Teaching Young Learners with the Ohio Early Mathematics

Teaching Young Learners with the Ohio Early Mathematics Standards in Mind Module Three Sponsored by the Ohio Department of Jobs & Family Services in collaboration with the Ohio Department of Education

Module 3: Overview of Session n n How do children develop geometric reasoning through play? What kinds of activities are developmentally appropriate for exploring measurement & data analysis?

Building Geometric Reasoning What are students learning by interacting with each of these center activities? (Backmapping) How would you adjust the activities for young learners?

Levels of Geometric Thinking n Level 0: Visualization • Recognizing and naming figures and shapes n Level 1: Analysis • Describing attributes of figures and shapes n Level 2: Informal deduction n Level 3: Deduction n Level 4: Rigor

Van Hiele Model of Geometric Reasoning n n Students need MANY experiences sorting materials AND explaining to others why they sorted the way they did Experience/play enables students to move through the levels

Geometry Standards Age 3 n n Begins to match and name 2 D and 3 D shapes, first only with same size and orientation, then shapes that differ in size and orientation Age 6 n n Uses shapes separately to create pictures n n Describes object locations with spatial words s. a. under/behind and builds simple “maps” with toys such as houses, cars, and trees Box n Recognizes and names a variety of 2 D & 3 D figures in any orientation Describes basic features of shapes (e. g. , number of sides or angles) Makes a picture by combining shapes Builds, draws, or follows simple maps of familiar places such as the classroom or playground

Measurement n n How do children learn about measurement in your classroom? What does measurement mean for a young learner? How do your preschool children learn about measurement through their spontaneous play and investigation? How can you focus on measurement as an intentional teacher?

Measurement Activity Estimating and measuring with non-standard (and standard) units of measure

Measurement Standards n n Age 3 Recognizes and labels measurable attributes n Begins to compare and sort according to attributes n Age 6 Tries various processes and units for measurement and begins to notice results of different methods Uses nonstandard measuring tools

Wrap-up n Given all that we have discussed and all that we experienced … • How would you define “mathematical competence” in your preschool learner? • How do we help develop these competencies through our interactions with these young learners?

Mathematical competence (National Research Council, 2001) 1. Conceptual understanding 2. Procedural fluency 3. Strategic competence 4. Adaptive reasoning 5. Productive dispositions