The post Youth Digital Uses Minecraft to Teach Programming appeared first on Education News.

]]>Minecraft, a popular online game for all ages, has been put to creative use as a teaching tool since its inception. Now, its educational applications are getting even more sophisticated: an online course called Server Design 1 uses the game to give kids an introduction to computer programming.

The course was designed by Youth Digital, a company that focuses on the technology education of kids 8-14, including coding, app development, and 3D modeling. With the Minecraft course, students learn to make mods for the game.

10 year old Ronan, who is enrolled in the course, summarized the appeal of the course:

I can turn a blank screen into a virtual playground.

Minecraft is a sandbox-style game reminiscent of Legos, in which players collect resources and assemble cube-shaped blocks into houses to protect themselves from monsters. These can range from simple structures to stunning works of art. There are two modes that players can make use of: survival mode, in which they’re running from enemies who are particularly dangerous at night, and creative mode, in which they have unlimited resources to build whatever they can dream up.

Justin Richards, Youth Digital CEO, said:

This matches science and storytelling into a singular project. It’s exploratory and just plain cool to actually get to modify the code and change the game that you love.

For $250 a year, students gain access to a Java server, curriculum, tools, and hosting with Youth Digital. They can design their own settings, characters, and scenarios, writes Brett Murphy of CNET.

Ronan said:

You get to add things that you would never ever, ever, ever be able to do without a programming interface. You can create skeletons wearing iron doors. How weird is that?

The course is designed to be engaging for students, and includes traditional media like videos, questions, quizzes, and assignments, but students can also earn badges for their achievements.

Kim Boyarski, the parent of a student using the program, said:

I like that Server Design 1 teaches my son Java, a real programming language, in a way that is fun and interactive. It allows him to create his own world and share it with his friends. He has been very excited to show off his work thus far and what he’s been able to create. I’ve been impressed with what he could accomplish after a few short lessons.

Minecraft’s other applications as a teaching tool include the Australian government’s yearly competition in which children design their “perfect national park” with Minecraft and MinecraftEdu, a version designed specifically for the classroom.

Richards said:

If you tell 9-year-olds that coding experience will help them get a job in the future, they might not be too interested. But if you ask them if they want to create a video game, they’ll answer yes every time.

Minecraft was acquired by Microsoft for $2.5 billion in 2014, reports Tyler Lee of Uber Gizmo.

Youth Digital also offers other online courses, in addition to summer camps and enterprise partnerships.

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]]>The post Study: Recognition of Abilities Helps Drive Interest In Math, STEM appeared first on Education News.

]]>According to a new study published by Florida International University Professor Zahra Hazari in the journal *Child Development, *interest and recognition can help increase a student’s enthusiasm for math and their willingness to pursue a career in STEM fields.

The study, “Establishing an Explanatory Model for Mathematics Identity,” suggests that an increased interest in the area of math is not something a person is born with, as was previously thought. It continues to say that students who have an increased confidence level in the subject do not necessarily become interested in it.

“Much of becoming a ‘math person’ and pursuing a related STEM (science, technology, engineering or math) career has to do with being recognized and becoming interested – not just being able to do it,” said Hazari, who specializes in STEM Education at FIU’s College of Education and STEM Transformation Institute, according to the NEA blog. “This is important for promoting math education for everyone since it is not just about confidence and performance.”

Participants included over 9,000 college students enrolled in calculus courses across the country. Researchers discovered that students who were enrolled in higher-level courses were doing so mainly due to an interest in the subject that evolved from some form of recognition of their abilities previously given to them, as well as finding the topic interesting.

The survey asked participants whether they felt family, friends, and math teachers viewed them as a “math person.” Those who responded positively to the question were classified as feeling recognized.

“It is surprising that a student who becomes confident in her math abilities will not necessarily develop a math identity,” Hazari said. “We really have to engage students in more meaningful ways through their own interests and help them overcome challenges and recognize them for doing so. If we want to empower students and provide access to STEM careers, it can’t just be about confidence and performance. Attitudes and personal motivation matters immensely.”

