Tag Archives: math

Nathan’s Notes

Welcome to Nathan’s Notes, your monthly report from middle school! Each month I’ll share some moments from the classroom, curriculum thoughts from me and/or our amazing teachers, some ideas about education that I’m excited about, and more.

One thing that got me excited this month…

Janis Chun’s 5th-grade science class. The students were using ratio tables in conjunction with Google Maps to discover how eating different foods change the carbon footprint. The students collaborated in pairs as they used math, technology, and science concepts to create a poster that highlighted their findings. I loved how the kids were able to have an application of math to deepen their understanding of a real-world issue about the environment. They were able to work on collaboration skills while using technology in a thoughtful way. Most importantly, the kids were engaged and excited about what they were doing in class!

A curricular question I’m pondering is…

How we can continue to build confident math students? The other day I heard one of our teachers say, “I am not a math person.” Immediately after she said it, she recognized that this statement is something that we have been actively working to vanquish from our language at Prospect Sierra. A growth mindset, especially in math education, is a topic we have discussed regularly by sharing our own personal math stories. Many of the stories that exist within our educational community are of struggle, self-doubt, and external factors that took away our math confidence. We understand that these are the kinds of experiences that lead towards the declaration of believing one is a “math person” or not. For the past few years, the math department has been working hard to unpack not just personal stories of discouragement in someone’s math journey, but also discussing how larger movements of math education in our country have contributed to self-doubt in this subject. How do we continue to foster confident math students? How do our own math journeys as adults impact our children’s experience in math?

One moment that made me think, wow what a special community this is…

When I spoke to the students from the “Be the Change” elective about the climate strike. To be honest, I was worried about this day. How do I support student activism while still upholding the integrity of the middle school? In this case, the activism the kids wanted to take directly impacted school because it required them to miss school. This question rattled in my mind. One day a group of 10 mixed-grade students appeared at my office door. They were from the “Be the Change” elective and were hoping to organize a Prospect Sierra group at the climate march in San Francisco. I wasn’t sure exactly what to say, but as we dove into dialogue it became clear to me that these students truly understood the tough situation that I was in as an administrator. They had empathy for me, and they also made clear that this was an event that they felt very passionate about. The way that these students engaged in discussion showed that they had been given a Prospect Sierra education. They spoke with empathy, respect, organization, and passion. We came to an agreement through thoughtful discussion, and we decided how to move forward. What initially felt like a stressful conundrum ended up being an inspiring moment.

Abby’s Corner: Summer Learning Fun

Summertime Fun

Happy summer to you all! Hopefully, you have already found some ways to relax. The heat wave that hit El Cerrito was an intense way to start our summer, and my hope is that you all were near a pool or beach on those 100 degree days.

Summer work is already underway at Tapscott and at our new Gatto/TK campus. Teachers have cleaned up and gone home, and some of our new faces are already here and getting a lay of the land, ordering materials, and thinking about how to support kids next year. It happens quickly, and I am getting excited to welcome our transitional kindergarteners to Prospect Sierra in late August.

In the meantime, if you are like me you have made a list of summer reading, eating, and relaxing that must be done! Wishing you a fabulous summer filled with joyful moments.

Worth Remembering: The “Summer Slide” is Real

While summer is super fun, it’s also a time that kids can lose some of the gains they made this past year in both reading and math, also known as the summer slide. Our approach as a school is to encourage parents to find ways that are fun and engaging for your child, and to keep them reading regularly as well as working their math brains this summer. Whatever way works for your child and your family, the goal is to promote lifelong reading and application of math skills in real life! When they buy ice cream, make them calculate the total or figure out how much change they will get back. When there is downtime for the family, have a family reading time for 20-30 minutes. There are lots of ways to “disguise the learning” so kids are still flexing those muscles!

The Tapscott Reading Challenge: We will once again attempt to read 400,000 minutes this summer! I encourage you to carve out some family reading time, and read some great books yourself or with your child this summer! Ideally, kids should be looking at books, listening to stories read aloud to them, or independently reading for 20-30 minutes every day this summer.

Practicing math skills during the summer:  This article from the Harvard School of Education highlights that, on average, kids lose 2.6 months of math learning over the summer. Below you’ll find the article’s suggestions for ways to integrate math into summer activities.

