sti course a closer look at singapore math by yeap ban har
Post on 03-Sep-2014
2.571 Views
Preview:
DESCRIPTION
TRANSCRIPT
June 2010usinganchorproblemsinsingaporemath
Yeap Ban HarScarsdale Teachers Institute
New York USA
Problem 1
Arrange cards numbered 1 to 10 so that the trick shown by the instructor can be done. In this problems, students get to talk about the positions of the cards using ordinal numbers. They get to use ordinal numbers in two contexts – third card from the left and third card from the top. The problem itself is too tedious to describe using words. Just come for the institute next time round!
Teachers solved the problems in different ways.
The above is the solution. What if the cards used are numbered 1 to 9? 1 to 8? 1 to 7? 1 to 6? 1 to 5? 1 to 4?
Problem 2
This is a game for two players. The game can start with any number of paper clips, say, 24. The rule is that a player removes exactly 1 or 2 clips when it is his / her turn. The winner is the player who removes the last lot of paper clips. Find out a way to win the game.
Problem 2
In this anchor problem and its variant(s), the concept of multiples emerges. Anchor problem does that – to emerge a mathematical concept.
It turns out that the winning strategy is to leave your opponent with a multiple of three. What if the rule is changed to removing exactly 1, 2 or 3 clips? The winning strategy is to leave your opponent with a multiple of four. Did you notice a pattern?
Problem 3
The initial textbook problem was changed into the second one. Anchor problems and its variants allow students to encounter a range of problems with mathematical variability (Dienes). In this case students encounter both arithmetic and algebraic problems, and also problems with continuous as well as discrete quantities. Although both problems involve the same bar models, the mathematics involved are different.
273
Najib
Goggle
Pascal
Gittar
297
Problem 4
The anchor problem was varied systematically so that students get to learn different skills in bar modeling. Notice the different bar modeling skills needed to solve the problem when is changed from half to three-eighths to four-sevenths.
This problem is taken from a Singapore school’s mock examination to prepare students for the national examination at the end of grade six.
Mrs Liu spent 1/5 of her monthly salary on a handbag, of the remainder on a vacuum cleaner and saved the rest. She saved $1890. Find her monthly salary.
= half = three-eighths = four-sevenths
Three methods to solve the third problem.
73
Problem 5
Think of a 4-digit number, say, 1104. Jumble the digits up to form a different number, say, 0411. Fin d the difference between the two numbers (1104 – 411). Write the difference on a piece of paper. Circle any digit. Tell me the digits you did not circle and I will tell you the one you circled.
How can you tell what the circled number is given the numbers which are not circled?
Problem 6
Piece the pieces together so that two adjacent values are equal. Initially students can be asked to simply piece any two pieces together. Later they can be asked to form a single ‘snaking’ figure. Finally they can be challenge to form a square.
Problem 7
Place digits 0 to 9 in the five spaces to make a correct multiplication sentence – no repetition. 2-digit number multiplied by 1-digit number to give a 2-digit product.
x
Why are there so few odd products?
Summaryanchorproblems
Roles• To emerge the idea of multiples• To provide opportunities to use ordinal
numbers in varied situations• To provide opportunity to solve arithmetic
and algebraic problems that involve continuous and discrete quantities
• To provide opportunity to learn different skills in using bar models
• To provide opportunity to do drill-and-practice while
Participants working through anchor
problems they created.
workshopactivity
Referencestheoriesandmodels
PolyaProblem-Solving Stages• Understand• Plan• Do • Look Back
Polya
NewmanDifficulties in Word Problem Solving• Read• Comprehend• Know Strategies• Transform• Do Procedures• Interpret Answers
Newman
Dienes• Principle of Variability–Mathematical Variability– Perceptual Variability
Dienes
Krutetskii• The ability to pose a ‘natural’
question as a form of mathematical ability
Krutetski (1976). The psychology of mathematical abilities in school children. Chicago, IL:University of Chicago.
Krutetskii
Big Ideas• Visualization• Patterning• Number Sense• Metacognition• Communication
Big Ideas
Mathematics Curriculum Framework
Mathematical Problem
Solving
Attitudes
Metacognition
Proc
esse
s
Concepts
SkillsNumericalAlgebraic
GeometricalStatistical
ProbabilisticAnalytical
Reasoning, communication & connectionsThinking skills & heuristicsApplication & modelling
Numerical calculationAlgebraic
manipulationSpatial visualization
Data analysisMeasurement
Use of mathematical tools
Estimation
Monitoring of one’s own thinkingSelf-regulation of learning
BeliefsInterest
AppreciationConfidence
Perseverance
top related