As most teachers do, I often look for different ways to increase thinking in my mathematics classroom. Over my 26 years in education, I have picked up many tidbits of information that contribute to my daily classroom routine. Two resources in particular have helped transform my classroom into a thinking classroom.
Over a decade ago, my school decided to purchase student devices for every student in high school, and teachers were challenged to transform their teaching using technology. At first, this seemed like an impossible task, until I learned about Desmos Classroom Activities. I was amazed at how fun and interactive these lessons are. Students could explore a math concept in a way that was not possible without technology. Over the years I’ve discovered other platforms with digital lessons, such as GeoGebra Classroom and Eureka Math Squared.
Many years later, I started hearing the buzz about students working on Vertical Non-Permanent Surfaces (VNPS), but it wasn’t until after the pandemic that I started looking into what all the fuss was about. I understood immediately as I read Building Thinking Classrooms in Mathematics by Peter Liljedahl and started incorporating the 14 practices into my classroom.
Now, after two years of building a thinking classroom, I see similarities in how digital lessons and “BTC” lessons, the types of lessons Liljedahl describes in his book, encourage students to think about mathematics.
Start with a thinking task.
BTC
“Good problem-solving tasks require students to get stuck and then to think, to experiment, to try and to fail, and to apply their knowledge in novel ways in order to get unstuck.” (Liljedahl 19)
Digital Lesson
The Desmos Guide to Building Great (Digital) Math Activities lists several ways a digital lesson might launch a thinking task.
Create an intellectual need for new mathematical skills.
Create problematic activities.
Give students opportunities to be right and wrong in different, interesting ways.
Use visibly random groups.
BTC
Students work in random groups of two or three on a VNPS.
Digital Lesson
Students can be randomly assigned in pairs with each pair sharing one student device.
Use nonpermanent surfaces.
BTC
Students are more likely to engage in the activity quickly because the vertical non-permanent surface allows them to erase their mistakes quickly and start over.
Digital Lessons
Digital interactives allow students to quickly adjust answers, which builds their confidence by reducing their concerns about making mistakes.
Student work is visible.
BTC
The teacher can see student work from anywhere in the room.
Digital lessons
The Teacher Dashboard allows the teacher to see all student work at once.
Knowledge is mobile.
BTC
Students can see other students’ work on the VNPS. As students observe each others’ work, knowledge spreads throughout the classroom.
Digital Lesson
Students can share their thoughts with each other, which also allows for knowledge to be passed on.
Consolidate each lesson.
BTC
The teacher can use student work on the VNPS to help consolidate a lesson and point out interesting ideas. Students can compare different methods of solving the thinking task.
Digital Lesson
The teacher can display student responses or select a sampling of student work to highlight during a class discussion.
Teacher Moves
Both BTC and digital lessons allow the teacher to become a facilitator of learning. While students are working on the lesson, the teacher is walking around and answering only thinking questions and either helping or challenging students to keep them in “flow”.
While these similarities give evidence of how digital lessons can build thinking in the classroom, it is the differences that make it necessary to use both VNPS and student devices when teaching mathematics. When writing on VNPS, students can show work and manipulate mathematical equations and computations very easily. Students can create diagrams and pictures to represent their thinking, which would be very time consuming typing on a student device.
Using digital interactives on their devices allows students the opportunity to interact with graphs and figures in a way that they cannot do with static images. Digital interactives give students interpretive feedback. Every action has a consequence, which allows students to make and test conjectures quickly.
When planning lessons, I decide between VNPS and student devices and choose the best tool for bringing out the mathematics. Lately, I’ve been veering away from traditional digital lessons, where students use their device for the entire lesson, and have instead been developing lessons that use VNPS and digital interactives on student devices interchangeably. I plan on writing about this experience in a future post.
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