Despite the fact that our current high school math curriculum is often outdated and not preparing students for the current societal and workplace realities, change is slow to come.
Today, we hear from Steve Leinwand and Eric Milou, longtime champions of high school math instruction reform and authors of Invigorating High School Math. Steve starts the conversation with his thoughts on what the roadblocks are that prohibit this critical change.
To dive deeper into this topic, you can join Steve and Eric in Chicago for an in-person workshop based on their book: Planning High School Mathematics Reform.
Transcript
Steve:
Those are some of the mindsets that are missing in our schooling, both middle school, high school, college, universities, that are essential for citizenship and not just employment. That's why we've taken this on so forcefully, because it really transcends just mathematics. It's not just about STEM fields, it's about the viability of this crazy democracy that we live in.
Edie:
Hi, this is Edie. Welcome to The Heinemann Podcast. Despite the fact that our current high school math curriculum is often outdated and not preparing students for the current societal and workplace realities, change is slow to come.
Today, we hear from Steve Leinwand and Eric Milou, longtime champions of high school math instruction reform and authors of Invigorating High School Math. Steve starts the conversation with his thoughts on what the roadblocks are that prohibit this critical change.
Steve:
I think that there is the issue of inertia, there's the issue of a lack of direction, and there is the unpleasant likelihood of opposition.
The inertia is very real. Why bother, why make these changes? We're happy. Everything worked for me, why should I change things? Change is slow, this is mathematics, it's been this way for years, and years, and years. In fact, what we are now dealing with with algebra geometry, algebra II has been entrenched since 1894, when the Committee of Ten wrote their amazing report about the need for standardized comprehensive high schools. We did Latin, and Greek, and algebra, and the geometry. Nobody misses Latin and Greek, but God forbid we recognize that there's this thing called statistics, that there's this thing called technology, that the world has changed dramatically. There just is inertia because it's like, "Well, this is not my responsibility. If somebody tells me to do it, if they change the tests, maybe I'll worry about it." That's the first order of business.
Second of all, there just has been so little guidance. We really had a gigantic change, particularly at middle school, in 2010 with the Common Core State Standards. We have a K8 math curriculum that is internationally benchmarked, that makes sense, that's built on progressions, built on trajectories, that rearrange things to be far more coherent, far more teachable. And nothing happened at high school. You have to do all of the same stuff you always did, all the same symbol manipulation because there's this AP calculus test that somehow is honored so greatly. There is no international benchmarking. We added on modeling and statistics. In the process, we just have not given people some clear guidance about it. Any time you start changing math, you know that you're going to have opposition, and the opposition becomes a real, serious obstacle. Why take it on? Why bother?
I think that's a place to start. Each of those reasons is flawed, but they don't really move out of the way in terms of providing incentives for people to say, "Wait a second, we need to take the bull by the horns and we really need to recognize the obsolescence and the unfairness of the current program." I think I've left you a whole lot of ideas in there, Eric.
Eric:
Thanks, Steve. I just want to pull out a couple points you made there, specifically about the need for data science, data analysis and statistics in today's world. If we haven't learned anything from the pandemic, it's the fact that we were inundated with data, graphs, charts, non-stop during it, talking about bending the curve, talking about maybe inflection points. Talking about looking at data. What's the double-blind study do? Talking about so much data during the pandemic. When are we going to return? What does a mask do? Does it help, does it not help? It was all about that analyzation of data to make decisions.
But yet, our curriculum in the mathematics world is still factoring quadratics for weeks, upon weeks, upon weeks. Why? Because we've always done that. And also, the race to calculus. Let's not pretend that there's not a race to calculus in American education. Steve and I are not arguing against calculus, we are arguing against the race to calculus. But we just would like to see an alternative to calculus for students not majoring in STEM careers. Psychologists, and sociologists, and arts, and trades, and hospitality, where data is so much more important to be studied. In nursing, and especially in nursing and medicine, where data analysis and data science are the hot thing right now and they will continue to be that way.
If you look at sports teams and the number of data scientists that they have to hire to look at all the data that's going on in sports right now, those are tremendous jobs. Gosh, as a frustrated young athlete, I would have loved those jobs back in the '90s.
Steve:
Let's just deal with the elephant in the room and that's time. We talk about statistics and people say, "Yes, it's important. We believe in statistics. But when do I do it?" Eric and I both believe that we need to stop and look at the obsolescence of a whole lot of things that we built into the curriculum. We spend two weeks factoring, sometimes three weeks factoring trinomial expressions. There's just no reason to spend that much time on it. It is not a preferred method for solving quadratic equations. We believe that the idea of sine squared plus cosine squared equal one is absolutely essential. It's the Pythagorean Theorem in the world of trigonometry. But the time spent on trig identities is just completely wasteful. We can graph them and be done. There are a whole lot of things that can come out of the curriculum that allow us to do more of the statistics, a more integrated approach.
