**ERIC Number:**EJ1156937

**Record Type:**Journal

**Publication Date:**2017-Oct

**Pages:**8

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-1073-5836

**EISSN:**N/A

Stimulating Base-Ten Reasoning with Context

Bray, Wendy S.; Blais, Tanya Vik

Teaching Children Mathematics, v24 n2 p120-127 Oct 2017

When asked to determine the number of tens in twenty-five, most second graders who have had instruction on place value can quickly provide the correct answer of two. However, when asked to show how the numeral 2 is represented in a set of twenty-five objects, many children struggle to draw a connection between the digit 2 and twenty objects in the set. Similarly, some children who use skip counting by tens to successfully determine that ten dimes can be traded for 100 pennies have been observed to have no idea how many stacks of 10 pennies can be made from 100 pennies without actually building the stacks. These examples highlight the challenge of teaching place-value concepts such that children develop deep understanding of the base-ten structure of numbers. Yet we know that developing fluency with base-ten thinking is critical. Understanding the base-ten structure of multidigit numbers is the gateway to conceptualizing large quantities and operating on multidigit numbers. In the early elementary grades, the authors want children to move from thinking of large quantities purely as sets of ones to simultaneously "seeing" sets of 10 ones as units of tens, sets of 10 tens as units of hundreds, and so on. Moreover, the authors want children to understand how the position of digits relates to these different sizes of units. One high-leverage teaching practice that serves as the starting point for developing deep understanding is engaging learners in using their current mathematical conceptions to solve and discuss task solutions that offer multiple entry points and promote mathematical reasoning (NCTM 2014). Through a detailed account of a carefully structured classroom discussion of student solutions in this article, the authors will illustrate the potential of using a contextualized problem involving groups of ten to assess and develop base-ten reasoning.

Descriptors: Mathematics Instruction, Elementary School Mathematics, Grade 2, Mathematical Concepts, Teaching Methods, Problem Solving, Mathematical Logic, Numbers, Concept Formation, Computation

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail: NCTM@nctm.org; Web site: http://www.nctm.org/publications/teaching-children-mathematics/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Elementary Education

**Audience:**Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Grant or Contract Numbers:**N/A