The early primary teachers at Westwind are focusing on an Innovation Grant project around developing the competency of communication in the area of mathematics. For my visit to the school last week, we focused on having the students communicate their mathematical thinking and understanding through materials, pictures, numbers and words.
In Dee-Ann Wozney’s kindergarten class, I did a demo lesson during which the other kindergarten teachers observed. After talking to Dee-Ann about what her students had been learning about, we did a short number talk involving ten frames and then I pulled the book Frog in the Bog out my bag and went with that. As I have with other classes this term, we asked the students to figure out how many critters were in the frog’s tummy. I had double ten frame mats available for the students, tubs of Unifix cubes and the students also had their math journals. We had the iPad cart in the classroom and I quickly showed an app that was familiar to the students – DoodleBuddy and how they could use that to draw to solve the problem. I introduced the ShowMe app and how they could use their voices to record how they solved the problem, accompanied by a drawing. The students made their choices and set off to solve the problem or prove their answer.
Interestingly, none of the students chose to use the blocks to model the problem. Many children chose to use the ten frames, using a different colour for each animal as I had modelled when I demonstrated how they could use DoodleBuddy. Several children drew a picture using DoodleBuddy – often of the frogs tummy with dots for the critters inside. Many children used ShowMe, with a few changing to another way to represent. It is difficult to be thinking about how to use a new app and solve a problem at the same time! One student drew ten frames as a model in her math journal and then recorded the number sentence for adding up the number of critters using numbers and symbols. Such range and variety in one kindergarten class!
We came together to show and share our mathematical thinking and the students were proud to show their different representations. What the teachers noticed is that most of the students had difficulty sharing their thinking orally. After a few students had shared, we stopped and asked the students to turn and talk to a partner so that they had a chance to orally rehearse what they would share. In our debrief after the lesson, the teachers felt the students might need some thinking frames modelled and practiced such as “I used….because” and “This helped me to think about the problem by…” to focus on process and metacognition. By having students share the different ways they solved the problem and thought about the mathematics also helps the class as a community build a repertoire of problem solving strategies, models and approaches.
In Erin Stapleton’s grade 1 class, I did a demo lesson on linear measurement, with a focus on communication. Another grade 1 teacher was able to also be in the class. I spent several minutes at the beginning of our time together looking at some of the illustrations from the picture book Actual Size by Steve Jenkins. We compared our eyes to the squid’s eye and our hands to the gorilla’s hand. The focus of this group time together was language development. I introduced terms like baseline, comparing, difference and the different terms we use when comparing horizontal length (long, short) versus vertical height (tall, short). The term difference was difficult for the students. When looking at the gorilla’s hand in comparison to the classroom special helper’s hand, I posed the question – how could we figure out the difference in size? A few of the students shared ideas about ways to measure the two hands but didn’t quite get at how to compare those measurements. We would re-visit that concept later in a more hands-on way.
To begin our measuring, I brought along a tub of “snakes” and a nesting set of owl dolls. I used them to line up along a baseline with other objects to compare which were longer, shorter, taller, etc. The students then chose and object and were tasked with finding something longer or taller and something shorter. The students use the iPads to take photographs and then the app PicCollage to compile and label their photographs.
As the students completed their PicCollage and put the iPads away, the next task they focused on was going back to two of their objects and finding the difference in their lengths/heights. The students recorded their observations using pictures and words with some starting to use numbers related to measuring as well.
Part way through the “finding the difference” challenge, the teachers and I realized the students were just developing an understanding of this concept so we paused and I used one student’s objects to coach the students through how they might find the difference. By measuring the height of the water bottle and owl doll with Unifix cubes, we could then line up the two towers of Unifix cubes side by side and see what the difference was, or how many more cubes taller the water bottle was than the owl.
The students were then able to continue on with this challenging task. We came together at the end of our two blocks of time together to show and share our findings. The students shared how they used drawings, often labelled, and words to show the measurements. Some of the students began to construct written sentences, using the language of measurement that we had been orally practicing during the lesson.
In both classes, the students were engaged in mathematical thinking during complex tasks for their ages and had many opportunities for talking about mathematics and showing and sharing their thinking and understanding.