For many parents, the pandemic brought school home — literally. For generations, we’d had established societal norms that we trusted that was suddenly blurred, with parents becoming teachers and tutors, managing their children, their time, and their daily academic learning. Sending their children to school wasn’t an option for most during the COVID-19 pandemic, and many quickly realized the enormity of the task of educating their children at home.
The assessments of that normative change are stark; we were bad at it. The National Assessment in Educational Progress (NAEP) report, the Nations Report Card (2022) for mathematics, showed the largest decline in NAEP mathematics scores in grades 4 and 8 since initial assessments in 1990. Many parents felt helpless.
While we all sometimes feel powerless as parents, this was different. Math was particularly problematic for parents, many claiming that the “new math” their kids were being made to learn was not valuable to their daily lives and development. Combine that feeling of powerlessness with the heavy responsibility of constantly caring for our children, and you often get anger, however misplaced it might be. In this case, parents took out their anger on what they perceived as “new math.”
There’s Nothing New to See Here
As a student of history, I learned early on that humanity hums along with a pattern worth understanding. Mark Twain is often credited with saying, “History doesn't repeat itself, but it often rhymes.” Humans naturally overemphasize the importance of our moment in time, so it is reasonable to expect that our perception of the mathematics changes that happen in “our time” is heightened. The reality, however, is that there has been a long history of “new math” evolutions.
In the US, you can find grumblings about “new math” traced as far back as the first public schools established in the 1630s in Massachusetts before we were officially a country. Since then, books have been written about the history of “new math” in predictable patterns starting in the late 1800s, with cycles of books and articles coming out about every 40 years. What changed wasn’t so much the mathematics being taught but which students gained access to the content and at what age they were first exposed to it.
1950’s - Sputnik Triggers More “New Math”
October 4th, 1957, was another central inflection point in our history of school mathematics. The Soviet Union launched a little artificial satellite called Sputnik, and that unanticipated successful launch was an ego shock to scientists, politicians, and citizens in the US. The loss of preeminence in scientific capability, which the US had dominated globally post World War II, came parallel to the scientific revolution of how we looked at mathematics. Following Sputnik, mathematicians turned their focus on school mathematics because societal changes required the effort to reconcile the centuries of advancement in the discipline with the static nature of what children were being exposed to in school mathematics.
This event triggered the Space Race as part of the Cold War, a scientific arms race, and eventually led to the release in the 1980s of the text A Nation at Risk. A Nation At Risk was a report by the National Commission on Excellence in Education to the nation and the Secretary of Education of the United States Department of Education. Quoting from that seminal piece, “If an unfriendly foreign power had attempted to impose on America the mediocre educational performance that exists today, we might well have viewed it as an act of war.” Yikes! “New math” and subsequently evolving school mathematics are often tied to the drive of a country or culture to be the preeminent scientific and economic global force. This usually comes alongside the introduction of new and very powerful technology.
Does this sound familiar? Today, with countless objects in orbit, we are reconciling the utility of what we teach our young people in a world with powerful computers, a ubiquitous internet, and the emergence of Machine Learning and Artificial Intelligence.
The Truth Is You Don’t Want “Old Math”
Let’s pause here for just a moment. I have read countless recent articles and debates about “new math” today where parents and others say, “Math is Math; stop trying to change it!” You may have said this exact phrase over the last few months. I’d like to illustrate the absurdity of this claim while not disparaging those claiming it. The mathematics concepts we teach our children date back to the early Greeks, from around the third century BC. You may be surprised that those genius Greeks didn’t recognize or define numbers other than natural numbers (1,2,3,...). They didn’t have ways of talking about units of measure like 1 1/2, other than a ratio of natural numbers. So
1 1/2 , to the Greeks would have been represented as 3/2, which works but is cumbersome. The Greeks didn’t explicitly mention in their surviving texts that they were aware of the shortcomings of their advancement of the sciences and that their concept of numbers had some issues. I’d be willing to bet if we were hanging out, though, they would be sweating it.
For example, if you only have natural numbers and ratios of natural numbers, what would you call the length of the diagonal of the ordinary square below?
