~ Sweetwater Union High School District ~
Otay Ranch Senior High School Summer Bridge Math for incoming 9th graders
- Dates: June 6 - 9, 2023
- Number of students: 11 incoming ninth graders
- Teachers: Anne Maria Almaraz, Melody Morris
Fig. 3. Approximately one in three Otay Ranch High School students are from socioeconomically disadvantaged families.
Sweetwater Union High School District has a short, six-week summer due to a year-round schedule so Summer Math Academies were shortened to one week. Two teacher professional development days were held each Monday followed by a four-day Summer Math Academy called “High School Summer Bridge Math for Rising 9th graders.” Week 1 (June 6-9,) was held for incoming Otay Ranch High School students. Week 2 (June 13-16) was held for incoming Hilltop High School students.
Summer Math Academy Teacher Leaders Anne Maria Almaraz and Melody Morris, mathematics teachers at Otay Ranch High School and Olympian High School respectively, led the Week 1 academy. Six SUHSD teachers observed their instructional practices and provided additional learning support to students. For the Week 2 Summer Math Academy, the six teachers would then co-teach the same academy curriculum to incoming Hilltop High School students.
Students at both Summer Math Academies tackled The Glowing Cubes problem, which required students to engage in Standards for Mathematical Practice 3 (SMP 3): Construct viable arguments and critique the reasoning of others.
Summer Math Academy Teacher Leaders Anne Maria Almaraz and Melody Morris, mathematics teachers at Otay Ranch High School and Olympian High School respectively, led the Week 1 academy. Six SUHSD teachers observed their instructional practices and provided additional learning support to students. For the Week 2 Summer Math Academy, the six teachers would then co-teach the same academy curriculum to incoming Hilltop High School students.
Students at both Summer Math Academies tackled The Glowing Cubes problem, which required students to engage in Standards for Mathematical Practice 3 (SMP 3): Construct viable arguments and critique the reasoning of others.
Problem: The Glowing Cubes
For this activity, students were given time on their own to model the problem using snap cubes and generate their own conjectures. Teachers encouraged students to communicate their problem-solving approaches and solutions to their peers and learn how others at their table had reached their own conclusions. Moving from table to table, teachers asked the students about how they planned to persuade others of their final solution and problem-solving approach.
Teacher Leaders Anne Marie Almaraz (above) and Melody Morris co-taught the Week 1 Otay Ranch High School Summer Math Academy, while fellow SUHSD teachers observed how they implemented DNR-based mathematics instruction and pedagogy. Eleven incoming ninth graders from SUHSD feeder middle schools attended the program.
“Who wants to explain this journey?” Almaraz asked the students. As the students responded, Almaraz asked “why” questions and asked for meaning. “What would taking away the 19 mean?” “I want you to think about that.” “How many cubes in figure three?” “Can you write that down? I want to ask you about that.”
Students started to wonder: “Why so many questions?”
“Because we’re trying to get you to convince us of your solutions,” Morris stated. “Let’s relate this to a court of law. If I’m the defendant in a case, I'm convinced I'm innocent. And the attorney I have paid to defend me is also somebody who's on my side. However, a jury, the people who are going to decide my innocence, they're going to be a little bit harder to convince. I have to provide them with some evidence. I have to say ‘There's no way I could have committed the crime and here’s why.’
“Then there’s the prosecutor who's on the other side who's not defending me,” she continued. “Ms. Almaraz and I are playing the role of the prosecutor. We're playing the role of the person who says ‘Maybe I can’t fully commit that you’re correct until I can't find any holes in your argument.’
“That's a little explanation of why we're asking so many questions. And why do we want to encourage you to ask yourself those questions? Am I just writing this on my paper because my eighth grade math teacher told me this is the thing to do? Or do I really understand what I'm doing? Do I understand the significance of these numbers and what they mean in the context of the problem?”
“Because we’re trying to get you to convince us of your solutions,” Morris stated. “Let’s relate this to a court of law. If I’m the defendant in a case, I'm convinced I'm innocent. And the attorney I have paid to defend me is also somebody who's on my side. However, a jury, the people who are going to decide my innocence, they're going to be a little bit harder to convince. I have to provide them with some evidence. I have to say ‘There's no way I could have committed the crime and here’s why.’
