## Triton Summer Math Lab Academy for incoming 9th graders

UC San Diego

- Dates: June 26 - July 7, 2023
- Number of students: 16 incoming ninth graders
- Number of professional development teachers: 9
- Facilitators: Dr. Curtis Taylor, Yekaterina Milvidskaia

Fig. 5. Teachers and students attending the Triton Summer Math Lab Academies were from schools with high percentages of socioeconomically disadvantaged and Hispanic students.

Sixteen incoming ninth graders and nine middle school mathematics teachers from low-income/high-need middle schools across San Diego County attended the Triton Summer Math Lab Academy, a highly interactive mathematics enrichment class for students and a professional development program for teachers.

“The Triton Summer Math Lab Academy is a space for students to (re)consider their relationship to mathematics and where teachers can learn about their role in helping students create a more positive disposition toward math as a human endeavor, not just a set of rules to be applied. People create math,” said Dr. Osvaldo “Ovie” Soto, executive director of Math for America San Diego.

The Triton Summer Math Lab Academy was held June 26 - July 7 at UC San Diego’s Center for Research on Educational Equity, Assessment and Teaching Excellence (CREATE). Teachers and students who attended the Math Lab Academy were from schools with high percentages of families identified as socioeconomically disadvantaged and/or serving a high percentage of Hispanic students. The Triton Summer Math Lab Academy was funded by Math for America San Diego (MfA SD), The Mara W. Breech Family Foundation, and the US Department of Defense’s DSEC initiative.

“The Triton Summer Math Lab Academy is a space for students to (re)consider their relationship to mathematics and where teachers can learn about their role in helping students create a more positive disposition toward math as a human endeavor, not just a set of rules to be applied. People create math,” said Dr. Osvaldo “Ovie” Soto, executive director of Math for America San Diego.

The Triton Summer Math Lab Academy was held June 26 - July 7 at UC San Diego’s Center for Research on Educational Equity, Assessment and Teaching Excellence (CREATE). Teachers and students who attended the Math Lab Academy were from schools with high percentages of families identified as socioeconomically disadvantaged and/or serving a high percentage of Hispanic students. The Triton Summer Math Lab Academy was funded by Math for America San Diego (MfA SD), The Mara W. Breech Family Foundation, and the US Department of Defense’s DSEC initiative.

Participants

Dr. Curtis Taylor and Yekaterina Milvidskaia (MfA SD Teaching Fellow Alumnae 2014) facilitated the Triton Summer Math Lab Academy. Taylor and Milvidskaia are Improvement Coaches for High Tech High’s Graduate School of Education’s Center for Research on Equity and Innovation.

In addition to the 16 students, nine teachers attended the Triton Summer Math Lab Academy including Vanessa Medellin, mathematics teacher, and Chris Olivas, mathematics teacher, High Tech Middle North County; Gemma Rubi mathematics and science teacher, High Tech Middle; Claudia Pruitt, mathematics teacher, Knox Middle School, San Diego Unified School District; Vicki Bauer, mathematics teacher, Bonita Vista Middle School, Dr. Ivette Sanchez, district mathematics resource teacher, and Taffy Tom, mathematics teacher, Chula Vista Middle School, Sweetwater Union High School District; Daniel Gonzales, mathematics teacher, King-Chavez Neighborhood of Schools and Cynthia Patino, mathematics teacher, Literacy First Charter School.

Fig. 5 shows the demographic information of the schools these teachers serve throughout the year.

Dr. Curtis Taylor and Yekaterina Milvidskaia (MfA SD Teaching Fellow Alumnae 2014) facilitated the Triton Summer Math Lab Academy. Taylor and Milvidskaia are Improvement Coaches for High Tech High’s Graduate School of Education’s Center for Research on Equity and Innovation.

