2023 was a year filled with new learnings for me. It was the first time in my 33 year educational career I was able to solely focus my efforts on supporting educators and searching for new learning I could share with them. I was able to work with a variety of school districts with varying demographics, a variety of student needs to be addressed, and problems of practice which stretched my learning. Therefore, I thought it would be fitting to focus my first blog of 2024 on sharing my discoveries from 2023. Keep in mind the term ‘discoveries’ is relative. These things were new learning for me but you might have discovered them a while back and are already an expert. I hope at least one of these resources can be a benefit to you and your students.
Polypad from Mathigon
Polypad is a completely free, no sign in required, set of virtual, visual models that can provide a wide variety of options for your students to ‘see’ the mathematics. Students significantly benefit from creating and working with a variety of visual models that represent mathematical concepts and Polypad provides access to those visual models without the cost of concrete manipulatives, which can be expensive. Keep in mind a concrete model is always beneficial for students, but the visual model can be as meaningful in building conceptual understanding. Polypad could be used as a teacher demonstration tool, or a student directed tool. I love that students don’t have to sign in and the tool is completely free to teachers, students, and parents.
Open Middle Tasks
Although Open Middle tasks were not new to me, 2023 was the first time I was actually able to use these tasks with students and see the power of these ‘open’ tasks. These fantastic ‘thinking’ tasks, designed initially by Robert Kaplinsky, encourage students to really stretch themselves and think outside the box. Many teachers have embraced the work of Peter Lijedahl in Building Thinking Classrooms (2020) and I have found the Open Middle tasks to be amazing ‘curricular thinking tasks’. The website allows you to sort by grade level, K-12, and by content domain. Over the years other educators have contributed to the task repository and now there are tasks to match most of the standards we teach. These tasks are great for group work or as an individual challenge task. Give them to all your students, don’t get caught thinking only the students who are high achieving can do these tasks.
Geogebra
Geogebra has been around for several years but they have transformed the resources, activities and task repository to include some outstanding ‘thinking’ tasks. As our standards move to more of a modeling and conceptual approach (WooHoo!) we need tasks that will provide opportunities for our students to see the math, to manipulate components and explore connections among math concepts. Geogebra provides those resources and activities. The website has grown the number of activities they offer as well as the types of activities. This is not just a geometry tool! Most content domains such as probability/statistics, algebra, number sense, and algebra activities are offered as a large repository of DOK 3 tasks. If you haven’t been back to Geogebra for a while it is worth a visit.
Hexagonal Thinking
Hexagonal Thinking was completely new to me in 2023 and I love it! This activity can be used in any grade level for any content area. It provides a way for students to process connections between and among ideas. You could use this to review concepts for an upcoming assessment, summarize the ‘big idea’ of a novel, chapter, and concept. This activity is easy to prepare and it lends itself to imaginative and creative conversations from students and adults. I would encourage you to use this activity in your next PLC meeting to analyze connections in data you see from students or break down a standard to make meaning of it for your students. The applications are endless. Don’t limit yourself to the examples shared in the blog post linked above, stretch your thinking.
Math Talks
By far, the number one concern I hear from K-12 math teachers and administrators is that students have a significant lack of number sense. Number sense can encompass a variety of symptoms, but here a a few:
- Students aren’t fluent in their math facts.
- Students can make careless arithmetic mistakes.
- Students can struggle to consistently work through a procedure or algorithm.
- Students aren’t flexible in their thinking about mathematics.
Although Math Talks are certainly not new to me, I did discover a variety of websites/resources that stretched my ideas about math talks. I began to see that real world images can spark some deep conversations when we ask students, “What do you see?”. Math Talks don’t have to include numbers at all. I also discovered the less you say and the more the students talk the more they will benefit from a math talk. Take a look at a few of the resources I used with students this year. I was blown away by the students’ thinking and insight.
I love end of the year lists and I hope you find this one helpful for your students.