The document discusses using math journals in elementary school classrooms to teach mathematical concepts. It describes a framework for teaching mastery that involves anchor tasks, guided practice, and independent practice. Journaling is presented as one part of this process where students explore concepts, structure their understanding, and reflect on their learning. Examples are provided of kindergarteners recording number bonds in their journals to master basic counting and addition. The journal entries allow teachers to assess understanding and provide differentiated instruction.
MCI Worchester State University Singapore Math InstituteJimmy Keng
Register at www.si.mcinstitute.com.sg
This exciting institute features a line-up of Singapore and US experts on Singapore Math, led by Dr. Yeap Ban Har and Dr. Richard Bisk.
ECM101 Development of Early Childhood NumeracyJimmy Keng
This course is offered to pre-school teachers by Pre-School Unit, Ministry of Education Singapore. This is Day 1 of the 12-hour course. Forty participants enrolled for the class which is the 4th Cohort.
These were the materials covered in last year's professional development. This year's session is a follow-up with revisiting of core ideas and extension of others.
Solves Multi- step Routine and Non-routine Problems involving Division and an...Nerisa Herman
solve multi-step routine and non-routine problems involving division and any of the other operations of decimals, mixed decimals, and whole numbers including money using appropriate problem solving strategies and tools. M6NS-If-113.3
This is part of the professional development for the team that translate My Pals Are Here into Dutch and also people who are going to provide professionald evelopment for teachers using Singapore textbooks in the future.
MCI Worchester State University Singapore Math InstituteJimmy Keng
Register at www.si.mcinstitute.com.sg
This exciting institute features a line-up of Singapore and US experts on Singapore Math, led by Dr. Yeap Ban Har and Dr. Richard Bisk.
ECM101 Development of Early Childhood NumeracyJimmy Keng
This course is offered to pre-school teachers by Pre-School Unit, Ministry of Education Singapore. This is Day 1 of the 12-hour course. Forty participants enrolled for the class which is the 4th Cohort.
These were the materials covered in last year's professional development. This year's session is a follow-up with revisiting of core ideas and extension of others.
Solves Multi- step Routine and Non-routine Problems involving Division and an...Nerisa Herman
solve multi-step routine and non-routine problems involving division and any of the other operations of decimals, mixed decimals, and whole numbers including money using appropriate problem solving strategies and tools. M6NS-If-113.3
This is part of the professional development for the team that translate My Pals Are Here into Dutch and also people who are going to provide professionald evelopment for teachers using Singapore textbooks in the future.
Connect with Maths Early Years Learning in Mathematics is an online community to support the teaching and learning of mathetmatics Birth to 8 years old. This presentation by Louise Hodgson, a mathematics specialist addresses counting principles in early years learning.
Presentation used for professional learning workshop for Education Assistants and Aboriginal and Islander Education Officer run by Tracey Armstrong and Sharon Lee from the Make It Count Swan Cluster.
LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011Jimmy Keng
This plenary lecture on elementary school mathematics was given at the conference which marks the end of the three-year Leaders and Educators in Asia Programme.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Math Plus Kansas City
1. mathplus www.banhar.blogspot.com
Dr. Yeap Ban Har
Making Connections through Multiplication and Division | Grades 3 – 5
SYNOPSIS |Using the CPA Approach which is fundamental to Singapore schools, we will explore
the learning of multiplication facts as well as multi-digit multiplication and division. The extension
between multiplication and division in whole numbers and in factions will be discussed. We will also
look at anchor tasks for lessons where the emphasis is on practicing a previously-learnt skill.
The CPA (Concrete Pictorial Abstract) Approach is based on Bruner’s ideas of
enactive, iconic and symbolic representations. New concepts are learnt through
concrete experiences.
Stages in Learning Multiplication Facts
1. Counting
2. Figuring Out
3. Remembering
3 x 4 =
6 x 4 =
7 x 4 =
9 x 4 =
Let’s figure out!
3. Anchor Tasks for Multi-Digit Multiplication and Division
Source | Maths – No Problem! Year 4
4. A farmer sells his crops to 3 restaurants.
He divides 525 heads of lettuce equally among the 3 restaurants.
How many heads of lettuce does each restaurant receive?
