## ~ Oceanside Unified School District ~

## Oceanside High School Summer Math Academy for incoming 9th graders

*Fig. 8. Teachers and students from two OUSD high schools participated in this year’s professional development and Summer Math Academies.*

Twenty-one incoming ninth graders from OUSD feeder middle schools attended the Math for America San Diego Summer Math Academy at Oceanside High School, from June 21 - July 15. Gregory Guayante, a mathematics teacher at OUSD’s El Camino High School, and Frederick Griesbach a mathematics teacher at Carlsbad Unified School District’s Sage Canyon High School were the instructors. Both teachers are alumni of Math for America San Diego’s five-year Master Teaching Fellowship program. Mr. Guayante and Mr. Griesbach were joined by Jennifer Barnes, a special education/math teacher at El Camino High School.

Oceanside Unified School District (OUSD) and MfA SD’s Partnership Serving Military-Connected Families

As in past years, Teresa Collis, OUSD career technical education coordinator and former principal at Oceanside High School provided additional support and funding for the 2023 Summer Math Academy. OUSD has a high percentage of K-12 military students.

“On behalf of the Oceanside Unified School District, I am again very excited and proud to help support Math for America San Diego’s Summer Math Academies for our incoming sixth and ninth graders. These annual math academies are an invaluable resource for students who are about to begin their middle and high school mathematics journey,” Collis said. “The Summer Math Academies make a huge difference in how students see themselves in their freshman mathematics classes and a huge difference in overall mathematics achievement throughout high school.

“Summer Math Academy students have more confidence and less anxiety about math, about entering a new grade and a new school. I am so enthusiastic about the success of this work, I wish we could dedicate a whole high school campus to holding Summer Math Academies each year,” Collis added.

As in past years, Teresa Collis, OUSD career technical education coordinator and former principal at Oceanside High School provided additional support and funding for the 2023 Summer Math Academy. OUSD has a high percentage of K-12 military students.

“On behalf of the Oceanside Unified School District, I am again very excited and proud to help support Math for America San Diego’s Summer Math Academies for our incoming sixth and ninth graders. These annual math academies are an invaluable resource for students who are about to begin their middle and high school mathematics journey,” Collis said. “The Summer Math Academies make a huge difference in how students see themselves in their freshman mathematics classes and a huge difference in overall mathematics achievement throughout high school.

“Summer Math Academy students have more confidence and less anxiety about math, about entering a new grade and a new school. I am so enthusiastic about the success of this work, I wish we could dedicate a whole high school campus to holding Summer Math Academies each year,” Collis added.

Content Focus

Guayante and Griesbach participated in this year’s OUSD Summer Institute. Inspired by the topic of study--Analytical Geometry--they designed a three-week curriculum for the Summer Math Academy centered on the Pythagorean Theorem. Knowledge of the Pythagorean Theorem is important for incoming ninth graders because of the connection it makes between algebra and geometry, and its usefulness in Algebra I, Algebra II, and geometry classes. Students at this level are expected to know, use, and be able to prove the theorem.

Starting this fall, OUSD will begin using the Illustrative Mathematics (IM) curriculum for secondary mathematics. Guayante and Griesbach wanted to try out the IM Grade 8 lessons on the Pythagorean Theorem with students to provide their teaching colleagues with field notes and suggestions about what worked and what could be improved when teaching these new lessons. Guayante had previously presented the IM Unit 8 Pythagorean Theorem lesson at the Summer Institute. He was excited to try out the lesson with students.

In Unit 8, lessons on geometric and symbolic representations of squares and cube roots precede learning the Pythagorean Theorem. For the Summer Math Academy, Guayante and Griesbach planned to quickly cover Lessons 1 and 2 (“The Areas of Squares and Their Side Lengths” and “Side Lengths and Areas”, respectively) and then spend time exploring the Pythagorean Theorem with the class.

Guayante and Griesbach participated in this year’s OUSD Summer Institute. Inspired by the topic of study--Analytical Geometry--they designed a three-week curriculum for the Summer Math Academy centered on the Pythagorean Theorem. Knowledge of the Pythagorean Theorem is important for incoming ninth graders because of the connection it makes between algebra and geometry, and its usefulness in Algebra I, Algebra II, and geometry classes. Students at this level are expected to know, use, and be able to prove the theorem.

Starting this fall, OUSD will begin using the Illustrative Mathematics (IM) curriculum for secondary mathematics. Guayante and Griesbach wanted to try out the IM Grade 8 lessons on the Pythagorean Theorem with students to provide their teaching colleagues with field notes and suggestions about what worked and what could be improved when teaching these new lessons. Guayante had previously presented the IM Unit 8 Pythagorean Theorem lesson at the Summer Institute. He was excited to try out the lesson with students.

In Unit 8, lessons on geometric and symbolic representations of squares and cube roots precede learning the Pythagorean Theorem. For the Summer Math Academy, Guayante and Griesbach planned to quickly cover Lessons 1 and 2 (“The Areas of Squares and Their Side Lengths” and “Side Lengths and Areas”, respectively) and then spend time exploring the Pythagorean Theorem with the class.

