Change is happening in Pre-College Mathematics! Pressure is mounting to get students into certification and degree bearing tracks. The GED now demands more conceptual math understanding as well as more algebraic content. How Can Faculty Address These Shifts? After a brief overview of institutional responses, Carren Walker of Collaborative for Ambitious Mathematics presents online resources to support teachers who seek to change both content and pedagogy in their courses, with a focus on active learning and formative assessment and specific examples of tasks and approaches. Watch the Blackboard Collaborate Recording of "Transforming the Classroom through the Standards for Mathematical Practice."
STEM Process and Project-Based LearningTodd_Stanley
The STEM design process involves asking, imagining, planning, creating, and revising. This cycle fits nicely into the model of project-based learning where students are creating an authentic product to show what they have learned. This shows you how you can incorporate the STEM design process into your projects to ensure maximize learning can take place. Part of this is creating a safe classroom environment where students are permitted to take risks. By doing this, you are giving students permission to fail, which is where the most learning takes place.
In this webinar we will present a collection of classroom-based formative assessment techniques for elementary and middle grade mathematics teachers to not only consider, but also to use effectively—everyday. Our guest, Skip Fennell, will also discuss how particular formative assessment techniques can bridge to summative assessments and the preparation for such measures. Fennell will address the suggestion from the National Council of Teachers of Mathematics’ Principles to Actions: Ensuring Mathematical Success for All (2014) that educators leverage assessment opportunities to improve teaching and learning at the classroom and school level.
STEM Process and Project-Based LearningTodd_Stanley
The STEM design process involves asking, imagining, planning, creating, and revising. This cycle fits nicely into the model of project-based learning where students are creating an authentic product to show what they have learned. This shows you how you can incorporate the STEM design process into your projects to ensure maximize learning can take place. Part of this is creating a safe classroom environment where students are permitted to take risks. By doing this, you are giving students permission to fail, which is where the most learning takes place.
In this webinar we will present a collection of classroom-based formative assessment techniques for elementary and middle grade mathematics teachers to not only consider, but also to use effectively—everyday. Our guest, Skip Fennell, will also discuss how particular formative assessment techniques can bridge to summative assessments and the preparation for such measures. Fennell will address the suggestion from the National Council of Teachers of Mathematics’ Principles to Actions: Ensuring Mathematical Success for All (2014) that educators leverage assessment opportunities to improve teaching and learning at the classroom and school level.
Expand Your Toolkit: Teacher Strategies for Deeper Math LearningDreamBox Learning
The road to conceptual understanding in mathematics is difficult. Through this journey, our students are required to demonstrate this understanding at every step. With the integration of technology in the classroom, blended learning can support student growth and understanding in math.
Of course, preparing students to model math concepts is problematic if teachers are struggling with the concepts themselves. Blended classrooms can provide support for both the learner and teacher. Want to learn how?
In this webinar, Courtney Foreman showed you how to expand your teaching toolkit by exploring new strategies and techniques for introducing traditionally difficult mathematics concepts to your students. Explore tools to promote the following in your blended classroom:
How to implement tasks that promote reasoning and problem-solving
How to use and connect mathematical representations
How to build procedural fluency from conceptual understanding
Real-time Assessment: A Guide for Emergency Remote TeachingFitri Mohamad
This is a set of materials from a webinar held for Universiti Malaysia Sarawak's lecturers (UNIMAS), to guide the transition from f2f teaching to emergency remote teaching - specifically on conducting Real-time Assessments.
An introduction to team based learning.
Prepared for Human Performance Technology course.
Presented at Multimedia University, Malaysia by Ali Mohammad Hossein Zadeh, 2012.
JiTT - Blended Learning Across the Academy - Teaching Prof. Tech - Oct 2015Jeff Loats
A four-person panel discusses the implementation of Just-in-Time Teaching in 18 courses across 5 disciplines. Participation rates and correlations with other outcomes are discussed.
Organic Online Discussions: Advantages and Implementation TipsD2L Barry
Organic Online Discussions: Advantages and Implementation Tips (5pm–5:45pm ET)
Presenter: Beth René Roepnack, eCampus, University System of Georgia
D2L Connection: Worldwide Edition
Wednesday, January 8, 2020
Totally Online
Gamification Techniques to Engage StudentsD2L Barry
Gamification in D2L, Leslie Van Wolvelear, Oakton Community College
Presentation given on Dec 13, 2019 at DePaul University for the D2L Connection: Chicago Edition.
Expand Your Toolkit: Teacher Strategies for Deeper Math LearningDreamBox Learning
The road to conceptual understanding in mathematics is difficult. Through this journey, our students are required to demonstrate this understanding at every step. With the integration of technology in the classroom, blended learning can support student growth and understanding in math.
