El Camino High School, Lincoln Middle School, North Terrace Elementary K-8, Oceanside Unified School District; Sagebrush Canyon High School, Carlsbad Unified School District; Marston Middle School, San Diego Unified School District.

*Fig. 7. With nearly 75% of its student population identified as socioeconomically disadvantaged, OUSD and Math for America San Diego have partnered for the past 9 years to offer professional development to district teachers and Summer Math Academies to incoming OUSD ninth graders.*

The Summer Institute mathematics professional development program was held for the 9th time this year for the Oceanside Unified School District (OUSD). Hosted by Math for America San Diego, the weeklong PD ran from June 20 - June 23, 2023 at Oceanside High School. Eight mathematics teachers participated. The Summer Institute was led by UC San Diego’s Dr. Guershon Harel, a distinguished professor in the Department of Mathematics, and Dr. Osvaldo “Ovie” Soto, Math for America San Diego executive director.

Participants

2023 Summer Institute teachers included OUSD mathematics teachers Gregory Guayante, an MfA SD Master Teaching Fellowship alumnus, and Jennifer Barnes, El Camino High School; Jennifer Levine, mathematics and science teacher, North Terrace Elementary School; Torrey Goldberg and Dustin Long, mathematics teachers, Oceanside High School; and Jeremy Robydek, mathematics teacher, Lincoln Middle School. Also attending were MfA SD Master Teaching Fellowship alumnus Fred Griesbach, mathematics teacher, Sagebrush Canyon High School, Carlsbad Unified School District; MfA SD Master Teaching Fellowship alumna Trang Vu, mathematics teacher, Marston Middle School, San Diego Unified School District; and Danny Saldivar, intern, 2023 STEMULATE program, UC San Diego; current MiraCosta college student, and future math teacher.

2023 Summer Institute teachers included OUSD mathematics teachers Gregory Guayante, an MfA SD Master Teaching Fellowship alumnus, and Jennifer Barnes, El Camino High School; Jennifer Levine, mathematics and science teacher, North Terrace Elementary School; Torrey Goldberg and Dustin Long, mathematics teachers, Oceanside High School; and Jeremy Robydek, mathematics teacher, Lincoln Middle School. Also attending were MfA SD Master Teaching Fellowship alumnus Fred Griesbach, mathematics teacher, Sagebrush Canyon High School, Carlsbad Unified School District; MfA SD Master Teaching Fellowship alumna Trang Vu, mathematics teacher, Marston Middle School, San Diego Unified School District; and Danny Saldivar, intern, 2023 STEMULATE program, UC San Diego; current MiraCosta college student, and future math teacher.

Content Focus

“Advancing Mathematical Ways of Thinking through the Study of Analytic Geometry” was the topic of study at this year’s institute.

“Analytic geometry connects algebra and geometry by using algebraic symbols and methods to represent and solve geometry problems,” Soto said.“ Participating middle and high school mathematics teachers at the PD had the opportunity to explore analytic geometry through the lens of conics.”

Conics, the result of intersecting a plane with a double cone and producing circles, lines, hyperbolas, and parabolas, provides a useful framework for understanding analytical geometry.

For this summer’s professional development work in the Oceanside Unified School District (OUSD), Prof. Harel designed a set of specific activities that explored mathematical problems in the physical world (e.g., Given any three points on a page, how can I compute the area of the triangle formed by them?).

“Advancing Mathematical Ways of Thinking through the Study of Analytic Geometry” was the topic of study at this year’s institute.

“Analytic geometry connects algebra and geometry by using algebraic symbols and methods to represent and solve geometry problems,” Soto said.“ Participating middle and high school mathematics teachers at the PD had the opportunity to explore analytic geometry through the lens of conics.”

Conics, the result of intersecting a plane with a double cone and producing circles, lines, hyperbolas, and parabolas, provides a useful framework for understanding analytical geometry.

For this summer’s professional development work in the Oceanside Unified School District (OUSD), Prof. Harel designed a set of specific activities that explored mathematical problems in the physical world (e.g., Given any three points on a page, how can I compute the area of the triangle formed by them?).

According to Prof. Harel, a deep understanding of analytical geometry is important for secondary mathematics.

“We frequently encounter geometry problems in our world. For example, if you want to know exactly where a satellite is in its orbit, you use an algebraic tool to solve a geometry problem,” Harel said. “This is a good summary of what analytical geometry is: When algebra comes to the rescue to solve a geometry problem.”

“We frequently encounter geometry problems in our world. For example, if you want to know exactly where a satellite is in its orbit, you use an algebraic tool to solve a geometry problem,” Harel said. “This is a good summary of what analytical geometry is: When algebra comes to the rescue to solve a geometry problem.”

Using Ways of Thinking to Connect Math Content and Curriculum

Mornings at the institute were devoted to teachers working by themselves and with each other on a series of analytical geometry problems that addressed quantitative questions about objects in space, e.g., “How can we determine the distance between two given objects? Will two objects moving along a given trajectory collide? If so, when?”