*At a Week 1 pre-brief session, Griesbach (in black) and Guayante outline their lesson plan with Jennifer Barnes, mathematics teacher, El Camino High School (left), OUSD’s Teresa Collis, and Guershon Harel, distinguished professor, UC San Diego Department of Mathematics and director of the OUSD Summer Institute.*

Daily Pre-Academy Briefings

Each day before students arrived, Guayante and Griesbach held a pre-brief meeting to prepare and talk through the lesson plan for the day. In week 1, Guayante and Griesbach were often joined by Jennifer Barnes, a mathematics teacher at El Camino High School and 2023 OUSD Summer Institute participant, Prof. Harel, who led this year’s OUSD Summer Institute on analytic geometry, and Teresa Collis, OUSD career technical education coordinator and former principal at Oceanside High School.

Although students learn the Pythagorean Theorem in middle school mathematics, it remained a priority for the Summer Math Academy teachers to find out the students’ level of knowledge about triangle theory to gauge their instruction.

Each day before students arrived, Guayante and Griesbach held a pre-brief meeting to prepare and talk through the lesson plan for the day. In week 1, Guayante and Griesbach were often joined by Jennifer Barnes, a mathematics teacher at El Camino High School and 2023 OUSD Summer Institute participant, Prof. Harel, who led this year’s OUSD Summer Institute on analytic geometry, and Teresa Collis, OUSD career technical education coordinator and former principal at Oceanside High School.

Although students learn the Pythagorean Theorem in middle school mathematics, it remained a priority for the Summer Math Academy teachers to find out the students’ level of knowledge about triangle theory to gauge their instruction.

*(From: Illustrative Mathematics, Grade 8, Unit 8, Lesson 1.1: Two Regions)*

Lesson 1 Warm-up Activity

Guayante and Griesbach presented the class with the Warm-up activity from Lesson 1 (The Areas of Squares and Their Side Lengths) and asked the students to compare which shaded region was larger. Students would first work with the problem themselves and then be asked to convince their table mates how they reached their conclusions. Table groups would then present their answers to the class while the teachers would point out variations in student thinking and challenge students on how they knew their answer was correct.

When presenting these types of problems, students at first may believe they can visually determine the answer without calculation, cautioned Prof. Harel at the morning pre-brief session.

Guayante and Griesbach presented the class with the Warm-up activity from Lesson 1 (The Areas of Squares and Their Side Lengths) and asked the students to compare which shaded region was larger. Students would first work with the problem themselves and then be asked to convince their table mates how they reached their conclusions. Table groups would then present their answers to the class while the teachers would point out variations in student thinking and challenge students on how they knew their answer was correct.

When presenting these types of problems, students at first may believe they can visually determine the answer without calculation, cautioned Prof. Harel at the morning pre-brief session.

“In mathematics, it’s important to instill doubt. ‘Are we trusting only our eyes?’” Prof Harel asked. “Teachers must instill doubt, so students can prove why they reached the conclusions they reached.”

____Next, students worked on the Tilted Square problem to find the area of each shaded square (in square units). This required students to decompose (break down a whole number into parts), rearrange, surround, and subtract to find the answer.

*Students share how they found the area of the first tilted square.*

Taking A Student-Centered Approach to the Implementation of New Curricular Resources

After the class ended, teachers debriefed on the day’s activities. After assessing the students’ responses to the Lesson 1 Warm-up exercise, the teachers agreed many of the students were struggling to access the curriculum as written. They also discussed the different approaches students tried for solving the Tilted Square problem, such as tilting the graphic to count (an unproductive approach); or translating squares within the figure (a more productive approach), but also providing an incorrect answer. They agreed they needed to slow down the teaching pace for the students to get a firm grasp on the underlying concepts.

This would require modifying the original lesson plans for the Summer Math Academy.

“The plan was to explore IM’s Grade 8, Pythagorean Theorem Unit, the new curriculum for the district starting next year,” Guayante said. “This was the goal, and it came from the Summer Institute’s geometric Pythagorean Theorem focus. Originally, we wanted to start with Lesson 6 (Finding Side Lengths of Triangles) or Lesson 7 (A Proof of the Pythagorean Theorem) and work our way back to Lesson 1. From Lesson 1, we could fluidly go to Lesson 2 and 3, but we found it didn’t fit well with how students were thinking.

After the class ended, teachers debriefed on the day’s activities. After assessing the students’ responses to the Lesson 1 Warm-up exercise, the teachers agreed many of the students were struggling to access the curriculum as written. They also discussed the different approaches students tried for solving the Tilted Square problem, such as tilting the graphic to count (an unproductive approach); or translating squares within the figure (a more productive approach), but also providing an incorrect answer. They agreed they needed to slow down the teaching pace for the students to get a firm grasp on the underlying concepts.

This would require modifying the original lesson plans for the Summer Math Academy.

“The plan was to explore IM’s Grade 8, Pythagorean Theorem Unit, the new curriculum for the district starting next year,” Guayante said. “This was the goal, and it came from the Summer Institute’s geometric Pythagorean Theorem focus. Originally, we wanted to start with Lesson 6 (Finding Side Lengths of Triangles) or Lesson 7 (A Proof of the Pythagorean Theorem) and work our way back to Lesson 1. From Lesson 1, we could fluidly go to Lesson 2 and 3, but we found it didn’t fit well with how students were thinking.