A separate study performed at Washington State University looked at 122 undergraduate students as well as 184 other participants who were all asked to complete a math test and then take a guess as to how well they did. One group received feedback pertaining to their scores prior to giving their guesses, while the other group had no feedback, and were also asked to state whether they held any interest in pursuing a career related to math.

While male participants repeatedly overestimated their math exam scores, women tended to predict their scores more accurately. However, it was found that more men wanted to pursue a math-related career than women, suggesting that the belief that a person is competent in a subject is directly related to the decision to follow a career path in that field, writes Dana Dovey for Medical Daily.

Researchers hope to use the study findings in order to get more girls interested in careers in math and science. To date, women in the United States make up almost half of the work force, although they account for only 24% of STEM positions, or those in science, technology, engineering or math jobs.

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]]>The post U Maryland, Georgia Tech Top NASA Concepts Competition appeared first on Education News.

]]>A team of students from Georgia Tech have taken first place in a recent NASA and National Institute of Aerospace contest that asked competitors to solve a variety of real-life space exploration challenges.

Overall, sixteen teams competed in the 2015 Revolutionary Aerospace Systems Concepts Academic Linkage (RASC-AL) Competition. This year NASA asked its participants to create a mission that would bring together new technology and innovative approaches in order to allow astronauts to become less dependent on materials and resources brought from Earth. Research and designs were presented to the judges, who took three full days to determine the winner.

“Some of the teams had ideas that NASA might be able to use as we venture out beyond low-Earth orbit,” said Pat Troutman, Human Exploration Strategic Analysis lead at NASA’s Langley Research Center in Hampton, Va. “The judges and I were impressed by the students’ engineering skills and innovative thinking.”

Top honors went to a team of students from the University of Maryland, College Park. The team created plans that would use the moon as a fueling stop on the way to Mars. The fuel would be created using lunar surface materials.

Meanwhile, the team from Georgia Institute of Technology placed first in the graduate division. Teams focused their missions on one of four themes that would allow astronauts to become less dependent on resources brought into space from Earth, including using materials on Mars, using materials on the moon, a Mars moon prospector and large-scale Mars entry, descent and landing, writes Carla Caldwell for *The Atlanta Business Chronicle.*

According to NASA, missions to Mars ask astronauts to travel long distances for extended periods of time, living and working far away from Earth without the luxury of readily available resupply shipments. This makes understanding how to best utilize resources found on both Mars and the moon to be of the utmost importance. Determining the usability of the resources will ensure that human exploration may continue.

Through their participation in the event, sponsored by NASA’s Advanced Space Exploration Division (AES) at NASA Headquarters and the Space Mission Analysis Branch at NASA’s Langley Research Center, student teams gain real-world experience with NASA’s current human space exploration mission design planning, which could influence future NASA missions.

A separate contest offered participants the opportunity to create a digital 3-D model of a space tool with the potential to be created by a Zero-G 3-D printer aboard the International Space Station to be used by astronauts while in space.

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]]>The post Purdue University to Open STEM-Focused Charter School appeared first on Education News.

]]>Purdue University has announced that it will be opening the Purdue Polytechnic Indianapolis High School in August 2017, a STEM-focused charter school that will offer classes designed and developed by the Purdue Polytechnic Institute faculty. The venture aims to be a Purdue university pipeline that will help more low-income and minority students continue at Purdue.

Purdue University president Mitch Daniels announced the university’s plan to open a new charter school by the summer of 2017. Initially the school will open for 9th graders only and then welcome about 300 to 400 students. The high school will:

“[P]rovide a bridge for inner-city students and others to succeed in high school and to be admitted directly to Purdue University,” Daniels said during the high school announcement June 18.

Faculty from Purdue will create a new curriculum that will be a fusion of K-12 and postsecondary education with a focus on industry leadership and participation according to Gary Bertoline, Purdue Polytechnic Institute dean.

Purdue faculty from both the Polytechnic Institute and the University will mentor the school’s teachers.

For the first two years, freshmen and sophomores will participate in problem- and project-based learning. The curriculum will focus on science, technology, engineering and mathematics, always in connection with real-life challenges.

