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Learning Moments CD - Early Mathematical Thinking

ITEM #: 5500348

These CDs can be used on PC or Mac platform.

Permission is granted for use of the CD by one individual program director, trainer, or college educator presenting the material in an in-person setting.

For use online or by multiple individuals in one organization (including large early childhood organizations, colleges, and other training institutions), please email requests to [email protected].

This Learning Moments CD (for use on a computer) presents 10 real-life video files that are the perfect compliment to workshops, lectures, and online courses on how young children spontaneously engage in mathematical thinking and learn by investigating and pursuing early math concepts during play. The clips include children from one to five years of age.

Young children spontaneously pursue mathematical interests and questions during everyday play. It is important to understand that children are intrinsically motivated to explore mathematical concepts well before entering formal education. By understanding the mathematical problems that capture young children’s interest we are better able to create learning experiences that build upon and extend children’s developing mathematical knowledge.
In the 10 clips on this CD, you will observe:

  • How a 21-month-old child’s instinctual interest in establishing one-to-one correspondence and creating a relationship between two different kinds of objects is an early form of logic and a precursor to math.
  • How toddlers engage in size estimations and enjoy testing limits by creating conditions where one object very nearly fits inside another.
  • How preschoolers reveal their understanding of counting principles, what numbers mean, and their emerging strategies for counting effectively during an invented game with tiles.
  • How young preschoolers define a sorting rule, classify objects, and discriminate objects that are simultaneously similar and different while working to sort a collection of materials.
  • How preschoolers define the phrase, “How tall I am,” use their world knowledge to measure more accurately, decide what types of numbers make sense when measuring a person’s height, and find a concrete way to confirm the equivalence of their height.
  • How a group of pre-kindergarten children investigate the relationship between slope and interval by rolling a ball down ramps, lined with wind chimes spaced apart.
  • How two four-year-old children carefully apply their incomplete knowledge of the conventional number sequence, and the principle of one-to-one correspondence, while counting approximately 40 seeds, and the strategy they use when they are unable to recall what number comes after 29 in the counting sequence.
  • How two four-year-old boys explore mathematical concepts by counting small sets of blocks and then combining them to double the count.
  • How two five-year-old boys work to make a length of string taut, from the table to the floor, so imaginary animals can safely slide down. How the children are enticed to persist in their efforts by a string that is just barely too short, and how the children ultimately manage their problem.
  • How a five-year-old boy is surprised when unequal weights can balance, and how he investigates this unexpected scenario.

Table of Contents

  • Introduction
  • A Clothespin for Every Side " Math at 21 Months
    Runtime 2:00
    What materials in your classroom promote logical-mathematical learning by supporting the young child’s intrinsic motivation to construct relationships between and among objects?
  • Too Big
    Runtime 1:10
    What other materials could support children’s investigation of things that appear to fit but don’t quite? In what other ways might you invite children to explore the threshold of limits such as maximum and minimum?
  • Pajama Count
    Runtime 2:07
    What do you make of the fact that the boys are not surprised that their individual counts of the same tiles yield such widely different numbers?
  • Sorting by Size
    Runtime 4:19
    The children successfully differentiate small and large objects. In what ways might you encourage them to sort medium objects, and thereby consider the two-way relationship between objects that are smaller than “large” and bigger than “small”? What could you do to invite the children to add additional attributes to their sorting rules (small heavy circle)?
  • Measuring Tape
    Runtime 3:17
    In what other ways could you invite the children to measure and compare the sizes of objects? What would you do to extend the children’s understandings about units of measurement, and the relationship of numbers to length and height?
  • The Sound of Slope and Speed
    Runtime 4:41
    If the children create songs of equal speed, can we then assume that they understand this pattern (song) is a combination of two variables? Given that it was difficult for the children to compare the two songs, how could you use a computer to improve this investigation? Or, in what ways could you help the children create a record of the speed and rhythm to better judge the differences?
  • Counting " Stuck in the 20s
    Runtime 4:53
    Ethan shows he is able to reflect on his own thinking when he says, “I don’t know how to finish, so I just did it again, and again, and again.” Verbalizing a problem helps to bring it to a conscious level for the group. What would you do to help support the children’s efforts to count effectively? And why?
  • Math " Combining Sets
    Runtime 4:18
    Speculate on the good reasons children have even when making a mistake.
  • A String Too Short
    Runtime 5:21
    Discuss the geometric concepts needed to solve the conflict between the angle of the string and its ultimate length. Speculate on what Henry understands, in addition to his memory of having anchored it once that causes him to persist with the original string. Comment on the children's knowledge of steep and shallow slopes, i.e. early geometry.
  • Unequal Weights Can Balance
    Runtime 2:30
    Do you think this set-up can teach the boy something new about fulcrums, or is it more likely to confuse him about how a balance beam works (such as knowing how a light­weight girl can see-saw with a heavier boy by sliding back on her side of the see saw)? Would you give the child a different set-up the next day? What new set up might make sense?
  • Appendix

The Learning Moments Series is produced by Videatives, Inc.