Uncovering Math Using Observational Drawing

 "When we as teachers are purposeful about bringing nature into our classrooms, we create opportunities for curiosity, questioning, observation, collecting and analyzing information."

(Nenia & Clucas Walter, pg. 8)

I recently read the article 'Exploring Nature Indoors with Observational Drawing and Scientific Thinking' by Kendra Nenia and Melissa Clucas Walter in the Fall 2021issue of Teaching Young Children. In it the authors discuss the many literacy benefits for children who carefully observe and draw objects from nature. As I was reading I was also considering the rich mathematical wonderings and connections that observational drawing can offer children. 

Observational drawing is when children draw what they see. If they are observing and exploring a natural object they are creating a realistic portrayal of the object in a drawn format. Children can sketch black and white representations using only pencil or marker, or draw their outlines first and then add colourful details after. 

       

As children explore ask them to consider what they see. Use varied questions to prompt a deeper exploration of the object including:

• What shape is this object?
• What size is this object?
• What textures do they feel when they handle the object?
• How heavy/light is the object?
  
• Are there any patterns on the object?
• What colours can be seen on the object?
• Does sunlight or artificial light affect the object? 
• Are there any shadows created on the object when it's placed in the light?
• What contours can be observed? 
• Of what does this object remind you?
  

Ask children to consider how they can draw the object in order to highlight their observations and ensure they are represented. What other drawing tools can be used to help in this artistic representation (e.g., pastels, watercolours)? What math is uncovered in this process? Engaging in supportive discussions with children throughout the drawing can help them to 'notice and name' the math they see. Educators can enhance this mathematical understanding by scaffolding the conversation and highlighting additional math concepts (e.g., proportional reasoning, perspective, reflections, symmetry) and encouraging children to include these in their drawings.

Once a child is satisfied with his or her drawing, encourage the child to represent the object in another way using a different artistic medium such as clay, Plasticine or wire.

When we tried observational drawing we first examined and drew a small pumpkin.

               

We also explored dried hydrangeas from the garden.

      

As children draw, ask them to look back and forth between their drawing and the object to ensure they are including any interesting nuances that will help give character to their artwork. Remind children that there is no right or wrong way to create art, and that repeated practice over time (even with the same object) helps us to refine our skills. Observational drawing should not be rushed. Encourage children who might become fatigued or frustrated to take a break from their work - they can tuck their object and drawing away and return to it when they feel inspired again.  

 

The interest in observational drawing in our classroom continued as the children became curious about some different leaves that had been collected and donated to our science table. Notice how the children became comfortable drawing the object using pencil first, and then added additional colourful details to show the shapes, lines, and patterns they saw.

Once children are satisfied with their drawings encourage them to share these with their peers. Children can reflect upon their experience - How did their mistakes help them to learn and improve their work? What did they enjoy about the experience? What might they do differently next time? How might children like to display their work? Sometimes children enjoy gifting their art to others, or displaying it in a public space like the school library. These drawings can be added near the shelf where books about nature are housed. Perhaps children will be inspired to create a documentation display to share the process of their observational drawing, and the final pieces, with others in the school or community. 

 

Observational drawing is an incredibly rich artistic experience that is infused with science, literacy and math. As each season brings new treasures, it can be revisited over and over throughout the school year.

Autumn Math Walk

 “I'm so glad I live in a world where there are Octobers.”
― L. M. Montgomery, Anne of Green Gables 

What a beautiful time of year it is in Southern Ontario! We have been spending much time outside each school day exploring the changes in our school yard. The children are curious about the world around them and ask many questions about their surroundings and the autumn treasures they find. Many of their wonderings have been mathematical in nature - Why is there a pattern on the sunflower's seed head? What are those holes in the stump and where did it come from? Why is a Daddy Long Legs an arachnid and not a spider?  How do leaves change colours? Why are the clouds moving so fast in the sky?

There is math everywhere. If one looks deeply enough, there is always a mathematical connection in nature. The sunflower seeds follow the Fibonacci Sequence - a numerical pattern meant to help maximize space and fit as many seeds into the head as possible. The perfect little circles in the stump might have been caused by a wood boring insect or bird looking deep into the bark for food. Daddy Long Legs have a different body than spiders even though they have eight legs. Leaves change colour because the amount of sunlight they need to create their own food lessens in cold weather (as the Earth's axis tilts us away from the sun), resulting in a chemical change in the leaves. 

I've been motivated to continue to look for rich mathematical wonderings and opportunities for inquiry each time I'm outside - even on the weekend with my own children. I find it fascinating to see math applied in an authentic, interesting, real world connection. The math in nature is beautiful! Inspired by this mathematical beauty I have written a book called Autumn Math Walk that includes photos and narrative to help readers delve deeply into exploring math in the outside world. I've appreciated the interest in this book and loved seeing the ways educators have used the text in their classrooms. Learning from one another is so inspiring!

 

    

I'm so very excited to partner with Pembroke Publishers and offer a free teaching resource to complement my book Autumn Math Walk!

Autumn Math Walk Teacher's Guide is a free resource that can help educators understand the math that exists in the natural world, and use this information to provoke conversation and understand with children as they explore nature. Perhaps children will be inspired to author and illustrate their own Autumn Math Walk book unique to their specific surroundings!

Pumpkin Math

Autumn is such a wonderful time of year! The colours and textures can inspire such rich math conversation! This past weekend we visited a few farm stands in the area and all I saw was math around me! I'm hoping that these photos will be useful as math prompts for 'math talk' conversations with children.

Show children a photo and ask them to share what they 'see, think and wonder' about each photo. The 'see, think, wonder' thinking routine can be used to help children delve more deeply into exploring and articulating what they notice in a specific situation. As children notice and name what they see, they can make connections to their own experiences and ideas, and form questions for further exploration and math research. 

Educators can also ask children specific math questions to guide their thinking. This can be especially helpful if the math concepts in the photos are geared towards an existing exploration the children are having, or if specific curriculum and assessment investigations are needed by the children. Sample math questions are provided below!

How many bumps are on this pumpkin?

 How big around is the stem?

What patterns do you notice?

How are these gourds organized?

What other ways can you sort the objects?

How many do you think are in each bushel? How do you know? 

 

What patterns do you see?

Why is the pumpkin more narrow at the top?

How big around might this be in the largest part?  

How many pumpkins do you estimate are in this box?

How many pumpkins might fit in the box if it was filled to the top?

How much money do you think the farmer should charge for the entire box of pumpkins? Why?

If these pumpkins are $3.50 each, how much would all of these cost? 

Should bigger pumpkins cost more than smaller ones? Why?

Which do you think is the biggest? How do you know?

 

Which pumpkin would you pick if you only had $2? Why? 

If you had X dollars, how many pumpkins could you buy?

How much money do all these pumpkins cost altogether?

What symmetry do you notice?

What patterns do you see?

How many pumpkins would a full crate hold?
 

Which gourd does not belong? Why?

How could you sort these? What's your sorting rule?

How many gourds do you think are in this bushel?

 

Halloween Math uses the 'see, think, wonder' thinking routine to explore seasonal objects and experiences in a mathematical context and is now available from Amazon!