Eleventh grade students will then have to choose which skills to expand on further and will be able to earn college credit while expanding their industry credentials.

Seniors will complete an internship in the STEM field of their choice. Upon graduation, successful students can enroll directly in the Purdue Polytechnic Institute.

At the moment, too few black and other minority students are graduating from public high schools prepared to study at Purdue.

“Our two basic objectives are to offer an alternative learning environment designed to better prepare students for today’s workplace and to increase significantly the unacceptably low number of Indianapolis Public School students who are qualified to succeed at Purdue.”

The school will be located in downtown Indianapolis. Purdue University partnered with EmplyIndy, the city of Indianapolis and USA Funds to open the school. The latter donated $500,000 for the school’s planning.

“Purdue Polytechnic Indianapolis will accelerate completion of a rigorous curriculum, saving students time and money, and better preparing them for rewarding careers with the skills that central Indiana employers value,”William D. Hansen, USA Funds president and CEO said.

The Purdue Exponent surveyed students on their opinion on the new STEM high school, with reactions mostly in favor of the school.

“Do I think it will work? Yes, but I would caution against bringing kids without being able to financially support them during and after college (i.e. reducing student loans),” Jake Brosius, a senior in the College of Liberal Arts said.

“I feel as though if inner city students knew more of the opportunity that they have as well as the capability to obtain the opportunity, then more students would be willing to try. I feel like this school will help students realize that they can become something better and instill in them the willpower to do so,”Jordan T-Moore, 2012 alumnus of the College of Engineeringresponded.

The school will partner with local businesses to offer its students internships and other hands-on learning opportunities. This concept could be widely adopted, Daniels says.

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]]>The post Autodesk Offers Free Software for 3D ‘Makers’ appeared first on Education News.

]]>As the second annual Week of Making begins with President Obama calling for a nation of ‘makers,’ Autodesk has responded with the creation of the free and open learning platform Project Ignite, which offers students hands-on experience with design in the areas of 3D printing and electronics.

The project will focus on the entire education spectrum, from kindergarten through the 12th grade, incorporating the custom design software offered by Autodesk through a variety of step-by-step projects, in addition to hardware options that can be purchased by individuals or educational institutions.

“Bringing 3D design and literacy into the classroom is an important step in preparing our next generation to be innovative and creative thinkers,” Autodesk PR Manager Jennifer Gentrup explained to us. “Project Ignite encompasses every aspect of the design experience and available options include free design software, step-by-step projects and hardware purchasing options including 3D printing and electronics kits.”

Teachers will be able to set their classes up inside the program through the web platform. A class profile can be created online, ready-to-teach 3D printing, 3D modeling or electronics projects can be chosen, and the simple web interface allows for easy management.

The platform can be used through Autodesk’s free software Tinkercard and 123D Circuits, as well as optional for-purchase hardware such as MakerBot 3D printers and Circuit Scribe pens/modules. It can also be used by parents at home for a weekend project in an effort to transform the educational experience.

Other companies such as Pearson, Arduino, Microsoft and Electoninks Writables also plan to support the initiative by bundling their hardware for schools in order to help educators use the program faster, writes Brian Krassenstein for 3DPrint.com.

“Project Ignite has been a wonderful addition to the classroom and I love what it does for my students’ excitement, engagement and overall interest with design and 3D printing technology,” said Kim Coyle, educator at Middle School of Plainville, in a prepared statement. “Our goal is to inspire and prepare the students to be the next generation of innovators, so we’re expanding Project Ignite into other grade levels and looking into creating a makerspace next year to provide an environment that nurtures the students’ curiosity and creativity.”

The 3D design software offered through Autodesk is used in thousands of schools and maker communities across the country. The company, who has been interested in 3D printing lately, views technology as not only a use for manufacturing, but also as an essential tool for learning.

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]]>The post Univ of Cambridge Receives £4 Million for Lego Professor, Education appeared first on Education News.

]]>The Lego Foundation has donated a £4 million benefaction to the University of Cambridge, and the University is investing £2.5 million for the creation of a Lego professorship to start in October, 2015. The professor will be head director of the Research Centre on Play in Education, Development, and Learning.

