I have the best job! Part of my professional portfolio is facilitating professional learning in mathematics. I work alongside amazing teachers who are willing to take pedagogical risks and try new approaches. These amazing educators are as concerned with ensuring that fundamental concepts are deeply learned as they are concerned that we are building mathematical agency in our students. The desire is that our classrooms are places of learning where girls say: I can do this; This struggle is good; Mistakes help me move towards understanding; I am flexible; Your thinking will help me with my thinking; I am a listener; I am a collaborator; I am NOT a denominator! (yes, this requires some explanation…read to the end of this blog post)
Our Grade 4, 5 and 6 classes are all exploring fractions. In Grade 4 and 5, students were able to name the parts of a fraction with ease – especially when the whole was pizza or a chocolate bar!
Misconceptions started to reveal themselves when students were challenged to explain the meaning of fractions. I mean, what exactly is the denominator anyways? The bottom number? There must be more to it than that! And the numerator? Always smaller than the denominator and always on top. Always smaller? Can you prove that? Students knew the names but they did NOT understand the meaning.
In order to get to rich learning for students, teachers at our school design their lessons according to an understanding by design framework (UbD). Further, I am a four-part math lesson kind of teacher and it is my experience that 4-part lessons lend themselves to deep learning. The kind of learning where students can confidently name the learning goal of the lesson at the end of the period(s). You can read more about the 4-Part Math Lesson from Kyle Pearce.
The design of the lesson was important. The plan was critical. How could I move girls in their understanding of fractions? How would I set the stage? How could I lead them into deeper learning? How will I know what they now know? And lastly, how will students assess their own core competencies (Collaboration and Communication)?
You can check out the lesson plan here. I used Van de Walle’s resource, Teaching Student-Centred Mathematics: Developmentally Appropriate Instruction for Grades 3 – 5, to help lay out a path and set the questions to present to our students. I love this resource and it is a “go-to” for me whenever I am beginning to lay out a UbD plan.
Something really interesting happened in this lesson. The core competencies and the big idea (denominator is a divisor) came together in an unexpected way. When I use the word denominator, I ask students to accompany the word with an action. For denominator: students stand, bend low, form a two-fisted arm flex and say loudly in a low voice: DENOMINATOR!!! (Check out the Blue Power Ranger for a visual with this :))
After we had established that the denominator acts as a divisor – divides up the whole into parts – students quickly connected that our core competency learning goals (collaborate and communicate) would NOT happen if people acted like a denominator in their small groups. This was a significant light-bulb moment! And, I think that it will stick! We are on the road to deeper learning and enduring understanding. Who would have thought that learning about fractions would lead us to life lessons along the way?