Monthly Archives: March 2014

Brain-based Research to Assist Students!

 This is still a top selling book on how learning best takes place in the classroom.  Download it from Amazon.  You won’t be sorry!


Research-Based Strategies to Ignite Student Learning is the first book for educators written by an author who is both a neurologist and a classroom teacher. Dr. Willis used her neurology expertise to examine the past two decades of learning-centered brain research. Using her background and experience as a clinical neurologist and neuroscience researcher, she sifted through the abundance of neuroimaging and brain mapping information. She assessed what information was both valid and relevant to education. She then employed her training and experience as a classroom teacher to provide strategies for implementing the best of this research in the classroom. She brings this knowledge to life in a comprehensive and accessible style.

Teachers will be introduced to strategies that will work in their own classrooms. These strategies will help teachers improve student memory, learning, and test-taking success. Teachers will also learn how to captivate and hold students’ attention.

Dr. Willis takes a reader-friendly approach to neuroscience, describing instructional strategies that are adaptable for grades K through 12. Through statistical data, individual student stories, and her own experiences using these strategies with elementary and middle school students, Dr. Willis provides teachers with a wealth of information they will want to start using in their classrooms before finishing the book.

The book includes learning strategies that have come from research about how stress and emotion affect learning. Willis describes assessment techniques that not only assess authentically and with diversity, but also teach while assessing. This book will become one that teachers will return to again and again to pick up new strategies to make their ow

Need Problem-Based Fun for your Classroom or Home?


 These are some of the best proven problems on the market !

We’ve got something we think you’ll like—a special two-book package just for you – Getting Into Geometry and Solve It! K-1, both filled with a ton of attention-grabbing, hands-on activities.


We’re so confident you’re going to love and find value in our activities that we want to give you the opportunity to try them at an unbelievable price.


Together, these books normally cost $42.90, but for a limited time you can get the digital versions of this package for only $4.97, an 88% savings. Prefer print? No problem. $14.97 gets you hardcopies of both books with free shipping (within US only), and you’ll still be saving 68%. Not bad, right? Click here to check it all out.


AIMS Education Foundation is a non-profit dedicated to helping excellent teachers like you with math and science.


The AIMS Family


Share the Beauty of Mathematics!

How our 1,000-year-old math curriculum cheats America’s kids

By hiding math’s great masterpieces from students’ view, we deny them the beauty of the subject

Rubik's CubeYou can use a Rubik’s Cube to explain symmetry groups: Every rotation of the cube is a “symmetry,” and these combine into what mathematicians call a group. (Jeffrey F. Bill / The Baltimore Sun)
By Edward FrenkelMarch 2, 2014

Imagine you had to take an art class in which you were taught how to paint a fence or a wall, but you were never shown the paintings of the great masters, and you weren’t even told that such paintings existed. Pretty soon you’d be asking, why study art?

That’s absurd, of course, but it’s surprisingly close to the way we teach children mathematics. In elementary and middle school and even into high school, we hide math’s great masterpieces from students’ view. The arithmetic, algebraic equations and geometric proofs we do teach are important, but they are to mathematics what whitewashing a fence is to Picasso — so reductive it’s almost a lie.

Most of us never get to see the real mathematics because our current math curriculum is more than 1,000 years old. For example, the formula for solutions of quadratic equations was in al-Khwarizmi’s book published in 830, and Euclid laid the foundations of Euclidean geometry around 300 BC. If the same time warp were true in physics or biology, we wouldn’t know about the solar system, the atom and DNA. This creates an extraordinary educational gap for our kids, schools and society.

PHOTOS: From the Fed to GM, 5 top-tier women trying to fix man-made messes

If we are to give students the right tools to navigate an increasingly math-driven world, we must teach them early on that mathematics is not just about numbers and how to solve equations but about concepts and ideas.

It’s about things like symmetry groups, which physicists have used to predict subatomic particles — from quarks to theHiggs boson — and describe their interactions. Or Riemannian geometry, which goes far beyond the familiar Euclidean geometry, and which enabled Einstein to realize that the space we inhabit is curved. Or clock arithmetic — in which adding four hours to 10 a.m. does not get you to 14 but to 2 p.m. — which forms the basis of modern cryptography, protects our privacy in the digital world and, as we’ve learned, can be easily abused by the powers that be.

