Last week the New York Times published, “ Make Your Daughter Practice Math. She’ll Thank You Later. The way we teach math in America hurts all students, but it may be hurting girls most. ”
It’s the sort of article that leads me to write a Comment, but many people beat me to it. Typical were responses about a father forcing the child to memorize times tables, which the child resented at the time, but boy was dad proud the day that PhD was earned (this Comment was an ‘NYT Pick’).
The editorial compares learning math to learning a musical instrument. Just like learning to play the guitar, “Simply understanding how a chord is constructed isn’t the equivalent of being able to play the chord….The word “rote” has a bad rap in modern-day learning”.
The piece argues that math teaching places too much emphasis on conceptual understanding, and not enough on the kind of drill that makes reciting times tables automatic.
The problem is that the author here doesn’t take the analogy far enough. True, the goal of playing a guitar is not understanding why a chord is a chord, but the goal of playing a guitar is also not playing chords.
The goal is to make music.
So what’s the object of doing math? It’s not doing times tables. It’s conceptual understanding itself.
Now, I don’t actually disagree that kids need to be fluent mathematically, just as there is value in learning to play individual chords on a guitar as a route to playing a full piece. But memorizing times tables is actually the equivalent of memorizing where your fingers go rather than actually placing those fingers properly on the fret board.
So how do you learn to ‘play’ math the right way?
What is 9 x 7? 63. How do I know this?
- 10 x 7 is 70. To get 9 7’s, 70 – 7 = 63.
- 5 x 7 = 35 and 4 x 7 = 28, and 35 + 28 = 63.
- 10 x 10 = 100. 9 x 11 = 99. 12 x 12 = 144. 11 x 13 = 143. I see a pattern. Since 8 x 8 = 64, multiplying 1 less than 8 by 1 more than 8 is 63. Later in Algebra I’ll be able to connect this to the full generalization that (x + 1)(x – 1) = x^2 – 1, a special case of what’s called a, “Difference of squares.”
- It’s 63 because I have it memorized.
The memorization came after I made connections. This result fit into an overall structure, with the truth of any one piece fitting into a larger picture. And, moreover, it fit into a future picture. When it came time for Algebra, my experience learning arithmetic fit. I didn’t go on to memorize the distributive property and the difference of squares pattern, I connected them to prior learning.
“Rote” has a bad rap in modern math learning for good reasons. The article goes on to say, “But girls especially could benefit from some extra required practice, which would not only break the cycle of dislike-avoidance-further dislike, but build confidence.”
My 25 years of teaching experience tells me the opposite. When students learn by rote, they are two years away from never being successful in math again. When the math you know is a disconnected, unstructured house of cards, you don’t know when it will fall apart, but you know that it will.
Every once in a while we're lucky enough to get a tenured professor to lead math circles. What's even more unusual is when that professor represents MC2 and travels around the city to run math festivals at Chicago elementary schools. Keigo Kawaji recently won the The Center for Learning Innovation Digital Teaching Innovation Award at the Illinois Institute of Technology. He's also MC2's Teacher of the Month! 1) How long have you worked for Math Circles? I have been a member of our Math Circles since 2019. 2) What made you start working for Math Circles? I was part of the math circles organization in my hometown through high school. By my high school senior year, I got to serve teaching in their programs, this then led to my first paid positions in teaching at summer math camps. So it has been quite natural to join our Math Circles of Chicago once I became an educator here. 3) Why do you teach? I have been inspired by mentors who have guided me to this nice recognition. Influenced by three such mentors during my high school years. So I teach to pay forward. (And thank you Steffi, Tom, and Richard). 4) What is your favorite thing about teaching? I see teaching as my own means of performing music, or creating an artistic piece (though I am good at neither). As a college professor, I was just recognized at my home university (Illinois Tech) for my teaching innovations in both digital and beyond digital platforms. Sharing these teaching innovations with similarly minded educators is truly rewarding for me. 5) What is something you wish more parents knew? There is no such thing as the 'only way'; there are many ways to solve a problem. Oftentimes, in hindsight, we realize that this was the only way we knew. This offers some food for thought. 6) What is something you want people to know about Math? When attempting to solve a challenging problem, start by finding one solution. Then, sometime later — or perhaps someday — try exploring a different, alternative solution. 7) How has Math Circles impacted your teaching career and your perspective as an educator? For the past 7 years, I have met many fellow educators, parents, and students through the Math Circles. In fact, I recently tried to count how many, and realized that I connected with almost one thousand people in the greater Chicago area community. I now wonder how many readers here and I might have already crossed paths (I'd be honored!). For each connection that I have made, I have grown as an educator. 8) Should Pluto be given back its title of planet? In fact, I do not know. I am curious as to what sets of rules should be used to define inclusion as planets. Maybe there are more than one defined set of rules for inclusion. And it is okay to say I don't know.
