Mathematical Ways of Thinking: Summer Math Academies Spotlight Common Core Learning

SMA Blog Post Pics

“Each day we ask ourselves, ‘did the kids have a chance to think critically?’  We try to shift the mathematics to the kids’ point of view to elicit a student-produced solution, bringing them to the board and facilitating that kind of conversation.  The Summer Math Academy gave us the freedom to follow different pathways until kids were saturated.  Our goal was to figure out how much value we could get from each problem.”  – Aurmon Harchegani, SMA instructor

If you happened to stop by bungalow TMC 102 on the UC San Diego campus this July, you’d likely find a group of highly engaged middle and high school students busy solving problems like “the handcuff puzzle,” “the toothpick problem,” and “the clock hands problem.”  These and other intriguing mathematical challenges were a part of the first UC San Diego Summer Math Academy (SMA).

The SMA is a new student-centered project developed and taught by Math for America San Diego fellows, a corps of selected, exemplary math teachers.  Launched in 2008 and housed in CREATE, UC San Diego’s Center for Research on Educational Equity, Assessment, and Teaching Excellence, MfA SD is a mathematics fellowship and teacher professional development program dedicated to improving regional mathematics education.  MfA SD supports a variety of K-12 mathematics activities including projects developed through the CREATE STEM Success Initiative, a UC San Diego effort to leverage university resources to support high need students to succeed in Science, Technology, Engineering and Mathematics (STEM).

At the Summer Math Academy, middle and high school students explore mathematics concepts in an open, supportive and interactive setting.  Students learn by working in groups in order to strengthen their math content knowledge and share problem-solving strategies.

The SMA is part summer school, part professional development; students attend the academy in the mornings and Math for America San Diego fellows debrief in the afternoon to discuss the lessons from the morning and plan for the next day.  SMA curriculum features learning and teaching approaches of the new Common Core State Standards – Mathematics (CCSS-M), including eight mathematical practices designed to prime students for their next math course.

The SMA middle school teaching team included Gen Esmende, MfA SD Master Teaching Fellow and teacher at Wangenheim Middle School; and Eunice Lee and Brett Patrick, MfA SD Fellows and teachers at Madison Middle School and Bethune Elementary and Middle School, respectively.

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Middle school students spent part of one morning understanding patterns and expressions.  Eunice Lee, pictured above and below, worked with students by asking them to reflect on how they reached their solution and then to articulate their thinking processes with others.

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Throughout the week, middle schoolers in the middle school academy worked closely, forging friendships over math challenges.  Students talked with each other as they worked, thinking out loud and answering each other.  Deeply engaged with the process, students discovered there were no wrong answers — just answers that could be clues to finding the right answer.

“It’s great that the Summer Math Academy gives students the time to think about the problems,” said Lee.  “Usually the first idea they come up with is not the correct idea; however, students find it leads to other ideas, which lead to the solution.”

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“With the pattern activity, we really wanted students to be able to make sense of how the structure was growing and connect that to an algebraic expression,” said teacher Esmende, above.

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“We believe the students gained deeper reasoning skills by engaging in these types of pattern problems, and especially with our emphasis on the “PPG” — how the general expression directly connects to the meaning of the pattern, picture, and its growth,” added teacher Patrick, pictured above.

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The high school Summer Math Academy focused on arithmetic sequencing and motion and rate problems that incorporated CCSS-M ways of thinking.

“We selected more holistic problems for the high school group,” said Fred Griesbach, SMA instructor, MfA SD Master Teaching Fellow and teacher at Mira Mesa High School (pictured above).  “We wanted to work with problems that gave us the opportunity to ask a student, ‘what are you trying to find, why are you trying to find it and what does this element mean?’  We aimed for more open-ended, sophisticated problems allowing students to go to different levels and have multiple solutions.”

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The SMA encourages usually reticent students to step forward and explore new ways of understanding concepts presented by each problem.  Here Aurmon Harchegani, SMA instructor, MfA SD Fellow and teacher at High Tech High Chula Vista, helps explain the track meet problem.

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As part of the learning process, the UC San Diego Summer Math Academy asks students (like the two pictured here) to explain to others how they reach their solutions.

“At this level, understanding mathematics on a technical level is the students’ job; however, developing social behaviors in the classroom that include articulating what and why they know what they know, can advance their options as they grow,” Griesbach said.  “And if they can articulate and collaborate socially, these are the skills they’ll use in real life.”

The UC San Diego Summer Math Academy is one way the CREATE STEM Success Initiative is helping to leverage campus-housed programming to regional K-12 students.  MfA SD plans to offer the UC San Diego Summer Math Academy for incoming seventh through tenth graders next year, and the Academy’s teachers are excited to share their work with other teachers.  For more information, contact Math for America San Diego at

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