In addition to the 16 students, nine teachers attended the Triton Summer Math Lab Academy including Vanessa Medellin, mathematics teacher, and Chris Olivas, mathematics teacher, High Tech Middle North County; Gemma Rubi mathematics and science teacher, High Tech Middle; Claudia Pruitt, mathematics teacher, Knox Middle School, San Diego Unified School District; Vicki Bauer, mathematics teacher, Bonita Vista Middle School, Dr. Ivette Sanchez, district mathematics resource teacher, and Taffy Tom, mathematics teacher, Chula Vista Middle School, Sweetwater Union High School District; Daniel Gonzales, mathematics teacher, King-Chavez Neighborhood of Schools and Cynthia Patino, mathematics teacher, Literacy First Charter School.

Fig. 5 shows the demographic information of the schools these teachers serve throughout the year.

Observing the Triton Summer Math Lab from Two Perspectives

Math for America San Diego’s summer academies serve two constituencies at the same time. Following is a description of this robust experience, first through the teacher-participants’ lens, and then from the standpoint of students.

The teachers’ experiences were framed by Geoff Krall’s “Necessary Conditions”, Carol Dweck’s work on “Growth Mindset” (described below), and Guershon Harel’s “DNR-based Instruction”. From the students’ perspective, important Summer Math Lab Academy experiences included the value of searching for and justifying patterns, developing a growth mindset in approaching math content and understanding the benefits of working in groups.

Math for America San Diego’s summer academies serve two constituencies at the same time. Following is a description of this robust experience, first through the teacher-participants’ lens, and then from the standpoint of students.

The teachers’ experiences were framed by Geoff Krall’s “Necessary Conditions”, Carol Dweck’s work on “Growth Mindset” (described below), and Guershon Harel’s “DNR-based Instruction”. From the students’ perspective, important Summer Math Lab Academy experiences included the value of searching for and justifying patterns, developing a growth mindset in approaching math content and understanding the benefits of working in groups.

“Necessary Conditions” PD for Teachers

The teacher professional development focus at the Triton Summer Math Lab Academy centered on the work of Geoff Krall (1).

Krall’s work posits three elements, or “Necessary Conditions,” that should be implemented by teachers to achieve highly effective mathematics instruction and student learning. These include 1) Academic Safety - addressing student race and gender equity issues for cultivating an identity as a mathematician; 2) High Quality Math Tasks - use of math problems that can be accessed by students at a variety of levels of mathematical understanding; and 3) Effective Facilitation - implementation of pedagogical strategies that promote student agency and persistence.

Math Lab teachers had the opportunity to observe Dr. Taylor and Ms. Milvidskaia model the instructional approach with students while reflecting on the significance of their own teaching practices. Daily structured anticipatory and debriefing sessions, before and after each day’s instruction, included the use of protocols ensuring equal airtime for all teachers.

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(1) Krall, G. (2018). Necessary Conditions: A Self Study Guide for Teachers and Coaches on Improving Math Discussions. Stenhouse Publishers.

The teacher professional development focus at the Triton Summer Math Lab Academy centered on the work of Geoff Krall (1).

Krall’s work posits three elements, or “Necessary Conditions,” that should be implemented by teachers to achieve highly effective mathematics instruction and student learning. These include 1) Academic Safety - addressing student race and gender equity issues for cultivating an identity as a mathematician; 2) High Quality Math Tasks - use of math problems that can be accessed by students at a variety of levels of mathematical understanding; and 3) Effective Facilitation - implementation of pedagogical strategies that promote student agency and persistence.

Math Lab teachers had the opportunity to observe Dr. Taylor and Ms. Milvidskaia model the instructional approach with students while reflecting on the significance of their own teaching practices. Daily structured anticipatory and debriefing sessions, before and after each day’s instruction, included the use of protocols ensuring equal airtime for all teachers.

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(1) Krall, G. (2018). Necessary Conditions: A Self Study Guide for Teachers and Coaches on Improving Math Discussions. Stenhouse Publishers.

