This blog post is the third in a series of four blog posts exploring the student experience of problem-based learning. The first two posts are available here: “How Do Students Perceive Problem-Based Learning?” and “Inviting Students to the Mathematics.”
Once students have an invitation to the mathematics and understand the situation, how do they get started answering questions?
Continue reading “Concrete Representations that Give Students a Way to Get Started”
How do we invite students to the mathematics, and explicitly signal to kids that they have ideas that matter in math class?
In this series of blog posts, the first of which is available here, we’re exploring how, in order to be successful in a problem-based classroom, students have to shift their thinking about what being a good math student looks and sounds like. What do you notice about your own students’ beliefs about how they should participate? What are you curious about now, as you think about what it takes for students to be successful in a problem-based classroom?
Continue reading “Inviting Students to the Mathematics”
Does problem-based learning mean students need to forget everything they knew about how to act in math class?
As a teacher, and then as a coach and teacher-educator, I’ve been thinking for a long time about the shifts teachers need to make when using a problem-based curriculum like the IM Math curricula. Recently, though, I’ve gotten to be in classrooms not as a coach or a teacher, but just to observe. Sitting with the students, experiencing math class from their perspective, I’ve been reflecting a lot on the demands placed on them as learners in a problem-based setting.
Continue reading “How Do Students Perceive Problem-Based Learning?”
Linda Richard, Curriculum Writer
I used to teach my students a catchy song to memorize the distance formula. We all had fun goofily singing this song. My students hummed it to themselves during tests and successfully calculated distances. I was pleased with this outcome—but what did my students actually understand about distance in the coordinate plane? In retrospect, very little.
Continue reading “Making Sense of Distance in the Coordinate Plane”
Illustrative Mathematics
It was great to see so many of you at NCSM and NCTM in San Diego. If we missed you, or you weren’t able to attend, read our NCSM and NCTM round-up below.
Kristin Umland,VP Content Development
A great conversation I had with the IM elementary school curriculum writing team got me thinking: What is a measurable attribute? That is, when given an object, what can we measure about it? Before you jump in with your own answer, consider these questions:
Is “redness” a measurable attribute? Why or why not? Does this picture help you decide?
Kate Nowak, Director of 6-12 Curriculum
When I was teaching high school mathematics, my local colleagues and I spent a whole lot of time creating problem-based lessons. We were convinced that this style of instruction was a good way to learn, but the textbooks in use at our school simply contained definitions and theorems, worked examples, and practice problems. One day I was talking to my dad about how much time I had been spending lesson planning. His response was, “People have been teaching geometry for, what, 3,000 years? Shouldn’t the lessons be, like, already planned?”
Continue reading “Presenting IM Algebra 1, Geometry, Algebra 2”
By Greta Anderson & Patti Drawdy, IM Certified Facilitator
I read the lesson three times through, but was still unsure why the number line below shows $3 – 7$. My aha moment arrived courtesy of the grade 1 standards.
By William McCallum
When I was a child, I used to get puzzle books out of the library. One of the puzzles was the twelve-coin problem, the most difficult of all coin weighing problems. My mother and I worked on it separately at the same time, and she solved it first. Some time later that evening she came into my room to find me in tears of frustration. Instead of helping me, she asked: “Do you want me to tell you the solution?” I said no and she left. I will never forget the joy when I finally figured it out.