University of Cambridge vice-chancellor Sir Leszek Borysiewicz said in The Reporter, the university’s magazine that:

“[H]e has accepted with gratitude a benefaction of £1.5million from the Lego Foundation, payable over three years, of which both the capital and the income may be used to support a Research Centre on Play in Education, Development, and Learning within the Faculty of Education over the same period.”

The Lego Foundation, which owns 25% of the Lego company, is a foundation with a mission to improve learning through play. The Foundation highlights in its vision statement:

“Play helps children develop the intellectual, emotional, social and creative skills that are of lifelong benefit to them and their communities. . . . That is why our work is about re-defining play and re-imagining learning.

The Lego Professorship is the first of its kind and it is expected to launch October 2015. The academic/director will be chosen by a board of electors and his professorship will be within the university’s Faculty of Education. The Lego Foundation has a clear mission as far as education is concerned:

“To re-imagine learning we want to work with parents, carers, school systems, institutions and governments to use the transformative power of play to improve learning for millions of children all over the world.”

The NASA Space Grant Consortium has recently made an endowment to the Robert C. Byrd Institute for Advanced Flexible Manufacturing, the Herald Dispatch reports. The grant will support the First Lego League regional qualifiers in southern West Virginia.

The NASA grant will fund the qualifying competitions in Huntington, Parkersburg, South Charleston, Lewisburg and Weston and overall about 60 teams with students ages 9 to 14 will participate for a chance to qualify for the state-level tournament.

The Lego Robotics program FLL was founded in 1998 and has been taking place in eighty countries with more than 25,000 participating teams. The program’s mission it to get young learners interested in STEM through play and experimentation with robotics.

RCBI’s Director and CEO Charlotte Weber says the First Lego League is an education promoting opportunity for the institute. She added:

“I encourage others to get involved with FLL. It’s truly amazing to witness the level of excitement at these friendly competitions as children demonstrate their knowledge of the STEM fields while also learning valuable character-building skills. We’re proud to be a part of such a worthwhile endeavor.”

The First Lego League starts September 19, 2015 and on November 7 about 15 teams will compete at the FLL qualifier competition.

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]]>The post Code.org Expands Partnerships for Computer Science Education appeared first on Education News.

]]>Code.org has announced eleven new partnerships to help educators select the best material for their students and which will also help qualify educators to teach computer science through professional development workshops and courses.

The new partners of Code.org include: Bootstrap, Codecademy, CodeHS, Amplify Education, Beauty and Joy of Computing, Project Lead the Way, Technology Education and Literacy in Schools, Globaloria, the National Math and Science Initiative, Tynker and ScratchEd.

With these partnerships, Code.org will bring computer science education to more schools and will encourage more female students and unrepresented minority students to choose a career in Computer Science. Already, over 70 of the biggest school districts in the country collaborate with Code.org to offer computer science classes.

These districts receive professional development training and instruction on how to integrate computer science classes into their existing curricula, Taylor Soper of GeekWire.com notes.

Hadi Partovi, Code.org co-founder told Geek Wire:

“Code.org’s courses already reach millions of students globally in grades K-8,” he said. “But as we expand in high school, we work region by region, and we can’t do it all. We’re leading a movement and we need partners to help.”

School districts and educators can now choose among the eleven new partners of Code.Org or the nonprofit’s own materials.

The partners offer educator resources for elementary, middle and high school students. Code Studio offers four no-cost courses that blend online tutorials and unplugged activities for elementary school students and also provides one-day weekend workshops for educator development.

Globaloria, another new Code.org partner, offers six courses on game design and a three-day training and ongoing online professional development for educators.

Among the schools choosing Code.org to integrate computer science education into their schools is Forsyth County Schools, who hope to increase participation in computer science by female students and minority ethnic groups by rolling out Code.Org’s free curriculum and teacher development courses next year. The partnership will allow all five public schools in the county to teach computer science, ForsythNews.com reports.

