# data[].attributes.body
You still hear it too often: ” The right side of your brain is responsible for creativity and the left side for logic”. This belief also claims that, depending on the person, one side is more dominant than the other. Although it all sounds catchy and “sells” easily by speakers and corporate trainers, neuroscience proves this is a myth

# data[].attributes.attachment_link.readable_text
You still hear it too often: " The right side of your brain is responsible for creativity and the left side for logic". This belief also claims that, depending on the person, one side is more dominant than the other. Although it all sounds catchy and "sells" easily by speakers and corporate trainers, neuroscience proves this is a myth.

What neuroscience data tell us?

Yes, there are specialized areas in the left and right hemispheres of the brain (especially related to vision and movement). However, tons of neuroscience research, including my own, has proven time after time that creative and analytical thinking are not strictly lateralized. Interesting as well is that your brain constantly communicates to both sides through a brain structure called corpus callosum.

In addition, you can apply both brain functions when needed. Otherwise you wouldn't be able to navigate this complex world, solve problems or come up with new ideas.

Take-home message

Although you might prefer analytical tasks over creative ones, you do have the ability to use both skills. Crucial is that you have the mental flexibility and reflective skills to adapt your processing strategies to face new and unexpected situations.

Learn more about the Left-Side Right-Side Brain Myth:

# data[].attributes.attachment_link.title
Brain Myth: Creative Right & Logical Left Brain | Academy 404

# data[].attributes.attachment_link.description
You still hear it too often: " The right side of your brain is responsible for creativity and the left side for logic". This belief also claims that, depending on the person, one side is more dominant than the other. Although it all sounds catchy and "sells" easily by speakers and corporate trainers, neuroscience proves this is a myth.

# data[].attributes.attachment_link.title
Trying 3-Act Tasks with Primary Students_tcm2017-10-112a

# data[].attributes.headline
Research Paper:                       3-Act Math Modeling

# data[].attributes.subject
Research Paper:                       3-Act Math Modeling

# data[].attributes.body
Check out this video that a Colorado Math teacher uses in her classroom to show what learning looks like!

# data[].attributes.attachment_link.title
Baby Giraffe Tries to Stand and Takes His First Steps

# data[].attributes.body
6th, 7th, 8th, Algebra, Geometry, Algebra 2

# data[].attributes.attachment_link.title
enVision Algebra I, Geometry, and Algebra 2 Program | Pearson High School Math Curriculum

# data[].attributes.attachment_link.description
Engage your students with Pearson's AGA Algebra I, Geometry, and Algebra 2 math programs. Learn more about Pearson's innovative math lessons and research-based instruction.

# data[].attributes.attachment_link.readable_text
What is 3-Act Math Modeling?
Math modeling is often misinterpreted as using manipulatives while solving math problems. Authentic math modeling requires the use of mathematics to make sense of real-world situations. "Making sense" is the key to such math modeling. Unlike traditional real-world problems, the 3-Act Mathematical Modeling lessons in do not set up the problem for students to solve. Students are presented with a collection of information and context for it, but they then determine what the question is that needs to be solved and what material is pertinent to solving that question. This connection to students' real lives and the ability to interpret that data is integral in helping students think mathematically.

3-Act Mathematical Modeling lessons are designed to engage students in mathematical modeling of everyday events to help students see that math really is all around them and that it can explain the events. These lessons present students with the opportunity to model conceptual thinking in real-world situations. They require students to identify essential variables, formulate models from those variables, perform operations using the model, interpret the results of those operations, and validate the conclusions of those results. It all takes place within three simple acts.

Dan Meyers says it well: "Storytelling gives us a framework for certain mathematical tasks that is both prescriptive enough to be useful and flexible enough to be usable. Many stories divide into three acts, each of which maps neatly onto these mathematical tasks."

For a more in-depth look at what Mathematical Modeling is, see Eric Milou's Mathematical Modeling Monograph. (Link to document here.)
3-Act Mathematical Modeling Lessons
In , stories were chosen for the 3-Act Mathematical Modeling lessons that require all manner of mathematical tasks. In the program, these lessons are organized into 3 parts:

Pose the Problem - ACT 1, The Hook: a multimedia presentation engages students (example video below) and then is followed up online by a brainstorm of possible question and answers situations.

The Model - ACT 2, The Model: Students develop mathematical models to arrive at a solution.

The Resolution and Sequel - ACT 3, The Resolution: a multimedia presentation (video example below) helps learners explain the differences between their own conjectures and the actual solution.

