Theresa Harrington/EdSource TodaySecond-grade teacher Mark Montero explains how students can use a number chart to solve math problems.Theresa Harrington/EdSource TodaySecond-grade teacher Mark Montero explains how students can use a number chart to solve math problems.Courtesy of Sean NankSean Nank with Presidential AwardSean Nank is a math expert who is helping teachers to implement the Common Core standards. He’s a professor at the American College of Education, created in 2005 to provide online graduate programs and professional development to educators. Nank received the Presidential Awards for Excellence in Mathematics and Science Teaching from President Barack Obama in 2009, the highest recognition that a K-12 math or science educator can receive for outstanding teaching in the nation. He has also authored two books on teaching math and testing: “Testing over Teaching: Mathematics Education in the 21st Century” and “The Making of a Presidential Mathematics and Science Educator,” both published in 2011.
Nank was appointed to represent the United States as a mathematics assessment expert at the 2012 International Congress on Mathematical Education in Korea.
Q. Do you think the Common Core is effective in preparing students for college and 21st century careers?
A. I think it is as long as we make the shift. In my first book, I said that teachers should be allowed to adapt rather than adopt curricula. With the Common Core standards, any type of curriculum that comes from it is only at its best when we’re allowed to adapt it to the strengths and weaknesses of our students – to really teach them from where they’re at.
The biggest thing I love about the Common Core is that for the first time, we can all talk about common standards from many states, not just California.
Q. What are some of the differences in Common Core standards and teaching strategies that may be unfamiliar to parents?
A: I have a daughter in 6th grade in a public school in the San Diego area of California. I can sympathize with what parents are feeling, but the biggest thing that makes me love it for my daughter is that I know there is a difference between a learning strategy and what students are actually going to do. They are still doing math problems such as long division, but there are different ways of teaching it so they understand it.
I like to tell people that I’m ‘classically trained’ in mathematics. I was brought up the traditional way, which is to never ask, ‘Why?’ – just be able to do the problem. You didn’t have to know the hows and the whys.
Q. What are some of the instructional shifts that teachers are making with Common Core math?
A. Now we have this opportunity to not stop, but slow down a little bit and ask how this works and why this works and see it in a different way.
I recently gave a presentation about timed tests in mathematics. We don’t want to lose automaticity, or fluency with mathematics, but we want to give teachers other options. Composing and decomposing numbers works better than rote memorization. A lot of people think of automaticity as recalling facts, but I like to think of it as more than the recollection. I would define fluency as being able to recognize patterns, so people can do math quickly – which is not to say memorization is bad. It’s still something that is needed. But, you can only memorize so many math facts. If you know the patterns behind them, you can break them down really fast.
There are people who do math like human calculators – who do math really fast. One of the strategies they use is decomposing numbers. For example, with 7+13, you want to be able to see the tens and ones. 10 + 3 is 13; 3 + 7 is another set of 10 and that’s 20. Being able to do that with addition, multiplication, division and subtraction lets you see patterns and it helps you through calculus. I was always thinking about the patterns in school.
I see the Common Core as a way to provide teachers with strategies so that students can see the beauty of math – the how it works and the why it works and the patterns.
Q. How do the Mathematical Practices emphasized in the Common Core fit in with the idea of a growth mindset, meaning the belief that intelligence can be developed through effort?
A: The Standards for Mathematical Practice include: make sense of problems and persevere in solving them. These allow us to understand that student success with the standards is more an indication of the effort they put into learning, as opposed to their inherent intelligence.
It’s difficult to get people to accept this. But I really believe with every fiber of my being that given enough time and given enough support, every student can succeed.
It’s a matter of changing that mindset from, ‘I’m no good at math because I couldn’t do it the first time, so I’m bad at it,’ to realizing that if I keep trying, then I’m going to get it. There’s going to come a time in anybody’s mathematical career when there’s something you’re going to have to work at. I haven’t met a person who succeeded without practicing and thinking about it and making mistakes.
Q. How can a growth mindset help teachers implement the Common Core?
A: There’s a perception that math teachers know every bit of math. But we’re like everybody else. Over time, you forget things. And even if you do know every bit of math, it’s really difficult to go back and relearn it.
From the time since I got my preliminary credential in 1996, I have had to go back and I have had to learn the hows and the whys. I think that’s one of the things that really holds people back, thinking, ‘What if my students ask a question that I don’t have the answer to?’ Many teachers like me were schooled in procedures, but not schooled in the hows and the whys. So, some teachers may be hesitant to do that because that might not have gone into their educational experience.
For that, I would say, teachers need to practice what we preach and have a growth mindset also. We don’t have all the answers, so let’s model that.