Previously, Code.Org partnered with College Board in order to urge high schools in 35 of the country’s biggest districts to offer Code.Org’s Computer Science education.

The Computer Science classes and funding offered through College Board are available to schools that pledge to use the PSAT standardized tests which help identify students with an inclination toward a computer science career.

Nintendo of America has also recently announced a partnership with Humble Dumble for raising money for Code.org. To this end, Nintendo launched the Humble Nindie Bundle promotion, a release of console games that have been up to now exclusively available for PC, MAC, Linux and Android devices. The promotion is available for console and handheld games.

For Hadi Partovi of Code.org, establishing computer science education across the US will ensure women and ethnic group minorities will have the chance to know if computer science is a career they’re good at and drawn to:

“Before leaving high school, all students deserve the

opportunityto learn computer science and understand how it can help them in any career, regardless of whether they want to be software engineers or not,” Partovi said. “Many girls and underrepresented students of color never even consider a future in CS because most schools don’t teach the class.”

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]]>The post Harvard Receives $400 Million from John Paulson appeared first on Education News.

]]>Harvard has received a $400 million endowment, the largest in the history of Harvard University, to support the School of Engineering and Applied Sciences from billionaire hedge fund manager John A. Paulson. The president of Harvard, Drew Gilpin Faust, said Paulson’s understanding of the importance of the engineering school will “change Harvard and enhance our impact on the world beyond.”

Tamar Lewin, reporting for The New York Times, writes that Paulson is 59, graduated from Harvard Business School in 1980, and manages a hedge fund of $19.5 billion for wealthy clients. He also oversees pension funds such as the New York State Common Retirement Fund.

In 2013, Paulson earned $2.3 billion, according to Institutional Investor’s Alpha magazine, by taking 1 to 2% of assets via management fees and a performance fee of 20% of annual gains, which is standard in the hedge fund industry. The walls of his office in Rockefeller Center in Manhattan are covered with watercolors by Alexander Calder.

Paulson’s gift was added to the university’s $6.5 billion fund-raising campaign, which started its public presence in September 2013. Mr. Paulson was not without his critics, who questioned his choice to add to Harvard’s expansive coffers rather than choosing to donate such a large gift to those in greater need.

The engineering school, which will be renamed the Harvard John A. Paulson School of Engineering and Applied Sciences, will be moved across the river to Allston, the site of a new science campus next to Harvard Business School and the Harvard Innovation Lab.

“For 379 years, Harvard has had a profound global impact across a multitude of disciplines that benefits all of humanity,” Mr. Paulson said in a statement. “SEAS is the next frontier for Harvard, and its expanding campus in Allston promises to become the next major center of innovation.”

This endowment could give Harvard a boost in the ongoing competition to enroll top students, particularly in the areas of computer science and engineering. Currently, Stanford University is making important strides in its wealth and standing, in part because of sharing the same locale as Silicon Valley, report Douglas Belkin and Rob Copeland of The Wall Street Journal.

This “extraordinary gift will enable the growth and ensure the strength of engineering and applied sciences at Harvard for the benefit of generations to come,” Faust said in a statement.

Paulson’s generous gift follows two other very large donations. One came from hedge fund manager Kenneth Griffin, who gave $150 million to the university to be used for financial aid. The other was from the family of Gerald Chan, a Harvard-educated investor, who gave $350 million to the school of public health.

Paulson’s donation is not for buildings on the new extended campus, but instead will be used for programs and personnel at the school of engineering. Officials at Harvard say that Paulson’s gift will be the start of a new era at the school – the collaboration of the business and engineering schools.

Harvard’s engineering department grew into a school in 2007. Now the student enrollment has more than doubled, along with a 30% growth in faculty. Last year, Steven Ballmer, a Harvard graduate, gave approximately $60 million in order to hire 12 faculty members to the engineering school’s existing team of 24, writes John Lauerman of Bloomberg.

Paulson’s gift may be proof that the wealthiest US institutions of higher education are on the receiving end of more than their share of philanthropy. Last year, Harvard received $1.16 billion, and Faust is on his way to raising $6.5 billion by 2018.