Source | Math in Focus 4
Hundreds tens Ones
Note | In Partitive Division, you know the number of groups. Example – Four children
shared 12 cookies equally. In Quotitive Division, you know the number of items in
each group. Example – Twelve cookies are put in packs of 4 cookies.
5. Anchor Tasks for Practice Lessons
Source | Every Child Can Do Math
Fraction Connections
1. How many halves are there in
2
1
2 ?
Source | Math in Focus 4
2. Find the value of
4
3
of 20.
Source | Primary Mathematics 4
6. mathplus www.banhar.blogspot.com
Dr. Yeap Ban Har
Developing Number Sense through Counting, Adding and Subtracting |
Grades K – 2
SYNOPSIS |Using the CPA Approach which is fundamental in Singapore schools, we will explore
what students need to be able to do to be proficient in counting, adding and subtracting. How can
teachers of younger children develop deep understanding using small numbers? The use of ten
frames, number bonds and bar models will be emphasized. We will also learn several mental
computation strategies.
The CPA (Concrete Pictorial Abstract) Approach is based on Bruner’s ideas of
enactive, iconic and symbolic representations. New concepts are learnt through
concrete experiences.
Teaching kids to count is fine, but teaching them what counts is best.
Bob Talbert
A fundamental idea in counting is that you can only count things in the same set i.e.
having the same ‘noun’. It is obvious that four oranges and an apples does not make
five apples. You don’t count different nouns!
In the same sense, 1 ten and 4 ones do not make 5 tens. Or, 1 half and 4 fifths do
not make 5 fifths. Or, worse, 5 sevenths!
Implications – integrate sorting with counting rather than teaching those as isolated
skills.
1. Sort the fruits.
2. Count how many in each basket.
7. Source | Earlybird Kindergarten Mathematics Reader
Let’s look at the use of ten frames for counting numbers less than 10 and numbers
greater than ten.
Implication – Help students progress from counting in ones to counting in tens and
ones.
Count, “1, 2, 3, 4, 5, 6, 7, 8, 9, 10. 1, 2. 10 and 2 is twelve.”
Instead of “1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.”
8. Anchor Tasks for Counting, Adding and Subtracting
1. Count 4 square tiles. Make a shape using 4 square tiles.
Source | Earlybird Kindergarten Mathematics
9.
10. 2. 8 + 6
Source | Maths in Focus 1
3. Subtract 28 from 300.
Source | Primary Mathematics 2 Third Edition
Number Bonds
Two children starts with a small pile of beans. They take turn to remove either one
or two beans until all the beans have been removed from the pile. The winner is the
child who takes the last bean(s).
12. mathplus www.banhar.blogspot.com
Dr. Yeap Ban Har
Key Note | The Big Fives in Mathematics Classrooms
SYNOPSIS | What are five things that students who are good in math do? What are five key
competencies that students need to have by the time they start middle school? Who are the five
wise guys who can answer most of the questions we have in mathematics education? What did they
say about mathematics learning?
In his engaging and thought-provoking keynote, Ban Har will offer a simple framework that guides
good mathematics instruction. You will learn how students develop ability in visualization and
generalization, number sense, metacognition and communication. We will see that "it is fine to teach
children to count, but it is best to teach them what counts!" (Bob Talbert)
13.
14. visualization
generalization
number sense
metacognition
communication
I can show.
I can draw.
I can explain.
I can write about it.
I can find ways to challenge myself.
Piaget
Dienes
Vygotsky
Skemp
Bruner
explore
structure
journal
reflect
practice
core
competencies
good
at math
elements of
effective lessons
learning
theories
15. model
scaffold
let go
explain
counsel
Yulin wants to make 14 small identical stars and 20 large identical stars using wire.
She has made 12 small stars and 7 large ones using 960 cm of wire. The length of
the wire she used for 3 large stars is the same as that for 4 small stars.
What is the length of the wire she needs to make the remaining stars?
Source | Primary School Leaving Examination
tools
pedagogical
16. mathplus www.banhar.blogspot.com
Dr. Yeap Ban Har
Developing Foundations for Multiplication and Division | Grades K – 2
SYNOPSIS | Using the Problem-Solving Approach which is fundamental in Singapore schools, we
will explore the acquisition of multiplication facts. What are some things that young children do that
prepare them for formal learning of multiplication and division. The role of visuals such as dot
diagrams and language will be emphasized.
