New Math - What (I think) it is, why you want it, and how to find it

This past week I attended Curriculum Night at my children’s school, the school that I happen to lead. While all the presentations were informative and inspiring, what I heard from Huck and Harrison’s math teachers – and what I see happening in all grades of math instruction at MTS – has kept me thinking. I now have a much richer understanding of what some might call “new math” and want nothing else for my own boys.

“New Math” – What (I think) it is.

Outstanding math teaching, especially in the early years, is focused on numeracy and “number sense” rather than algorithmic computation. We want our students to understand why math works rather than simply how to do math. Though great math teachers have been teaching this way for decades, this holistic approach to math has been labeled “new math” by some. While I am no expert on the math wars (“new math” versus “old math,” I presume, here are two sample problems shared at Curriculum Night that shed some light on the subject.

C+G

First-grade math is focused on understanding numbers to 20 and addition to 20. While these topics seem so basic – my son has been counting well past twenty since before kindergarten – one problem his teacher shared demonstrated why students need to have mastery of these simple fundamentals. 

As an analogy, try solving the following equation. C+G. Excuse me? C is the third letter of the alphabet. G is the seventh letter. So what is the tenth letter? For most adults, we have to count on our fingers to see that C is 3 and G is 7. Then we have to add to 10 (the easy part) and count again with letters to get J, the answer. As adults we can easily say all the letters to 26 but we don’t have a rapid familiarity with C and G in a way to see their relationship to J. The child who can count to 20 (or higher!) starts with the same lack of familiarity with 3 and 7. By counting things often, working on number bonds  that make five, ten, and twenty, students gain the ability to quickly see 3+7=10. They also know that 2+8 = 10. This ability to “know it when I see it” and spot other connections (6+4=10) is “number sense.”

32 x 14

In an “old math” third-grade class students would learn to approach this problem by lining it up like this (insert image) and then completing four single-digit math multiplication problems (4x2, 4x3, 1x2, 1x3) and a three-digit addition problem (128+320) while remembering to put a zero in the ones place value after the first two multiplication steps. If all goes well (did you line up all the numbers properly?), you get the answer 448. Even if the answer is right, do you know why you put a zero in the ones place in the second step of the algorithm?

At Curriculum Night we were introduced to a “problem string” that arrives at the same correct answer and can largely be done in your head:

32x10 = 320

32x 5 = 160 (half of the answer above)

32x15 = 480 (add those two together)

32X14 = 448 (480-32 = 480-30-2)

Problem strings are just one technique that “new” math teachers use to build rich numeracy and computational skills. Yes, they also teach traditional (read “old”) algorithm for really nasty problems and to show your parents that you can still do the “math that they learned.” We also have calculators for those really nasty problems!

Our kindergarten through eighth-grade math teachers – we have math specialized teachers in the youngest grades – were eager to share countless more such approaches and problems. They love all the ways students can approach a problem with the focus on understanding and the right answer. New math teachers are way more interested in how you got there and relish seeing a new strategy being used.

New Math - Why You Want It

While old math served many of us well, there are three reasons why I think we should all want this “new math” for our children.

1. A robust foundation. Math skills build on one another throughout the years – scaffolding in education-speak. If the foundational skills are not robust enough, students experience far more difficult challenges in the later years. On numerous occasions, I have seen a seventh-grader who had strong algorithmic skills advanced to a higher-level math class only to experience frustration and failure in Algebra 2 or Trigonometry because they did not have the robust foundational skills and numeracy. A student who once thrived in math was soon hiring a tutor and dropping math as soon as the Calculus AB exam was over. 
2. Positive math identity. Diverse approaches to problem-solving and a strong sense of numeracy allows all students to experience success in math. Done right, every third grader sees themselves as a “math person” not just the child who completes the times tables worksheet first. “New math” curricula and pedagogy with its focus on process – how you thought – also develops a growth mindset that can positively impact all academic areas.
3. It’s how we actually do math. I do math all the time in my job. Five minutes ago I was reviewing a proposed budget for an upcoming event. That “back of the envelope” math – it didn’t actually require any writing – allowed us to quickly assess the scope of our plans and could have easily been a math problem in a class here at school. New math is how most of us actually do math. 

New Math - How to Find It

Few schools will say “we do new math” on their website. A school administrator might give a guarded answer if asked “do you teach old math or new math?” There is a war between the two, remember? So how do you find outstanding math instruction? You find teachers who talk math. Look for teachers who talk about math and math instruction with enthusiasm. Great math teachers will quickly go beyond the name of the set program their school uses and the worksheet pages assigned for a given lesson. Inspired math teaching is curated from numerous sources and has far more games, projects, and group work than individual worksheets. Talking with such a teacher you might hear names such as Jo Boaler, Cathy Fosnot, and Dan Meyer. If you can, find out what professional development the math teacher has done recently. Outstanding math teachers I know listen to math teaching podcasts and do workshops at Stanford’s YouCubed program. Even more than the names dropped and courses taken, listen for excitement. A teacher who is passionate about teaching math will, in turn, inspire passion in your child. This needs to be the case in 2nd grade just as much as in 7th grade. Math is cool, and a great teacher can make that a universally known truth.

My boys are incredibly fortunate to attend Mount Tamalpais School where every student learns math from a math specialist. Our math teachers – I am the Head of School at MTS – regularly trade emails and recommendations for projects, games, and problem-solving strategies. I am confident that our students are building an incredibly robust foundation and identity that will set them up well for a bright math future.

- Andrew Davis