Summer Math Preview: High School For high school students interested in our two weeks of summer programs at Benito Juarez high school , here's a preview of the math content! What is Category Theory? Perhaps it's best to hear about the subject from your instructor, Dr. Eugenia Cheng [ watch until at least 8:25] :
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In February we interviewed Louisa Shannon, who leads an MC2 After School Program at Murray Elementary School and who has been a lead teacher at MC2 summer camps, both at Back of the Yards and in her own school. She's now in her 4th year at math circles! 1) What made you start working for Math Circles? I started working for Math Circles after participating in a Formative Assessment Lesson (FAL) Professional Development Cohort that Doug O'Roark co-organized during virtual learning. 2) Why do you teach? I teach because it is a vocation and a privilege. Being entrusted to provide equitable access, cultivate identities, and prepare community members is an honor of which I aspire to be worthy every day. 3) What is your favorite thing about teaching? Facilitating and witnessing a Eureka moment of clarity when someone synthesizes the pieces of information into a new understanding that they take with them as far and wide as they wish. 4) What is something you wish more parents knew? I wish more parents knew how resilient, capable, creative, and joyful children can be when we empower them to struggle with challenging tasks they find interesting for knowledge's sake. 5) What is something you want people to know about Math? Regardless of our previous academic performance, we are all math people. Math is fundamentally about exploring and solving problems that help us identify patterns and understand relationships. Doing math cultivates problem-solving. Problems are growing exponentially; we need as many problem-solvers as possible. 6) How has Math Circles impacted your teaching career and your perspective as an educator? Math Circles has challenged me to seek, promote, and expect joy for every learner. It has helped me recommit to a career as an educator. 7) Should Pluto be given back its title? Although nine is divine, eight is pretty great! I think Pluto should remain a dwarf planet.
In January, we interviewed Lisa Cash, MC2's most experienced teacher. Lisa led our first ever After School Program at Goudy Elementary (which continues to this day), and also leads sessions at our Lane Tech Hub, along with summer sessions at Payton HS. 1) What made you start working with Math Circles? I wanted to do interesting and engaging math with my students after school. However, I started teaching at the Pilsen Hub first. I brought it to my school later and have been running it there ever since. 2) What is something you wish more parents knew? I hope parents realize how much their enthusiasm shapes their child's experience. It is a joy to teach Math Circles because of this. 3) How has Math Circles impacted your teaching career and your perspective as an educator? I have spent the last 7 years learning and growing with Math Circles. Working with the team at Math Circles has broadened my ability to help students think deeply about math.
Greetings MC2 Folks! While it still feels very much like winter here in Chicago, many families are beginning to think about their plans for Summer math enrichment. There are math programs all over the country, some free, some not. A few admit everyone they can fit, others ask applicants to complete an application, write an essay, or submit a math problem set. The table below can help you make a choice. Some things to note: Camps in Chicago -- MC2, UIC, and UChicago -- tend to have later deadlines than national camps, and the UIC and UChicago websites are usually updated in March or April. If you are on MC2's mailing list you will get updates. If you need any advice, email us at info@mathcirclesofchicago.org or hit the 'Contact' button on this website!
