1. 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

2. Introduction
Research findings
Solving Existing Problem
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3. 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
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4. 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
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5. 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).
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6. 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.
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7. 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).
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8. Instructional Model
Place Value & base ten counting System in different countries
Instructional model of two digit numbers( p9)
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9. 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
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10. 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.
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11. 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.
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12. 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)
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13. 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
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14. v   Manipulative
This project is designed to work with two different manipulative.
First will be concrete objects as:
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: (
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15. Results v Children’s single-digit addition sums to 18
v    Children’s conceptual structure of two-digit number:
Children’s invented procedures
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16. Discussion Analysis References:
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