What's so great about 3-Act Math Modeling?
There are three significant reasons 3-Act Math Modeling lessons are making an impact in math classrooms. Math modeling lessons offer an embedded learning opportunity for students to connect what they are learning in class to real-world situations. These lessons present an engaging, high-interest situation for which students propose a mathematical model to help them get resolution. The situations featured in these lessons are relevant to students, making math personal. 3-Act Math Modeling lessons answer the commonly asked question "when will I ever need this math skill in real life?"

With 3-Act Math Modeling lessons, students control identifying the problem to be solved, determine the relevant information, and choose how they solve the problem. When students are given the opportunity to make choices in their classwork, they are more invested. They are more interested and motivated, which increases their effort toward understanding math concepts.

Not least is that these lessons are low threshold, high ceiling activities. The work during these problems is far more significant than the answers themselves. Students of all abilities can work and contribute to solving problems. Though students can work at their own pace and depth, rich discussions result during each Act that challenge all students. No matter their level, the cognitive demand remains high, so that all students have the opportunity to stretch their mathematical understanding and skills.

Take a look at some of these enVisionmath 2.0 3-Act Math Modeling lessons and use them in your classroom today. No matter what program you are currently using, click here to download everything you need to get started using these lessons with students.
Download our FREE 3-Act Math Modeling Lessons Today!

# data[].attributes.attachment_link.title
Engaging Students with 3-ACT Math Modeling - Fresh ideas for teaching blog

# data[].attributes.attachment_link.description
What is 3-Act Math Modeling? Math modeling is often misinterpreted as using manipulatives while solving math problems. Authentic math modeling requires the use of mathematics to make sense of real-world situations. "Making sense" is the key to such math modeling. Unlike traditional real-world problems, the 3-Act Mathematical Modeling lessons in enVisionmath2.0 do not set up ...

# data[].attributes.headline
NCTM: Promoting Growth Mindset with 3-Act Math

# data[].attributes.subject
NCTM: Promoting Growth Mindset with 3-Act Math

# data[].attributes.attachment_link.description
I train mathematics educators who want their students to be better problem solvers.

# data[].attributes.attachment_link.readable_text
Folks, if you teach stats in middle school or high school, 2019 is your time to shine.

Here are a couple of items where the world needs your help and one way where the world (a/k/a Desmos, the New York Times Learning Network, and the American Statistical Association) is here to support you.

Marginal Tax Rates

Here is a clip from 60 Minutes in which Congresswoman Alexandria Ocasio-Cortez proposes a 70% top marginal tax rate.

And here is a ranking of the last five words of that sentence for "concreteness of meaning to average Americans":

1. 70%
2. tax
3 [tie]. rate, top, marginal

A 2013 YouGov poll convincingly illustrates how little Americans understand our marginal tax rate system. YouGov posed the following scenario:

Suppose that your income put you at the very top of the 28% tax bracket and you earned one more dollar such that you were now in the 33% tax bracket.

They asked 818 respondents to choose between two options:

1. My tax bill would go up a very small amount.

2. My tax bill would go up substantially.

Only 52% of respondents correctly answered that their tax bill would go up a very small amount. Democrats answered that question correctly nearly twice as often as Republicans, a difference which is amply explained by all the Republican leaders who are smart enough to know how marginal tax rates work lying to people about how marginal tax rates work.

Explaining tax rates before Reagan to 5th graders: "Imagine if you did chores for your grandma and she gave you $10. When you got home, your parents took $7 from you." The students said: "That's not fair!" Even 5th graders get it.

- Scott Walker (@ScottWalker) January 15, 2019

We need to help our students - whatever their political inclinations - believe fewer lies.

There are lots of interesting questions our students (and their teachers!) should ask about taxes and the kind of society they want to live in, questions like " What are the upsides and downsides of making Dwayne 'The Rock' Johnson pay 70% of the money he makes above 10 million dollars in taxes?" But we cannot answer those interesting questions if we don't have a basic command of the facts of our tax system, if we allow our leaders to deceive us about how marginal tax rates work.

Stats teachers: you have the power to make your students smarter about taxes in a day than fully half of Americans have been in their entire lives.

1. Take a few representative individuals from the world - real or imagined, but definitely including The Rock.

2. Hypothesize their income. Just make up numbers across an income distribution.

3. Use our tax brackets to calculate their tax bill.

4. Create a new set of brackets that are more just.

What's Going on in This Graph?