Source | Maths - No Problem!
17.
18. Stages in Learning Multiplication Facts
1. Counting
2. Figuring Out
3. Remembering
Stories for Multiplication
Equal Groups
Array
Comparison
Rate
Combination
Stories for Division
Sharing
Grouping
Note | In Partitive Division, you know the number of groups. Example – Four children
shared 12 cookies equally. In Quotitive Division, you know the number of items in
each group. Example – Twelve cookies are put in packs of 4 cookies.
3 x 3 =
6 x 3=
7 x 3 =
9 x 3 =
Let’s figure out!
20. mathplus www.banhar.blogspot.com
Dr. Yeap Ban Har
Fractions | Grades 3 – 5
SYNOPSIS | In this session we will look at two key ideas in learning fractions and consider strategies
to teach addition, subtraction, multiplication and division of fractions.
Example 1
Share among 4 friends. They all get the same amount.
21. Example 2
Example 3
Grace arranged
2
1
,
3
2
,
4
1
in order, from the greatest to the smallest.
Is she correct?
23. 3
1
Example 9
Find the value of 12
5
4
.
Give your answer as a fraction in the simplest form.
Source | PSLE Singapore 2013
Example 10
The total cost of a pen and a book is $32. The cost of the pen is
5
3
the cost of the
book. What is the cost of the book?
Source | PSLE Singapore 2013
Example 11
Kai Li spent
3
1
of her money on 5 magnets and 11 postcards.
The cost of each magnet is 3 times the cost of each postcard.
She bought some more magnets with
4
3
of her remaining money.
How many magnets did Kai Li buy altogether?
Source | PSLE Singapore 2013
24. Example 12
Mr Lim had a total of 540 long and short rulers. After selling an equal number of
both types, he had
3
1
of the long rulers left and
6
1
of the short ones left.
What was the total number of rulers left?
Source | PSLE Singapore 2014
25. mathplus www.banhar.blogspot.com
Dr. Yeap Ban Har
Math Journals| Grades K – 2
SYNOPSIS | In this session we look at a framework for teaching to mastery and examine the role
of journaling in the process. How does journal entries look like? What do we do with them? How
does it help in assessment and differentiation?
Teaching to Mastery
To master counting, Kindergarteners should be able to tell the number of a set of
objects. Fluent at counting means able to do it with accuracy, confidence and some
degree of flexibility. It does not mean count fast!
To master number facts, First Graders should be able to recall 1 + 4 = 5 and, in
cases, they cannot recall (8 + 9), they should be able to figure out (8 + 9 = 10 + 7).
Fluency is not mere speed. When one is fluent in a language, it does not mean one
speaks fast, does it?
Anchor Task
o Explore
o Structure
o Journal
o Reflect
Guided Practice
Independent Practice
The framework for teaching to master involves several stages and journaling is one
of them.
26. In an open lesson for students who had just completed Kindergarten, the anchor task
was to use unifix cubes to explore the number bonds of 5. Later, they extend their
investigation to the cases of 3 and 7.
The journal writing was to look for and write down two numbers that add up to a
given number. Owen was given 6, for instance.
Source | Owen’s Journal
Source | Alex’s Journal
Owen looked for two numbers that add up to 6.
He tried to record his results in his journal.
Owen was able to make number bonds for 6.
He was also able to see possibilities – 5 and 1,
3 and 3 as well as 4 and 2. Is recording was
less successful as his ability to form numerals was
still not developed. He also attempted to use
symbols (not used in this lesson) that he had little
understanding of.
Although not required, Alex had chosen to record the results of the
investigations in his journal. It can be seen that he went from random
recording to making a systematic list. It is interesting to observe the
case of 0 continued to elude many students.
Journal allows advanced learner to experience differentiated
lesson. In this case, Alex went to explore cases involving negative
numbers while waiting for the class to complete their investigation..
27. In an open lesson for students who had just completed Grade 1, the anchor task was
to add three single digit numbers such that the vertical sum equals the horizontal sum.
After working on it with their friends and discussing it, students document how it is
done.
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