EC.8. Creating Positive Early Childhood Learning Environments
Well-prepared beginning teachers of mathematics at the early childhood level create mathematical learning environments characterized by exploration, reasoning, and problem solving; they draw upon children’s mathematical, cultural, and linguistic strengths thereby developing conceptual understanding and positive mathematical identities. [Elaboration of C.4.2 and C.4.3]
Classroom learning environments provide contexts to shape the ways children experience and learn mathematics. From the visual displays on the classroom walls to the arrangement of desks and the accessibility of instructional materials, the learning environment indicates how a teacher views mathematics and what children are expected to learn and do. Well-prepared beginners understand that learning environments affect young learners' developing mathematical identities and can either support or hinder children's abilities to learn mathematics. By using classroom routines as opportunities to explore mathematics, these teachers create learning opportunities in which all children feel invited to participate. For example, when kindergartners are lined up for lunch, a teacher might facilitate an exploration of the various meanings of counting, such as ordinal numbers (e.g., first, second, third in line). Similarly, a teacher may further develop first graders’ understandings of measurement ideas by asking the children to compare the heights of those in line and order them from tallest to shortest. Second graders may be asked to examine patterns and concepts of odd and even when they consider whether every child has a partner when they form two lines. Whether children are counting out snacks to place in baggies or dividing classroom supplies for a mathematical task, well-prepared beginners learn to attend to these events to deepen young children’s learning of mathematical concepts.
Well-prepared beginners understand the role of manipulative materials in helping young learners represent mathematical concepts and communicate their thinking. They select and use a variety of manipulative materials and encourage children to use these tools to explore mathematical ideas without always telling them when and how to use the materials. Materials are easily accessible for young learners to use when they explore mathematical concepts, solve problems, and communicate their mathematical thinking for themselves and others. Well-prepared beginners also know that the type of manipulative materials and the names they give to them support children's later learning of mathematics. They use manipulatives to help young children make connections among concrete counters, number names, and symbols when children transition from play-based, real-world knowledge of quantities to formal base-ten number systems (Morin & Samelson, 2015).
Well-prepared beginners establish classroom norms that reflect their valuing of the various ways children explore and reason about mathematical situations and support young learners’ development of mathematical explanations (Yackel & Cobb, 1996). They know that language and communication patterns are functions of a person’s culture and understand that children enter classrooms speaking the language and language vernaculars used by their families and friends outside of school. These teachers treat children’s language as a resource, not a deficit, and support all children, regardless of their English proficiency, to participate in class discussions (Moschkovich, 2010). Well-prepared beginners see their roles as helping young learners connect their out-of-school communication practices with the academic and mathematical language they are expected to use in schools. They engage their children in classroom discussions and encourage children to use their existing communication patterns while they teach them the language of mathematics, including vocabulary, symbols, and materials. Consider Vignette 4.4.
Vignette 4.4. Solving 21 + 32
A class of first graders is finding the total number of stickers in two different-sized packages. One package has 21 stickers, and the other package has 32 stickers. The children can use connecting cubes, base-ten blocks, or paper and pencil to solve the problems. After the children solved the problem, the teacher, Mr. Walker, engages the class in a discussion.
Teacher: Who would like to share how they solved the problem? Rebecca?
Rebecca: I used the sticks and cubes [Points to base-ten blocks]. I got two sticks and one cube and three sticks and two cubes and put them together. Then I got 53.
Teacher: How did you know to take out 2 tens and 1 unit to equal the number 21?
Rebecca: Cause the stick is 10.
Teacher: The stick is 10 what?
Rebecca: Ten tinies. So one stick is 10, and two sticks are 20, and I needed one more to equal 21.
Teacher: Will you count the tens and ones for us?
Rebecca: [Touches each block when she counts] Ten, 20, 30, 40, 50, 51, 52, 53.
Teacher: Thank you; I see what you did now. Did anyone solve the problem a different way? Jamaal?
Jamaal: I did it in my head. I plussed 20 and 30 and got fiddy. Then I plussed the one and the two and got three. So my answer is fiddy-three.
Teacher: [Writes 53 on the board]. So let me see if I understand what you did. First you added 20 and 30 and got the sum of 50. Then you added one and two and got the sum of three. Then what did you do?
Jamaal: I plussed, I mean added, fiddy and three and got fiddy-three.
Teacher: I see, thank you for sharing.
In this exchange, Mr. Walker builds on Rebecca's and Jamaal’s everyday language and provides them with the mathematical terms to use when they communicate. Rather than correcting children when they speak, he revoices their statements using mathematical terms. More important, in the case of Jamaal, Mr. Walker realizes that he said “fiddy” instead of “fifty” but does not correct his language because he understands what Jamaal means and does not want him to feel uncomfortable in sharing his thinking. Instead Mr. Walker uses the correct mathematical pronunciation and continues the class discussion. Well-prepared beginners build on children’s mathematical, cultural, and linguistic strengths to promote the positive and mathematical dispositions of every child.