Mathematical concepts and activities for early childhood
When we think about math we often think about numbers. Yet, mathematical thinking for young children has a completely
different meaning. Children naturally use an array of concepts and skills that enable them to see, as well as to process and
organize relationships and connections among different elements in the world (McWhorter — Colvin, 1996). Mathematical
concepts, such as comparing, measuring, and patterning help children understand phenomenon, solve real life problems,
appreciate design, and make predictions about the future. In this context math should definitely be something that is enjoyed
by young children.
As children come to understand mathematical relationships in a quantitative manner, which involves numbers and formal
operations (such as adding, subtracting, multiplying, and dividing), they need many opportunities to think and make
qualitative judgment about the world around them using the following concepts:
Classifying: sorting into groups by discovering likeness and differences (from strong contrast to subtle differences).
Take advantage of real life opportunities to sort objects; e.g. clean up time, sorting laundry. Create sorting games: sorting
stones collections by color, sorting cars by size. "How else can we sort these?" Involve children in decisions about
classification: "Are these farm or wild animals?" "Are these reptiles or mammals?" "Is a whale a fish?"
Ordering: arranging in a sequence by size, amount, or time (from a few objects to many).
Ask questions such as: "Which one comes first, second, third?" "Why" "Which one is the longest, shortest, heaviest?" "How
can you tell?"
Patterning: a form of ordering that contains an element of repetition (from becoming aware of patterns to extending and
then creating patterns).
Focus children's attention on patterns in daily routines, songs, rhymes, artwork, nature (night and day, seasons, snail spiral,
zebra's stripes). Encourage children to notice and describe patterns in the world, extend dialogue about patterns, translate and
identify relationships among objects and phenomena. Is there repetition? Does this geometrical pattern symmerical? Extend
children's thinking by asking to predict how the pattern will evolve (will it change?). Ask children to make up a pattern.
Shape and space: understanding positions, distances, boundaries, and recognition of form (from experimenting with space
and shape to planning a structure).
Allow children to explore the environment and use vocabulary that relates to child's or object's position in the space: up,
down, above, under, behind, in front. Provide puzzles with varied degrees of difficulty. Help identify, name, and compare
shapes through games, books, and objects in the environment. Explore properties of regular (circle, triangle, etc.) and
irregular shapes. "Which shape has pointy edges?" "How many sides does it have?" Round things roll, squares don't —
"Why?". Provide building materials and ask about balance, strength, and design of structures.
Non-standard Measurement: compare length, weight, volume (from direct comparison side by side to using non-standard
tools and estimation).
Start with simple comparisons of less than and more than, as big as my hand, as tall as the teacher by direct comparison.
Provide non-standard measuring tools to extend children's interest in measuring. They can measure their height by using
blocks, a string, or tape. Involve children in making decision about measurement: "How long do you think it will last?" "How
much should I add?" "Is this bowl big enough?"
Counting and naming numbers: counting by rote, counting objects, recognizing numerals. Play rhyming games with
numbers. Play age appropriate board games. Ask questions or make suggestions that make children think numerically and
make qualitative judgment: "Did you get as many as I did?" "Count again and see if you get the same number!" Encourage
children to count in a meaningful context. "Do we have enough cups for everyone?" "Count how many trucks you take
outside so that you will know how many to bring back." Counting can help solve a conflict if the dispute is about who has
more. Ask children to figure out how many children are missing, how many sit around the table, etc.
http://earlychildhood.educ.ubc.ca/community/research-practice-mathematical-thinking-early-years