The teachers who are most apt to be the early adopters of reforms, honestly, are the people who have a lot of these ideas without even knowing they’ve really embraced and embodied that growth mindset.
One of the things we desperately need is to just give teachers time and resources to be able to learn this. Right now, teachers work a lot. Hours are pretty long, and there are not enough hours in the day to teach all of your classes and really dive into this. The districts doing the best are the districts that have built in teacher release time for summer planning and after-school sessions to really figure it out.
Q. How do you think the Common Core may evolve in the future?
A. I got a chance to talk to Bill McCallum, one of the three authors of the Common Core, while I was in Korea in 2012. One of the two things he said was that in K-8, they nailed it. But in terms of grades 9-12 high school Common Core, “It’s good, but it (Common Core) needs some work.’
The second thing he said, which I was absolutely interested in and excited about, was that the authors’ intention was to revisit the Common Core standards and continue to make them better. There hasn’t been a process for that in California, as far as I know. The one thing that was done was the 85-15 rule, where 15 percent could be added by the state. But no one has looked to revamp them based on how they’re going so far.
Q. What advice do you have regarding curriculum adoption?
A. I would say if there was one magic bullet I would suggest, is if everybody in the process thought of the curriculum they were thinking of adopting from the students’ perspective. What is it going to look like for the students? Because, for the students, you’re really setting up a frame of reference for what mathematics is for them.
I do like the idea, with textbook adoptions, of having a lot of different people in the room who can evaluate it from different perspectives, including a student representative.
In my opinion, there are some textbooks that do it right, and there are some that miss the mark entirely. But if you do it right and integrate it, it’s definitely the right way to go.
John Dewey wrote a bunch of books in the early 1900s, and they’re just as applicable today. He talked about how we isolate subject matter instead of integrating it. What we do in the education system is we break them apart. Separating Algebra I and Geometry is breaking apart what is intricately connected.
I like the integrated math approach more than traditional, as long as it’s done right because you’re letting the different branches of mathematics talk to each other, which is the way it was originally used. Integrated includes algebra, geometry and other math concepts combined each year in a three-year progression of courses. Traditional separates Algebra I, Geometry and Algebra II out each year. If you take away algebra from geometry, you’re losing a component.
Q. What is your view of integrated science instruction, which combines different branches of science that have traditionally been taught in isolation, such as biology, chemistry, physics, earth science and marine biology?
A. In terms of integrated science, I have a personal background in science and my wife is a department head and has been teaching science for 13 years in high school. Honestly, the biggest worry in the state of California is if we go integrated, what does that mean in terms of a credential? Can a biology teacher teach integrated science with chemistry and earth science? Or are they going to have an integrated credential? All the credentialing has to be figured out. What do we need to do in order to get teachers ready for that? Now, if you get a science credential, it’s in biology or physics or chemistry.
But, if you have a full math credential like I have, you can teach everything in secondary school from Pre-algebra up to Pre-calculus.
Q. Can you please elaborate on why you consider math to be ‘beautiful’?
A. I think that’s the way I view every single subject that you could ever learn from pre-k though college. I think of all of them as different ways of viewing our world and making sense of our world. You can look at it from a historical perspective, through literature, scientific discovery or psychology.
But from the mathematical perspective, you get to see the beauty and the patterns of people and interactions and the physical environment around us.
In the movie, ‘A Beautiful Mind,’ mathematician John Forbes Nash Jr. is standing by a punch bowl and the light’s hitting the punch bowl and glittering in a pattern up to this guy’s tie and he says, ‘There’s a mathematical reason I could tell you your tie’s ugly.’
There are things that happen in the natural world. For people, understanding those patterns is a logical way of thinking about the world. I think it’s a way we can make a lot of sense about the world around us.
In the last chapter of my first book, I wrote about the Fibonacci Sequence, which is found in nature. You can see it when you look at a rose, the way the petals unfold. Or in the snail-like shell of a nautilus. Or in the seeds in a sunflower. They spiral out according to the Fibonacci Sequence (a series of numbers in which the next number is found by adding the two previous numbers, ie. 0, 1, 1, 2, 3, 5, 8…). Understanding that pattern brings more beauty to it.
A few years ago, I decided to learn the guitar. At first it was all about numbers to me – based on the strings and the frets. Like the song, ‘Smoke on the Water’ was 3-6-8. I still remember it mathematically.
Teachers can help students make connections between math and the real world through interdisciplinary lessons that combine math and science and English, with one overarching question driving why we’re learning what we’re learning.
I just hope that the Common Core allows students to see mathematics the way people who love mathematics see it.
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