How should the mathematics we teach students change over time? Should students learn the same things in 2020 as they will in 2070 or 2120? What about 2520? I believe that how a person answers these questions depends a lot on how he or she see math’s purpose.

If math’s purpose is giving students basic foundational skills, this might lead someone to believe that math’s foundational skills stay the same so we’ll always be teaching roughly the same mathematics.

If instead math’s purpose is giving students the skills they need to be productive members of society, this might lead someone to believe that what we teach should change over time. After all, the workplace skills people needed in 1920 differ from those needed in 1970 which still differ from those needed in 2020.

By 1970 though, as calculators became more common, employees could use this tool to compute the sales tax and instead spend their time considering different problems that used to be so complicated that they were previously unrealistic to do.

For example, consider this story about Lewis Fry Richardson who in the 1920s created a formula to predict the weather six hours ahead of time. The problem was that he had to make so many calculations that “he needed six weeks to produce a weather forecast for the next six hours – and even then it was not very accurate.” So by the 1970s, as calculators and computers became more commonplace, less time could be spent on computing the numbers and more time spent on making better formulas to predict the weather.

Now in 2020, we have a new wave of technology including apps that can instantly solve math problems for us. This is amazing to me because the idea that something like this would ever exist was unimaginable when I was a kid… and it should make you wonder what currently unimaginable innovations await future generations.

What do you think? What am I wrong about? What do you agree with me on? Please let me know in the comments.

SO SO Wrong! In everyday life we need to know how to add/subtract/multiple/divide. We do not have a calculator glued to our hands. You need to understand what is a logic answer. Junk into the calculator is Junk out. But my students do not recognize that because they have no understanding of numbers. As a former engineer, I appreciate the use of technology but NOT until they know their basics.

Hmm. In this age of people with cell phones, I feel like now more than ever we have calculators metaphorically glued to our hands.

So you think that we should be teaching math the same way in 100 years? 500 years?

Do you need to actually know how to multiply and divide or just estimate? I estimate the sales tax to see if I have enough or if I was charged correctly. I estimate to see if my answer makes sense. I think estimation is an underrated skill. Sometimes we tell students its a guess. When asked to estimate, I’ve seen students figure out the answer and then round it! The actual skills of estimating are something we should teach in the future!

It’s not my intention to say that estimation is not important. It’s a great tool for checking for reasonableness. However, many cases require the person doing the math (for example the business charging the sales tax) and now we have computers that can do it.

One current example might be coin counting in second grade. I firmly believe children should be able to fluently and flexibly combine 5’s, 10’s, and 25’s. But torturing kids with endless (blocked) work on coin identification and counting coins in the first month of school when most children have no background with coins to make connections is a foolish waste of time. Time would be better spent building place value understanding through the hundreds and solving tasks.

This is a FANTASTIC example. In 100 years I’d be shocked if coin usage was still common. So, that’s at least one standard I’d hope would go away. Personally, I can’t remember the last time I even used coins.

I am going to whole heartily agree with Robert on this one. It is disappointing to see how little the classroom of today has changed from 50 years ago. Instead of teaching how we were taught we need to teach how we wish we would have been taught. We have so many tools that can be utilized to help student UNDERSTAND what they are doing instead of memorizing and believing that math is magic or a bunch of tricks. If the way we taught math in the past why do so many people to day say that they do not enjoy math and delight in saying that “I am not a math person” When I started teaching in 1975 calculators were just becoming available. Through the next several years NCTM and others worked to ensure that calculators and technology were used to help students learn. The conclusion statement is the direction that we need to be going.

Robert, I love that you pose these questions. I recently engaged in the same type of questions around time spent teaching kids dividing by decimals and using analogue clocks, 5th grade and 3rd grade teachers respectively. I’m always reminded of Andrew Stadels classroom clock and managing our time on the practices that our students will use today and in their future. I continue to find ways to guide my students to use all appropriate tools to support the authentic tasks that make up the majority of our time. I suspect those that follow a prescribed curriculum might find it difficult to relate the subject they teach to the students that are in their classes in 10-20 years. My hope is our colleges are making the appropriate shifts in the way they provide guidance to those entering our incredible profession.

Yeah I really hope that these changes are happening too, but I don’t really know and that’s concerning.

It’s obvious we aren’t teaching the way we should right now. But I’ll be honest, with 5 preps, I don’t have the time to totally revamp my curriculum into something that is up to date. Students should be programming and using spreadsheets all the time in math class starting in second grade. But there’s no curriculum that matches it. Our curriculum is 35 years behind where it should be but someone has to create better curriculum and someone else has to adopt it for things to change.

This isn’t just a math issue. Social studies should be taught through video/stage production, science through design process, and ELA through publishing.

I agree that the content of what we are teaching should be flexible enough to change with the changing times, but we also need to make sure our students have a good conceptual understanding of math. I believe that focusing on the 8 mathematical practices during teaching builds the flexibility in thinking that students will need as grow up in a world that is evolving so quickly.

Marc, it’s not my intention to say that it is TEACHERS’ job to rewrite the standards. I think that STANDARD WRITERS need to give teachers updated standards that can be reasonably completed in a year. Somehow there continues to be this disconnect.

Brilliant- all subjects taught w respect to the greater stage of application. I completely agree.

I agree with Marc and Robert. It’s a standards issue AND a curriculum issue. The standards are getting better, especially in secondary, at demanding that students understand the conceptual…but unless teachers have a good support that balances both (conceptual and procedural), it won’t happen. So much is demanded of teachers these days, they don’t have time to write rewrite curriculum. Some curriculums are getting closer such as Illustrative Mathematics and Mathematics Vision Project. If we want teachers to teach this way, there needs to be more support to teach this way…. As a district math specialist I’m trying to help HS teachers make this shift, but its hard without curricular support and not having taught this way myself, it’s even harder. We need high quality curriculum that supports this way of teaching so teachers can have a life outside of school.

I agree with you. As a homeschool teacher, I teach math to each student. While I require 80 percent to move on we strive for 100 percent understanding. I allow multiplication tables while they are learning because standardized tests do not allow calculators yet. Way back when I took the SAT, the first thing I did was scribble out the multiplication table on my allowed scratch paper. I have just not been able to memorize it completely. I was able to score very high on the test because I understood how to do the math but just had a block in memorizing. It’s a timed test so figuring it out would have lowered the results quite a bit.

Allowing our students to use the technology that is available will allow them to accomplish more in the long run and open more opportunities.

Definitely a lot of research and anecdotal experience that points to speed having very little impact in real life, while having deep conceptual understanding and the ability to apply math being much more important.