“At the Triton Summer Math Lab Academy, teachers observed a dynamic mathematics teaching environment that keeps students interested, involved, and curious, while simultaneously creating a safe environment that promotes intellectual risk-taking, excitement, and energy in mathematics learning,” Soto said.

Instruction-Centered Growth Mindset in Mathematics for Students

The Triton Summer Math Lab Academy instruction centered on the importance of cultivating a growth mindset in students when teaching and learning mathematics. Growth mindset is a concept developed by Carol Dweck (2), Professor of Psychology at Stanford University, that views intelligence and abilities as changeable and learnable. Approaches for achieving a growth mindset in math at the Math Lab Academy included 1) the use of content and pedagogy to expand students’ beliefs about mathematics; 2) attending to students’ perception of themselves as mathematical; and 3) fostering an understanding in students about what means to ‘do mathematics’ and ‘be smart’ in mathematics.

“A growth mindset in math for students and the Necessary Conditions modality for teachers are two frames that complement each other for effective mathematics instruction,” Milvidskaia said. “We wanted students to experience how cultivating a growth mindset can help them with math.

“This means understanding that everyone is capable of learning math. Understanding that although it’s often a struggle to learn math, it’s actually a positive endeavor, as struggling when learning creates new synapses in a student’s brain. Most of all, we wanted the students to find joy in learning math and to experience it as an open and creative subject,” she added.

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(2) Dweck, C. S. (2006). Mindset: The new psychology of success. Random House.

The Triton Summer Math Lab Academy instruction centered on the importance of cultivating a growth mindset in students when teaching and learning mathematics. Growth mindset is a concept developed by Carol Dweck (2), Professor of Psychology at Stanford University, that views intelligence and abilities as changeable and learnable. Approaches for achieving a growth mindset in math at the Math Lab Academy included 1) the use of content and pedagogy to expand students’ beliefs about mathematics; 2) attending to students’ perception of themselves as mathematical; and 3) fostering an understanding in students about what means to ‘do mathematics’ and ‘be smart’ in mathematics.

“A growth mindset in math for students and the Necessary Conditions modality for teachers are two frames that complement each other for effective mathematics instruction,” Milvidskaia said. “We wanted students to experience how cultivating a growth mindset can help them with math.

“This means understanding that everyone is capable of learning math. Understanding that although it’s often a struggle to learn math, it’s actually a positive endeavor, as struggling when learning creates new synapses in a student’s brain. Most of all, we wanted the students to find joy in learning math and to experience it as an open and creative subject,” she added.

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(2) Dweck, C. S. (2006). Mindset: The new psychology of success. Random House.

How Triton Summer Math Labs Integrated Theory and Practice

Professional development for teachers at the Triton Summer Math Learning Lab included daily pre-brief sessions before students arrived. Teachers discussed student work and classroom observations from the previous day and previewed the upcoming day’s math and instructional goals through the lens of the Necessary Conditions framework.

At daily debriefs after the student Math Lab, Taylor and Milvidskaia led discussions on the day’s instruction on what went well and/or what needed improvement. Teachers journaled on a Necessary Condition of focus they had observed that day; e.g., “How did the facilitators attend to the necessary condition, ‘Academic Safety’ for students? What ‘wonderings’ do you have?” When reviewing student work samples, teachers answered prompts such as, “What mathematical strengths do we see? What are the next steps for students in their learning?”

As an example, teachers responded to the following prompt:

Professional development for teachers at the Triton Summer Math Learning Lab included daily pre-brief sessions before students arrived. Teachers discussed student work and classroom observations from the previous day and previewed the upcoming day’s math and instructional goals through the lens of the Necessary Conditions framework.

At daily debriefs after the student Math Lab, Taylor and Milvidskaia led discussions on the day’s instruction on what went well and/or what needed improvement. Teachers journaled on a Necessary Condition of focus they had observed that day; e.g., “How did the facilitators attend to the necessary condition, ‘Academic Safety’ for students? What ‘wonderings’ do you have?” When reviewing student work samples, teachers answered prompts such as, “What mathematical strengths do we see? What are the next steps for students in their learning?”

