Nurturing Learning in Three- and Four-Year-Olds: Mathematical and Scientific Thinking

Preschoolers are rapidly developing the mental abilities to think in mathematical and scientific ways in order to explore and understand their favorite topics.

Topic: Mathematical and Scientific Thinking


The preschool years, ages three and four, are a busy time for young children’s minds. When given encouragement and support, they can become immersed in extensive explorations of topics that interest them. Whether it’s dinosaurs or rainbows or airplanes that capture their attention and imagination, preschoolers are rapidly developing the mental abilities to think in mathematical and scientific ways in order to explore and understand their favorite topics. Preschoolers are also seeing evidence of math and science concepts in everyday life, from laying out the right number of napkins for snack to predicting and testing the direction a ball will go when it’s kicked. In this Nurturing Learning we’ll look at the abilities that preschoolers are developing that help them think in more complex ways.


Taking Apart and Putting Together

What children are doing:

Threes and fours are playing with the concepts of parts and wholes. They are fascinated by the insides of both mechanical things and living things and how the different parts make the whole thing work. They are also gaining in their understanding of how to put many parts together to make a whole. Everything they create becomes more complex and elaborate: the structures they build, the stories they tell, and the artwork they create.


What caregivers can provide:
  • Puzzles, including floor puzzles, with a range of difficulty.
  • Building sets with a variety of parts, marble mazes, “found” materials (cardboard and wood scraps, heavy-duty tape) to build with.
  • Discarded small appliances and real tools to take them apart.
  • Books that illustrate the insides of animals, plants, buildings, machines, etc.
  • Opportunities to take apart and examine the insides of plants, seeds, etc.; tools for exploration (magnifiers, tweezers); and paper and pencils to record what they see.
  • Cooking and baking experiences, allowing children to participate in combining ingredients to make a finished dish.

What caregivers can say and do:

  • Encourage children to continue their work over multiple days by setting apart a place for continuing work to be kept where it won’t be disturbed.
  • Model and extend children’s curiosity ( “I wonder what it looks like inside. What do you think we’ll find in there? How could we find out?”).
  • Ask children to describe their thinking and decisions as they build ( “What did you do next?” “That’s interesting. What does that part do?” “What else will you need?”).

Observing Changes in Themselves

What children are doing:
Preschoolers are keenly curious about themselves. They love seeing and talking about pictures of their younger selves; they express pride in how they’ve grown and changed. This fascination with personal growth is a wonderful context in which to introduce measurement, charting, recording observations, and other math and science skills.

What caregivers can provide:

  • Tools to measure height and weight (start with non-standard ways of measuring and then introduce standard measurement tools, such as rulers, later).
  • Opportunities to record their measurements and observations.
  • Photo displays of children as babies and toddlers.
  • Children’s books, both fictional and nonfictional, that focus on growth and change in children.

What caregivers can do and say:

  • Adults put so much emphasis on getting bigger that young children, in comparing themselves to each other, put more value on being taller than others, which can result in hurt feelings for those who are on the shorter side. Emphasize that people come in all heights and weights and that what is worth getting excited about is noticing and recording their own growth over time, rather than being taller than other children.
  • Size is the most obvious aspect of growth, but help children focus on other ways that they have changed, too. Record their responses.
  • Extend children’s interest in their own growth to the growth and development of other living things. Invite children to investigate the growth of animals from babies to adults and talk about how their development is different. Encourage measuring, counting, charting, and recording.

Creating Representations

What children are doing:

  • As preschoolers get older, they become more skilled and interested in recreating accurate models of things they’ve observed. Drawing or sculpting a representation to be incorporated into a scientific exploration can actually help young children focus their attention on details they otherwise might have missed. When they are intent on drawing the insect, fish, or flower exactly the way they see it, they notice much more detail, which in turn fuels more curiosity. Even young preschoolers show an amazing level of attention, focus, and interest when representational drawing and sculpting is part of their investigation.

What caregivers can provide:

  • Drawing and painting tools that support more detailed drawing: colored pencils, fine-point markers, etc.
  • Firmer modeling clay (instead of play dough) and tools to encourage detailed sculpting.
  • An area where children can display their work without danger of being destroyed, or offer to take a photo that the child can keep, talk about, and reproduce if desired.

What caregivers can say and do:

  • Talk to children about creating models from observations and how it’s different than creating from their imagination. Consider showing examples of illustrations from children’s books that show each.
  • Talk to children as they are recreating what they see; comment on the details that the adult notices represented in their model. If children are stuck, adults can help them focus on specific parts of the animal or plant by talking about shape, line, and color to help children think of how they could be recreated.

Recognizing Numerals

What children are doing:
At some point during the preschool years, children make the connection that a particular written squiggle – “5” for example – represents an amount and corresponds to the verbal word for that amount. Since there’s nothing about the squiggle (or, more accurately, symbol) that looks like the amount it represents (there aren’t five lines or dots in the symbol “5”), children can only learn the names and symbols for each amount through lots and lots of exposure and use in the context of play and everyday activity.

What caregivers can provide:

  • Games that include written numerals.
  • Puzzles, books, charts and other materials that link written numerals with their amounts.

What caregivers can say and do:

  • Incorporate counting, verbal labels, and written symbols in everyday activity. (“How many children want strawberries on their yogurt? One, two, three four – okay ‘four’ children. Let’s write that on our chart – here’s the number ‘4’ and I’ll put four dots next to it so we can remember.”).
  • Give children models of numerals that they can refer to, but don’t be concerned about the accuracy of their early attempts. Curved and diagonal lines are difficult for little fingers to make. Children will write numerals backwards and sideways as they learn. Over time they will improve as they find meaningful ways to practice. What won’t help is a lot of correction or meaningless repetition/practice, which only makes children fearful of making a mistake and less motivated to write on their own.

Keep in mind

Scientific thinking involves making predictions about what will happen next, testing those predictions and observing the outcome, recording that outcome in some way, and telling others about what’s been discovered. Mathematical thinking includes not only knowing numerals and counting, but also creating patterns, recognizing geometric shapes, measuring, and organizing numeric information using charts and graphs. Although all of that sounds far beyond the capabilities of most preschoolers, it’s really not! Preschoolers can learn all of these skills, and will do so eagerly, if those skills are embedded in activities and explorations that are centered on children’s interests and curiosity.





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Nurturing Learning in Three- and Four-Year-Olds: Mathematical and Scientific Thinking

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