Adding advanced mathematical concepts to young math students and subtracting lessons with no real-world application equals more math success, said panelists during a recent Tech & Learning webinar hosted by Dr. Kecia Ray.
“Moving Beyond Algebra-Ready to Algebra-Excited: Cultivating Algebraic Reasoning from Kindergarten to High School” was sponsored by DreamBox.
During the event, educators shared real-world, actionable tips for making math classrooms more joyful and productive places.
Watch the free webinar on demand here.
Early Algebra for All Students > Early Algebra for Some Students
Research shows that only 35 out of every 100 eighth graders are proficient in math, said Kirsten Keels, professional development specialist at DreamBox Learning and Ph. D candidate who conducts research aimed at getting all students ready for algebra at an early grade level.
“I want to situate algebra as a civil right for all of our students,” said the former fourth- and fifth-grade math and science teacher. “When we think about the life outcomes that are attached to taking algebra and successfully completing this in high school, or even in eighth grade, it can either be a gateway for students to their educational opportunities and financial security, or it can be a gatekeeper barring students from those life outcomes.”
To ensure that all students are ready for algebra, Keels advises preparing students for algebra as soon as possible. “I tend to reframe algebra as a sense-making activity,” she said. “We know that students enter our classrooms, even as early as kindergarten, curious about their world, wanting to know more about it, so why not take their lived experience and help them mathematize. So a part of early algebra is helping them see that mathematics can be used to model the world around them.”
Subtle Shifts + Better Word Problems = Student Success
Students can start learning pre-algebra as early as kindergarten. “They can start thinking about functions and variable notation at those grade levels, as long as we think about how to present it in a meaningful way. We can reorganize arithmetic and highlight the algebraic nature of this content that's already in our K-5 classrooms,” Keels said.
She shared her research with fifth-grade students, including special education students, and how she was able to teach them principles of algebra with word problems that were open to various possibilities. For example: “John has some pieces of candy inside of a box. He has three pieces on top. How many pieces of candy does John have?” Students were then able to learn that the number of cookies within the box was a variable and could be represented by “N.”
“For these students, we had subtle shifts that made a big difference,” Keels said. “So now instead of focusing on two numbers and figuring out whether or not we're going to add, subtract, multiply or divide, we're focusing on sets of numbers and making generalizations. We're highlighting those key relationships, and there's a body of literature that talks about how special education students benefit from focusing on problem structure. So instead of giving them traditional word problem after traditional word problem, I gave them one word problem and they got to explore and come up with their own solution in different ways.”
Make Your Math Problems Add Up In the Real World
Dr. Tim Hudson, chief learning officer at DreamBox Learning, spoke about the problems with how studying math is often framed, noting that most Algebra I descriptions are dry and not focused enough on math’s many applications. “If students are curious about their world, and they want to mathematize their lived experience, the only things in these course descriptions that speak to that are like, ‘You're doing this to succeed in advanced courses,’ which is not terribly motivating. It’s like, ‘Why would I want to do well in this thing I don't like just to do well in things that I'm also not going to like down the line?’” said Hudson, a former high high school mathematics teacher and K-12 mathematics coordinator and strategic planning facilitator for the Parkway School District in suburban St. Louis.
These problems often extend from the course descriptions into the way the course is actually taught. “It feels like the way we treat math a lot of times when we're teaching it, is to break it up into a bunch of pieces. It's just a list of polynomial functions, simplifying expressions, and different things,” Hudson said. “If we taught driver's ed like we taught math, we would break it up into disconnected pieces, like one day is the stick shift. Tuesday is the clutch. Wednesday is the gas and the brake. Thursday is the steering. And then we send students off to real world driving situations, and it's not going to go well because you can't break it up like that, and have it make sense and be able to put it back together.”
Hudson advised creating word problems that actually relate to the real world and inspire students to pull all their math skills together. “Driving is fun, but just doing one repetitive thing with the gas pedal is not, it's all got to be put together,” he said.
Better Pedagogy = More Joy and Success in Math
K-12 educators Denise Trakas and Sarah Knox spoke about how they put these ideas into practice within their districts.
Trakas, the K-5 mathematics program coordinator for Washoe County School District in Nevada, said her district has been working on bringing a resilient math pedagogy and joy to the mathematics classroom. “We started by developing the K-5 mathematics philosophy,” she said.
The district’s new math philosophy is built around being responsive to where each student is at a given time. “So it's not just about being teacher-centered, or student-centered,” Trakas said. “It's really about using our great instructional practices that we have as teachers and making it learner responsive.”
Trakas used data gathered from DreamBox to celebrate students' math milestones at each of the schools in her district, awarding certificates to the students who completed the most lessons completed with understanding and the student who had the most growth. “I haven't received so much positive feedback from schools as I did from that, it took something off the school's plate, and they're recognizing students' hard work and effort,” she said.
Knox, the director of intervention and prevention in the Instructional Support Services Division of Napa Valley USD, talked about her own struggles with math as a student, and how she was told by an educator that she would never be good at the subject, which is of course not the message you want to send to any student. “We've been working on a two-fold approach to support students like myself, who really struggled with math,” she said. “One is to have a growth mindset be a core component of our math approach, and then also that we have pathways that are mindful and are appropriate for students at different places in their math skills.”
Within Knox’s district a majority of students are Latinx and math programs are designed to be responsive to each student’s individual needs. “We are committed to long term learning solutions for students and data is really important in determining what's working for our students,” Knox said.