Don’t break out your calculators. This is the application of that wonderful theorem attributed by name to Pythagoras or the cult of Pythagoras but predates the pesky Greeks by 3000 years (Babylonians). The diagonal of a square is the hypotenuse of a right triangle, so the diagonal of this square is length √2. That number cannot be represented by a ratio of natural numbers. Which means the Greeks had no answer to it. You can easily create the square above using any unit of measure you would like, and with the limited tools of the Greeks, you couldn’t precisely name the distance from one corner to the opposite. That’s a problem!
For a reason, it's called an irrational number – mathematicians had to create new tools to understand and represent this distance. Then, we could apply that understanding as a new perspective to what the ancient Greeks understood as “math.” This is only one example of how math changes all the time. Another quick example is that decimals, as number representations, weren’t invented until the 15th century by Jamshid al-Kashi, followed by the representations we know today by Simon Stevin in the 16th century. If math never changed, we wouldn’t have the math you wish wasn’t changing.
The Common Core as “New Math”
Okay, back to the task at hand. Why are there the claims of “new math” today? What did the Common Core Standards have to do with it, and why is it such attractive fodder for memes and righteous parental anger? The Common Core standards resulted from a question of preeminence happening in our society today. The US consistently scores 28th out of 38 countries on the Program for International Student Assessment (PISA) test. PISA is an international assessment that measures 15-year-old students' reading, mathematics, and science literacy. The 2023 results were the lowest US math scores recorded in the history of the PISA math test since it began in 2003. The decade before the launch of the Common Core Initiative, around 2010, researchers studied the countries beating the US in mathematics, looking for reasons our children weren’t performing well. These researchers concluded that the US mathematics curriculum must become more focused and coherent. The “mile wide and an inch deep” approach was weak and did not empower US students to compete globally with their peers. We can’t have that!
The Common Core brought about best practices for learning mathematics for diverse student populations. Rather than the previous approach of teaching just how to do procedures of mathematics, it provided US students with a platform to better understand what mathematics is and why those procedures work. It was a change in perspective, similar to the other “new math” revolutions we have discussed.
The Missing Paradigm: Who Is Doing the Teaching Matters
Perhaps one of the most important points in this newsletter is the missing paradigm in many of the historical trends we have discussed with “new math” revolutions. The pattern we have described is always a top-down, policy-driven approach. What matters for widespread support and implementation is stakeholder buy-in, which requires an understanding of who is teaching mathematics and why. This means that anyone teaching mathematics must understand that the perspective for and implementation of mathematics and school mathematics is changing.
Some would call our current world the knowledge economy, or that what you know—and your ability to bring it to bear in any given circumstance—creates economic value for you. Others would say that the rise of Large Language Models (LLMs) is the end of the knowledge economy and the beginning of the allocation economy. Here, humanity will go from makers to managers, from doing the work to learning how to allocate resources. When LLMs have access and can consolidate information from millions of humans in microseconds, what may become more important is choosing what effort is to be done, deciding whether the machine-driven work is good enough, and editing one’s prompts when it is not. Here, the change in assumption and perspective of the utility of mathematics and school mathematics plays an important role in the future of what our children learn.
The Common Core Standards (CCS) and the Principles and Standards from the National Council for the Teachers of Mathematics (NCTM) set a profoundly powerful foundation for this. The mathematical habits of mind, pervasive throughout embodied mathematics, are the exact skills that the knowledge or transition allocation economy will require for our future workforce. Students do not acquire these skills by being taught the “top ten math habits of mind.” Instead, they learn them by doing them when engaged in mathematical tasks. Skills like reasoned guessing, challenging outcomes, pattern recognition, alternative representation, testing edge cases, and classification are habits that have lasting power in our dynamic world. This means that teachers must be able to understand and build learning environments that foster and model these behaviors with their students.
A direct example of this may be helpful. Here is a snippet of a social media post that was reshared thousands of times with thousands of comments.
First, you should notice that the teacher and the parent are intimately involved in mathematics teaching for this student. They are both key stakeholders, and both need to be aware of how and why mathematics is being taught – especially how this task asks students to learn. This task is designed for students to understand the fluency and robustness of our base-ten number system as it exists today. The base-ten number system is incredibly powerful, allowing for the ability to represent any number that can be dreamed up with only 10 numbers and the idea of place value. Genius! You can now define the number of grains of sand on all the beaches on earth… it's roughly a septillion, which we can write because of the base-ten number system. Once the user understands the power and fluency, the system becomes very efficient with arithmetic. Knowing that 27 means 27 ones is powerful, and understanding that this means the same thing as 2 groups of 10 ones and seven additional non-grouped ones is equally powerful. This isn’t new math; it is just mathematical representations that lead to robust and deep understandings of numbers and arithmetic.
