The ICE model summarizes the key components of learning as Ideas, Connections, and Extensions. Ideas refer to basic facts and skills. Connections involve linking ideas together and applying ideas in new contexts. Extensions represent using ideas creatively and making novel inferences. The model suggests assessments should weigh Ideas less and Connections and Extensions more to align with curriculum goals of deep understanding over simple recall. It also helps ensure grades reflect higher order thinking beyond isolated skills or facts.
Algebra Readiness: Equipping K-8 Students for SuccessDreamBox Learning
As the focus on standards-readiness grows, educators need reassurance that they’re not just teaching students how to pass a test, but also supporting their exploration, creativity, and deep understanding of applied knowledge. Joe Trahan, former middle school teacher, will discuss the pedagogical approach to preparing students for formal algebra. He'll share opportunities educators have to introduce the exploration of abstract concepts at an early age—at a time when students are more focused on concrete mathematical concepts.
Algebra Readiness: Equipping K-8 Students for SuccessDreamBox Learning
As the focus on standards-readiness grows, educators need reassurance that they’re not just teaching students how to pass a test, but also supporting their exploration, creativity, and deep understanding of applied knowledge. Joe Trahan, former middle school teacher, will discuss the pedagogical approach to preparing students for formal algebra. He'll share opportunities educators have to introduce the exploration of abstract concepts at an early age—at a time when students are more focused on concrete mathematical concepts.
There is overwhelming evidence that students face serious challenges in learning mathematical proof. Studies have found that students possess a superficial understanding of mathematical proof. With the aim of contributing to efforts intended to develop a comprehensive conception of mathematical proof, literature search was conducted to identify areas where research could be directed in order to increase proof understanding among students. To accomplish this goal, literature on modes of reasoning involved in proof construction, ideas on the classification of activities that constitute a proof path, and categories of proof understanding are exemplified using mathematical content drawn from Real Analysis. These exemplifications were used to illustrate the connections between modes of reasoning and levels of proof understanding. With regard to students’ fragile grasp of mathematical proof this critique of literature has revealed that many previous studies have given prominence to proof validations while there is lack of crucial interplay between structural and inductive modes of reasoning during proving by students. Hence, it is suggested in this paper that current research could also focus on mechanisms that promote an analytic conceptions of mathematical proof that are comprehensive enough to allow students to engage in more robust proof constructions.
Secondary mathematics wednesday august 22 2012brearatliff
Using CSCOPE for Instructional Planning - a PowerPoint outlining how to use the YAG, TEKS Verification Document, IFD, VAD, and EITG for effective lesson planning.
There is overwhelming evidence that students face serious challenges in learning mathematical proof. Studies have found that students possess a superficial understanding of mathematical proof. With the aim of contributing to efforts intended to develop a comprehensive conception of mathematical proof, literature search was conducted to identify areas where research could be directed in order to increase proof understanding among students. To accomplish this goal, literature on modes of reasoning involved in proof construction, ideas on the classification of activities that constitute a proof path, and categories of proof understanding are exemplified using mathematical content drawn from Real Analysis. These exemplifications were used to illustrate the connections between modes of reasoning and levels of proof understanding. With regard to students’ fragile grasp of mathematical proof this critique of literature has revealed that many previous studies have given prominence to proof validations while there is lack of crucial interplay between structural and inductive modes of reasoning during proving by students. Hence, it is suggested in this paper that current research could also focus on mechanisms that promote an analytic conceptions of mathematical proof that are comprehensive enough to allow students to engage in more robust proof constructions.
Secondary mathematics wednesday august 22 2012brearatliff
Using CSCOPE for Instructional Planning - a PowerPoint outlining how to use the YAG, TEKS Verification Document, IFD, VAD, and EITG for effective lesson planning.
Dr. Jere Confrey explains the challenges of building and implementing learning trajectory-aligned diagnostic assessments for early algebra, grades 6-8.
Learning Trajectory-Aligned Diagnostic Assessments for Early Algebra, Grades ...Basia Coulter
A learning trajectory connects what students bring to instruction, to a target concept, and delineates a set of landmarks and obstacles that students are likely to encounter as they move from naïve to sophisticated understandings.
EdD and EdS ProgramDiscussion Expectations and ProtocolOne of .docxSALU18
EdD and EdS Program
Discussion Expectations and Protocol
One of the learning principles of the EdD and EdS programs is the development of a learning community composed of both students and Faculty Members. Therefore, we expect you to engage in dialogue with your colleagues on Walden EdD and EdS Discussion boards. However, an advanced graduate-level Discussion is much more than just an assignment in which you fulfill your obligations by posting once and responding twice. Rather, the Discussion board is the heart of the learning community, a dialogical space in which you explore one another’s thinking and expand your own ideas. Ways to respond meaningfully to posts include:
· Suggesting a different perspective
· Asking a probing or clarifying question
· Sharing an insight you gained from having read the post
· Expanding on the post (e.g., validating an idea with your own experience)
· Making a relevant suggestion (e.g., recommending a website)
At this point, it is your turn to reflect on the responses colleagues made to your original post, noting what you have learned and/or any insights you have gained as a result of their comments. Although there is no requirement to do so, we urge you to continue with any dialogues that have potential for further development of the learning community and for your own learning.
Digital Communication and Scholarly Discourse
Digital communication poses a new challenge for EdD and EdS candidates, as it may be the only way that you present yourself to colleagues and faculty. In the following weeks, you will be studying scholarly writing and discovering that communication with a scholarly audience carries different expectations than other types of communication. For the purpose of your program, it is important to establish guidelines for acceptable and appropriate communication via threaded messages and e-mail with your colleagues and faculty.