“If given a geometric description of a set of points, is there a way to express that set on a coordinate plane using algebra?” asked Soto. “Changing a problem situation from geometry to algebra, or vice versa, calls for an important set of ways of thinking students can--and should--learn in high school mathematics.”

An important launch point of study at the institute was Pythagorean’s Theorem. By ninth grade, students are expected to know about this theorem, not only because of its usefulness but because it shows a connection between algebra and geometry.

Mornings at the institute were devoted to teachers working by themselves and with each other on a series of analytical geometry problems that addressed quantitative questions about objects in space, e.g., “How can we determine the distance between two given objects? Will two objects moving along a given trajectory collide? If so, when?”

“If given a geometric description of a set of points, is there a way to express that set on a coordinate plane using algebra?” asked Soto. “Changing a problem situation from geometry to algebra, or vice versa, calls for an important set of ways of thinking students can--and should--learn in high school mathematics.”

An important launch point of study at the institute was Pythagorean’s Theorem. By ninth grade, students are expected to know about this theorem, not only because of its usefulness but because it shows a connection between algebra and geometry.

Teachers, working in groups, were instructed to select, “test drive” and present a lesson to the group featuring analytic geometry. Teachers Guayante and Robydek chose a lesson on the Pythagorean Theorem from the district’s newly adopted Illustrative Mathematics curriculum, which will be implemented in the fall.

After Guayante and Robydek reviewed the lesson’s teaching guide elements, (the suggested content and student-facing teaching approaches), and walked the group through the lesson, they shared their concerns about the lesson structure. Using a DNR, student-centered framework, they believed the curriculum instruction to label the problem (the Pythagorean Theorem) was given too soon in the lesson, i.e., labeling the problem before the students had a connection to meaning.

In the group discussion, Prof. Harel offered a correction and suggested presenting a generic proof so students could reason in general terms. A generic proof is an example that allows someone to see, for that particular example, the general structure of the proof.

“This is the incredible power of the Summer Institute,” Soto said. “When teachers work and solve mathematical problems together ‘as students,’ they have a better understanding of how to teach that mathematics, the challenges students may encounter, and the ways they may complement or enhance student learning.”

After Guayante and Robydek reviewed the lesson’s teaching guide elements, (the suggested content and student-facing teaching approaches), and walked the group through the lesson, they shared their concerns about the lesson structure. Using a DNR, student-centered framework, they believed the curriculum instruction to label the problem (the Pythagorean Theorem) was given too soon in the lesson, i.e., labeling the problem before the students had a connection to meaning.

In the group discussion, Prof. Harel offered a correction and suggested presenting a generic proof so students could reason in general terms. A generic proof is an example that allows someone to see, for that particular example, the general structure of the proof.

“This is the incredible power of the Summer Institute,” Soto said. “When teachers work and solve mathematical problems together ‘as students,’ they have a better understanding of how to teach that mathematics, the challenges students may encounter, and the ways they may complement or enhance student learning.”

Takeaways

At the end of the Summer Institute, the teachers and Prof. Harel participated in a debrief session to share a summary of what they had learned.

“Each year, Summer Institute teachers discover that the decisions they make about their pedagogical approach and ‘teaching moves’ for a particular problem come from a deep understanding of the mathematics content and of student thinking. It’s a valuable approach for strengthening mathematics instruction,” Soto said.

“From the math, you extract pedagogy, and not the other way around,” Harel added.

Here are some sample takeaways and responses from the teachers with Prof. Harel’s and Dr. Soto’s commentary at the institute wrap-up:

Analytic Geometry was a great example of the challenge.

At the end of the Summer Institute, the teachers and Prof. Harel participated in a debrief session to share a summary of what they had learned.

“Each year, Summer Institute teachers discover that the decisions they make about their pedagogical approach and ‘teaching moves’ for a particular problem come from a deep understanding of the mathematics content and of student thinking. It’s a valuable approach for strengthening mathematics instruction,” Soto said.

“From the math, you extract pedagogy, and not the other way around,” Harel added.

Here are some sample takeaways and responses from the teachers with Prof. Harel’s and Dr. Soto’s commentary at the institute wrap-up:

**Teacher 1:***The pedagogical aspects/demonstrations about how math is more meaningful when we had time to think about them and collaborate. Not wanting to interrupt the mathematics of students; that ideas in math don’t come from nowhere.***Harel:**Students’ reasoning must be taken seriously. Efficiency comes out of inefficiency.**Teacher 2:***I’m excited to implement the Math 8 Pythagorean Theorem unit at the upcoming Summer Math Academy.*

**Soto:**It’s wonderful when we can get the content of the Summer Institute and Summer Math Academy to align.- T
**eacher 3:***I like doing math. It’s beneficial to create a lens [for student thinking] and pick the important things to focus on.*

**Harel:**Incorporating middle school and high school [teachers and topics into the same Summer Institute] can be challenging.Analytic Geometry was a great example of the challenge.

Next, read how teachers applied their new knowledge at the Summer Math Academies at Oceanside High School and Rancho Margarita Elementary K-8 .