The way the parent and the teacher talk about “new math” here is predictable. The representation is new… to them. Parents and teachers are both part of the child’s academic development. When COVID forced education into the household, parents were asked to become teachers in ways they were never trained to be. They did not receive the stakeholder awareness necessary to implement this approach to mathematics with fidelity. The teacher shortage crisis means that teachers, at least over the last two decades, likely lack the training and preparation to fully embrace something they would call“new math,” — landing them in the same boat as many parents. This represents the gap between the intended and enacted curricula, which are well-researched in mathematics (Boesen, Jesper, et al., 2014). The way that this parent and teacher feel, at least my interpretation of that from their words, is how all new teachers or relatively new teachers feel. If you do not have the opportunity to unpack and study mathematics-for-teaching, then you haven’t seen the purpose or power behind the tasks you are trying to help your children or students learn. The last time a teacher or parent studied place value was likely when they were in grade school as students.
New Math is Not a Problem to be Solved; It’s an Opportunity
MathTrack Institute trains and develops the capacity of our educators and parents through the opportunity for continuous improvement and learning. Framing it through the Growth Mindset work of Dr. Carol Dweck and the Mathematical Mindset work of Dr Jo Boaler is productive for our writing. Growth Mindset is all about the idea that you can be better at the things you currently don’t know or are not good at. People with a growth mindset believe that their success depends on time and effort and that their skills and intelligence can be improved with effort and persistence. Mistakes are learning opportunities and not a reflection of their ability or self-worth. This is the opportunity for parents and teachers who run into what they label “new math.” If it feels scary at first, that doesn’t reinforce that you aren’t a math person or that you aren’t a good parent. It's not a threat to your identity within those roles. Contrastingly, if you bring a fixed mindset, you will believe that your intelligence is something you were born with and cannot be changed. This is a difficult mindset and can be very discouraging for parents and teachers. It does not feel good to think that you are just not good at something regularly, and those with a fixed mindset often put a lot of effort into hiding these perceived shortcomings. Those of us who care about our children would never want to model for them that they are born to be smart or not.
How We Can Help Administrators When Confronted with “New Math”
- Be patient and empathize with parents who are frustrated with “new math” because it is new to them, and they want to be able to help their kids. Without understanding the importance of parents' roles as stakeholders, you can lose much of your progress with your curriculum and strategic plans.
- Be patient and empathize with your teachers who are frustrated with “new math” because it is likely new to them, too. Almost all traditional and alternative mathematics educator training programs do not prepare them with a sophisticated understanding of mathematics-for-teaching.
- Growing your own (GYO) talent with an apprenticeship-based approach will enable consistent, in-house expertise with the required sophistication to attend to today's and future math.
- If you want to read more about the scientific evolutions discussed in this article, we highly recommend reading Thomas Kuhn’s (1970) seminal work, The Structure of Scientific Revolutions. This will enable a further understanding of the discussion of the scientific revolutions involving an interplay between changes in assumptions and perspectives.
How We Can Help Teachers When Confronted with “New Math”
- Be patient and empathize with your student's parents and your students. They feel the same way you feel when you are confronted with a new topic. Your first reaction is to question its validity, and then, when not provided with good information, you rebel against it.
- When confronted with new topics or new approaches, develop the mathematical habits of mind to ask several questions of yourself that you can find the answers to and also model this for your students:
How Can We Help Parents When Confronted with “New Math”
- You, as a parent, are a teacher. When you think of yourself this way, your evolution of understanding what your children are learning is less about how it is relevant to you as a career-working adult and more about your fractional position as a high-quality teacher.
- Pursuing a deeper understanding of these topics makes you a model for your kids. Model a growth mindset so your kids can apply the same framework to their own lives. Parents don’t know everything; your kids already know that. Don’t expend energy hiding it; learn with them and be courageous enough to share it.
- Be confident that how you learned mathematics decades ago may have been useful, but it lacks utility now. The world you are raising your children for didn’t exist when you were a kid.
