I have been a math educator for about twenty years and Building Thinking Classrooms in Mathematics by Peter Liljedahl has more potential to improve the way we teach mathematics than any other book I have ever read. These are not words I say lightly. This book is an absolute game changer for all math educators…
I’ve recently started exploring what education and professional development could look like in the virtual reality Metaverse after my friend Mike Flynn suggested that we try it out. I made a series of eight videos to demonstrate this as a proof of concept. Consider that while this might seem crazy or unnecessary right now, if…
I love reading (and especially listening) to books that help me learn new ideas or realize how what I thought I knew was wrong. I think this is especially important for anyone responsible for leading or inspiring others. I especially love stories and metaphors that I can think about and incorporate into my presentations and…
I recently saw that Charlie and the Chocolate Factory musical, and one song really caught my attention. It took the common saying of “you have to see it to believe it” and gave it a twist in the song It Must Be Believed to Be Seen. One of the verses is: Beyond this door’s a…
[Looking for other grade levels? The button below allows you to download all of them or you can look here.] If you’ve been looking for a way to challenge your students that was simultaneously accessible for all students but still challenged your high flyers, then you’ll love the problems on my Open Middle Depth…
[Looking for other grade levels? The button below allows you to download all of them or you can look here.] If you’ve been looking for a way to challenge your students that was simultaneously accessible for all students but still challenged your high flyers, then you’ll love the problems on my Open Middle Depth…
[Looking for other grade levels? The button below allows you to download all of them or you can look here.] If you’ve been looking for a way to challenge your students that was simultaneously accessible for all students but still challenged your high flyers, then you’ll love the problems on my Open Middle Depth…
[Looking for other grade levels? The button below allows you to download all of them or you can look here.] If you’ve been looking for a way to challenge your students that was simultaneously accessible for all students but still challenged your high flyers, then you’ll love the problems on my Open Middle Depth…
[Looking for other grade levels? The button below allows you to download all of them or you can look here.] If you’ve been looking for a way to challenge your students that was simultaneously accessible for all students but still challenged your high flyers, then you’ll love the problems on my Open Middle Depth…
[Looking for other grade levels? The button below allows you to download all of them or you can look here.] If you’ve been looking for a way to challenge your students that was simultaneously accessible for all students but still challenged your high flyers, then you’ll love the problems on my Open Middle Depth…
[Looking for other grade levels? The button below allows you to download all of them or you can look here.] If you’ve been looking for a way to challenge your students that was simultaneously accessible for all students but still challenged your high flyers, then you’ll love the problems on my Open Middle Depth…
[Looking for other grade levels? The button below allows you to download all of them or you can look here.] If you’ve been looking for a way to challenge your students that was simultaneously accessible for all students but still challenged your high flyers, then you’ll love the problems on my Open Middle Depth…
[Looking for other grade levels? The button below allows you to download all of them or you can look here.] If you’ve been looking for a way to challenge your students that was simultaneously accessible for all students but still challenged your high flyers, then you’ll love the problems on my Open Middle Depth…
One question I often get about problem-based lessons is “What should I do if students finish a problem early?” The conversation often shifts to ways to extend the problem so that students who are done and want more challenge have something to do. So in this blog post I want to dive into a distinction…
[This is one of a series of posts that explore real world examples of mathematical modeling to help educators better understand its applications. This is not intended to be a context for a student lesson. To learn about Spies and Analysts, I recommend watching this webinar (with elementary, middle, and high school versions) or reading…
Have you ever noticed that you can accept tough feedback from one person, but if another person gave you the exact same tough feedback, it would make you feel judged or criticized? Giving tough feedback is challenging and may feel like an impossible choice: say something and offend the recipient or sugarcoat your message into…
As I’ve mentioned in many blog posts, I struggled a lot in my first years as a teacher. I began my teaching career at a time when schools were desperate for math teachers. I got an emergency credential and was allowed to teach before ever taking an education class or doing any student teaching. I…
Note: This blog post is based on Juli Dixon‘s work on “just-in-time” scaffolding versus “just-in-case scaffolding”. Whenever I plan to teach a lesson, I try to anticipate the foundational skills students will need to know to complete it. For example, if students have to determine which slope is steeper, I think about how they will…
My favorite of all the Depth of Knowledge (DOK) levels, as I define them in these matrices for elementary and secondary mathematics, is DOK 3. I’ve always found it challenging to give a short and sweet reason as to why I felt that way… until I heard Bushnell’s Law. This “law” was created by Atari…
When I was learning math as a student, I had no idea that math was a beautiful and interconnected story. Sure, I could do mathematics. I even graduated from UCLA with a Bachelor of Science in Mathematics. But I didn’t deeply understand mathematics. For example, I had never noticed how simple single digit multiplication progresses…