We often hear or use the phrase, “paying it forward.” This usually pertains to doing a good deed for others or a random act of kindness. We’ve been using this phrase the past couple weeks at the Manhattan Country School Farm to reflect on our gardening practices.
Our students, first and foremost are soil farmers. It’s necessary to supply new, organic matter to our vegetable gardens. The basis of preparing and building soil with a balance of nutrients each plant requires is vital in providing healthy and delicious foods for our community.
The past two weeks our 8-9’s Oeste and Este classes were at the Farm. Oeste was busy in the gardens, harvesting the last of our root crops like potatoes and carrots. They pulled weeds and fed them to our chickens and turned the soil over by hand. During meal preparation, each class added potato peels, fruit skins and egg shells to our compost bucket. When cleaning our cow stalls the kids dump the manure, old sawdust and hay into the spreader which is either broadcast on our hay fields or piled in the compost barn. The mix of animal and plant waste is then turned periodically to aid the decomposition process which creates rich organic soils.
The Este homeroom arrived with the task of adding the nutrient rich compost to the garden beds during Farming class. With the bucket of our tractor full of compost, some kids shoveled it into wheelbarrows while others dumped it into the beds and spread it around. This process continued throughout the week, seeing most of the lower garden finished. Almost every meal served at the MCS Farm has direct connections to our garden. However, this week we enjoyed an ingredient connected directly to the process of decomposition.
In September, our 5th grade class inoculated logs with oyster mushroom spores and stacked them totem style in the farmhouse basement. As the mycelium spread through the logs and began the process of breaking down the wood fibers it also “fruited” providing us with beautiful mushrooms. Wednesday evening dinner was pizza prepared by kids in cooking class. The topping choices were sweet Italian sausage made from our pigs and beautiful oyster mushrooms growing in our dark basement.
Even though every student a MCS doesn’t perform each task in the garden due to the seasonality of their trips, they do have knowledge that someone has come before them. The 9-10’s and 6th grade will do the bulk of the planting on their spring trips in May, but every member of our MCS Farm community will enjoy the fruits of all labor and our practice of paying it forward.
An important feature of an early childhood math curriculum that parents may not know about is something called subitizing, which is a large word for a very simple phenomena: the ability to recognize the number of objects simply by looking at their arrangement. If you have every rolled a pair of dice and recognized 12 pips by seeing two sets of boxcars, then you know what it feels like to subitize.
Subitizing helps us count objects quickly using familiar patterns: the first set of dots directly above is completely disorganized, so the brain cannot discern a pattern. The second card shows the dots organized, but not in a way that the brain can count easily. The third card enables us to actually carry out subitizing by seeing two distinct groups of five.
While subitizing is something that occurs in newborns, as well as primates, dolphins, birds and even amphibians, it is a fertile area to explore numerical reasoning with young children. In the Manhattan Country School Lower School math program, we do a series of three tasks that develops and explores this important concept.
The first exercise is to look at small groups of dots arranged in different patterns and instruct students to photograph and develop pictures of dots. A dot pattern is shown for a very brief amount of time, students shut their eyes to record what they’ve just seen, and then reproduce the remembered pattern using magnetic dots on a board.
This exercise stimulates provocative discussions about how we recognize quantities. Some children visualize numbers as shapes, while others see them as patterns, and these patterns take on different interpretations. A set of four dots can be seen as a square of four dots, or two sets of two vertical or horizontal dots. A group of 10 dots arranged in a triangle can be remembered as an ascending pattern of one, two, three and four dots.
In the second exercise, students are shown a number and asked to arrange the dots in patterns or shapes that can be remembered easily. Students will arrange dots as two rows of three, three rows of two, or as two sets of three dots arranged in a triangle. By putting dots into groups like this, they are exploring concepts like multiplication (in that the dots can be skip counted by two), or addition (3 + 3 = 6 dots.)
In the final exercise, students use their understanding of subitizing to play the game Compare, where they take a set of dot cards, split them into two piles and then flip them over one at a time and call “mine” if the set of dots on their card is larger than their opponent’s. The idea here is to further refine their estimation and numerical reasoning skills by comparing two sets of dots and deciding which has more. Students are discouraged from counting the dots one by one, because the activity emphasizes numerical perception, which is an important component of developing number sense.
If you’d like to know more about subitizing and it’s importance in early childhood mathematics, you could do no better than perusing Douglas Clement’s article, “Subitizing: What Is It? Why Teach It?” If you want to practice subitizing with your child at home, you need look no further than a set of dominoes or playing a board game that uses dice.