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Procedural vs. Conceptual Learning
Conceptual learning provides models, ideas and multiple ways to understand how to solve the math.
Procedural learning provides a formula, trick, or method to solve a particular kind of math without understanding how or why the formula, trick or method solves the problems.
CONCEPTUAL LEARNING What is budgeting as a low income worker?
Read this brief article as you will be answering questions about it. DO NOT OPEN LINKS IN THE ARTICLE unless you are interested.
If you have any trouble opening the link, put this url in your browser. Change browsers if you cannot get to it free. I access it in Chrome and Bing.com https://www.marketwatch.com/story/most-americans-are-one-paycheck-away-from-the-street-2015-01-07
1. DO YOU KEEP HAVE A BUDGET and have you budgeted for unexpected expenses?
2. Bullet list three facts you learned reading "One Paycheck Away From the Street."
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Workshop 1 GAMES AND GAMING |
Spent captures interest and attention with Montessori's point of interest, self-correction and continuous learning w/each play.
A 7th grader in Quincy, MA, explained to his math teacher why playing the game more than once was so important.
He said, "This game is going to teach me how to be an adult!"
Kids and adults LEARN from game play that is interesting to them and contains Montessori's Principles.
They experience learning in the Flow Zone.
The next video shows students learning math playing online games--Motion Math is a favorite of theirs.
View
Motion Math in the Classroom
Math games, board games, computer games, sports and dance, are ways to teach students math procedures and concepts.
Sports, dance, interactive resources, games must NOT over-emphasize procedural facts instead of conceptual learning or students will STOP learning from BOREDOM, FRUSTRATION, OR DISINTEREST.
4. Which of Montessori's Principles do you see in the games in Motion Math?
Point of Interest-- something inviting draws the learner's focus and attention to the experience
Self Correcting Feedback-- the materials offer self-correcting information
Continuous Learning-- every experience playing a game or creating or making, increases learners' knowledge, skills, understanding
Qwirkle is MATH WITH NO NUMBERS THAT WE LEARN BY MAKING MISTAKES.
To try the free online version with friends or someone you are tutoring, here is the link- Qwirkle Freeware
5. Throughout K-12, did you play online games or use a gaming system in math classes to learn math?
If so, did the games keep you in a flow zone OR out of the Flow Zone?
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Workshop 2 Math and Gender |
Researchers in psychology have been studying STEM fields (science, technology, engineering, and math) and a marked gender gap phenomenon. Girls are less likely to major in these fields in college or enter them in the job market.
A recent study from the University of Illinois at Urbana-Champaign suggests that "children can adopt beliefs from information they hear about their gender," through literature, television and media, toys, and conversations with adults.
"A girl who hears that “girls are bad at math” can internalize that message, believe she IS bad at math, and do worse at math because of it."
-Maggie Severns, Future Tense, June 14, 2012
What games and toys are for young children to use and call their own? How do toys influence beliefs?
ADD a question about toys.
Hear
How One College Is Closing the Tech Gender Gap
How One College Is Changing the Tech Gender Gap reports 18% of U. S. in computer science graduates are female.
6. Bullet list four initiatives to teaching and learning Harvey Mudd College instituted to attract women to the computer science program and keep them learning.
7. If you were expanding this program to attract and interest all kinds of students in computer science, mathematics and engineering design courses, what would you CREATE THAT IS NOT PRESENTLY THERE to add to Harvey Mudd's initiatives?
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Workshop 3 Stop Motion Animation Videos |
Stop Motion Animation Videos by elementary school students!
View 1st, video
View
She speaks quickly but the ideas shown are helpful.
View
https://www.exploratorium.edu/tinkering/blogs/getting-started-with-stop-motion-studio
This shows how to make a 2 frame video.
Create Your Stop Motion Video
Download an stop motion video making app.
We use the FREE version of Stop Motion Studio
Email your video to me or upload it your learning log.
Google drive does not allow you to insert video into a google doc.
A solution to this is to record yourself on your phone or computer.
Take the video file and upload it to google drive.
Once uploaded to google drive, set the permissions for the video to anyone with the link can view--click the three dots in the top right corner, then click share.