The other piece to all this, when people start arguing about time, is 20 years ago, there was very little algebra in middle school. The Common Core has changed all that. We're doing equations in sixth grade, more equations in seventh grade. We are evaluating expressions and using formulas in seventh grade. We're doing functions and systems of equations in eight grade. The days of having to reteach all of algebra I in the first half of algebra II was real. It's not anymore. When we've had so much math, so much algebra prior to algebra I, and then have the algebra I in ninth grade, we don't have to repeat it all because we've seen it.
We think that just a whole lot of ideas that you can see in spatterings around the country that we really would like to bring to the fore, and make over the next five or seven years, the actual way that math is done because it makes sense, and because it's right, and because it serves the most kids.
Eric:
Let's not forget one other thing here, maybe two other things. It's that we are talking about curriculum change, yes. We know that's a longterm process. There's some great examples of states out there, like in Idaho and in Oregon, doing great things on longterm curriculum change. But the high school classroom has to change more than curriculum. High school classroom has to change instruction, and the high school has to change assessment. We don't just sit here to say curriculum's got to change, and we can't do that, so we can't change anything else. No. We can change instruction tomorrow if we want to. Outdated modes of instruction still sit in most high school classrooms, where the teacher is the purveyor of knowledge and the teacher shows how to do things, and kids copy notes. It's an outdated scribe mode of instruction that still permeates most of our classrooms.
Assessment still looks like the same it still does. 10 questions on the test, some are worth seven points, some are worth nine points, and the last question's worth 12 points because it's got to add up to 100. These things are obsolete. Not just the curriculum, but instruction and assessment. We need full term change in all of these areas.
Steve:
What we're really proudest of with Invigorating High School Math is we didn't just say those things, we tried to give examples. There are some sample unit assessments that we are very proud, that we think are models for what a quality, highly aligned and rigorous assessment for a unit would look like. We have a whole bunch of examples of modeling, and about tasks, and about the aspects of pedagogy that we think need to permeate high school.
Edie:
I was happy to hear you mention, Eric, that there are some states and some really good models out there for change. I'm curious to dig into that a little bit more. Where is the entry point you see where educators start to build momentum around this change?
Steve:
It's top down and it's bottom up. We see a whole lot of local control states where a district has strong leadership, a superintendent or assistant superintendent that says, "This is ridiculous. We've been doing the same thing for 130 years. It isn't working very well, it's screwing a lot of kids and we need to find some ways to do it differently." Gets into meetings with their math department, have two math teachers who agree with all this stuff, and they build a plan. Chapter 10 in our book is about implementing change. It has a five-year plan. It's like teachers are never given five years to implement something like this. We believe it takes five years to do. It's a year of study, and it's a year of planning, and a year of gradual implementation, and all that stuff.
It's in lots of places, this bottom up. We have lighthouses. You can go to places like South Burlington, Vermont. You can go to places like Downey, California and see some of these things taking place, some of these things in action. I was in Singapore last week at the Singapore American School and they have an integrated program for basically eight grade and ninth grade, that makes just a whole lot of sense. They realized that algebra I, algebra II is just not particularly useful.
Then, in other states, you have the more top down leadership. Utah is a classic example. Utah has really moved things ahead. They have the test scores to show that it's making a difference. But they've been doing this for almost 10 years. Not all states are going to be like Utah, but more and more states are saying, "What's Utah been doing? How did they do it? How do we encourage this at the state level?" In most places, because it's local control, it's like it's an option, you don't have to do it in the short term. But I think that as people see that it takes root and it makes a difference, and it's happening in both the higher performing and the lower performing districts, that it's likely to grow.
Eric:
Yeah. Let's just add one practical point here about how a local district can make some change. The first thing to look at is okay, senior year electives. Most schools have an AP calculus, maybe even a non-AP calculus, and maybe a statistics or an AP statistics. But the first place of entry, I think, is putting out a fourth year data science course. Free materials, completely free out of Stanford, youcubed, and Jo Boaler, should be looked at by every high school teacher. Put a fourth year elective in data science.
Then eventually, and I think the tough discussion, about the third year mathematics, the third year of high school mathematics specifically is alternatives to algebra II. Should we discuss alternatives to algebra II, where all kids take algebra I and all kids take geometry. All kids have a common two years of high school. But then, maybe there's some pathways, some options for kids. Traditional option, of course, goes through the algebra II, and maybe even an advanced algebra II as Steve was talking about earlier, to calculus. Then, a pathway number two starting in 11th grade would be a data science pathway. Then, on pathway number three, where kids going into vocational careers, quantitative literacy.