Registration Information and Forms Update! The next time you login to your MC2 account to register your child for an MC2 session, you'll be asked to update some information about each child you enroll, and complete our standard forms. Updating information about your student--what's new/different: You'll be asked to give your child's date of birth. We're now collecting gender and race/ethnicity information here (which is optional) rather than having a separate registration form (this will reduce the number of signed forms we collect by one). If your child is in high school, we ask for your child's school (with our old system this information was often not updated). Form notes: We know that most families have completed our forms previously; we're asking you to do so again, but once you've done so that should be the last time (or at least the last time for several years)! The CPS data form is an exception--it will need to be completed once a year. Families are free to not share their child's CPS data (and, of course, some of our students do not attend CPS); if your child does not attend a CPS school or if you prefer to not share their data with MC2, simply answer 'no' to the two questions on the form. Of course, we would encourage you to answer yes if you can, as it's helpful for us to collect as much information as possible so we can analyze the overall impact of our programs. We never share individual student data with outside groups . Individual student data is also not shared with our teachers. We only use collective student data for evaluating our programs; we do NOT use individual student data for any purpose other than to calculate these averages.
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MC2 Changes Welcome to MC2, Fall 2024! As we launch our fall programming, we have several announcements to make! 1. High Schoolers Welcome! MC2 offers a rich set of programs for high school students, and we are eager to have students with us in middle school to return during their high school years. Cantor-A1/G: This program is for students in Algebra 1 and Geometry, typically enrolling students in 8th, 9th, and 10th graders. We've redesigned each Cantor semester around specific Big Mathematical Ideas that will be particularly appealing to those aspiring to those planning to go on and take advanced math courses in high school in college. This fall Cantor will focus on sequences and series (key concepts for prepping for Calculus) and probability (great prep for Statistics courses). Kovalevsky-A2/PC: For students further along in the high school math sequence, Kovalevsky will also include activities related to probability, and give students to some undergraduate level mathematics--Game Theory. As we hinted at last year, MC2 is working on establishing a program tentatively titled 'MC2 Scholars' that will incentivize high schoolers to stay engaged with us through 12th grade. MC2 Scholars will be strongly encouraged to participate in the Cantor and Kovalevsky programs; they'll also get support to apply for math summer camps, produce math research (to be presented at QED, Chicago's Youth Math Symposium), and to become assistant teachers in MC2 Classrooms. And, yes, we are looking to raise money to give scholarships to those students! Keep an eye on our newsletters as we look to launch this program at the end of the school year. 2. Hub Changes We have one location & week day change, a possible winter addition, some extra sections, and we're stepping back from online. We're taking a step away from online programming this fall. We expect to return either in winter 2025 or fall 2025; for now we're making sure we back up our plans, many of which include Google Jamboard, which is being discontinued as of October 1st. Our Chinatown location has switched to Bridgeport. We continue to partner with St. Therese Catholic School; this year we will be operating out of their St. Barbara's location. Also, these Bridgeport sessions will now convene on Wednesdays rather than Tuesdays; see all locations and times on our Locations webpage . At our Payton and UChicago sites we are hoping again hold a second section of our Brahmagupta-7/8, so that sessions will run from 1PM-2:10PM (like last year) as well as 2:20PM-3:30PM. We're also expecting to add a Cantor-A1/G session from 10:00AM-11:15AM at the Saturday Back of the Yards High School Hub. Finally, we are looking to open a west side hub this winter; stay tuned! 3. Festivals Galore! Last school year we surprised ourselves, holding 30 Julia Robinson Math Festivals. This year we are going for 40! If your school might be interested, have a teacher or school leader complete our festival interest form ! 4. Stepping away from partnering this year Over the past several years MC2 has partnered with homeless shelters, refugee programs, and community centers to hold math circles in a wide range of spaces across the city. Currently our organization is working on creating a strategic plan to determine how our organization will continue to grow. For now we are focused on doing fewer things better. We expect this to be a pause, and we'll reach out to these partners in the future when we have the capacity.
Our math summer camp list has been updated, with one new addition (Campersand). There are math camps all over the country, some free, some not. A few admit everyone they can fit, others ask you to complete an application, write an essay, or do a bit of a math 'try out'. The table below can help you make a choice. Some things to note: Middle School parents, Math Path is recommended and relatively close (Kansas City this year). If you are interested have your child apply right away. While they will take applications through April they have rolling admissions and the longer you wait the lower your chances are you'll be admitted. Camps in Chicago--MC2, UIC, and UChicago--tend to have later deadlines than national camps, and the UIC and UChicago websites are usually updated in March or April. If you are on MC2's mailing list you will get updates. If you need any advice, email us at info@mathcirclesofchicago.org or hit the 'Contact' button on this website! UPDATED MARCH 11, 2024