Of course, preparing students to model math concepts is problematic if teachers are struggling with the concepts themselves. Blended classrooms can provide support for both the learner and teacher. Want to learn how?
In this webinar, Courtney Foreman showed you how to expand your teaching toolkit by exploring new strategies and techniques for introducing traditionally difficult mathematics concepts to your students. Explore tools to promote the following in your blended classroom:
How to implement tasks that promote reasoning and problem-solving
How to use and connect mathematical representations
How to build procedural fluency from conceptual understanding
Real-time Assessment: A Guide for Emergency Remote TeachingFitri Mohamad
This is a set of materials from a webinar held for Universiti Malaysia Sarawak's lecturers (UNIMAS), to guide the transition from f2f teaching to emergency remote teaching - specifically on conducting Real-time Assessments.
An introduction to team based learning.
Prepared for Human Performance Technology course.
Presented at Multimedia University, Malaysia by Ali Mohammad Hossein Zadeh, 2012.
JiTT - Blended Learning Across the Academy - Teaching Prof. Tech - Oct 2015Jeff Loats
A four-person panel discusses the implementation of Just-in-Time Teaching in 18 courses across 5 disciplines. Participation rates and correlations with other outcomes are discussed.
Organic Online Discussions: Advantages and Implementation TipsD2L Barry
Organic Online Discussions: Advantages and Implementation Tips (5pm–5:45pm ET)
Presenter: Beth René Roepnack, eCampus, University System of Georgia
D2L Connection: Worldwide Edition
Wednesday, January 8, 2020
Totally Online
Gamification Techniques to Engage StudentsD2L Barry
Gamification in D2L, Leslie Van Wolvelear, Oakton Community College
Presentation given on Dec 13, 2019 at DePaul University for the D2L Connection: Chicago Edition.
Weather safety is important as it affects everyone, both inside and outside of the office setting. Thunderstorms, lightning, flodding, and tornadoes can impact us all. This presentation is to bring awareness to my colleagues at ERM.
Iterating over the Traditional - Legal Approaches to Smart Contract DevelopmentCasey Kuhlman
Designing smart contracts could follow many routes. Here are some thoughts from traditional lawyers as to how we often design contracts which could be used by smart contract designers.
This PowerPoint by Dr. Dee McKinney & Katie Shepard was presented as a workshop for the East Georgia State College Center for Teaching & Learning for interested faculty & staff in January 2018.
A four-year-old asks on average about 400 questions per day, and an adult generally asks much much less. Our school system is often structured around rewarding giving the "right" answer and not asking smart questions. The result over time is that, as we grow older, we stop asking questions. Yet asking good questions is essential to finding and developing solutions - an important skill in critical thinking, innovation, and leadership.
This workshop will support teachers to explore their current habits and practices of formulating and asking questions, discuss with their colleagues a range of practices from research and articles, and then develop some new practical approaches they can use with their students.
The flipped classroom - and interactive workshop plus key ideas. presented at ALDinHE 2014. What to flip, what to replace it with, how to do it #aldcon
NCTM 2014 Presentation: Citrus Grove Elementarykrzavack
Take a look at how this elementary school whose teacher leaders facilitated a math book study that increases standardized math test scores tremendously!
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.
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.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
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
3. Overview
Review of Changes in GED
• Curricular
• Assessment
Review of Institutional Response
• Structural Change and Curricular Change
What about Pedagogical Change?
• Practices
• Norms
• Important Ideas
• Getting Started
• Content Resources for Assessment and Learning
4. GED shifts in Curriculum
• Algebra – More of it!
• A lot more– graphs, lines, polynomials,
inequalities, radicals…
• Requires foundational conceptual understanding
• Big Idea Understanding Necessary
• Demands Symbolic Knowledge as well as Vocabulary
5. GED Shifts in Assessment
• Conceptually demanding Problems
• Foundational Skills assessed only in the
accomplishing of Problem Solving Tasks
• Calculator Use – YES! (five no calculator problems)
• Calculator on-computer with user guide
• Formula sheet available
• “tips and tricks” will not be enough
• This might feel overwhelming!
LOTS of people and institutions are Working on
Responses!