8. Where is math involved in stop motion animation video making? What concepts are we using?
BIG IDEA Closer Mindsets--How do we change ours to help us learn?
9. Applying your knowledge about factors that produce growth and fixed mindsets, analyze in a few sentences the mindset you have about learning mathematics. How did you get this mindset?
10. DO YOU THINK having choices of multimodal resources to learn with as you did in this assignment-- using stop motion animation video production, playing Spent, and learning math with game play would positively help you to enjoy learning math?
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Not Part of the Assignment
Animations and Storytelling from Young Writers Bookcase
A Ingham's List of Technology & Teaching Resources, Updated Frequently
Link to Using the Google Suite for Student Centered Teaching of Mathematics, Maddy Hill Slide Deck (Spring 2021)
Link to the Tutoring Math Digital Choice Board
More information about money and the state of our economy: https://www.marketplace.org
What happens when poor families are given SMALL guaranteed incomes monthly?
Find out what happened in this pilot study w/ Stockton, CA families.
https://www.pbs.org/newshour/show/stockton-ca-gave-residents-a-guaranteed-income-heres-what-happened
View
GoldieBlox, a toy company determined to raise the number of female engineers, uses their innovative toys to draw interest in the STEM subjects in young girls, which is often lost as they get older.
Does this commercial upend the argument of the judges in the next story OF A FEMALE? For your consideration and discussion in the Zoom conversation.
A game for tutoring yourself or others!
Qwirkle: Math Without Numbers
- Math is the least favorite of more than one-third of students, the highest unfavorable rating of any subject.
- 34 percent say math is least favorite in 2017 report What Teens What From Their Schools: A National Study of Student Engagement
- See chart from Grant Wiggins
- Math is only subject among all the least favorite choices in which the leading response was "I am bad at it!"
Today we are going to play a game of shapes and colors that promotes mathematical thinking and mathematical learning, both procedurally and conceptually.
It is called Qwirkle
- Used to teach math problem-solving skills
- Improve children's capacity to think logically and solve problems in novel situations
- Promotes visual-spatial reasoning
- Math concepts of sets with characteristics
Activities
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Qwirkle consists of 108 wooden blocks of six shapes and six colors.
- Briefly explain and demonstrate rules (procedures) for playing the game
- Use game from the previous group to show how rows are built and points are scored
- Create teams of 2 or 3
- Ask each team to create a team name
- Draw 6 blocks and begin game play
- 4th Grade Rules: Play as many blocks as you can during each turn
- Ask team players to call the points as they get them
Play Qwirkle Against the Computer with the Qwirkle APP
- Qwirkle App from the App Store
What is the procedural and conceptual learning in the game?
Math TUTORIALS
Khan Academy, is an online tutor for elementary, middle, high school, and college students learning astronomy, biology, calculus, chemistry, geography and more, has the mission "to provide a world-class education" experience free online to everyone.
Video
View TED talk: Kahn Academy
Salman Khan's original intent for creating his tutoring site completely changed when users he had not planned for found the videos.Summarize Khan's initial intent for his videos and compare that to what Khan Academy is now.
Would you conclude that this change resulted because of amistake, having a growth mindset,creating a change of purpose or something else entirely?What is Khan Academy offering schools and students to positively influence teaching and learning? (View 11:00-15:20)
Interactive TimesTable from NCTM
Motion Math, the Definitive Review
Why Play Math Games? Kitty Rutherford, Teaching Children Mathematics (April 27, 2015)
Read and hear One Teen's Story of Science Sexism
5. What ACTIONS might you do to TURN AROUND THE JUDGES' DECISION AND HELP her GAIN a different outcome FROM WHAT HAPPENED?
Tutoring Others
Who are you tutoring?
What are you tutoring?
Self-Tutoring
What are you self-tutoring?
Are you taking 2 hours/week to pursue this learning?
In 1-2 paragraphs describe TEAMS’ words, ideas or actions from the list above that you are using from the TEAMS’ weekly classes to assist tutoring others.
In 1-2 paragraphs describe TEAMS’ words, ideas or actions from the list above that you are using from the TEAMS’ weekly classes to assist your self-tutoring.
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