*Teachers worked closely with students to get them started on problems and to have them clarify how they reached their solutions. “You’re on the right track, very good,” Guayante said.*

“So, we took a different approach. We moved from Lesson 1 and built from what they learned in that lesson. For example, regarding the area of a Tilted Square, we thought, ‘Why would a student need to know the formal reason for using the Pythagorean Theorem at this point?’ So we never mentioned the Pythagorean Theorem by name, never mentioned right triangles. We decided the students would be fine without ‘formally’ learning the Pythagorean Theorem at this point; that we could somehow fit it into the instruction when the students were ready. The students were driving the decisions of where to go next,” Guayante added.

“There were two distinct methods for finding the area of the square, and we wanted to get into it with the students: Method 1 and Method 2,” Griesbach said. “We didn’t want to leave and move on; we needed to stick with this internalization of a concept. So, half the students were comfortable with solving it one way and the other half the other way, and we stayed on that.

“We got them comfortable with the process of learning without using labels. We introduced symbolic representation later, after the generalization of the arithmetic. This methodology got them to the notion of the Pythagorean Theorem.”

“We got them comfortable with the process of learning without using labels. We introduced symbolic representation later, after the generalization of the arithmetic. This methodology got them to the notion of the Pythagorean Theorem.”

*El Camino High School math teacher Jennifer Barnes helped students walk through their thinking to arrive at an answer.*

“We wanted students to understand not only how to ‘do’ the problem, but the how and the why — ‘why does this make sense?’ — the cause and effect,” Barnes said. “Summer Math Academy students have the opportunity to really explore problems and gain a deeper understanding of the mathematics they’re learning.

“In some mathematics classes, students are shown a shortcut, and not taught the way it really works,” she continued. “At the Summer Math Academies, students experience the ‘process of understanding,’ and experience tangible reasoning about why they reach a solution. They’re not just memorizing mathematical formulas. When a student says, ‘I get it’, I know they will never forget it.”

“In some mathematics classes, students are shown a shortcut, and not taught the way it really works,” she continued. “At the Summer Math Academies, students experience the ‘process of understanding,’ and experience tangible reasoning about why they reach a solution. They’re not just memorizing mathematical formulas. When a student says, ‘I get it’, I know they will never forget it.”

*“We have the opportunity to work closely with students, get them to talk things out, ” Griesbach said. “Students in regular classrooms might hide a little bit; we prioritize things like confidence and fostering skillful communication and dialog with one another.”*

Takeaways

Working with the newly adopted curriculum, Guayante and Griesbach made recommendations and suggested lesson adjustments for district colleagues to consider as they worked their way through Unit 8. For the Warm-up and Tilted Square problems, their notes included:

Working with the newly adopted curriculum, Guayante and Griesbach made recommendations and suggested lesson adjustments for district colleagues to consider as they worked their way through Unit 8. For the Warm-up and Tilted Square problems, their notes included:

- Overarching mission of the lesson: addition and subtraction strategies.
- Confirmation of student thinking: theorize and then convenience yourself.
- Making sure students understand. Presenting two strategies, with half the room using Method 1 and the other using Method 2.

On reflection, Griesbach observed, “The idea of implementing a curriculum that’s translatable felt at times like a juggling act, but prioritizing things like increasing student confidence and communication with one another was always in the forefront of our decisions. We were always looking for ways we could use the curriculum, but also get student growth. This meant making different decisions about the curriculum, teasing out and deciding what worked and what did not.”

“The fluidity of how Greg and Fred were able to adjust and change their teaching goals midstream was based on their teaching practices and shared experience as MfA SD Master Teaching Fellows,” said Dr. Osvaldo “Ovie” Soto, Math for America San Diego executive director. “These two teachers, steeped in Prof. Harel’s DNR mathematics instruction framework, were able to successfully collaborate and control the curriculum through this common lens. It’s hard to capture the effect of this kind of professional development on teachers who participate in the Summer Math Academies, but I can say the effects are deep and long-lasting.”

“I’m always honored and humbled to teach at the OUSD Summer Math Academy each year,” Guayante said. “I just learn…. I can’t put my finger on it, but I’m always a little bit better teacher than I was come fall.”

“The fluidity of how Greg and Fred were able to adjust and change their teaching goals midstream was based on their teaching practices and shared experience as MfA SD Master Teaching Fellows,” said Dr. Osvaldo “Ovie” Soto, Math for America San Diego executive director. “These two teachers, steeped in Prof. Harel’s DNR mathematics instruction framework, were able to successfully collaborate and control the curriculum through this common lens. It’s hard to capture the effect of this kind of professional development on teachers who participate in the Summer Math Academies, but I can say the effects are deep and long-lasting.”

“I’m always honored and humbled to teach at the OUSD Summer Math Academy each year,” Guayante said. “I just learn…. I can’t put my finger on it, but I’m always a little bit better teacher than I was come fall.”

Read about the 2023 OUSD Middle School Summer Math Academy here.