Little Kids – Powerful Problem Solvers:
Math Stories from a Kindergarten Classroom
By Angela Giglio Andrews and Paul R. Trafton
Washington, DC: NAEYC, 2002
www.naeyc.org
This book discusses “ the daily intricacies of launching kindergarteners on a life of what they call mathematical sense making”. They “provide a mathematically rich environment and classroom climate and challenge the children to solve the mathematical problems around them”
Children learn and use intellectual dispositions, including “making sense of experience and observations, estimating, predicting, hypothesizing, analyzing, and applying a variety of mathematical concepts.”
Children assist as well as challenge one another. Children sometimes refer to their experiences as “hard fun”. “Mathematics allows us to generalize beyond the seen to the unseen”.
The book “celebrates the mathematical capabilities and achievements of kindergarten children” and shows what they can do in “a mathematically rich classroom.”
Little Kids – Powerful Problem Solvers
Most students enter school confident in their own abilities and they are curious and eager to learn more about numbers and math objects. They make sense of the world by reasoning and problem solving and teachers must recognize that young students can think in sophisticated ways. Young students are active resourceful individuals who can construct, modify, and integrate ideas by interacting with the physical world and with peers and adults. They make connections that clarify and extend their knowledge, thus adding new meaning to past experiences. They learn by talking about what they are thinking and doing and by collaborating and sharing their ideas. - Principles and Standards for School Mathematics
September – Which Holds More
Teachers should guide student’s experiences by making the resources available, Planning opportunities to measure and encouraging student to explain the results of their actions.
October – The Dilemma of Sharing Cookies
The challenge at this level is to build on children’s innate problem-solving inclinations and to preserve and encourage a disposition that values problem solving.
November – It’s not Fair – They’ve got more blocks
There is great potential for geometric thinking and learning in working with unit blocks.
Representing ideas and connecting the representation to math lies at the heart of understanding math.
December – When is a Triangle, not a Triangle
Geometry can involve exploring ideas and learning about shapes as the children work with attribute blocks, pattern blocks and geoboards.
Language is a very powerful tool and should be used to foster the learning of math.
January – Soup with Chicken Inside
Through their investigations, young students should develop the idea that data, charts and graphs give information. They can be powerful learning tools. Devote at least 2x the time to analyze as to make the graph.
February – The Secret of the Hearts
The 100th Day of School allows teachers to highlight 100 as an important benchmark number.
March – Ms. McGill’s Challenge
When students compute with strategies they invent or choose because they are meaningful, their learning tends to be robust; they are able to remember and apply their knowledge.
April – Aaron and the Tall Tower
By learning problem solving in math, students should acquire ways of thinking, habits of persistence and curiosity and confidence in unfamiliar situations that will serve them will outside the math classroom.
May – “Dear Bus Barn”
Young students can engage in substantive problem solving and in doing so develop basic skills, higher order thinking skills and problem solving strategies.
June – Revisiting the Rice Table
By allowing time for thinking, believing that young students can solve problems, listening carefully to their explanations, and structuring an environment that values the work that students do, teachers promote problem solving and help students make strategies explicit.