This swirly mess is basically what math started to look like in my brain.

At 41 years old, I watched a Montessori instructor in Chicago demonstrate dynamic addition with the Golden Beads. In a Montessori classroom this work is introduced at the primary (pre-K and kindergarten) level.

My heart jumped a little as he worked through adding the two addends and arriving at a sum. So that's what carrying the one meant! Really meant. Of course, it's a base ten number system! I see it. I was giddy as math became much more dynamic for me. I could see why dynamic addition problems were... dynamic. And in true Montessori fashion, that concrete knowledge led to a new conceptual understanding of base ten.

As a small child, I carried the one faithfully on my papers, repeating exactly what my teacher put on the board to come to the correct calculation. I was good at following directions. For me, mimicking the teacher's steps and carrying the one was easy enough.

I now realize, I wasn't taught math. I was taught a series of directions to follow to arrive at a correct calculation. As long as I could memorize and apply that, it looked like I was learning math. Memorizing math facts is useful and necessary, but it doesn't necessarily mean you will be good at higher math.

This is why my math skills deceptively seemed to wane in some areas of math as I got older. I say deceptively because I had never really been "good" at math. How could I be good? I had never been taught math. I was taught to memorize and execute a set of directions.

I continued to consistently receive pretty good grades in math and was on a higher math track (we tracked in the 80s), so why would anyone intervene? I was leaning on my ability to memorize and follow instructions. I was not picking up mathematical thinking. In math classes, this was enough for the tests and plenty for the college entrance exams. But it was definitely not enough to excite me to explore a math or science field beyond high school. Plus, if I had, I'm sure I would have done horribly without a proper foundation.

I was happy to leave more complicated math behind. I remember many times when I had no idea what was going on. Any time we deviated from the memorized steps, it was a language I didn't speak. Lipstick (good planning and processing skills) on a pig (my actual critical thinking math skills).

Were my planning and processing skills at a young age such a known/comfortable strength that I leaned into them to never turn back, no matter the class, curriculum, or instructor? Or could a different kind of math curriculum and instruction have opened me to the language of math, not just the rote processes? Who knows? Maybe my brain was not ready until the ripe old age of 41. Maybe the rote processes were so ingrained in me that I was blind, put to sleep. But what a joy it was to discover the beauty in math, even if it was late. Math is one of the things I most enjoy in my work today.

I hope the changes from Common Core and the ways math is now taught will give children a better math experience than my rote calculation experience in the 80s. Instruction has changed a lot in traditional school settings. Many manipulatives are available these days that work similarly to the Golden Beads, and there are curriculums that focus on problem-solving instead of rote repetition. It certainly requires a willingness to engage your mind and stick with challenging problems, but taking on a math curriculum that fosters critical thinking will prepare you for more than just a test. It's a great time to be a math learner!

A recipe for growth is to fail early, cheaply and often. How comfortable are you with seeing your child fail?

For some parents, it's as natural as breathing. They don't even see the struggle as struggle, they just see growth.

For some parents, it takes a lot of work, but they want to give their child the gift of struggle, so they accept that they (as parents) will have some struggle in the process, too.

For some parents, it is too uncomfortable. It is not where they want to be.

The reality is you cannot remove all failure and struggle from your child's life. Life will test them for the skills of independence and resilience at some point, even if you won't. It's coming. 

Adapting to new skills and experiences is easier when you are younger (early). The stakes are lower when you are younger (cheaply). Failure is guaranteed with some frequency if you participate in an environment that asks for independence, mastery and excellence (often).

Are you ready to fail?

In a traditional classroom, subjects are presented each year, and everyone moves in lockstep. How well you learn this material based on the yearly timeline is recorded as a grade. In our studio, learners work on their Core Skills (reading, math, grammar/spelling) based on their own timeline. They create daily, weekly and session goals to keep in step with their yearly goals. Learners do not move on until they have mastered the material. This is a much higher level of accountability than the traditional model of grades. 

In the traditional model, you could spend a year getting B's or C's, moving to the next grade level, and progressing while not understanding a good chunk of the material. Requiring mastery is asking for more accountability. 

It also allows learners who love to learn the freedom to challenge themselves and move more than one grade level a year.

How can learners be accountable to parents if grades aren't sent home? Parents can see their learners' progress anytime on Mastery Book, our transparent tracking program. Tracking mastery is a higher level of accountability and transparency.