Gosh, we've talked about quantitative literacy in this country for more than 20 years. But is there any good quantitative literacy courses out there? Yes there are. There's stuff coming out of the Dana Center and UT Austin, University of Texas Austin. I encourage people to look at the quantitative reasoning out of UT Austin and also, as I said previously, the data science coming out of Stamford. These can start as fourth year options, and then eventually, the tough discussion about third year pathway options to algebra II.
Steve:
I hate to be a Debbie Downer about these kinds of things, but we do need to acknowledge the fact that the system is really not suited to be able to make these kinds of changes. We currently have four distinct silos. There are high school math teachers, separate and distinct from high school guidance counselors. They often don't communicate. They often don't have the same values. The issue of making changes in the high school curriculum without having the guidance counselors understanding it is a real problem. Then, we have the two other groups. We have the college admissions officers, and we have the college math professors and math department heads. We have all four groups that don't really talk to each other and it becomes a real problem in terms of building a coherent system.
Edie:
In the book, you speak to preparing students for societal and workplace realities. Do you think that, when school districts are making change like you've mentioned, is that a driving question about how are we preparing students?
Steve:
I don't think there's any question that it should be a driving question, but it's not one that people ask. They say, "What percentage of your kids are getting fours and fives on the AP? What percentage of your students are going to four year colleges?" They're not asking questions about are students being prepared to wrestle with the really tricky statistical and mathematical issues of our time. We live in an unbelievably complex society. Given, full stop. We know that. We live in a society that is so filled with ambiguity, and we live in a society that demands nuance. And yet, we have this sense of, "Let's just simplify it. Let's just spoonfeed it. Let's just get high test scores."
We forget that the only chance we have in this world of AI, in this world of complexity, in this world with all of the scientific revolution, with all of the moral issues around biology, and about drugs, and about healthcare and all, you need to understand that there are not simple answers to those things. We are not preparing kids to wrestle with problems and recognize that there are confidence intervals, and that there models that are good but not perfect.
Eric:
When I give presentations, I ask teachers in the room, "What percent of adult's last experience with mathematics was negative?" I ask the teachers in the room to give me a number. Then, I unveil on my slide the answer is 98.5%. Then, I tell them, "Actually, I just made that number up. It's not true at all." However, everybody in the room wouldn't disagree with that number. Everybody in the room would say, "Oh, that's probably right."
Steve:
This is me.
Eric:
Even though I just completely make up that number, 98.5%. I think that has a lot to do ... We've got to reflect upon that. Why are so many adult's last experience with mathematics negative? If it's true and we believe it's true, and usually all the people in the workshop with me, the math teachers in the room agree. That means we got to do something about this. We got to take steps. Whether it's curriculum, instruction, or assessment.
Steve:
Change in education in the current world is incredibly hard. Change takes time. Change takes study and discussion. There are not mechanisms for high school math departments to have two days off over the course of a year to come and wrestle with that, to have an outside person, to do readings, to argue and agree with what they agree with and what they disagree with, and how they move ahead. Change takes some allocated time for where do we start, and what do we then do? The whole change process that gets mocked in education a great deal, because we just ignore it. It's a whim, it comes from top down. Teachers close their door and ignore it half the time. It's not serving the needs of both society and kids in mathematics.
Edie:
I think that's one of the components of your book that I really appreciate is the amount of reflective questions. I know there can be a time issue, but those are such incredible resources.
Steve:
But we pose those questions because we don't have the answers. We have partial answers. We have a bunch of ideas. But that whole book was written and in places that we see it being used, it's being used as a resource. It's being used as a study guide. It's not being used as, "Here are the answers, here's the directions, here's what we go and do." It's really nice to hear you say the questions are really helpful. We think the questions are, with some of the background information, the heart of the change process.
Edie:
Thanks for tuning in today. To read a full transcript, and for more information on their book, and to hear about an upcoming conference with Steve and Eric where you can dig deeper into high school math reform, visit blog.heinemann.com.
Steve Leinwand is Principal Research Analyst at American Institutes for Research in Arlington, Virginia and the author of Accessible Mathematics and Sensible Mathematics, and coauthor of Developing Numerical Fluency. Steve served as Mathematics Supervisor in the Connecticut Department of Education for 22 years and is a former president of the National Council of Supervisors of Mathematics. In 2021, he was awarded the National Council of Teachers of Mathematics' Lifetime Achievement Award.
Eric Milou is Professor of Mathematics at Rowan University in Glassboro, NJ and co-author of Daily Routines to Jump Start Math Class and EnVision Math A|G|A. Eric served as President of the Association of Mathematics Teachers of New Jersey and on the Board of Directors of the National Council of Supervisors of Mathematics..
