Open Connections

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Sharing a Passion for Math in Group Tutorial II

Written by Amy Hertzog, Facilitator. Originally published in the Winter 2019-20 issue of the "Open Connections Magazine"


I spent most of my school-aged years in Japan, attending traditional American schools on U.S. military bases. My dad was a high school math teacher. He was my high school math teacher for several years. He loved math and thought everyone should love math as much as he did. He was able to share this passion with his students on a daily basis. His dry sense of humor and ability to break down complicated mathematical concepts would make the subject of math feel more approachable and accessible to his students. I truly feel lucky to have had him as a teacher, even if I did not fully appreciate it in that moment. (How many kids in traditional schools had their dad asking if they had finished the math homework he had assigned in school that day? Kind of ironic now that I am a homeschooling parent!) I would say that most math came fairly easily to me, but I never loved math when I was in school. And there were two areas that I have struggled with my entire life: measurement conversions and word problems. The anxiety these two areas caused me continued into adulthood. I can honestly say that it is only in my recent years as a homeschooling parent and OC Facilitator, and after learning new strategies to use with the youth in my programs, that I can approach these two mathematical areas without feeling myself freeze up.


As a parent of three children who were traditionally educated in a public school setting and two children who are homeschooled, I have seen a wide range of attitudes towards math even in my own family. For one child, math is their passion. They see themselves having a career with a strong math focus in the future. For three of my children, math came easily to them, but they were content when their math classes in high school (and college) were completed. And I have one child who has struggled with math and told himself and others that he is “no good at math” and that he’s just “not a math person.” As a parent, I was concerned with his math story and began to wonder how to approach math in a way that would change his outlook, knowing from my own experience how math anxiety can continue into adulthood.


When I began facilitating Group Tutorial II here at Open Connections, I encountered many youth with this same negative attitude toward math. I can’t tell you how many times I have had youth say to me, “I hate math” or when they see that we are starting a math task, I hear “Ugh! I am just no good at math.” The tipping point for me happened on the first day of Thursday Group Tutorial II last year. I was walking with a youth who was brand new to OC and within our first few minutes together, she said, “I’m really stressed that Thursday’s focus is on Math and Science. I am really bad at math.” I don’t know if I can adequately express how these words from this 10 year old youth made me feel. The closest I can come is sad and disheartened. This inspired me to delve into research about math anxiety and to search for new ways to approach math not only with my own children, but with youth I facilitate here at OC. I truly believed that there had to be another way to present math that would decrease anxiety and show youth that math is not just memorizing math facts and working through a problem in search of the “right” answer. Math is a beautiful thing.


In my quest to find a new way to approach how I present math as a parent and Facilitator, I stumbled upon the work of Jo Boaler, a Professor of Mathematics Education at Stanford University and British education author. Dr. Boaler has written numerous books including—my personal favorites—Mathematical Mindsets and What’s Math Got To Do With It?. She has been featured in news outlets such as the New York Times, TIME Magazine, and The Wall Street Journal, She is the founder of YouCubed, a free online K-12 math resource offered by Stanford’s Graduate School, “to give parents, teachers, and students the resources they need to inspire and excite students about mathematics.” When I read that sentence, I knew that I would become a Jo Boaler “groupie.” I poured through her books and the YouCubed website and began to excitedly prepare activities to introduce in Group Tutorial II this past year.


One thing I value about Open Connections as both a parent and a Facilitator is their Partnership Education Model. The topics we explore in Group Tutorial II offer exposure that can then be taken deeper at home. We can dabble in a variety of mathematical concepts, offering a positive, supportive atmosphere and experience which will translate to youth being more comfortable when they approach math at home.


An activity we explored in Group Tutorial II was The Four 4’s. The task instructions are: Can you find every number between 1 and 20 using just four 4’s and any operation? (An example for the number 16 would be 4 + 4 + 4 + 4. An example for the number 8 would be 4 x 4 - 4 - 4.) The possibilities are endless and this is an example of a task that can be scaled up or down depending on the age of youth. Youth wrote the numbers 1 through 20 on a sheet of paper and began exploring. Consider pausing here, grabbing a sheet of paper, and trying this task for yourself.