“Then there’s the prosecutor who's on the other side who's not defending me,” she continued. “Ms. Almaraz and I are playing the role of the prosecutor. We're playing the role of the person who says ‘Maybe I can’t fully commit that you’re correct until I can't find any holes in your argument.’
“That's a little explanation of why we're asking so many questions. And why do we want to encourage you to ask yourself those questions? Am I just writing this on my paper because my eighth grade math teacher told me this is the thing to do? Or do I really understand what I'm doing? Do I understand the significance of these numbers and what they mean in the context of the problem?”
Ms. Morris gives directions on how to use the yellow and pink post-it notes for the Swap Meet math task.
Next, table teams participated in the Swap Meet activity. Students began by presenting and justifying their Glow Cube solutions at their table. Then two students from each table were instructed to travel from table to table to “swap” information on how they came to their conclusions and to share their remaining questions.
“What we want you to do is swap ideas about something you are 100 percent convinced about,” Morris said. “You're going to state something that you know to be true about the problem and back it up with evidence so we cannot put any holes in your argument. The second thing you're going to do is to identify any questions you have, where you're not fully convinced about the answer, or that there's a little piece of it that you just don't have; some little question about where it was extra confusing to you.” Students listed the ideas they were confident about on a yellow post-it note. Any Ideas they still wondered about were listed on a pink post-it note.
After returning to their tables and making adjustments based on what they learned, teams mounted the post-its on whiteboards for students to make their case to the teachers.
Dr. Osvaldo “Ovie” Soto led daily debriefs with Summer Math Academy Teachers. Debriefs are a valuable component of the Summer Math Academy experience. Teachers identify and discuss issues of teaching and learning. Then they decide how to approach the next day’s lesson based on students’ thinking.
Daily Debriefs
After class, teachers debriefed and shared what they noticed during the day’s activities. Many students were challenged by the Glowing Cubes problem. Students had trouble relating the parts of the linear functions/equations they wrote to the context of the problem. Teachers also noticed mimicry of problem-solving without understanding.
Based on debrief input from the previous day, Morris decided the students needed more time to think alone and to work in pairs, so she revised the Day 3 curriculum to accommodate this observation.
Based on debrief input from the previous day, Morris decided the students needed more time to think alone and to work in pairs, so she revised the Day 3 curriculum to accommodate this observation.
Takeaways
On the final day of the academy, incoming Otay Ranch High School students shared with teachers what they had learned, and what they would like to take with them as they enter ninth grade math classes:
Teachers who observed the academy throughout the week shared their thoughts with students:
Read about Week 2 at Hilltop Senior High School Summer Math Academy here.
- When I get an answer, I will think about it more.
- Show my answers and how I got it.
- Use your own way to solve a problem.
- You want us to know how you solve it, not just ask us to solve it. I respect that you care about how I think.
- It was better than I expected. I thought you’d be telling us more, but you helped us and you gave us a lot of time on our problems.
- Being able to do math in situations where I didn’t think I needed it. Being able to associate math with global problems.
- The teachers and the people around me and the games and the help took some pressure off.
Teachers who observed the academy throughout the week shared their thoughts with students:
- It’s cool to see that students can be involved without incentive. It’s not about being good or bad. You’re all mathematicians. You worked toward it. You are hard workers and very intelligent.
- You were teaching me how to be a better teacher. Teachers make mistakes. You had “ah-ha moments.” I thought you wouldn’t have fun, but you disproved that. Thank you for providing many moments of learning.
- Thank you for being brave. You signed up for something you didn’t know anything about.
- Applaud the bravery. Congratulations on coming! You all said something positive about this [experience].
- I would choose all of you [as students next year] if I could. You are awesome, cool, brave, and good problem solvers.
- Resilience. Classes should be more student-centered. Problem-solving is crucial.
Read about Week 2 at Hilltop Senior High School Summer Math Academy here.