Listening, Learning, and Teaching: A Virtuous Cycle (include the word "math" in the title?)
Thinking vs. doing
Math for Adventurous learners
The Impeded Stream
Learning from students
Looking Forward, Look Back
Student Work Samples (including the five mixed number subtraction strategies)
Racing to the Finish? (acceleration)
Noticing and Wondering (multiple parts)
"I'm not a math person..."
Motivation and Mindset
A rule of thumb for math acceleration: "If you have to teach them how to do it, then you shouldn't."
What makes a lesson exciting (not always the superficial). It happens when students ideas are at the forefront
The role of and issues with "real-world" problems - necessary? sufficient? implementations that do and do not work; contrived problems; "messiness" of realistic problems; being clear about purpose (motivation, application, using context to develop conceptual understanding, understanding modeling process, etc.)
How To Bring This Private School Teaching Method Into A Public School Classroom (about the Phillips Exeter Academy in San Diego)
How does this article related to "Noticing and Wondering"? How can these teaching methods be adapted to math?
https://giftedchallenges.blogspot.com/2017/07/six-reasons-to-stop-treating-gifted.html (Focus on needs. Services that meet needs are not rewards. Different work for gifted students is not special treatment. Just like all students, it is gifted students job to do work that moves their learning forward.
https://www.theatlantic.com/education/archive/2017/07/the-underrated-gift-of-curiosity/534573/ (The importance of curiosity in achievement, happiness, etc. and the fact that it is missing from gifted ID (and programming?): 'Motivation should not be considered simply a catalyst for the development of other forms of giftedness, but should be nurtured in its own right,” note the Gottfrieds. Stimulating classroom activities are those that offer novelty, surprise, and complexity, allowing greater autonomy and student choice; they also encourage students to ask questions, question assumptions, and achieve mastery through revision rather than judgment-day-style testing.'
Ten Plus One: concrete strategies for enriching routine math tasks
Even basic math tasks contain deep ideas that are worthwhile for advanced and adventurous learners to explore. Learn some alternatives to simply accelerating bright students into “the next topic in the book.”
What Does It Mean to “Do the Math”?
A few simple shifts in the way we frame the questions in our math classrooms can engage advanced learners and set all students on a path to deeper learning.
Nurturing Adventurous Mathematical Learners
Adventurous learners have two key qualities: curiosity and a willingness to take risks. Bring out the mathematical adventurer in your students.
“I’m not a math person…”
Is it true that some people just aren’t math people? What does it even mean to be a math person? How do our beliefs on this subject affect the way we teach?
Intrepid Math: Challenging bright math students without rushing them
All mathematical topics are brimming with potential for deep and meaningful learning. Explore example of problems and projects that engage upper-elementary gifted and talented math students in truly deep and meaningful learning.
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Ask Nick about the best coding platform for learners (include W3)
3 Act Problems
great pages (and videos) for motivating topics: group theory, fractals, prime numbers, higher dimensions, golden ratio,
Dan Brown TED talk
Notes about double number lines (for Perplexing Percentages):
Double number lines are recommended in the Common Core and other places. There are a few things to keep in mind. The double number lines are a thinking tool, not a task to memorize and perform. They help kids do three things:
- Visualize relationships.
- Develop strategies.
- Explain thinking.
They are also great for helping kids estimate.
Don't make too many rules about how kids draw or use them. Let them decide how carefully they should draw them. Let them decide how much detail they need to show. As long as the number lines help kids do the three things above, then they are working the way they should.
In class, show students very briefly how the two lines are drawn so that matching numbers are vertically above/below each other. Stress the importance of figuring out the 0% and 100% parts. Maybe ask them to compare to tables to double number lines (just like tables, the lines show which numbers match to which, but the lines also show amounts in between). Have kids collaborate to solve the problems. Have groups share and compare their number lines and their thinking strategies. Get them talking about advantages and disadvantages of different ways that different groups make their double number lines and the different strategies they use to solve the problems.
All of this is about getting kids to create their own strategies for doing percent problems instead of memorizing rules such as "to find a percent, divide the two numbers and then multiply by 100" or "to find the percent of a number, turn the percent into a decimal and multiply it by the number." Kids forget these rules, because they don't usually understand why they are doing them. When they use estimation, visuals, and common sense to create their own strategies, they retain their knowledge.
IDEAS FOR "COOL STUFF"
http://www.scientificamerican.com/video/epic-math-battles-legos-versus-trees/?WT.mc_id=SA_SP_20160328 (Epic Math Battles Video)
Mechanical Binary Counter (Notice and wonder what this is without seeing the title!) @fermatslibrary
animated pictures of prime factorizations: http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/
Thoughts for the day (N&W)
Patterned lists of equations help students discover meanings and make connections. (E)
Don't tell students anything when you first display a prompt. Just ask them what they notice and wonder, and let their ideas flow! (E)
Noticing and wondering prompts are great tools for differentiation, because students naturally respond at their own level of thinking. (E)
Sometimes, you can use noticing and wondering prompts to suggest problem-solving ideas—but now the students participate in creating the problem! (E)
Patterned lists help students discover meanings and make connections between math concepts (M)
The meaning of fraction division may be the most challenging concept in arithmetic. Give students plenty of time to think! (M)
Help students learn to feel comfortable sharing their "noticings" and "wonderings" by accepting all ideas without comment at first. You can discuss them later. (M)
Inserting blank spaces into a multiplication table encourages students to predict products of fractions or decimals before they learn the rules. (M)