Often with math inquiries in Group Tutorial II, youth begin by working on the task individually for a period of time. Then they are encouraged to work with a partner or small group to brainstorm different possibilities. I love walking around the room and hearing youth share their thinking with their peers. Witnessing the “aha!” moments happen, when youth grasped something unexpected or see a pattern for the first time, helped me realize that this approach could make a difference. After youth worked on this task in small groups for some time, we gathered together as a large group to share thoughts, noticings, and wonderings. Talking as a large group allows youth to see that there are multiple ways to approach the same task. It also shows that everyone has something to bring to the table. When discussing the Four 4’s task, the concept of Order of Operations came up. For some youth, this was a concept that they had explored, but for others, this was new learning. This was a great opportunity to put a pause on the Four 4’s task and delve into the Order of Operations. My favorite moments are when we branch off into another mathematical concept during a task.


Other examples of math inquiries we have explored in Tuesday and Thursday Group Tutorial II include:

  • Determining how many squares are on a chessboard? (Hint: it is more than 64!)
  • A Fibonacci Exploration—youth explored the Fibonacci sequence and used graph paper to create their own Fibonacci spiral.
  • Pascal’s Triangle task—youth were given a copy of Pascal’s Triangle with numbers missing and asked to find the missing numbers. This led to a discussion about triangular numbers.
  • Real-life Math including cooking and measuring OC’s Wildflower Meadow.
  • Spending a morning playing a variety of math and logic board games.
  • Celebrating Pi Day!


I have changed my math story and the way I approach math with youth. I have learned that being slow at math is okay. In Group Tutorial II, we take our time when we explore a mathematical task, purposefully slowing down to think about the task, listen to our peers, and ask questions. I have also learned that the path to an answer is just as important as the answer itself. The language I use with my own children and with youth in programming is still new for me. You might hear me say things like, “When we struggle with a problem, our brain is growing.” or “Anyone can learn math and everyone is a math person.” I encourage the use of manipulatives when working on a task and youth are asked to show their work to clarify how they are thinking through a task. Youth in my programs know that I do not always have the answer. Often we are puzzling through a task together.


After finishing my first year approaching math in this way at home and in Tuesday and Thursday Group Tutorial II, I feel encouraged and even more passionate about helping everyone see the beauty in math and creating more positive math stories for themselves. I have seen youth express less anxiety and disdain for our math tasks, including my own child. After his own math explorations in his Group Tutorial program, he frames his words about math in a much more positive tone. And the youth who told me on that first day of program last year that she was stressed about our math focus on Thursdays became more confident throughout the year. She even shared a fun math task with her peers in program that she had discovered at home. And I continue my own learning—reading and looking for new ideas and tasks to share with youth in my programs. I am excited to use new vertical, non-permanent writing surfaces (i.e. whiteboards!) for our collaborative math inquiries and to try visible random grouping when creating groups for math tasks.


One final thought. John Urschel, a Ph.D. candidate in mathematics and former professional football player wrote an article for the New York Times titled Math Teachers Should Be More Like Football Coaches. In it he says, “And no one expects math teachers to talk with the kind of fire, or to demand the kind of commitment and accountability, that football coaches do. But I wish they did. A growing body of research shows that students are affected by more than just the quality of a lesson plan. They also respond to the passion of their teachers and the engagement of their peers, and they seek a sense of purpose. They benefit from specific instructions, constant feedback and a culture of learning that encourages resilience in the face of failure—not unlike football practice.” If you ask youth in my programs what I am passionate about, I imagine you would hear things like mushrooms, Japan, the Olympics, and math (maybe Pi Day in particular!). I’ve learned that it is never too late to change your math story and that it is time for us all to become passionate about math and share that passion with the youth in our lives. So...what is your math story?