  • Highlight the math in everyday activities. When shopping, help kids calculate change or discounts. When watching a baseball game, talk about what players’ statistics mean. When cooking, try halving or doubling a recipe, and assist kids in figuring out the new proportions.
  • Read short math stories together. Studies have shown that reading math-focused stories to children, such as Bedtime Math books or the Family Math series, can help boost math scores in school.
  • Play math games. Games like Yahtzee, Racko, Blokus, Monopoly, and Set all rely on skills necessary for math, such as counting, categorizing, and building. Even playing with blocks and assembling jigsaw puzzles can help kids learn spatial skills and recognize patterns.
  • Find small ways to practice math at home. While worksheets alone won’t solve the summer math slump, small amounts of practice with basic formulas can help. Problem-of-the-day math calendars are a great way to practice basic math problems on a small scale. Parents can also find resources on Investigations about what types of mathematical procedures they should be practicing with their children.

Additional resources for math at home:

  • The founder of Bedtime Math, Laura Overdeck, describes how and why this series of daily math problems works as a family engagement tool in mathematics.
  • YouCubed resources for parents and apps/games/problems for students
  • YouCubed online course for students. This self-paced course is designed for any learner of math and anyone who wants to improve their relationship with math. The ideas should be understandable by students of all levels of mathematics. Parents who have children under age 13 and who think their children would benefit from some of the course materials should register themselves (i.e., parent’s name, email, username) for the course. The parent may then choose to share course materials with their child at their own discretion.

Worth Reading

Celebrate Pride this month with two great books. I love both of these! Pride: The Story of Harvey Milk and the Rainbow Flag is great for upper elementary students and provides some understanding of the flag as well as the local changemaker Harvey Milk. This Day in June is a great picture book, appropriate for all ages, and provides some background information on different aspects of this month’s SF Pride Parade.

Dr. Jo Boaler Opens Minds

The PSPA Authors & Lectures team recently brought Dr. Jo Boaler to campus to talk about maths. We intended to write “maths” because Dr. Boaler, who is British, refers to “math” as “maths.” Further, the “s” on “math” makes the subject expansive and full of possibilities and “expansive” and “full of possibilities” is exactly what we want for our students when they’re engaged in maths. To nurture the idea that maths is full of potential, and most importantly, accessible to all, students need a belief that they can do maths. Dr. Boaler’s talk focused on how to cultivate this type of mathematical mindset.

Growth Mindset

At Prospect Sierra, we’ve been implementing Carol Dweck’s work around growth mindset for many years. Dweck posits that in a growth mindset people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment. A growth mindset is integral to Dr. Boaler’s work as well, and underpins the research she does showing the brain’s plasticity and extensive brain growth during hard work and struggle in particular.


Dr. Boaler’s work is pivotal in helping students believe they are capable math problem-solvers. In Dr. Boaler’s work there are no “math people” and “not math people.” She knows that every student will hit a roadblock and struggle, whether they’re told they can do math or not, or whether they’re good at math or not.

The Pit

Speaking of struggle, another powerful strategy from Dr. Boaler’s talk is her idea of “the pit.” The pit is the place of struggle where students are grappling with hard problems to solve. They often want a way out, or want a teacher to carry them over the pit. But in actuality the pit is the place where the brain is growing the most. The more we can help kids get more comfortable with the discomfort of the pit, the more they will grow and learn.

Helping Your Child

So what can parents do to help their child develop this flexible, ever growing math mindset?

  • When you see your child struggling with a math problem you could ask “What are some other strategies you can use?” You could also remind them that “Struggle is good; it means your brain is growing!”
  • Praise hard work rather than attributing success to being smart or gifted. You might say “You tried very hard and you used the right strategy,” or “What a creative way to solve that problem!”
  • When your child has made a mistake or feel like they’ve failed you can remind them that mistakes are an important part of the problem solving process and that they ultimately help improve understanding. Further, to normalize mistake making, you could ask “What mistake did you make that taught you something?” Or, “What did you try hard at today?”


If you’d like to learn more about the growth mindset, there’s lots of great information specifically for parents on this website. And if you’d like to learn more about Dr. Boaler’s math mindsets, click here. Thank you to the PSPA Authors & Lectures committee for bringing us such a thought provoking maths leader!

Introducing…Middle School Matters: Math!

