Math Methods - Putting it into Practice
To help more students prepare to excel as math instructors, WGU Teachers College Elementary Math Methods faculty have begun hosting webinars that invite current, future, and former students to engage in hands-on practice using new, innovative math tools and online applications to teach specific math subjects.
“Each webinar focuses on a different math topic, such as telling time, working with fractions etc.,” said Megan Rzyski, Senior Instructor, Math Methods.
“Participants in the webinars get to explore virtual math tools to solve problems, model how to teach concepts, brainstorm how to help students with misconceptions, and more. These are interactive sessions full of discussion and idea sharing.”
Math Methods faculty state that students in the webinars say they have come away from the sessions with concrete ideas to help them prepare to teach these concepts in their classrooms once they graduate.
Putting it into Practice
“As a team of Math Methods Instructors, we recognize that sometimes students do not understand how to implement math tools in their instruction. For example, they know they can use a specific tool to teach a concept – like base ten blocks can be used to teach place value or that fraction circles can be used to teach fraction addition, but they may not understand HOW to actually do that,” said Rzyski. The webinars are designed to help build that understanding.
Math Topics Covered in Webinars
While all Math Methods instructors collaborate to plan the webinar sessions, faculty members take turns leading each webinar. The enthusiastic WGU Teachers College faculty who have led these sessions along with Rzyski include Amy Barrett, Adam Hiebel, Carol PeQueen, Jen Wallender, and Kristie Remaly.
These faculty are supported by program mentors who assist with moderating the sessions and helping students one-on-one including Morgan Swearingen, Katie Bush, Makenzie Gurss, Brenda Wesley, Laura Hendrickson, and Christy Katz.
The highly-interactive sessions have included the following topics so far:
o Understanding fractions with pattern blocks
o Telling time
o Math operations with money
o Integer operations
o Place value with base ten blocks
o Math expressions with algebra tiles
o Probability
Demonstrating Use of Virtual Tools
The webinar leader helps participants on the call understand how this all translates to students in an elementary education classroom. “We show webinar participants – who are mostly current or former Math Methods students, but also some future Math Methods students - what this will look like in their classroom as they teach these topics."
Pictured (on right) are some visuals of how these applications can be used online to help demonstrate concepts such as Base Ten Blocks to develop number sense, and Spinner to develop probability and data analysis concepts.
"We give them questions we anticipate their students will ask so they can prepare to use the tools to demonstrate the concepts and help their students learn,” said Rzyski.
Authentic Learning Experiences
During each webinar WGU Faculty put a problem on the screen and give participants a link to an application that can be used to help solve the problem. Students are given a few moments to explore the application and then the group engages in conversations. “We give them time to explore a little before we show them how to interact with the tool,” said Rzyski. By giving the participants time to practice first, they can bring their experience to the conversation. The faculty also use the webinars to help participants anticipate some of the common errors students will make in learning these elementary concepts.
"It is clear that the chief end of mathematical study must be to make the students think." — John Wesley Young, American mathematician
Nurturing the Creative Constructivist
As WGU students progress on their degree path, they build a solid foundation of math theory, but nationally, there’s a move away from the narrower focus of the past to a broader, more constructivist view of math teaching happening across the country today says Rzyski. “Today, educators are not taught that there is just one way to solve a problem, and if people can find unique ways to get to the solution, that’s celebrated. The education landscape is changing, and we need to train future teachers to be creative constructivist educators,” said Rzyski.
In Elementary Math Methods, students learn about many math tools, such as fraction circles. Fraction circles are either plastic pieces that come together to form a circular shape but can also be assembled in parts such as a ¼ circle, or a half circle to demonstrate how the pieces fit the whole. Many online applications exist to demonstrate the same concept. “Fraction circles are easily understood as tools used to explore the concept of fractional parts of a whole and operations with fractions. However, how to use these fraction circles to demonstrate such a concept, such as multiplication of fractions, is not intuitive,” said Rzyski. “We want to help students see effective ways these tools can support their teaching by problem solving together through actual math examples. These webinars get students over that hump where they can marry theory with practice and use these apps in a hands-on, safe learning environment that supports learning in a classroom,” she said.
The figure to the left demonstrates how fraction circles can be used to explore fraction multiplication.
The circle first shows 8 total slices with 2 slices shaded in to represent 2/8. This example was used to model ½ x 2/8.
When thinking of this as “1/2 of 2/8”, students can then use this representation to find half of the shaded region. Because the shaded region is two equal pieces, half of it would be just one shaded slice.
This allows students to see that the product is 1/8.
“I had one webinar on telling time that turned into what felt like a magical session because the students were so engaged and so into it,” said Rzyski. “There were so many realizations from them on how they could take what we were using in these tools and use it to bolster their future classroom instruction for their students. We took the clock and then put fractions over top of the clock to demonstrate what a quarter of an hour looked like for a student trying to align fractions and time telling, and many other practical examples. We have students who have completed the course coming back for these webinars now because these learnings will be so relevant to them as teachers. “
In another example from the session on telling time, the instructors showed how to make the visual switch from minute hands to second hands, from digital to roman numerals and more. Students on the call are encouraged to ask questions all along the way and share discoveries and ideas. While the instructor is demonstrating the use of the tool, WGU program mentors are also staffing the webinar and assisting in answering chat questions and fielding individual student inquiries for immediate 1:1 support.
“By the end of the webinar some participants said that even though they had completed the Math Methods course they would keep coming back to pick up these skills for their classrooms,” said Rzyski.
There should be no such thing as boring mathematics. — Edsger W. Dijkstra, Dutch systems scientist
Rzyski has been with WGU Teachers College since 2016, and first served as a program mentor, and then moved into the instructor role in 2018. Speaking with her makes it very clear she’s found her passion. “I love unpacking math and I love when I can help others see why we do what we do!” said Rzyski. “Many students have memorized traditional strategies for solving math problems but have not been shown how to unpack those strategies, as well as explore others, to find the “why” behind mathematics. I think that anytime we can help students build a strong conceptual understanding and help them see how math is all woven together it becomes very exciting. “Math” and ”exciting” may seem like opposites, but I feel differently,” said Rzyski. “Math has always been my favorite subject, and I always knew I wanted to teach it and to make it exciting for people. Take for example when I was learning area of a trapezoid. It was so dull. I just plugged-in numbers to a memorized formula that was long and confusing. But then I was shown why the formula for determining the area of a trapezoid actually worked, and I was amazed! I want to make that kind of exciting discovery possible for our future teachers so they can share that with their future students.”
Moving forward
While the team of faculty intend to revisit popular topics, they are also always bringing on new topics. For Spring of 2022, they are exploring topics including perimeter area, 2D and 3D shapes, and much more. While the webinars are not recorded in order to protect student privacy, as well as to encourage students to freely ask questions, the Math Methods instructors have begun to record the monthly concepts and demonstrations of the tools in order to build a library of these topics in shorter ‘explainer’ videos. Here is a sample of one of those sessions. (Please note, this link requires WGU student, faculty, alumni or staff sign on credentials.)
To learn more and register for upcoming sessions, enrolled students can register via a link in their Math Methods course, or email mathsciencemethods@wgu.edu for the registration link.
