Math Beyond the Numbers

When many people think of math they think of memorizing their multiplication tables, learning the formulas for area and solving for x. These are important skills to master but they are not the true purpose of math; instead, they are the tools learners use to think critically, solve problems and explore the world around them. Mathematicians are willing to think abstractly, fail and persevere in making sense of problems. At TVS we are working to help learners develop into lifelong mathematicians.

How do we help learners accomplish this? We integrate technology, challenging problem solving activities and lots of games to develop the skills and mindset needed to persevere in math! Khan exposes learners to new content in a way that requires them to think deeply, analyze mistakes and persevere when they make mistakes. When learners are working on problem solving activities they have the opportunity to talk about their strategies and work to communicate effectively with their peers. They also get to see how math can help them solve problems in the world around them.

Math games provide learners with a fun way to practice fluency skills which usually take time and repeated exposure to master. When learners are able to practice skills in fun ways they are more willing to make mistakes, learn from one another and practice for more time than they would using a worksheet. Additionally, studies have shown that learning in a low stress environment aids in storing information in long term memory and games provide the perfect low stress environment for learning!

So what is my role in all of this? Am I here to take the place of Khan? Or create a more traditional math classroom? The answer to both of those questions is NO! I am here to enhance the amazing work that is already happening at TVS! Learning math can be challenging and that is overall a good thing. We want learners to struggle and persevere but sometimes that struggling can shift from a learner’s challenge zone to panic zone. When this happens, I’m here to provide a quick hint, a reminder of a tool or manipulative they could use to support their thinking or simply to cheer them on as they build up their confidence.

Another enhancement I am excited about for next year is providing students with companion math labs to enhance the learning they are completing on Khan. These math labs will help learners build fluency skills that can easily be overlooked when focusing on Khan mastery alone. For example, learners in Discovery are first introduced to fractions in Arithmetic Unit 4. Based on my experience as an elementary math teacher and someone with a masters in mathematics education, fractions are best introduced using manipulatives and hands on experiences which is simply not possible to do using Khan. Next year, learners will be required to master a math lab, in addition to unit 4, where they will explore a variety of fraction concepts using manipulatives, drawings and math discussions. The goal of this lab is to supplement the learning they will gain from Khan for a more holistic understanding of fractions.

One of my favorite TV shows is Numb3rs, an early 2000s show where a mathematician helps the FBI solve crime. In the show’s introduction it says “Math is more than formulas or equations; it’s logic, it’s rationality, it’s using your mind to solve the biggest mysteries we know.” This is my passion and goal with the learners at TVS- to help them have the tools and mindset they need to use logic and rational thinking to solve the problems of tomorrow.

P.S. Want to help your learner continue practicing math at home this summer? Check out these games!

Learning to Learn Math in Spark

If you have school-aged children, you might have noticed that learning math today looks nothing like it did when you were in school. Unlike the approach we experienced as students and the approach that still persists in many conventional schools, The Village School learning design prioritizes deep understanding over rapid rote memorization. Our goal with math (and other subjects!) is that learners are equipped with a sense of math efficacy that comes from learning to learn instead of simply learning. Spark Studio Guides have designed a math curriculum that nurtures a growth mindset creating space for young learners to feel capable and excited as they deepen their numerical fluency.

Learning at TVS in Spark Studio and beyond is based on mastery and not bound by age or time. Similar to the literacy curriculum in Spark, the Spark math curriculum is highly-structured, multi-sensory, and research-based. The Spark Math Map is a visual representation of the most important mathematical skills that Spark learners work to master, and are foundational for any young learner in providing them with both the understandings they need for our elementary math curriculum and equipping them to learn how to learn math as they encounter it in their daily lives.

You can probably remember seeing a toddler determined to hold the right number of fingers up to show their age demonstrating their earliest counting skills. Hands and toes serve as everyone’s first math manipulatives. After fingers and toes comes blocks, and in Spark Studio we introduce an engaging collection of Montessori math manipulatives. The intentionally designed manipulatives allow our youngest learners to learn math through natural play – a pedagogy we lean heavily on here at TVS.

One of the most memorable math manipulatives in Spark is called the long bead chain. Visit any Montessori classroom and you’ll see the beautiful wooden display case of carefully hanging colorful chains of beads. These color-coded beads are used to master several basic mathematical fluency skills including linear counting, skip counting, multiplying, and squaring and cubing. By physically holding and counting the beads, learners are able to internalize the idea of quantity and pattern recognition, two foundational math concepts necessary for developing math fluency. As learners string together bead chains of various lengths, they visually and kinesthetically experience mathematical progression. This process fosters independence and encourages learners to approach math as a logical, engaging journey rather than just memorization.

The bead chain is just one example of how the math curriculum in Spark Studio is both playful and purposeful. In addition to the available manipulatives, Spark learners often engage in math games that promote numerical reasoning and thinking. The benefit of multi-age learning really shines through when learners are engaged in math-based games: older learners are able to model and articulate their thinking about math in a way that inspires and influences younger learners more than any adult could ever achieve.

