Kindergarten students are amazing. They begin school at the age of three or four, and by the time they graduate two years later, they can read, write, count, tell you stories and the names of shapes. When doing simple repeating patterns, though, our kindergarten teacher wondered if there was a way to help the students create something more complex than the simple ABAB patterns she always seemed to get. By circumventing the mathematics and teaching patterning through the arts, we managed to do just that. Through the processes of creating and discovering, our kindergarten students not only created complex patterns, but patterns of complexity that were beautiful and pleasing to see, do, and hear.
In kindergarten, “early learning experiences have a profound effect on their [students’] development. These early interactions directly affect the way connections are made in the brain.” (Queen’s Printer, 2006, p.1) Providing open-ended problems and activities for students to experience, think about, and enjoy, sets up these very young children for success in their future learning. We did not want to have an activity that showed an example and encouraged copying or a closed set of ‘correct’ responses. We wanted to provide a series of experiences that would let the kindergarten students be able to create and understand patterns that were more complex than simple ABAB repeating patterns. The methods we developed to address this problem were to have the students create patterns through music that they could play on an instrument and sing with their classmates. These songs then became the basis for a dance and a work of visual art. Through this the students gained a robust idea of the nature of repeating patterns and familiarity with the role of a pattern core in the creation of patterns.
Through the kindergarten years, the mathematics of patterning that the students need to know is, on the surface, seemingly straightforward. Students need to be able to:
identify, extend, reproduce, and create repeating patterns through investigation
identify and describe informally the repeating nature of patterns in everyday contexts
Three key ideas in these curriculum expectations guided us in how we wanted to try teaching pattern. Investigation, everyday contexts and creation of patterns. How we approached the learning that we wanted the students to have is to literally reverse the order of how we would usually approach teaching a new concept. Instead of starting at the lowest level of identification and moving through extension, reproduction, and finally arriving at creation, we started with creation. Putting this creation into the everyday context of music, dance and visual art allowed us to let the students creatively investigate repeating patterns.
The kindergarteners were presented with an Orff xylophone with only four tone bars [left] chosen from the pentatonic scale [see sidebar]. On each tone bar, we placed one each of a green, red, yellow and blue sticker. These would become the names of the notes. The students were split into three groups and sent to a xylophone. An adult at each xylophone facilitated the creation of a short phrase that each student played on the instrument while the other members sang along. Repeating this phrase made a song that was easily remembered by each creator.
Once all of the students in a group had created, played and sung a song, we introduced 4-colour foam mats [right]. The students were invited to dance to each others’ songs hopping from colour to colour as indicated by their songs. The creator played the xylophone, one volunteer danced, and the rest of the group sang along.
The whole class was brought together and a few of the students’ songs were shared with the whole group. Again the leader played, a volunteer danced and everyone else sang. The students were firmly situated in the role of creators having made a song and dance from a repeated pattern. Few of the students’ songs used only two notes (pattern elements), and of those some varied from a simple ABAB pattern by using different rhythms such as AA B, AA, B.
The role of the teacher throughout these math and art experiences was that of a facilitator and guide. A conscious effort was made to talk less, but to question more, replacing closed instructions with open guidelines as much as possible. When facilitating, the teacher encouraged students to talk about what they were creating, to tell the members of their group how to sing their songs. Through these small group as well as large group discussions, the students were asked to think critically about what it was that made up their songs. During this process, they decided that the core of their songs, the pattern core, should be called ‘the repeating part.’
The students were guided to create a record of their songs using long strips of chart grid paper and different coloured bingo dabbers. [above & left] These were to become the basis of a work of visual art that reinforced the concept of a pattern core.
Reinforcing the Core Concept
With the records of their music firmly in hand, the students shared their songs and dances. The idea that we can record and reproduce patterns of music and dance came easily to the students. Next we asked them to use these strips of patterns to create a work of art [left]. The students cut apart their patterns at the pattern core. These parts were then glued to construction paper in a way that reinforced further the idea that the ‘repeating part’ was the core of their pattern.
The pattern art was sent home to share with the parents. The students were asked to explain their patterns and what they had learned, and the parents were invited to give feedback on their child’s learning. The responses indicated that the students’ sharing ranged from a simple retell to parents and children making connections to other mathematics.
“She shared with me that she learned today how to make patterns from her math learning activity. Today they cut strips of three boxes and with bingo dabbers she painted it in the same sequence and pasted it on the orange paper.”
Using language relating to pattern
“Our daughter clearly understands the work done here. She use the word ‘pattern’ to describe this work and also explain different patterns using colours, shapes, and numbers.”
Making connections to arithmetic
“We learned from this activity. The pattern had a rule such as multiplication or addition. Multiplication is hard to my children [sic]. She understood addition.”
Making a video documentary
We decided that we would make a documentary of the teaching and learning we had done in order to show what kindergarten students are capable of achieving in mathematics. and to showcase some of the mathematics that the children performed as a song and dance. We entered our video into the Mathematics Performance Festival [mathfest.ca] so that it could be shared with a wide audience.
Implications for Practice
The kindergarten students demonstrated that they could indeed learn through investigation, and creation of mathematics through the arts. The patterns that they created were all different and most took forms more complex than a simple ABAB repetition. Through this creation of music dance and art, the students “discovered” the concept of the pattern core and were able to easily identify the ‘repeating parts’ of their own and their peers’ work. Clearly this is an effective method to teach mathematics in the kindergarten environment.
We now know that teaching mathematics through the arts in a way that highlights the everyday context of patterns is a viable proposition. In fact, we suspect that it is even more effective than traditional methods using linking cubes and other mathematics manipulatives. We wonder if the kindergarten students will retain the concept of the pattern core into grade one where they will be introduced formally to this concept. We also wonder if the creation of the video documentary of our learning might not have engaged parents even more into the learning of their children if we had not had to publish it to the Internet near the end of the school year. How might the conversations at home, around the dinner table, have turned to what they had learned in math today, and how much fun they had creating beautiful mathematics through song, dance, and visual arts? How might this, then, enhance the mathematical learning of the kindergarten students when they had mathematics worth talking about to their parents?