6. Structural Responses
• Delivery of learning
– Multiple options for the diversity of lives
– Accelerated Programs (Many examples)
– Learning labs with trained tutors
• Re-Define of Basic Skills Math
– High School 21 and I-Best
– Modular Approach (ie. Virginia)
– Side by Side support and Just in Time learning (Valencia)
7. Curricular Responses
Maricopa – Scottsdale College
• Faculty created-Creative Commons
• Attention to vocabulary and constructs
– Multiplication is “copies”
– 5/7 is 5 copies of 1/7
Pathways
Dana Center
Non Stem Quantitative Reasoning/Literacy
8. Mathematical Practices
Standard 1: Make sense of problems and persevere in solving them
Standard 2: Reason abstractly and quantitatively
Standard 3: Constructviableargumentsandcritiquethereasoningofothers
Standard 4: Model with mathematics
Standard 5: Use appropriate tools strategically
Standard 6: Attend to precision
Standard 7: Look for and make use of structure
Standard 8: Look for and express regularity in repeated reasoning
http://www.insidemathematics.org/index.php/mathematical-
practice-standards
9. First Steps..
What could a Practice Standard Look Like?
Demonstrate that:
• Student Thinking Matters
• All student thinking is valued
• Student voices and ideas will be heard
• Ideas will be valued
• NUMBER TALKS
– Public thinking about a do-able problem
– Example of a Number Talk
10. Formative Assessment
• Questions that inform your teaching
• Questions that reveal student understanding and emergent
learning need savvy design.
Example from Dylan William:
Which fraction is smallest?
a) 1/6, b) 2/3, c) 1/3 , d)1/2
Success Rate of 88%
Which fraction is largest?
a) 4/5, b) 3/4, c) 5/8, d) 7/10
Success Rate of 46%, 39% chose b.
11. Shifting Norms: Questioning Patterns
When students share their thinking, the classroom
script changes.
IRE/IRF
Not Working for Students
Probing Into Student Thinking and
Pressing students for ideas.
Feedback instead of Evaluation:
Inquiry: What is half of a fourth?
Response: 1/8
Evaluation/Follow-Up: Right.
Research says when the follow up is
evaluative, student engagement and
class participation lessens.
T: What is half of a fourth?
S: 1/8th
T: How do you know?
S: I just do
T: I want to understand about your
thinking.. Why 8ths?
S: I cut the fourth piece in half
T: How is that an 8th?
S: Now there are eight pieces
T: So why is eight mean eighths?
S: The whole has eight pieces and I
picked one of them. So an eighth.
12. Shifting Norms: Learning Focus
Observed “REMEDIAL PEDAGOGY”
Grubb, et al. (2011) Working Paper 2
Pedagogy Re-imagined
•Parts to Whole
•Procedures
•Rules
•Isolated Ideas
•Repetitive Practice of Skills
•Whole to Part
•Concepts
•Themes
•Context
•Problem Solving using
foundational skills
13. First Steps: Practices in the Classroom
Consider choosing one or two of these ideas to
try out in your classroom:
• Number Talks at the beginning of Class.
• Which of these are Equivalent?
• Card Sorts
• Pattern Recognition
• Meta-Cognitive Questions
• Limiting Scaffolding
14. First Steps..
What could a Practice Standard Look Like?
Equivalent to .3? Yes? No? Explanation
30/100
30%
0.300
.3%
15. Card Sorts
• Students sort cards in to sets of Equivalent
groups (Start with a total of 4 groups of 4
cards.
• Great work for groups of two.
• Ask groups of two-four to verify solutions and
be ready to explain sorting rule.
• Ask: What was easy about the sorting? What
was hard?
16. Scaling Up Card Sorts
• Introduce a card with an intentional error.
• Introduce blank cards. Students fill in.
• Card sorts that have 2 reasonable sorts
possible.
• Have students make card sorts as a study tool.
17. Pattern Recognition
• Number talks with Patterns
• Focus on how students see the pattern
• Values multiple ways of seeing
• Builds to generalization
• What is the 3rd Stage? The 10th, The 100th?
Stage 1 Stage 2 Stage 4
18. Meta-Cognitive Questions
• What would someone have to know to answer this question
efficiently and accurately?
• How confident are you that you can solve this problem? Why?
• What do you understand now that you did not know at the
beginning of the course?
• What advice would you give someone enrolling in this course?
• Which of the questions on this worksheet are similar?
• Write another problem this is like this one. How do you know
they are the same?
19. Limit Scaffolding
• Find out what students know – not what they
don’t know.
• Opportunity for formative assessment. The
instructor observes student knowledge as well
as problem solving dispositions.
• Invite student knowledge and experience into
the classroom.
20. Time in Hours Since Vehicles Started
VolumeofGasinTankinGallons Driver A
Driver B
Driver C
Driver D
What Can you Determine from this Graph?
4 cars started with full gas tanks and drove 60
miles per hour until the car ran out of gas.
21. Questions for Reflection
• What can you Determine?
• What Questions Do You Have?
• What Else Do You Want to Know?
Limit Scaffolding Prompts:
General questions meant to provoke student reflections opposed to calling upon
procedures.
22. Time in Hours Since Vehicles
Started
VolumeofGasinTankinGallons
(0,42)
(4,12)
Driver A
What can you determine given this Data?
