Effective teaching is more than a good lecture. In fact, it may be NO lecture at all. This presentation suggests dozens of effective structures. While many are not fully explained here, they are easily found in many locations on the internet and in the woks of Gardner, Tomlinson, Marzano, Sternberg, Costa, Solomon and others.
Making and Justifying Mathematical Decisions.pdfChris Hunter
In BC’s nearly-decade-old “new” curriculum, the curricular competencies describe the processes that students are expected to develop in areas of learning such as mathematics. They reflect the “Do” in the “Know-Do-Understand” model. Under the “Communicating” header falls the curricular competency “Explain and justify mathematical ideas and decisions.” Note that it contains two processes: “Explain mathematical ideas” and “Justify mathematical decisions.” I have broken it down into its separate parts in order to understand--or reveal--its meaning.
The first part is commonplace in classrooms. By now, BC math teachers—and students—understand that “Explain mathematical ideas” means more than “Show your work.” Teachers consistently ask “What did you do?” and “How do you know?” This process is about retelling, not just of steps but of thinking.
The second part happens less frequently. Think back to the last time that you observed a student make—a necessary precursor to justify—a mathematical decision. “Justify” is about defending. Like “explain,” it involves reasoning; unlike “explain,” it also involves opinion and debate.
In order to reinterpret the curricular competency “Explain and justify mathematical ideas and decisions,” I will continue to take apart its constituent part “Justify mathematical decisions” and carefully examine the term “mathematical decisions.” What, exactly, is a “mathematical decision”? Below, I will categorize answers to this question. These categories, and the provided examples, may help to suggest new opportunities for students to justify.
Effective teaching is more than a good lecture. In fact, it may be NO lecture at all. This presentation suggests dozens of effective structures. While many are not fully explained here, they are easily found in many locations on the internet and in the woks of Gardner, Tomlinson, Marzano, Sternberg, Costa, Solomon and others.
Making and Justifying Mathematical Decisions.pdfChris Hunter
In BC’s nearly-decade-old “new” curriculum, the curricular competencies describe the processes that students are expected to develop in areas of learning such as mathematics. They reflect the “Do” in the “Know-Do-Understand” model. Under the “Communicating” header falls the curricular competency “Explain and justify mathematical ideas and decisions.” Note that it contains two processes: “Explain mathematical ideas” and “Justify mathematical decisions.” I have broken it down into its separate parts in order to understand--or reveal--its meaning.
The first part is commonplace in classrooms. By now, BC math teachers—and students—understand that “Explain mathematical ideas” means more than “Show your work.” Teachers consistently ask “What did you do?” and “How do you know?” This process is about retelling, not just of steps but of thinking.
The second part happens less frequently. Think back to the last time that you observed a student make—a necessary precursor to justify—a mathematical decision. “Justify” is about defending. Like “explain,” it involves reasoning; unlike “explain,” it also involves opinion and debate.
In order to reinterpret the curricular competency “Explain and justify mathematical ideas and decisions,” I will continue to take apart its constituent part “Justify mathematical decisions” and carefully examine the term “mathematical decisions.” What, exactly, is a “mathematical decision”? Below, I will categorize answers to this question. These categories, and the provided examples, may help to suggest new opportunities for students to justify.
Multiplication -- More Than Repeated Addition and Times Tables.pdfChris Hunter
Multiplication is repeated addition... but it also means so much more than that! In this workshop, you will explore several fundamental meanings of this operation (e.g., equal groups, arrays and areas, how a quantity is “stretched,” etc.) through rich tasks that address each of these meanings. Also, you will explore and discuss relationships between the “basic facts.” More importantly, you will learn how to help your students see that these relationships extend to other types of numbers that they come across in BC’s intermediate and middle years mathematics curriculum (e.g., two-digit whole numbers, fractions, decimals, integers, etc.).
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
1. Curricular Competencies
Reasoning
I can make sense of mathematics.
Emerging Developing Pro
fi
cient Extending
recognize repetition
(patterns)
predict what happens next
(conjectures)
fi
gure out why repetition is
happening
(proofs)
look for new occurrences of
repeated reasoning
notice structures discover shortcuts discover generalizations discover insights;
fi
nd faults in generalizations
estimate a reasonable answer decide whether my actions
and answers make sense
(convince myself)
decide whether my actions
and answers make sense
(convince a friend)
decide whether my actions
and answers make sense
(convince a skeptic)
build a logical progression of
statements
2. Curricular Competencies
Problem Solving
I can
fi
gure out what do when I don’t know what to do.
Emerging Developing Pro
fi
cient Extending
plan a way to approach a
problem
use a strategy to solve a
problem
use multiple strategies to
solve a problem
select the most e
ffi
cient or
elegant strategy to solve a
problem
determine what is being asked
and what information is
needed to solve a problem
evaluate progress and revise
actions, if needed
persevere until a problem is
solved
pose and solve new problems
3. Curricular Competencies
Communicating
I can explain and defend my ideas and decisions to others.
Emerging Developing Pro
fi
cient Extending
participate in mathematical
discussions (pair, small-group,
or whole-class)
contribute to mathematical
discussions (pair, small-group,
or whole-class)
share my thinking with others
to advance collective knowing
revise how I communicate my
ideas to others, as needed
describe my process for
fi
nding answers
(play-by-play)
explain my process for
fi
nding
answers
(colour commentary)
back up my statements and
actions with examples and
reasoning
construct and assess
alternative arguments
listen to the reasoning of
others
critique the reasoning of others
use informal (but clear) intuitive
language
use formal (and precise) math
language;
attend to units, labels, etc.
edit and organize my written
work so that readers can
follow it clearly (e.g., left to
right, top to bottom;
appropriate symbolic notation)
4. Curricular Competencies
Representing
I can show mathematical ideas in many ways.
Emerging Developing Pro
fi
cient Extending
use concrete and pictorial
tools to approach problems
and explore concepts and
procedures
e
ff
ectively use concrete and
pictorial tools to solve
problems and make sense of
concepts and procedures
select appropriate concrete
and pictorial tools to solve
problems and make sense of
concepts and procedures
consider advantages and
limitations of a concrete or
pictorial tool
relate using concrete and
pictorial tools to using symbols
use prescribed symbolic
representations to encode
mathematical ideas
move between di
ff
erent
symbolic representations of
the same mathematical idea
select and use appropriate
symbolic representations to
encode mathematical ideas
consider advantages and
limitations of a symbolic
representation
5. Curricular Competencies
Connecting
I can connect math concepts to each other, use math to understand our world, and build on my prior
knowledge and experiences.
Emerging Developing Pro
fi
cient Extending
connect one part of math to
another
(within the same concept)
connect one part of math to
another
(across di
ff
erent concepts and
within the same strand)
connect one part of math to
another
(across di
ff
erent strands)
make math-to-math, math-to-
world, and math-to-self
connections that are novel and
have value
cite familiar “real-world”
applications of mathematics
use math to represent “real-
world” situations
use math to deepen my
understanding of “real-world”
phenomena
connect new problems to
previously solved problems
express how new concepts
and procedures are similar to
and di
ff
erent from prior
learning
(partial)
express how new concepts
and procedures are similar to
and di
ff
erent from prior
learning
(comprehensive)
