[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…
[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…
[This is one of a series of posts that explore real world examples of mathematical modeling to help educators better understand its applications. To learn about Spies and Analysts, I recommend either reading this blog post or watching this webinar (with elementary, middle, and high school versions).] For years I’ve been trying to find…
If you’ve ever asked students a question only to have tentative responses come back like “Yes… No… Uh… Yes…”, then you’ll enjoy this story. In the early 1900s, there was a famous horse named Clever Hans that amazed people because of his intelligence. At first Hans was able to count objects and then tap his…
You’ve probably heard that there are tournaments for board games such as Scrabble. These winners are often held in high esteem for their intelligence, knowledge, and strategic thinking which they use to propel themselves to victory. They are thought to be experts of the languages they use… but I wonder if that is always the…
Most teachers believe that there is not enough time to teach all their grade level standards in a single year. I’m guessing that this doesn’t come as a surprise to you. So, the question then is what do we do about it? I think that the most common reaction is to want to skip certain…
Many years ago I took a steak cooking class where the instructor told us, “If you’re not sure if the steak is done, it’s better to undercook it than overcook it. The reason why is because you can always throw the steak back on the grill if it’s undercooked, but you can never undo overcooking.”…
I had an interesting experience I wanted to share. I haven’t fully developed this idea, but I’m sharing it to see what you think… About a year ago I sat in the audience as Dan Meyer presented his take on problem-based learning. Now, I’ve seen Dan present at least a dozen times, and every single…
The 2017 College Football Championship game came down to the final play with six seconds left. Watch the first 14 seconds of this clip so you understand what happened. Next, I want you to read the excerpt below from a CNN article, and pay special attention to quarterback Deshaun Watson’s quote at the end. Think about…
One of my favorite takeaways from the book The Power of Habit: Why We Do What We Do in Life and Business was the origin story of the odor removing spray: Febreze. He begins by sharing how it was accidentally created by a chain-smoking Proctor & Gamble scientist. The day that scientist discovered it, he…
[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 called on students to ask them for an answer or explanation and gotten the feeling that they were just repeating what the earlier students had said? I’m guessing you have. You probably wished that students would state their own thoughts so you had a better idea of what they were thinking. This…
I’m really excited by how increasing numbers of educators are opening up their classrooms to their peers. I believe that the type of feedback they give and receive has great potential to help educators improve. Two of the biggest movements in support of that trend are #ObserveMe and Pineapple Charts. What I’ve been noticing though…
Many teachers often spend the first days of school working with students to set norms and expectations for the year. This is very helpful because it lays the foundation for a strong classroom culture where students feel safe to learn and make mistakes along the way. This is equally important for me in my role…
If you’re a professional development provider, it can be disheartening when you think about your training’s effectiveness. The participant evaluations written at the end of your training might be glowing with your praises, but when you check in with attendees a day later, a week later, a month later, or a year later, are the…
In last week’s blog post, I mentioned how I use a metaphor of a bench presser and a spotter to explain why I want to be the “least helpful teacher possible.” When I talk to students, however, I use a slightly different metaphor about personal trainers. Students will sometimes become frustrated if they think that…
When I work with teachers, I often tell them that my goal is to be the “least helpful teacher possible.” I believe I first had this goal after watching Dan Meyer’s TED Talk. While the idea of being the “least helpful” usually elicits a few laughs, I never mean it to be funny. To better explain…
Now that you’ve read about the three steps I often follow when trying to raise a math problem’s Depth of Knowledge level, I thought it might be useful to take you through the entire thought process of actually implementing those steps. The experiences I’m describing took place while preparing with some other teachers to teach…
Have you ever believed something about your students only to find out that you were not correct? This has happened to me many times and it doesn’t feel good when the reality kicks in that you were wrong. I remember a specific instance of this happening to me as I transitioned from teacher to teacher specialist.
If you’ve ever taught students how to find the area or perimeter of a shape, you won’t be surprised to read that students commonly confuse the two measurements. For example, if you ask a student to find the perimeter of a rectangle, they will often give you the rectangle’s area. Based on my experiences, this seems to be a pretty typical outcome for all math educators.
I realize that we’ve come to accept this as normal, but have you ever thought about why it happens? Does this also happen in real life? Could this possibly be a problem of our own creation? After all, when a person is buying grass turf and fencing for their home, does that person ever get confused as to which measurement is which? I can’t imagine that happening often.
This makes me wonder about whether it’s possible that the reason students confuse area and perimeter is because we often present problems with fake contexts. As a result, the terms “area” and “perimeter” remain abstract labels rather than something attached to a relatable meaning.