As an example, teachers responded to the following prompt:

*“For my teaching practice, what are three things that resonated with me that I need to practice? Identify one practice for each Necessary Condition: Academy Safety, Quality Tasks, Effective Facilitation.”*- Use of post-it notes (“You’re honoring a student’s think time - it’s a tool to communicate without breaking the silence of thinking time.” - Milvidskaia)
- Asking a student, “What do you understand, what was this person thinking? What are you thinking?”
- Addressing student anxiety with math stories (Dear Math task); we would do it as a mood board in my classroom.
- Use the Mathematically SMART slide that bullets 7-8 ways you can be mathematically smart today (Fig. 6 below).
- Use of quality time; “Meta Moments” to provide a transition between tasks.
- Have students take a deep breath as we transition. Being explicit and consistent on expectations. Appreciating the explanation of why for students.
- Eliminate the feeling of “this is a race” in math. I want to push students but alleviate “this is a race” thinking.
- Word use: Being careful with our use of words: using the words feedback, growth (not fail); “we can do hard things.” Words have a lot of power.
- Sequencing to make connections; comparing and contrasting; using playing cards as an effective tool to randomize calling on kids.
- Standing outside the classroom door and greeting students as they arrive (“The bell rings, you're setting a tone, I care, you belong, welcome. It can be hard in the chaos with everything going on. Students need to understand that they’re welcome here vs maybe at home. Do a quick check-in before they come in.” - Milvidskaia and Taylor)
- I will lean down to a student and say “I’m confused” - normalize saying “I’m confused.” (Now we’re having a dialogue, and the student doesn’t feel we're the holders of all the knowledge - Milvidskaia.)

Content Focus

Mathematical content at the Triton Summer Math Lab Academy focused on visual pattern problems. These problems were selected to build collaboration among the students while serving as a low pressure way for students to become accustomed to sharing their work with others. The open-ended, low floor/high ceiling visual pattern problems were used to introduce the mathematical concepts of initial value and rate of change.

The students’ experience was marked by pattern searching, argumentation, and learning to see themselves as capable doers of mathematics. They learned to work together and value each others’ ideas.

Mathematical content at the Triton Summer Math Lab Academy focused on visual pattern problems. These problems were selected to build collaboration among the students while serving as a low pressure way for students to become accustomed to sharing their work with others. The open-ended, low floor/high ceiling visual pattern problems were used to introduce the mathematical concepts of initial value and rate of change.

The students’ experience was marked by pattern searching, argumentation, and learning to see themselves as capable doers of mathematics. They learned to work together and value each others’ ideas.

“Even though the focus was on linear relationships. The teachers did a good job of mixing it up. Too often students investigate the same kinds of problems with too much repetition,” Soto said. “For example, they only study linear growth, or only exponential growth or decay, etc. Varying the way things can grow allows students to ask the more fundamental question, ‘How can I predict an amount at any given point in time given the evidence I’ve seen?’ The point is to incite curiosity and show that math gives us the power to make models.

“Pattern finding is fundamental to doing mathematics. Looking for patterns is doing mathematics,” he said.

“Pattern finding is fundamental to doing mathematics. Looking for patterns is doing mathematics,” he said.

For the Toothpick problem, students were first instructed to consider the problems visually without additional information, then asked, “What do you notice? Is there a pattern? What do you wonder?” Presenting a problem in this manner stimulates critical thinking and creativity.

This type of instruction prompts students to play a role in the creation of the questions themselves, not just the answers. As more information is provided, students start to understand what may be necessary to solve the problems posed; i.e., ‘What else they may need to know and what concepts can they use?’