We also need to convey to students that mathematical truths are objective, persistent and timeless. They are not subject to changing authority, fads or fashion. A mathematical statement is either true or false; it’s something we all agree on. To paraphrase William Blake, mathematics “cleanses the doors of perception.”

What distinguishes us from cavemen is the level of abstraction we can reach. Abstraction enabled humans to move from barter to money, and from gold coins to plastic cards. These days, what’s left of “money” is often just an account record we read on a computer screen, and soon it could just be a line of code in a bitcoin ledger.

Today, abstraction is all around us — and math is the language of abstraction. In the words of the great mathematician Henri Poincare, mathematics is valuable because “in binding together elements long-known but heretofore scattered and appearing unrelated to one another, it suddenly brings order where there reigned apparent chaos.”

For the next generation to operate effectively, they must gain proficiency with abstraction, and that means mathematical knowledge plus conceptual thinking times logical reasoning — all things that a wider view of math would bring to the math classes at our schools.

I recently visited students in fourth, fifth and sixth grades at a school in New York to talk about the ideas of modern math, ideas they had never heard of before. They were young enough that no one had told them yet that math was impenetrable, that they wouldn’t get it. Their minds were still uncluttered with misconceptions and prejudice. They hadn’t yet been humiliated by poorly trained math teachers for making mistakes in front of their peers. Every question I asked them was met with a forest of hands.

I used a Rubik’s Cube to explain symmetry groups: Every rotation of the cube is a “symmetry,” and these combine into what mathematicians call a group. I saw students’ eyes light up when they realized that when they were solving the puzzle, they were simply discerning the structure of this group.

We next studied the majestic harmony of Platonic solids using dice. And I told the kids about the curved shapes (such as Riemann surfaces) and the three-dimensional sphere that give us glimpses into the fabric of our universe.

These are portals into the magic world of modern math, starting points as surely as addition, subtraction and fractions are starting points. The added bonus is that they give us a perfect antidote to the common perception of the subject as stale and boring.

Of course, we still need to teach students multiplication tables, fractions and Euclidean geometry. But what if we spent just 20% of class time opening students’ eyes to the power and exquisite harmony of modern math? What if we showed them how these fascinating concepts apply to the real world, how the abstract meets the concrete? This would feed their natural curiosity, motivate them to study more and inspire them to engage math beyond the basic requirements — surely a more efficient way to spend class time than mindless memorization in preparation for standardized tests.

In my experience, kids are ready for this. It’s the adults that are hesitant. It’s not their fault — our math education is broken. But we have to take charge and finally break this vicious circle. With help from professional mathematicians, all of us should make an effort to learn something about the true masterpieces of mathematics, to be able to see big-picture math, the way we see art, literature and other sciences. We owe this to the next generations.

If we succeed, we will stop treating this crucial subject as if it were the equivalent of painting a fence, and we will do away with the question, why study math?

Edward Frenkel is a mathematics professor at UC Berkeley and the author of “Love and Math: The Heart of Hidden Reality.”

Copyright © 2014, Los Angeles Times,0,5177338.story#ixzz2vOAPb66a

Where is California going with school testing?

A New Era in Measuring Students’ Mathematical Knowledge Is Coming:

The California Assessment of Student Performance and Progress 

Is your school ready?

 In the spring of 2015, California students from 3rd through 8th and 11th grades will officially take the first California Assessment of Student Performance and Progress (CAASPP). This assessment—which replaces the STAR test—includes the Smarter Balanced assessment and reflects the California Common Core Curriculum and Practice Standards. Your school and your students can be ready! 

CMC hopes the following resources will be helpful in your preparations for the new assessment.

Each subtitle below is a live link to its respective web page. 

Smarter Balanced Assessment System

The most dramatic change will be the use of the computer-based Smarter Balanced Assessment. California is one of 23 states belonging to the Smarter Balanced Assessment Consortium. Our new tests will be based upon their system.

Read About One School’s Efforts to Be Ready

Wilson Middle School in Chowchilla shares how they prepared their school and students to be ready for doing well on the new Common Core-based state assessment.

