MA201 Example Presentation Section 2.3: The Hindu-Arabic System
Presentation Outline I.Presentation Theme: Theme: Understanding the role of the decimal point (Where does the “oneths” place go?) Why Challenging for Elementary Students: The meaning of the position of decimal point can be confusing. Mathematics for Elementary Teachers: Understanding the “mirror symmetry” of our place value system. II.Mathematics and Sharing my understanding: Explaining the mirror symmetry that exists in our place value system and the misleading position of the decimal point. Providing a solution that teachers can use to explain the regularity of the place value system from hundreds to hundreths.
Presentation Outline I.Presentation Theme: Theme: Understanding the role of the decimal point (Where does the “oneths” place go?) Why Challenging for Elementary Students: The meaning of the position of decimal point can be confusing. Mathematics for Elementary Teachers: Understanding the “mirror symmetry” of our place value system. II.Mathematics and Sharing my understanding: Explaining the mirror symmetry that exists in our place value system and the misleading position of the decimal point. Providing a solution that teachers can use to explain the regularity of the place value system from hundreds to hundreths.
Presentation Outline I.Presentation Theme: Theme: Understanding the role of the decimal point (Where does the “oneths” place go?) Why Challenging for Elementary Students: The meaning of the position of decimal point can be confusing. Mathematics for Elementary Teachers: Understanding the “mirror symmetry” of our place value system. II.Mathematics and Sharing my understanding: Explaining the mirror symmetry that exists in our place value system and the misleading position of the decimal point. Providing a solution that teachers can use to explain the regularity of the place value system from hundreds to hundreths.
Presenting My Presentation Theme (At least one slide clearly identifying the presentation theme or topic.)
Presentation Theme: Understanding the role of the decimal point.
By exploring a common elementary school misconception: “Where did the oneths place go?”
Problem: Where did the oneths place go? Find the place value of 8. a)6.781 Trissy says, “tenths”.
Problem: Where did the oneths place go? Find the place value of 8. a)6.781 Trissy says, “tenths”.
Problem: Where did the oneths place go? Consider the following number: : hundreds 2: tens 1:ones 1: tenths 2: hundredths 3: thousandths
Problem: Where did the oneths place go? Consider the following number: : hundreds 2: tens 1:ones 1: tenths 2: hundredths 3: thousandths
Problem: Where did the oneths place go? Consider the following number: : hundreds 2: tens 1:ones 1: tenths 2: hundredths 3: thousandths
Problem: Where did the oneths place go? Consider the following number: : hundreds 2: tens 1:ones 1: tenths 2: hundredths 3: thousandths
Problem: Where did the oneths place go? Consider the following number: : hundreds 2: tens 1:ones 1: tenths 2: hundredths 3: thousandths
Problem: Where did the oneths place go? Consider the following number: : hundreds 2: tens 1:ones 1: tenths 2: hundredths 3: thousandths
Problem: Where did the oneths place go? Consider the following number: : hundreds 2: tens 1:ones 1: tenths 2: hundredths 3: thousandths Where did the ‘oneths’ go?
Topic Justification For this specific problem: I found this problem described in a journal publication, “But what about the oneths?” by Amy MacDonald in Australian Mathematics Teacher, Trissy was a real student who asked this question.
Topic Justification Quoted from the paper: Many errors students make in mathematics are rational, “logically consistent and rule based rather than random.” The strategies constructed in order to assist in solving an unfamiliar problem are usually based on prior knowledge and experience. (It is natural to ask where the ‘oneths’ place is.)
Topic Justification Quoted from the paper: Many errors students make in mathematics are rational, “logically consistent and rule based rather than random.” The strategies constructed in order to assist in solving an unfamiliar problem are usually based on prior knowledge and experience. (It is natural to ask where the ‘oneths’ place is.)
Topic Justification In general: Elementary children have traditionally found place value to be difficult to learn, and their teachers have found it difficult to teach. Understanding place value requires a child to make connections among and sense of a highly complex system for symbolizing quantities. From Place Value: Problem solving and written assessment by Sharon Ross in Research, Reflection, Practice
II. Sharing my understanding
Explaining The Problem Mirror symmetry is a pattern in which there is a vertical line of reflection. The left-hand side and the right-hand are mirror images of each other.
Explaining The Problem A student knows that there is a mirror pattern, and expects that this patterns occurs symmetrically around the decimal point “If 7 is ones, then 8 is oneths.”
Explaining The Problem “If 7 is ones, then 8 is oneths.” However, ask Trissy: What would 8 oneths mean? Ones and ‘oneths’ would be the same!
Explaining The Problem “If 7 is ones, then 8 is oneths.” However, ask Trissy: What would 8 oneths mean? Ones and ‘oneths’ would be the same!
Explaining The Problem The “mirror symmetry” occurs around the ones place, not the decimal point. 7 = ones 2 = tens and 8 = tenths 4 = hundreds and 1 = hundreths Ones and ‘oneths’ would be the same!
Solution for elementary students: teach them the Endless Base 10 Chain
Discussion For Teachers The decimal place is not exactly ‘in the middle’. Is this different than what you thought? Exercise: Suppose that you have and would like to multiply this by Explain how you could solve this problem using the endless base 10 chain.
Discussion For Teachers The decimal place is not exactly ‘in the middle’. Is this different than what you thought? Exercise: Suppose that you have and would like to multiply this by Explain how you could solve this problem using the endless base 10 chain.
Implications for Teachers from “But what about the oneths?” Amy MacDonald suggests: Use the endless Base 10 chain (Steinle & Stacey) when explaining the structure of decimal notation. Encourage students to recognize that the symmetry of the decimal revolves around the ones. The decimal point indicates the ones place on its left.
Any questions?
References “But what about the oneths?” by Amy MacDonald in Australian Mathematics Teacher, Place Value: Problem solving and written assessment by Sharon Ross in Research, Reflection, Practice (Found online at AcademicOneFile via USA library.)