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]]>The post New Robot Learns Through Trial and Error appeared first on Education News.

]]>Researchers from Berkeley, California have created a robot named “Brett” (Berkeley Robot for the Elimination of Tedious Tasks) that can perform a number of tasks and gets better at them the more times they are tried.

In order to accomplish this, his programmers reward Brett with a numerical score after he successfully completes a task. The better he performs, the higher the number is. “We’ve had it learn on its own, how to put caps onto bottles,” Sergey Levine said.

Rather than programming the robot for each individual task, algorithms are used that allow the robot to use trial and error to learn the tasks in much the same way as a human learns.

So far, Brett has learned a variety of tasks, including the assembly of a toy airplane, placing the claw of a toy hammer under a nail, and discovering where a square peg belongs.

While Brett currently operates in a lab setting, he is meant to one day help people out around their homes. The challenge with that, says Trevor Darrell, co-researcher and director of the Berkeley Vision and Learning Center, is that while objects in a lab setting are always in the same position, these robots must adapt to the constantly changing environments of homes or offices.

A number of other robots like Brett have been trained to do everyday tasks including retrieving a beer from the fridge, purchase a sandwich outside the home, or even play a game of pool.

“If we can have practical household robots, we can have them go into your home, they can clean up your house, they can do the dishes, do the laundry,” Levine said.

Researchers say Brett has the capability to master tasks within 10 minutes of beginning to learn. However, if the robot needs to find where objects are located, and thus learn extra coordinates, it could take him up to 3 hours to learn a task.

Each robot is a Personal Robot 2 (PR2) built by Willow Garage from Silicon Valley, reports Jonathan Bloom for ABC 7.

“What we’re reporting on here is a new approach to empowering a robot to learn,” said Pieter Abbeel, a professor in the university’s department of Electrical Engineering & Computer Sciences, in a prepared statement. “The key is that when a robot is faced with something new, we won’t have to reprogram it. The exact same software, which encodes how the robot can learn, was used to allow the robot to learn all the different tasks we gave it.”

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]]>The post A Comparison of Common Core Math to Selected Asian Countries appeared first on Education News.

]]>Jonathan Goodman

Professor of Mathematics

Courant Institute of Mathematical Sciences

New York University

July 9, 2010

**Executive summary. **The proposed Common Core standard is similar in earlier grades but has significantly lower expectations with respect to algebra and geometry than the published standards of other countries I examined. The Common Core standards document is prepared with less care and is less useful to teachers and math ed administrators than the other standards I examined. I have reservations about the Common Core standards regarding statistics in grades 7 and 8.

**History and overview**. At the request of Bill Evers and Zeev Wurman, I examined the published math standards of (South) Korea, Singapore, Hong Kong, and Japan, and Taiwan, as well as the proposed Common Core US standard, which I simply call US below. Evers and Wurman expressed particular interest in the question of teaching of Algebra in grade 8. They told me that this might be a major difference between the proposed Common Core national standard and the California State math standard. I have not examined the California standard.

The foreign countries chosen were from a recent list of high performing countries. Other high performing countries whose standards I have not examined are Australia and Flemish Belgium (Walloon Belgium has separate standards and is not in the top group by performance). Neither of these standards was available to me. The Flemish standard is not translated into English.

The conclusions and opinions expressed here are mine exclusively. Evers and Wurman have their opinions, they emphasized that they are not mathematicians and did not try to influence me, which would have been futile. I agreed to do the comparison because I have a strong interest in math education. They did provide me with translations of the foreign standards.

In this report, I offer judgments and opinions. For example I judge the arithmetic standards for first grade to be similar across countries. I try to label opinions as such. For example, it is my opinion that the Common Core draft description of the “mathematically proficient student” is so unrealistic as to be detrimental.

My experience with mathematics comes foremost from my career of mathematics research and teaching in a department ranked among the top ten nationally (US News). I also have considerable interest in K-12 math education, and have been actively involved in mostly fruitless attempts to influence New York City Department of Education math curriculum. I am familiar with the NCTM standards and ongoing debates on the best ways to teach math to kids.