Practice and Pilot Tests

The Smarter Balanced Practice Tests provide an early look at sets of assessment questions aligned to the Common Core for grades 3–8 and 11 in both English language arts/literacy and mathematics. As a teacher, you owe it to your students to take the pilot test yourself. That way you will know what will be asked of your students.

Sample Test Questions

These sample tasks are intended to provide an early look into the mathematics understanding that will be measured by the new assessment system. While these items are not intended as sample tests, use them to plan instruction to help students meet the demands of the new assessments. Try them with your students.

2014 Smarter Balanced Field Test

This spring, students across California will experience a “no stakes” field test of the Smarter Balanced assessments.  The purpose for the Field Test is to establish levels of student achievement in the new assessment. Visit this site to learn all about the Field Test and the Achievement Level Descriptors for mathematics.

Teacher Resources

Many organizations have developed resources to explain the Standards and help teachers support student success in the classroom. These fact-sheets, videos, and instructional resources provide detailed information for educators, parents, and policymakers about the college and career-ready Standards.

Frequently Asked Questions

Use these FAQs to assist your school with transitioning from the former state assessments to the Smarter Balanced assessments. The FAQs may be used to ensure understanding among your staff regarding the universal tools, designated supports, and accommodations available for the Smarter Balanced assessments.

For More About the CA Common Core Implementation

If you would like to learn more about California’s implementation of the Common Core State Standards, visit the California Department of Education web pages. 

Please forward this message to teachers and administrators in your school district

For more CA Standards resources and articles for educators, visit

 CMC’s Common Core Resource web page

The Common Core Math Standards: Content and Controversy

Students will still spend time memorizing math formulas, but thanks to Common Core they will also be required to model the concepts they’re learning.

FE_PR_080725edublog_math.jpgThe Common Core math standards require students to spend equal time on memorization and modeling.

By One comment SHARE
A Guide to Common Core

When the “math wars” began in the 1990s, on one side were those who argued for a new focus on concepts and reasoning rather than drilling students on their times-tables. On the other were the traditionalists, who said the progressive approach allowed students to become unmoored from the building blocks of the subject, leaving them unprepared for more advanced mathematics.

The writers of the Common Core math standards have sought a middle ground.

“There are explicit expectations for knowing the times-table from memory, and that’s going to take dedicated work toward that end. So this isn’t fuzzy math,” said Jason Zimba, a professor of physics and math at Bennington College in Vermont and lead writer of the math standards. “On the other hand, some of the curricula we have are weak on applications, so kids don’t ever get to see what it’s good for, or what it’s used for.”

Students will spend time memorizing and practicing formulas in Common Core classrooms. And they’ll spend an equal amount of time modeling to understand concepts they’re learning about—using the seasons or a business cycle to understand trigonometry, for example.

“I think we’ve had curricula that swing too far to one side or the other on these things,” Zimba said. “The notion of rigor in Common Core involves equal intensity about conceptual understanding, procedural skill, and fluency and application.”

The creation of the math standards was in large part an editing process. Experts have mostly agreed that previously, American math classes tried to cover too much ground, leaving students without the deeper grasp of central concepts that would serve them best in more advanced mathematics. So the Common Core math standards tackle fewer topics, and also move students more slowly through arithmetic, subtraction, multiplication and the other operations that build up to more complex math, particularly algebra.

“These standards are focused in a way that we didn’t have before in the sense that they really try to say in each grade-level, this is what you need to learn so you can move on,” said William McCallum, math department chair at the University of Arizona and a member of the work team for the Common Core math standards. “A lot of curricula tend to keep teaching the same thing over and over again, and never doing it in a particularly deep way.”

Even critics have praised the focus, and also the way that the Common Core math standards address some of these basic areas, especially fractions.

“It’s based on pretty solid research on what is done in high-achieving countries,” said Milgram. “Mathematically, it’s summed up in one little phrase: Fractions are numbers. And it’s made emphatically clear in the Common Core standards.”

“They are not pieces of pizza and they are not little blocks, and they are not a certain number of dots in a bigger set of dots,” he added.

Using pizza to teach fractions isn’t banned, Zimba said. But the idea that fractions are actual numbers that fall on the number line—rather than pieces of something larger—is emphasized.

Other aspects of the Common Core math standards—mostly at the secondary level—have raised concerns among a handful of mathematicians, however.