However, most central to our math curriculum in Spark Studio is the development of a growth mindset. We know from research and our experience at TVS that a learners’ belief in themselves when it comes to learning math is the most powerful lever in shaping their experience and success. We also know that young people – especially our own children – will internalize and model the attitudes that are modeled for them. Do you talk about math fondly – or do you proclaim yourself “not a math person”? Expressing confidence about your own mathematical abilities will help your learner (and maybe even yourself!) realize that learning math is all about attitude, effort, and practice. Even when things get tricky – just take one bead at a time!

Learning to Learn Math

I’ve never considered myself a “math” person until I became a high school English teacher and realized that there was no such thing as a “math person” just like there was no such thing as an “English person”. Throughout the ten years of my career that I spent as an English teacher, I made a point to share my appreciation for math with all of my students, many who were shocked that a person who loved books could also love numbers. Friends who were math educators and well-known educational researchers also helped me shake this misconception – and so did the statistics classes that I took during my doctoral studies.

So where did I get this idea? I know for certain that it originated early on as a result of the messages I received in school. To be a math person at school you had to be good at math, and to be good at math you must learn fast and solve problems even faster. In fifth grade, my math teacher would pass out our tests in order – best to worst score. Each week I would cringe with scarlet cheeks as she placed the last test in her stack on my desk, face-down, of course. If I had only had the chance to take my time, learn at my own pace, and most importantly, build confidence in my ability to learn to learn math – maybe I would have been a math, not an English teacher.

The irony of the traditional math teaching approach is that math in the real world is meant to be slow – not fast. In a typical math class, the lessons are planned and scheduled before the school year begins leaving no time to plan responsively to the emerging needs of learners. Memorization is prioritized over conceptual understanding, and efficiency is prioritized over divergence. This type of learning is shortsighted, and as a result, turns many young people – myself included – away from understanding and appreciation for math.

One of the most frequent questions we get about our learning design is often in the form of a complaint about math and they go something like this… “But, don’t you need a teacher to learn math?” “My kid really doesn’t like learning math this way.” “Learning math that way doesn’t work for my kid.”

As a parent myself, I can relate to these sentiments – learning math is difficult and stretches a different part of the brain. I can also empathize with how difficult it can be to watch your child struggle to learn something, and how fear can creep in when I begin comparing my own children to their friends who attend different schools with a more traditional approach. When I slow down and think about the purposeful and research-based design of the math curriculum at TVS, my fears subside and I feel grateful for the opportunity my own kids have to learn how to learn math and develop confidence in their mathematical ability.

The goal of the math curriculum at TVS is much different than the typical or traditional math classroom. In fact, we would posit that the two are designed for completely different end results. The goal of our math curriculum at TVS is to build each individual learner’s capacity for learning how to learn math- or even, more broadly, how to solve problems, so when they encounter math challenges or difficult problems in their future schools, jobs, and life, they will have the ability to approach such challenges with confidence.

Most parents, educators, and learners can get on board with our ultimate goal of building the confidence and capacity to solve difficult problems. It’s the process that makes us uncomfortable.

For a learner, this process involves making mistakes, getting stuck, languishing a bit, feeling frustrated, avoiding asking for help, making more mistakes, complaining, figuring out what they need to learn, figuring out what tools they need, asking for help, finding momentum, making progress, feeling successful, making mistakes, getting stuck, (repeat, repeat, repeat!) Over time, the process of learning something new and challenging becomes far less intimidating, and learners draw on their previous experience to know what to do next.

Take an example of one of our oldest learners- a learner who has used Khan Academy to master arithmetic and pre-algebra, and is now halfway through Algebra I. Recently, this learner was making mistakes as he worked through the practice problems on Khan Academy. He was stuck. Feeling frustrated, he started avoiding math. Enter the languishing period. Noticing this, his guides and parents checked in with him. He responded by complaining about how difficult the problems were and how Algebra was a “different kind of hard” than he’d ever faced in math. He said he wasn’t sure what he needed to learn it but “Khan wasn’t helping”. Enter the complaining phase. Curious about his approach, a guide sat next to him as he worked through a problem. When he got stuck, she suggested going back to the video and modeled taking notes. Once back at the practice exercise, the learner referenced her notes as he solved the problem. Instead of the reassuring “ding” that indicated he got it right, his selected answer showed red and a “not quite” message. Before clicking “start over”, he clicked on the hints to see how they solved it. He looked back at the notes and discovered what he had done wrong. He solved the next four problems successfully and moved on to the next lesson. This time, he took out his notebook to take notes. At home, he confirmed with his parents that it is his goal to complete Algebra I this year. He made a weekly goal to stay on track and uses time outside of school to meet his goal if needed. Enter the finding momentum phase.

At TVS, we are deeply familiar with this process of learning how to learn math. The experience we share here is commonplace; the learner described is not alone in his process of learning to learn math. Mastery-based learning is hard and frequently uncomfortable and gratifying and confidence-building. All of this is by design. While our learners aren’t exempt from getting stuck, avoiding work, or complaining as they learn how to solve difficult problems, through our learning design they adopt a core belief that they are capable of learning hard things. They might need more practice, more support, or more tools, as they explore and master new concepts, but thankfully all of these are within reach.

As a result, I am certain that although some of our learners definitely enjoy math more than others, all of them would scoff at the idea that there is such thing as a “math” person. For this, I am so grateful.