Colorado teacher believes students should experience math–not just memorize it.
When Krista Borland, middle school math teacher at The Early College of Arvada in Colorado, was going through her teacher education program, she learned that the best way to teach math was through experiential, hands-on learning. And that most districts don’t offer this.
“Current math solutions that place students at the center of their own mathematical discovery just don’t exist,” her professors told her, “so while we know the best way to teach math, you likely won’t be able to do it.”
Borland was frustrated. Would she have to build her own curriculum from the ground up? Why didn’t more districts follow best practices?
And then she found Carnegie Learning Math, and everything changed.
The 6-12 school where Borland teaches started using the Carnegie Learning Math Solution at the beginning of the 2021-22 school year, and her excitement about the program is contagious. The math program is built on the idea that students need to develop their own mathematical understanding through active inquiry and conversations with each other. It was precisely the kind of student-led math curriculum she’d dreamed about in college—now in her own classroom.
Read on to hear how it’s going!
What first drew you to the Carnegie Learning Math Solution?
When I was in my teaching program, my professors talked about a great, natural way for students to learn math through an experiential approach, where they could take what they knew and build on it and experience math in real-life settings. But they kept saying that while this is best practice, many districts’ curriculums don’t do it.
So when our district previewed Carnegie Learning, I was so excited to see that it was an explorative math program! It allows students to truly experience math, not just memorize it. This really makes Carnegie Learning a cutting-edge math program.
How have your students responded to the Carnegie Learning Math Solution?
As my students have gone through the program, I’ve seen immense growth, mathematically and in other areas. They’ve gone from being afraid to take risks to speaking up confidently and really embracing math. They’ll say things like, “Hey, I see this occurring. Is that right? What do you think?” And they're genuinely discussing complex mathematical concepts. The first time they took a new problem and said, “Hmmm…this worked for a similar problem. I wonder if this will work here,” was an amazing experience–for them and for me.
It sounds like your students are enjoying a math classroom that’s more discourse-based and collaborative than many. Is that right?
Definitely. My students speak math all the time! The literacy component of the Carnegie Learning program is so amazing. My kids are using vocabulary I didn't learn until I was in college, and they're in middle school! We use words like ‘sample set.’ I didn't learn ‘sample set’ until I was in stats class! Carnegie Learning teaches them at such a high level, and they don't even realize it. And it’s not just that they’re speaking in mathematical terms; they’re also coming to grips with the math behind them.
How else has your classroom changed, for you and your students, since you’ve started using the Carnegie Learning Math Solution?
My classroom has changed from me being the center of attention to the students being the center of attention. It's not sit-and-get. At this point, students have taken over the classroom and started sharing their mathematical experiences. It’s just magic because these were largely students who were frustrated with math. But now, students all work on whiteboards. Everything's erasable, mistakes are allowed, and they’re not afraid to take chances.
Carnegie Learning knows that teachers shouldn’t act as vessels of knowledge where what they know simply gets dumped from one person to the next. To be a good teacher, I’ve learned that I have to let students lead. But that’s not the mindset most teachers leave their training programs with, and the shift that Carnegie Learning asks you to make is not a small one and takes some time. But once it takes root, oh my gosh!
My principal observed me once before I started using the Carnegie Learning Math Solution and once after. He told me the change in my classroom was like night and day. The second time he visited, he noticed that the students were talking about math, not sitting quietly and taking notes like before. When he asked me what had changed, I said, “It’s Carnegie Learning. That’s what’s changed my classroom.”
What are some of your favorite teaching moments with the Carnegie Learning Math Solution?
I had a group of students who were all on Accelerated Learning Plans. They were advanced kiddos who risked plateauing. They suddenly went from saying, “That's the answer. I got it right,” to giving detailed explanations of why the math worked and how it related to similar concepts they’d studied. And, from there, their test scores inevitably went up.