For one, experts have worried that the standards are encouraging a way of teaching geometry that may not only be above the heads of students, but also hard to grasp for teachers. The standards start with transformational geometry, a way of visualizing congruence by, for example, transposing figures over one another or flipping them into mirror shapes. The authors of the standards say it’s a way to help students grasp fundamental concepts in geometry. Mathematicians, though, worry that what may seem like a simple way of teaching students is actually a highly complex approach more appropriate for college math majors that could reduce the emphasis on the rules and formulas of geometry.

“It’s true that the transformations are the beginning of geometry,” said McCallum. But, he added, “They’re exaggerating what’s in the standards.”

The main critique of the math standards, however, is that they don’t include a full course of Algebra I until high school.

William Schmidt, the Michigan State researcher, has found that “internationally, the focus of eighth grade for all students in virtually all of the TIMSS countries—except the United States—is algebra and geometry.” A National Center for Education Statistics report in 1999 found that 40 percent of U.S. eighth-grade mathematics lessons included arithmetic topics such as whole number operations, fractions and decimals. These topics were much less common in Germany and Japan, where eighth-grade lessons were more likely to cover algebra and geometry.

Algebra in eighth grade prepares students to take more advanced classes in high school, which in turn better prepares them for college and a possible career in science, technology, engineering or math (what are known as the STEM fields).

Research has found that black, Hispanic and economically disadvantaged students are much less likely than their peers to take algebra in eighth grade. Those groups are also less likely to enroll in advanced math classes later in high school. The disparities have turned access to algebra into a civil-rights issue. In the last decade, more states have pushed eighth-graders to take algebra in order to close the gaps and also to meet demands that they better prepare students for STEM careers.

“If you do algebra in grade 8, then you have four years—and if you need to repeat, you can repeat, or you can reach calculus by grade 12. It’s not mandatory for being accepted to colleges, but selective colleges expect it,” said Ze’ev Wurman, a former U.S. Department of Education official under George W. Bush who participated in the creation of California’s highly regarded math standards. (In adopting the Common Core math standards, California rescinded its previous requirement that students take Algebra I by eighth grade.)

“If you don’t prepare everyone, then essentially you only have the privileged kids who are prepared to take [advanced math],” he added.

Research suggests teaching algebra to all students by eighth grade may be ineffective, however. Many students fail because they are unprepared, and even fall further behind. And Zimba says the standards include “an awful lot of algebra before eighth grade,” even if they don’t technically include an Algebra I course. “By the time you’re in eighth grade, you’re solving two equations and two unknowns. It’s highly rigorous,” he said.

McCallum said the eighth-grade standards, though not called Algebra I, cover “what happens in normal Algebra I in high school.”

But Zimba also acknowledges that ending with the Common Core standards in math could preclude students from attending elite colleges or pursuing STEM careers.

“If you’re a young person who wants to become an engineer, or who wants admission … to an elite university, you would be advised to take mathematics beyond the college- and career-level,” he said. “If you want to take calculus your freshman year in college, you will need to take more mathematics than is in the Common Core.”

He argued that it isn’t the role of the standards to close racial and socioeconomic gaps between those who go down that path and those who don’t. “You can simply graduate from high school, you can graduate college- and career-ready [via the Common Core], or you can graduate STEM-ready,” Zimba said. “It would be great if policymakers would make sure underprivileged communities were aware of these distinctions.”

McCallum said the standards make it easier to help students who want to push ahead, however. The Common Core includes directions for alternative pathways that are more advanced than the regular pathway, and which allow a student to complete courses in calculus or something equally rigorous, like statistics, by the end of high school. “It’s always been the case that you need to take more math if you want to be ready for a STEM career,” he said. “There’s always going to be differentiation in high school. So this is not a new thing.”

The main challenge with the new standards, McCallum said, will be ensuring teachers are ready to handle a tougher set of requirements for their students. “A lot of teachers who are used to teaching math as a sort of ‘do-the-math’ subject, they’re going to be called on to have a deeper understanding of what the math is all about,” he said. “For many states, these are simply higher standards than they had before. That in itself is a hard thing.”

This story was produced by The Hechinger Report, a nonprofit, nonpartisan news outlet based at Teachers College, Columbia University. It was written by Sarah Garland for the Hechinger Report’snational reporting project on the Common Core.