Please keep the following guidelines in mind:
· Slang, emoticons ( :-) ), and acronyms are frequently used in chat rooms and provide helpful shorthand between friends, but they are not acceptable in scholarly responses.
· Discussion postings and responses to colleagues are to be written in complete sentences with attention to correct punctuation and spelling.
· E-mails to Faculty must always contain the course title and section number in the subject line and your complete name at the end.
Attention to detail is one of the habits that will pay off as you begin developing your written assignments and advanced graduate-level projects.Thought Process Grid
Level of Thought Process
Explanation of Thought Process
Guiding Questions
Self-system thinking (Marzano; no corollary to Bloom)
“Knowledge is expressed in an interrelated system of attitudes, beliefs, and emotions” (pp. 50–54).
How strongly do you believe in ____? What questions come to mind?
Metacognition (Marzano; no corollary to Bloom)
“Knowledge is monitored, evaluated, and regulated by establishing clear goals a ...
Elementary mathematics wednesday august 22 2012brearatliff
Using CSCOPE for Instructional Planning: a PowerPoint outlining how to use the YAG, TEKS Verification Document, IFD, VAD, and EITG for effective lesson planning.
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.
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.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
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.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
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
1. The ICE Model
I(deas), C(onnections and E(xtensions).
Developed by Robert Wilson (Queen’s University).
Elaborated upon by Susan Young.
Ideas
the fundamentals of new learning
include building blocks such as the steps in a process, the
necessary terminology/vocabulary, definitions, details and
facts
Ideas are only information.
What do Ideas look like?
o recognizing numbers
o knowing that a triangle has three sides
o associating heavy clouds with the probability of rain
What do Ideas-level tasks look like?
o show a “greater than sign”
2. o identify the parallelogram
o state the slope of the line shown on the graph
o graph the ordered pair (2, 6)
o measure this angle using a protractor
o match the unit “cm” with the appropriate expansion
o or fill in the blanks for “in the expression 5x , 5 is called
2
the _______, x is called the ______, and 2 is called the
_______
Ideas are “bits and pieces” of knowledge that are best described in
terms of simple recognition or recall.
Ideas-level demonstrations are set as a basic minimum requirement
for success, fitting best with Level two of the provincial achievement
rubric. Major student errors and the continuous need for teacher
support set Level one achievement apart.
Connections
• between and among the discrete bits and pieces of knowledge
3. • made by the learner between the material and their own real-
world experiences
• ideas are integrated into webs of information and knowledge
that is tied together so that learners are not experiencing
isolated skills, concepts, rules or symbols.
ie. This number _ is
2 less than 9
1 more than 6
small compared to 73
Prime
lucky
the number of days in a week
large compared to one-tenth
Consider the concept of seven as constructed by a young child. It is
first likely connected to the counting procedure and understood to be
less than 10 and more than 2. However, the web of connected ideas can
grow large and involved. Van de Walle, p.29
Connections are webs
• Estimate the answer to 12/13 + 7/8
• Compare squares and rectangles
4. • or answer questions like In how many ways can two triangles
be different
• identify relationships between objects by stating shared
attributes
• use events from meaningful experiences to describe probability
• compare experimental results with predicted results
• discuss trends in graphs to draw conclusions about the data
Extensions
• students are able to use their learning in novel ways apart from
the initial learning situation to predict how …; state the
implications of …; propose solutions for …; or validate his and
others’ thinking
• evaluate arguments that are based on data analysis, ask “what
if” questions, discuss and defend the choice of a pattern rule, or
create problems giving rise to first-degree equations with one
variable
• the students’ ability to use old definitions and laws to predict
new generalizations and conclusions by relating knowledge
from several areas
• student is able to reorganize prior knowledge and skills
creatively or generatively to describe or illustrate new
generalizations or concepts across strands or disciplines
5. Strands Ideas Connections Extensions Totals
Number Sense & Typically scores from The verbs associated with The application of
Numeration quizzes, homework. Students see how “extensions” suggest that ICE ensures that a
Procedural skills remain mathematical ideas build children need grade is more than an
Expectations selected important but should be on one another in a useful opportunities to think average of scores.
from Ontario weighted in proportion to network of connected deeply,
Curriculum other goals that reflect what ideas.
Document and the curriculum values.
categorized by verb
as I, C or E.
Spatial Sense & Extension verbs challenge ICE helps to align
Geometry Ideas are at the beginning of Students apply ideas in a students to ask questions assessments with the
Expectations selected the learning continuum. context or situation. and reason about true goals and
from Ontario important ideas. objectives of the
Curriculum program.
Document and
categorized by verb
as I, C or E.
Patterning & Algebra Extension solutions The final grade is
Ideas (only information) are Students recognize that demonstrate a student’s dependent upon the
Expectations selected at the lowest level on a mathematics is not a facility in using a variety quality of the
from Ontario rubric. laundry list of isolated of mathematical instruments that are
Curriculum rules and formulae. representations to add to used to generate the
Document and their own understanding grade. ICE can serve
categorized by verb and to better communicate to keep a balance in
as I, C or E. ideas to others. those instruments.
Total 35 50 15 100
• the students’ ability to pose problems and to invoke informed
but original experimental designs or experiential methods
Generating a grade through the use of the ICE model reflects the developmental
nature of learning and can still fit nicely into administrative expectations about
marking.