Finding inspiration in a week of math

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Erin Chavez
erin.chavez@education.ky.gov

Some teachers in Kentucky started their year off this fall with a week full of inspirational math lessons from Jo Boaler’s youcubed, a website that offers five days of lesson plans and tasks designed to instill a positive mindset about math in students.

Boaler is author of “Mathematical Mindsets,” cofounder of youcubed and professor of mathematics education at Stanford University. She followed thousands of students through middle and high school, studying how they learn in an effort to find the most effective ways to unleash the math potential in all students.

What Boaler found was that scores of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. The students’ belief that they cannot do math hinders math-related pathways and STEM career opportunities.

Research has shown very clear methods to change this phenomena, but the information has been confined mainly to research journals.

“Mathematical Mindsets” provides a proven, practical roadmap to mathematics success for all students. The lessons include a short mindset video, designed with the help of Boaler’s class of undergraduates and some school children, that inspires all students to learn mathematics through a positive growth mindset method. Following the mindset videos are activities designed to invite students into a world of open, creative and visual mathematics.

A few Kentucky teachers wanting to change the mindset of students about mathematics began using these lessons recently. Here are a few examples of what they discovered.


 

Using inspirational math lessons from Jo Boaler’s youcubed website, students in Christy Drury’s 4th-grade mathematics class find different structures within a group. The students highlighted that grouping by either coloring or circling the way they visualize the number. Submitted Photo by Erin Chavez
Using inspirational math lessons from Jo Boaler’s youcubed website, students in Christy Drury’s 4th-grade mathematics class find different structures within a group. The students highlighted that grouping by either coloring or circling the way they visualize the number.
Submitted Photo by Erin Chavez

Christy Drury is a 4th-grade teacher at Collins Lane Elementary (Franklin County). She wanted to proactively change the mindset of her students in mathematics, and found that Boaler’s videos and engaging mathematical tasks had the potential to do just that, she said.

Many times, the typical textbook or worksheet promotes getting the right answer to computation problems. These five days of lessons are different, because they have students work with mathematics conceptually so that they are able to visualize the number.

In a particular lesson Drury used – Day 2 Mistakes are Beautiful Things – the students discovered patterns in a visual design to understand the quantity of a number. This teaches students to see different ways of combining other numbers to make a specific number.

This activity helped students realize the different and creative ways we can express numbers.

“Inspirational math was a great way to challenge my students with engaging math tasks,” Drury said. “As we are working on developing a growth mindset, these activities inspire students to work through challenging problems and see math through different math ‘lenses.’”


 

Kristen Oetken’s 2nd-graders work on ways to see numbers and how they see the structure. Some students are also visualize groupings in the visual representation of the number. Submitted photo by Erin Chavez
Kristen Oetken’s 2nd-graders work on ways to see numbers and how they see the structure. Some students also visualize groupings in the visual representation of the number.
Submitted photo by Erin Chavez

Kristen Oetken is a 2nd-grade teacher at Atkinson Elementary (Jefferson County).

Oetken found that the inspirational math week lessons helped her students see that mathematics is more than just computation and answers, and they should keep going even when the work gets more difficult and mistakes are made.

Using the Day 2 Mistakes are Beautiful Things lesson, the math talk that led into the activity helped open students’ eyes to see that numbers are more than a symbol, said Oetken, that they actually have quantity and value. With this understanding, students were able to learn from one another on how they saw a group of dots that represented a visualization of a number.

“While implementing week two of Jo Boaler’s inspirational math week, I saw that my students weren’t afraid to dive into the mathematics,” she said. “My students had valuable mathematical discussions on the way that they visualized the structure and quantity of numbers. They realized that math is not just symbols. Mathematics has meaning and value, and we can apply it to real-world problems.”


 

Michelle Praria’s 5th-grade students make their own conjectures and learn something about the history of mathematics while solving hailstone sequences. The hailstone sequence is part of the unsolved Collatz Conjecture. Working on an unsolvable problem, Praria said, helps her students learn to persevere on difficult problems. Submitted photo by Erin Chavez
Michelle Praria’s 5th-grade students make their own conjectures and learn something about the history of mathematics while solving hailstone sequences. The hailstone sequence is part of the unsolved Collatz Conjecture. Working on an unsolvable problem, Praria said, helps her students learn to persevere on difficult problems.
Submitted photo by Erin Chavez

Michelle Praria is a 5th-grade teacher at Northside Elementary (Woodford County).

Praria knows that in the 5th grade, her students are always going to be faced with challenging problems in mathematics. Because of this, she wants to help change their mindset so that they are prepared to never give up, even if the problem turns out to be unsolvable.

Day 4 Conjectures, Creativity and Uncertainty is about introducing students to one of the world’s unsolved problems in mathematics. It involves a sequence of numbers called a hailstone sequence, because the numbers go up and down again and again. This allows students to be introduced to the idea of conjectures, which are very important in mathematics.

Conjecture is when a person thinks something might be true, but it hasn’t yet been proved.

In this particular lesson, students make conjectures about this hailstone sequence to see what happens. After Praria’s students discussed multiple conjectures, she told them about a famous mathematician, Lothar Collatz, who proposed that if a number is picked, and if you follow the procedure enough times, you will eventually get to 1. This then became known as The Collatz Conjecture.

Since then, lots of mathematicians have been trying to prove or disprove it. So far, every number that has been tried has reached 1, and powerful computers have checked enormous numbers of numbers, but no one knows if there is a large number out there that might break the rule. So this is classified as an unsolved problem in mathematics.

Praria’s students were in awe, and it helped them see that mathematics is not all about solving a problem; it’s truly about persevering and making sense of mathematics.

“Inspirational math has helped my students experience math in a different way this year,” Praria said. “Mistakes have become a valuable and meaningful part of the learning process in our class. I see students take ownership of their learning by seeking to understand and learn from their mistakes. We have learned to value the process of learning in math.”

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