IM Certified® Blog
Why is 3 – 5 = 3 + (-5)?
By William McCallum You will never have to subtract again. Students sometimes learn about addition and subtraction of integers using integer chips. These are circular chips, with a yellow chip representing +1 and a red chip representing -1. You start with the...
Professional Learning Through a Fraction Task Progression
Teaching mathematics is a continuous cycle of identifying where each student is in their learning trajectory and determining meaningful ways in which to build on their current understandings. While we often have little control over students’...
Engaging All Students in Meaningful Mathematics
“At the end of the day, this wasn’t about focusing on the objective, it was about making the objective meaningful to him.” The work of teaching is both invigorating and challenging. We want to instill a love of math and learning in every student, and ensure that each...
Parent Math Night Using Illustrative Mathematics
Open House night; cue anxiety and sweaty palms! Hope my students’ parents don’t mind. I just began my seventh year of teaching middle school mathematics. Middle school is a limbo land filled with prepubescent pre-teens, drama, and students trying to find their...
Planning for Meaningful Practice
There is no shortage of available math resources for teachers to use in their classrooms. The difficult and time-consuming job for teachers is weeding through all of the tools to decide which best supports students in learning mathematics. It is a difficult job...
Say What You Mean and Mean What You Say
By William McCallum In one of our professional development workshops, there is an activity in which the facilitator asks teachers to skip count by $\frac34$. The facilitator records the count, $\frac34$, $\frac64$, $\frac94$, . . . and then asks for patterns they...
What Is Right About Wrong Answers?
When I first started teaching, at the end of each day, I would open my teacher’s guide, grab my pen, and thumb through the stack of completed worksheets. My eyes would dart quickly from the red answers in the teacher’s guide to the corresponding answers on each...
What I Learned Today: Scale Drawings & Maps
I asked my 15-year-old what she learned today at school. She paused for a moment and then answered, “What did you learn at school today?” It took me a while to think about what I had learned (which will make me more patient when I ask her again tomorrow), and then I...
The IM Curriculum Changed How I Think About Math Instruction
Growing up we usually think we are either a math person or not a math person. But, in preparing for this year I saw a picture that said ‘How to be a math person: Step 1: Do math Step 2: Be a person’ and I really started to look at math differently. I’ve been teaching...
Planning to Use Pre-Unit Assessments
Time to start a new unit! What do you need to know before your students enter the room? NCTM’s Principles to Actions names several productive beliefs about assessments that will promote mathematical success for all. At the top of the list is that the “primary purpose...
