Supporting First Grader’s Ten-Structured Thinking by addition problems Karim Ezzatkhah University of Illinois at Urbana Champaign Supporting First Grader’s Ten-Structured Thinking by addition problems Karim Ezzatkhah University of Illinois at Urbana Champaign 9/17/2018

Introduction Research findings Solving Existing Problem 9/17/2018

Literature Study Culture and Language v Language structure v     Concrete modeling v     Teaching method v     Children understanding of basic arithmetic Addition and Subtraction Situations in the Real world 9/17/2018

Literature Study continue1 Children’s counting strategies Using manipulative Finger counting Verbal counting (counting mentally) Derived facts counting (Derived fact strategy involves using memorized addition facts) Fact retrieval counting (Children quickly produce the answer, without overt signs of counting) Children’s Difficulties in identifying digits of Multi-digit Number: Instructional Materials 9/17/2018

Literature Study continue2 Children Conceptual Structures for Two-Digit numbers (Pp6-7) Present Textbooks and Teaching/Learning Two-Digit Numbers (p7) What is the problem? Many first graders in the U.S.A. do not understand the base-ten structure of multi-digit number words (Fuson, 1990). U.S. students have problem with grouping quantities and understanding place- value system (Miura, 1987). 9/17/2018

Literature Study continue3 There are irregularities in reading and writing two digit numbers. Thus, first graders need time and effective instruction to learn those numbers. Reading and writing multi-digit numbers is difficult for children because written numbers do not correspond directly with spoken counting numbers, for example fifteen is not one ten and five or thirty seven is not three tens and seven. 9/17/2018

Literature Study continue4 Children's counting knowledge from out of school is not like counting procedure that children learn at school. For example, children when count a collection, they get the result as a combination of ones (unitary concept), in fact we are expecting the result in base-ten system (multi-unit concept). ( Fuson, 1992). 9/17/2018

Instructional Model Place Value & base ten counting System in different countries Instructional model of two digit numbers( p9) 9/17/2018

Reading and writing Two-digit numbers in different countries English spoken and west Asian countries Ten written characters Base-ten counting and Place-value system Irregularity in first decade Different decade name East Asian Countries Multi-character in writing numbers Base-ten counting system No perfect place-value system No decade name Regularity between decades 9/17/2018

Purpose of this study It proposed, that the students those learn two-digit numbers by addition of the most difficult single-digit sums to 18, with unitary conceptual structures. And, they use appropriate manipulative or computer to model the learning situation. These students will be able gradually acquire multiunit conceptual structures and understand two-digit numbers sense. They also learn difficult single-digit addition sums to 18, with a deep understanding. 9/17/2018

Purpose of this study, Continue . Therefore, their understanding of two-digit numbers and single-digit addition sums to 18, would be better than students that are following textbooks based instruction in this field. 9/17/2018

Methodology 1- Participants and settings: 2- Teachers training 3-Design(p11) 4-Experimental Procedure v   Preliminary test: v   Pretest &Posttest v   Interview v   Process of the treatment (Pp13-14) Instructional Games (p15) 9/17/2018

Measure of Skills and Understandings v    Children’s single digit addition and subtraction tasks v    Children’s understanding of two-digit number v    Measuring the process of thinking v    Scoring policy and validation v    Test-Retest Reliability v    Validity 9/17/2018

v   Manipulative This project is designed to work with two different manipulative. First will be concrete objects as: 1- 100 wooden or plastic sticks. Tens Ones 2-Rubber bands. 3- a piece of paper illustrated the place-value mat. Second by computer assisted program: URL to computer program is: (http://www.mste.uiuc.edu/users/mmckelve/applets/Counting/done/counting.html). 9/17/2018

Results v Children’s single-digit addition sums to 18 v    Children’s conceptual structure of two-digit number: Children’s invented procedures 9/17/2018

Discussion Analysis References: 9/17/2018