Limited Scaffolding Extension 1:
a)Student Private think time. c) Share out in group discussion.
b) Work time with partner. d) Public charting of ideas, knowledge and wonders.
23. Based on what you know about Driver A’s vehicle, add ordered pairs to
the graph that make sense to you.
Time in Hours Since Vehicles
Started
VolumeofGasinTankinGallons
Driver A
Driver B
Driver C
Driver D
Limit Scaffolding Extension 3
This Extension might allow a revisit to the problem or an extension for
student groups who are ready for a new question.
24. Questions for Reflection:
Limiting Scaffolding Wrap Up: A teacher can facilitate the making of explicit
connections. The summary and reflection tasks are the opportunities for students
to reflect and summarize what they know and how they know it.
What math did you use today?
Where did you start in your thinking?
Where did you get stuck?
How did you get unstuck?
What are some general ideas about graphs do you think you
understand now?
How do you know you understand those ideas?
Did you learn any knew math skills while thinking about this
problem?
25. Providing Authentic Relevance
Dan Meyer –A math experience in three acts –
more than watching a video and seeing what
happens. His blog articulates his intentions:
http://blog.mrmeyer.com/2013/teaching-with-three-act-tasks-
act-one/
Examples:
http://www.101qs.com
This website has a selection of searchable “experiences”
Nana’s Milk is an example that requires thinking about
ratios. Search: Nana’s Milk and watch the 48sec clip.
See ACT 2 and ACT 3 on the web site below the video.
26. Pause
• Changing your Pedagogy is Hard, rewarding
work.
• You want a plan: change one thing at a time
• You want a buddy: plan to adopt a classroom
innovation idea with a colleague
• Visit each other’s classroom
• Commit to getting better.
• Remember to consider student buy-in
27. You are establishing
Sociomathematical Norms
• Students ask each other questions that press for
mathematical reasoning, justification, and understanding.
• Students use mathematical arguments when they explain
solutions.
• Mistakes are opportunities to rethink ideas around
mathematical concepts. Does this always work? Why or why
not? Mistakes lead to new learning about mathematics.
Yackel, E., & Cobb, P. (1996). Sociomathematical norms,
argumentation, and autonomy in mathematics. Journal for
Research in Mathematics Education, 27, 458-477.
28. Providing Authentic Relevance
http://www.gapminder.org
These are videos representing socially relevant
data using colorful information rich charts.
• What are the unit rates being used in this video?
• What does it mean if a circle is:
– Larger?
– Moves up or down?
– Moves to the left?
• What else do you want to know? Make a graph of your
own collected data.
29. Example
• Here is a “graph” from Gapminder
One Example
What questions might students ask?
What learning outcomes could you expect?
What skills do you need to use a resource like
this in class?
30. Interactive Resources
• Online manipulatives
– http://nlvm.usu.edu/en/nav/vlibrary.html
• Supporting “hands on learning”with online versions of common manipulatives
– http://www.geogebratube.org/?lang=en
• Geogebra has an abundance of user contributed resources, both worksheets and online tools.
It takes a little sifting to find appropriate tools
• Animated lessons
– http://www.ccsstoolbox.org/standards_content_mathematics.html
• Common Core lessons
• Online graphing Calculator
31. Lesson Plans
Illustrative Math Project
• http://www.illustrativemathematics.org
Growing site with lessons coordinated to Common Core Standards and Practices
Inside Mathematics
• http://www.insidemathematics.org
Tasks coordinated to the Common Core Standards supported by the Dana Center at UT Austin and
the Silicon Valley Mathematics Initiative
Scottsdale Community College
• https://score.scottsdalecc.edu/
Creative Commons Open source books
Math Assessment Project (MARS Tasks)
• http://map.mathshell.org/
Assessments, tasks, professional development support
Southern Regional Education Board
http://www.sreb.org/
Text available for download and use.
32. In Summary
• Responding to change requires dialogue.
• You are going to have questions and wonders.
• Create a professional community of practice.
• Elicit Support
Handouts: http://bit.ly/CarrenW_Practices
Email: carren@collaborativeforambitiousmathematics.org
Carren Walker
Editor's Notes
The sample tasks released demand students apply conceptual understanding of key ideas to form a problem solving plan.Calculators are available on the computer as students take the test.
Click to see examples of what these look like in practice
Wells, Gordon (1993) Reevaluating the IRF sequence: A proposal for the articulation of theories of activity and discourse for the analysis of teaching and learning in the classroom,Linguistics and Education, 5(1), 1-37Gutiérrez, K. (1993/94). How talk, context, and script shape contexts for learning to write: A cross case comparison of journal sharing. Linguistics and Education, 5 (3 & 4), 335-365.