At Desmos, we've been enormously enthusiastic about the partnership between the New York Times Learning Network and the American Statistical Association they call What's Going on in this Graph?

In that partnership, the NYT team selects a newsworthy and timely graph from their award-winning output. The ASA team hosts a conversation on the NYT website about what students notice and wonder about those graphs.

For the rest of the school year, my team at Desmos will be helping teachers host those conversations in their classrooms from our Activity Builder platform. A new graph and activity every week. Give them a try.

There's no time like 2019 to start all of this.

Featured Comments & Emails

Ben Orlin offers a useful lesson plan here:

One of my favorite parts of teaching Precalculus was a "Design Your Own Income Tax System" project, which went something like:

-Make up your own system (minimum: 5 brackets);
-Write a paragraph justifying your decisions;
-Make up 5 individuals (+ their professions) and compute how much tax each would pay;
-Express MTR as a function of pre-tax income (and graph it);
-Express tax owed as a function of pre-tax income (and graph it). (By far the hardest step.)

An unhappy email:

While the information about Americans misunderstanding taxes did not surprise me, your choice to bring politics into the situation did. How do you propose we use your information about the tax knowledge of Democrats vs. Republicans with our students? Should we poll the students on their political affiliation and spend twice as much teaching taxes to our Republican students as we do our Democrat students?

The difference in tax knowledge between Democrats and Republicans along with the propensity of Republican leaders to lie to their constituents about marginal tax rates is meant to heighten the importance of good instruction here. Whether students grow into Republicans or Democrats is irrelevant to me (in this particular moment). If they or their parents pay attention to Republican leaders or media, they are getting lied to about this particular issue and we can do something about that.

Another unhappy email:

You've made this particular mail also about politics. Roughly: "Dem/good Repub/bad" Does that serve your core goal (statistics pedagogy)? Thanks for this free service. I hope to read the next one.

FWIW I'm more inclined to believe "people/bad" than "Democrats/good" "Republicans/bad." But it certainly seems true that Republican leaders are willing to lie about this issue and that Republican voters are believing those lies. Teachers can and should subvert that relationship. Not necessarily converting Republicans to Democrats but making sure Republicans disbelieve their leaders when they lie.

Another:

This sort of proselytizing does nothing but polarize. You're taking advantage of those who follow you for your insights with math education to preach your opinion about complex, controversial political topics that require nuanced thought and discussion to resolve. Have you ever changed your mind due to other people smuggling in their unsolicited opinions about politics like this? If you're looking to change people's minds about politics, do it through an open, honest platform where that is your sole purpose. I hope you stick to math without trying to fit in other agendas that distract from this purpose in the future.

I get that it's a drag to see a) Republican leaders lying to their constituents, and b) their constituents believing those lies, but those aren't "opinions" of mine. They're the facts of the situation, and teachers need to work an overtime shift countering that deception. I hope that directly before or after you emailed me you emailed a complaint to the Republican leaders who are making your job harder.

Another:

When I was at university, we would have been required to present various viewpoints on an issue. Our professors would have required us to present pros and cons for each side. For examples, [dopey climate denier webpage] would give an alternative for our students to consider.

Thanks for the comment. Some issues are controversial enough that they deserve a hearing of multiple sides. Many other issues deserve no such hearing. The fact that " global climate change caused by human activities is occurring now, and it is a growing threat to society " is a settled issue by climatologists, our government, the military, and even for=profit insurance agencies. Now we need to decide what to do about it. By contrast, whenever I write my post declaring The West Wing the most overrated show of the 20th century, I will be sure to allude to opposing points of view.

Reader Bill Rider sent in his account of a lesson from his class:

I stated that this prompt came from a political discussion that revealed a lack of understanding about marginal tax rates among fellow politicians and pundits. Our learning about this idea would make us better informed that many adults. ( This enhanced their attention.)

In true Dan style, I didn't want to script this too much. Together, we wrote the seven marginal tax rates on the board.

I asked them how much tax one would pay (Individual) on a salary of $9,525. (Upper end of the lowest bracket.)

I then asked how much extra tax one would pay if they received a $10,000 raise. This allowed the kids to learn that some of the money is taxed at one rate and the rest at another.

We then considered someone who earns $520,000 a year. How much of that salary would be taxed at 37%?

In their groups, they collaborated to determine the total tax bill on $520,000.

Collecting each of the seven tax bracket computations allowed us to see things like: .32| 157,501 - 200,000| = tax for that portion of income

We determined that effective tax rate. Each class had at least one student who asked "why can't we just make life easy and use that effective rate for everyone?" Rich discussions ensued.