“In traditional mathematics instruction, students are told up front which concepts they’ll use to solve problems, limiting their own critical thinking by labeling the problem and identifying mathematical concepts at the outset,” Soto said. “However, a key component of learning to be a problem-solver is breaking the problem down into smaller parts for oneself. If teachers do it for students, the students lose valuable opportunities to make their own mistakes and understandings of mathematics.”

“In traditional mathematics instruction, students are told up front which concepts they’ll use to solve problems, limiting their own critical thinking by labeling the problem and identifying mathematical concepts at the outset,” Soto said. “However, a key component of learning to be a problem-solver is breaking the problem down into smaller parts for oneself. If teachers do it for students, the students lose valuable opportunities to make their own mistakes and understandings of mathematics.”

To help improve students’ confidence and mathematics skills, teachers implemented daily wellness check-ins, provided personalized notes on their math work, and celebrated successes large and small.

The Importance of Group Work

The Triton Summer Math Lab Academy curriculum included student group work to strengthen mathematical learning. Working together, students became aware that solving math problems with others helped them with their own understanding and knowledge of math. Throughout the course, teachers polled the students to track increases and decreases in their perceptions of how group work influenced their math progress. Taylor and Milvidskaia shared the results with students to help them see that working with others can improve their mathematical understanding.

“Today’s workforce is increasingly engaged in collaboration and groupthink,” Taylor said. “By emphasizing classroom group work, students learn the value of identifying and advancing good ideas from each other. It’s great to know theorems and mathematical concepts, but working well with others is also an important skill for improved mathematical understanding.”

The Triton Summer Math Lab Academy curriculum included student group work to strengthen mathematical learning. Working together, students became aware that solving math problems with others helped them with their own understanding and knowledge of math. Throughout the course, teachers polled the students to track increases and decreases in their perceptions of how group work influenced their math progress. Taylor and Milvidskaia shared the results with students to help them see that working with others can improve their mathematical understanding.

“Today’s workforce is increasingly engaged in collaboration and groupthink,” Taylor said. “By emphasizing classroom group work, students learn the value of identifying and advancing good ideas from each other. It’s great to know theorems and mathematical concepts, but working well with others is also an important skill for improved mathematical understanding.”

From the slide: “How can we continue to support others so that everyone feels and knows they are good at math? How has someone helped you in the past? Has someone helped you by asking questions?”

Student responses in class:

“In this age group, students think, ‘If I see it this way, then others must as well.’” Milvidskaia said. “Once they have their way of solving something, it’s really hard to see how others do it. So working in groups is helpful for reflecting on how others were correct.

Student responses in class:

- Thank people that help you and invite others. Explaining their thinking can support us.
- Listening all the way through even if you have a different idea or answer.
- We’re making everyone feel comfortable with math, we’re doing well. Listening and respecting each other.
- Being straight up with people. I like your thinking! Celebrating each other.

“In this age group, students think, ‘If I see it this way, then others must as well.’” Milvidskaia said. “Once they have their way of solving something, it’s really hard to see how others do it. So working in groups is helpful for reflecting on how others were correct.

*Students and teachers celebrate on the final day of the Triton Summer Math Lab Academy.*

*Dr. Ovie Soto with Triton Summer Math Lab Academy students at UC San Diego’s Social Sciences Public Engagement Building.*

“For two weeks, teachers observed two experts [Taylor and Milvidskaia] advance a growth mindset in this group of students,” Soto said. “Teachers had an immersive experience into what a mathematics classroom environment could look like that targets a growth mindset and implements the ‘Necessary Conditions’ framework for learning.

“Math content is perceived by most people in our country as black and white or right and wrong. The Triton Summer Math Lab Academy provided the substantive workings of a classroom with a different perspective,” Soto added.

“Math content is perceived by most people in our country as black and white or right and wrong. The Triton Summer Math Lab Academy provided the substantive workings of a classroom with a different perspective,” Soto added.

Explore other Summer Math Academies by clicking links on the Executive Summary Table of Contents