When my eighth grader asks for help with his algebra homework, I smile inside. I love doing algebra! I love doing math, grappling with a problem and sticking with it. That wasn’t always the case.  Growing up, even though I was fairly good at math, it wasn’t fun. It was an individual experience, never collaborative. If I asked the teacher for help, I wasn’t “smart” enough. If I asked a classmate for their strategy in solving a problem, I was cheating. On the contrary, in my home, we have an entire wall painted with whiteboard, and Dylan and I can each work on a math problem and step back to compare our thinking. As an adult, I so enjoy this. Now, I love making mistakes – screwing up a problem royally only for Dylan and I to examine my logic (or lack thereof) and discover where my thinking went awry. He, too, gets the same feedback. I’m inspired to stay with a problem whatever it takes. In this way Dylan watches me be “math resilient” and together we grow that muscle.

I’m delighted to report, I’ve learned math resilience and a growth mindset (failing fast and forward and sticking with it) from Prospect Sierra math teachers. Our math faculty is passionate about math instruction and learning. I’ve observed our math teachers as a parent and principal, and I’ve caught the “math fever” from them! To stay on top of best practices, our Avis math department and Division Heads have been attending conferences, workshops, and regional math meetings, as well as tapping renowned math thinkers to design the best K-8 math program in our region. Just like Tapscott reviewed various elementary programs and chose the Bridges curriculum to suit our K-5 learners, Avis, too, has been actively researching and piloting dynamic math curricula. Our goal? To graduate students who are able and resilient math problem-solvers, who are eager and ready to tackle any problem presented to them…with persistence!

Math education in the U.S. has gone through many transitions over the last half century – from the post-Sputnik era and “new math,” and the “back to basics” movement in the 70s, to the “math wars” of the 80’s and 90’s, followed by the assessment-driven accountability movement of the aughts typified by the infamous (and famously unsuccessful) U.S. policy of No Child Left Behind. These recurring national shifts in math education primarily affect public schools, and during these decades of debate over what math education should look like in the U.S., independent schools, such as our own, have enjoyed the freedom to choose the pedagogy and curriculum that suits their students, mission, and school community. Nonetheless, these phases of math pedagogy are noteworthy and relevant to us because they help us see the historical trends and inform our perspective on what we think math education should look like.

With the creation of the Common Core standards in 2010, math educators finally found themselves with a set of deeply researched, thoughtful, cohesive, and well-written standards. These standards include what content and skills should be taught, and embedded within them are also a consistent emphasis on developing students’ deep conceptual understanding of mathematics. The Common Core standards are a successful blend of procedural skills, problem solving, and deep mathematical understanding, and the philosophical underpinnings of  the Common Core math standards are consistent with what our math teachers at Prospect Sierra have been doing for many years.

Currently Prospect Sierra is aligned with the Common Core math standards in K through 7th grade. It took a few years for high-quality, Common Core-aligned curricula to become available, and as mentioned earlier, in 2015, we adopted the Bridges in Mathematics curriculum for our K-5th grade programs. Our middle school math department is currently conducting a curriculum review for 6th-8th grade, and last year piloted Eureka Math in 6th and 7th grades. This year we are piloting a new curriculum in 6th through 8th grades, Illustrative Math, which offers a balance of deep conceptual understanding with skills-based practice. So far, we are very pleased, and there will be more information to come on how our math pilot program is fairing.

Our math team (all of our math teachers plus Abby and Heather) recently attended the California Mathematics Council (CMC) Conference, where we learned from great math leaders including Jo Boaler who spoke about math best practices and in particular, building math resilience. We also met with Phil Daro, a local math leader and one of the writers of the Common Core. The conversation was incredibly informative and helpful, and we will be carefully considering our options as we continue to seek out the best practices for math instruction and course sequences in the years to come. Stay tuned for more!

Last week Dylan and I were stumped by an algebra problem. What did I do? I came to school and threw it up on the whiteboard in my office. I’d pull in teachers from all disciplines as they passed by office, prompting them to take a stab at the problem and show their thinking. By the end of the day, I had multiple ways to solve the problem (and not without a lot of head scratching mind you). Through multiple methods, I learned more about engaged problem-solving. It was an inspired, fulfilling math experience, and I grew my math resilience muscle. I’m watching your kids’ math resilience muscles grow too!

Here’s to math, enjoying it, and problem-solving for a better world!

Heather Rogers, Middle School Head
Aaron Moorhead, 5th Grade Math & Science Teacher