We discussed the many who fear moving into the next tax bracket and why such a fear was unfounded.

We discussed a representative's proposal to move towards a higher upper bracket of 70% , historical higher rates, the number of folks that might be affected and whether one would pay 70% on all income as a high earner.

I started to type up a worksheet but it seemed to scripted/guided... and it didn't come from their questions and their desire to be better informed than an adult.

# data[].attributes.attachment_link.description
Folks, if you teach stats in middle school or high school, 2019 is your time to shine. Here are a couple of items where the world needs your help and one way where the world (a/k/a Desmos, the New York Times Learning Network, and the American Statistical Association) is here to support you.

# data[].attributes.attachment_link.description
Dr. Milou's mathematics website of links, videos, assessments, and more for K-12 mathematics.

# data[].attributes.body
Today's traditional math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. Dan Meyer shows classroom-tested math exercises that prompt students to stop and think.

# data[].attributes.attachment_link.description
Today's math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. Dan Meyer shows classroom-tested math exercises that prompt students to stop and think.

# data[].attributes.body
GAIMME helps define core competencies to include in student experiences, and provides direction to enhance mathematical modeling education at all levels.

# data[].attributes.attachment_link.readable_text
Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME) Second Edition

Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME) Second Edition, a freely downloadable report, enables the modeling process to be understood as part of STEM studies and research, and taught as a basic tool for problem solving and logical thinking. GAIMME helps define core competencies to include in student experiences, and provides direction to enhance mathematical modeling education at all levels. The second edition includes changes primarily to the "Early and Middle Grades (K-8)" chapter. The GAIMME report is freely downloadable from both the SIAM and COMAP websites. View, download, or print the GAIMME report in color or black and white below.

Download Report Order Print Copy

Download Black & White Rubric Printout PowerPoint Template

Writing Team

with suggestions from many reviewers

What is Mathematical Modeling?

Early Grades (K-8)

High School (9-12)

Undergraduate

Resources

Contents

Example problems and solutions

Levels of sophistication

Discussion of teacher implementation

Suggestions for assessment

Key Components

Funded By

Consortium for Mathematics and Its Applications (COMAP) and SIAM with cooperation of National Council of Teachers of Mathematics and support from The Moody's Foundation.

GAIMME: Guidelines for Assessment and Instruction in Mathematical Modeling Education, Second Edition, Sol Garfunkel and Michelle Montgomery, editors, COMAP and SIAM, Philadelphia, 2019. View the entire report, available freely online, at https://www.siam.org/Publications/Reports/Detail/guidelines-for-assessment-and-instruction-in-mathematical-modeling-education

Questions? Contact us.

Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME) Second Edition

Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME) Second Edition

Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME) Second Edition, a freely downloadable report, enables the modeling process to be understood as part of STEM studies and research, and taught as a basic tool for problem solving and logical thinking. GAIMME helps define core competencies to include in student experiences, and provides direction to enhance mathematical modeling education at all levels. The second edition includes changes primarily to the "Early and Middle Grades (K-8)" chapter. The GAIMME report is freely downloadable from both the SIAM and COMAP websites. View, download, or print the GAIMME report in color or black and white below.

Download Report Order Print Copy

Download Black & White Rubric Printout PowerPoint Template
with suggestions from many reviewers

What is Mathematical Modeling?

Early Grades (K-8)

High School (9-12)

Undergraduate

Resources

Writing Team

Example problems and solutions

Levels of sophistication

Discussion of teacher implementation

Suggestions for assessment

Contents

Key Components

Funded By

Consortium for Mathematics and Its Applications (COMAP) and SIAM with cooperation of National Council of Teachers of Mathematics and support from The Moody's Foundation.

GAIMME: Guidelines for Assessment and Instruction in Mathematical Modeling Education, Second Edition, Sol Garfunkel and Michelle Montgomery, editors, COMAP and SIAM, Philadelphia, 2019. View the entire report, available freely online, at https://www.siam.org/Publications/Reports/Detail/guidelines-for-assessment-and-instruction-in-mathematical-modeling-education

Questions? Contact us.

Become a Member

Sign up for our Newsletter

Support SIAM

# data[].attributes.attachment_link.description
Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME) Second Edition, a freely downloadable report, enables the modeling process to be understood as part of STEM studies and research, and taught as a basic tool for problem solving and logical thinking.