One of my students, a seventh-grader who worked on eighth-grade math, was stagnant. Her Measures of Academic Progress (MAPS) scores had remained flat for a while. And this past spring, she jumped up ten points. I told her it was because she could now truly understand the math, not just follow rules to get the right answer. I still remember how brightly she smiled. It was a special moment because so often in math class, we hear girls say, “Well, I'm a girl. I'm not supposed to know how to do math.” And to watch these young ladies be starry-eyed and ecstatic about all the progress they’re making is just awesome.
You mentioned before the interview started that you work with many special education students. How has the Carnegie Learning Math Solution worked for them?
One special education student, in particular, comes to mind. He was labeled ID (intellectually disabled). He was in a regular classroom as much as we could have him there, and he experienced Carnegie Learning on grade level. He got a little extra sheltering and some notes, but he was able to step forward with it. He ended up being one of my top-achieving math students in my seventh grade and just loved learning this way. He was excited to come to math class and he was ecstatic that he got to try out new things when solving a problem and that it was okay to be wrong.
Another special education student will also stick with me. Math was where she was most challenged, but she also desperately wanted to learn and understand math. She struggled at the beginning of the year but slowly gained confidence when she saw that the curriculum encouraged her to bounce ideas off her peers and did not punish wrong answers. I watched her scores start to improve, but more importantly, I watched her enthusiasm for math grow stronger as the year progressed. Eventually, she reached a point where she could approach math problems with strategies she had not been directly instructed to use. This from a kid who, a year earlier, was struggling to understand the basics. Suddenly, she was applying her previous knowledge in logical ways.
When we were doing our MAPS testing at the end of the school year, she ran into my classroom while I had a class in session. She started jumping up and down; she was over the moon, and I asked, “What's going on? What happened?”
“I raised my MAPS score by 15 points,” she nearly screamed. She was beyond elated.
Watching my students, not just the “regular kids” but all my students, gain access to mathematical understanding and really learn to be comfortable with math is just indescribable.
What are you looking forward to as you keep working with the Carnegie Learning Math Solution?
I have the privilege of being in a 6-12 school where I teach middle and high school classes, meaning I get to watch my students grow all the way through and see the difference on the other side. I can’t wait to keep watching them go from being timid and afraid of math to owning the curriculum and finding solutions on their own. I know they will keep becoming stronger math students but also get stronger at looking at life. They'll keep learning how to problem-solve, and they won’t be afraid to look at something new and say, “Hmmm, could I try it this way? Let’s see,” and that’s such a valuable life skill.
Any words of wisdom for teachers, schools, or districts thinking of implementing the Carnegie Learning Math Solution?
Carnegie Learning is a fantastic math curriculum that allows students to explore and truly understand why math works. But it is a challenge to implement initially. However, the reward is worth every challenging minute.
I know some of my colleagues initially thought the curriculum would be too hard for their students, but they soon discovered that the program works if you break it down, piece by piece, and trust that the pieces build on each other, which they do. You have to allow the process to unfold, which can be difficult your first time through, but I was really upfront with my students about the fact that this was a new curriculum for me too, and that we’d be doing a lot of learning and growing together.
But ultimately, what Carnegie Learning does is allow a classroom to truly be a space where kids are excited to learn. And what teacher doesn’t want that?
Congratulations to Krista on her incredible year-and-a-half teaching with the Carnegie Learning Math Solution. She’s doing a phenomenal job, and her students are lucky to have her!
Before joining Carnegie Learning’s marketing team in 2021, Emily Anderson spent 16 years teaching middle school, high school, and college English in classrooms throughout Virginia, Pennsylvania, California, and Minnesota. During these years, Emily developed a passion for designing exciting, relatable curricula and developing transformative teaching strategies. She holds master's degrees in English and Women’s Studies and a doctorate in American literature and lives for those classroom moments when students learn something that will forever change them. She loves helping amazing teachers achieve more of these moments in their classrooms.Explore more related to this author
So often in math class, we hear girls say, 'Well, I'm a girl. I'm not supposed to know how to do math.' And to watch these young ladies be starry-eyed and ecstatic about all the progress they’re making is just awesome.
Krista Borland, middle and high school math teacher, Early College of Arvada, Colorado