**Educational philosophy.** All six of the standards documents I examined offer statements of educational philosophy. These statements have important similarities, including the need for understanding as opposed to rote, the need for research based age appropriate curricula, and the importance of higher level skills such as judgment, strategy, resourcefulness, and the ability to communicate. All of them state that high level skills do not come without learning facts and practicing algorithms.

I go through the standards grade by grade with comparisons, opinions, and some recommendations. I refrain from discussing many things the six standards have in common or that I do not think are significant differences. For example, all six standards call for first graders to “know their shapes”, but the details differ from country to country. I also mention what, in my opinion, are some strengths of non US standards documents that the US would do well to adopt.

In my opinion, the US standards are the least informative of the six. This will make it harder for US teachers and administrators to determine whether a particular curriculum or test meets the standard. By contrast, the Japanese standards (for example) give examples for almost every item to clarify precisely what the expectation is. The US standards are a study in bureaucratic ambiguity. For example, the US standard for grade 1 arithmetic (page 16) includes: “Add within 100, including adding a two-digit number and (*sic*) a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and*strategies based on place value, properties of operations, and/or the relationship between addition and subtraction*:…”. In light of the math wars, it is important to state whether *strategies* means an exercise in student problem solving or practice with some form of a traditional algorithm. An example would clarify this.

**Grade 1**. The six standards have much in common [1]. A major goal is addition and subtraction within a limited range: 0 to 20 for the US, and 0 to 100 for the others. All but Korea include carrying and borrowing. All mention place value and abstract properties of addition and subtraction.

The US and most others include pre-algebra problems such as 4 + __ = 9. The US standard emphasizes students’ ability to explain in words the reasoning in the solution of a math problem or calculation.Â An example of a correct explanation would be most helpful. The Japanese standard includes working with a number line, which I think is a great idea (in grade 2 for the US). There are expectations in the other standards that are not included (at least not explicitly) in the US standard.

*– Money*. All the other standards call for students to learn to manipulate the local currency. Some only use coins, in view of the overall restriction to numbers less than 100. Many call for students to practice place value and arithmetic with money, for example by exchanging pennies for nickels and dimes. Many call for students to read price tags and count out payments. The US standard calls for more abstract manipulatives rather than money. My opinion is that money is more natural. The US standard puts money in grade 2, but with less emphasis on coins as manipulatives.

*– Mental arithmetic*. Most of the other countries call for students to be able to add and subtract “mentally” (without paper or manipulatives) up to about 20. The US standard does not. Singapore calls for memorization up to 9+9. The US standard puts this in grade 2.

*– Calendar*. All but the US call for some understanding of the calendar. At least days, including the names of the days, and weeks. Some call or understanding the yearly calendar, including months. In my opinion, there is value in this, but one could argue that memorizing the names of the days is not math.

**Grade 2**. The six standards have much in common. Almost every major topic mentioned on one is mentioned in all. The biggest exception is that Hong Kong has nothing about fractions. Multiplication is receives less emphasis in the US standard than in the other five. It is not clear whether the US standard calls for the operation of multiplication, and the multiplication symbol, to be defined.

The US standard for addition is ambiguous. Quoting from page 17 (italics mine): “…(students) *develop*, discuss, and use different, *accurate*, and *generalizable* methods to compute sums and differences of whole numbers in base-ten notation, using their understanding of place value and the properties of operations.” Page 19 has: “5. Fluently add and within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 6. Add up to four two-digit numbers using strategies based on place value and properties of operations.” A standard should be clear on this point [2] but is not. Are second graders responsible for the column-wise addition algorithm or not? The wordings have much in common with the 1989 NCTM standards that deprecated algorithms. Will students develop the methods, or will teachers develop (i.e. teach) them? The terms *accurate* and *generalizable* also are from the math wars and (in my opinion) are out of place here. I refer the reader to the Japanese standard, page 71, which has a beautiful, clear, and precise suggestion of how to teach column-wise addition.

**Grade 3**. Again the six standards are similar. The most significant differences are as follows. The US emphasizes area more than the others. Japan, Hong Kong, and Korea omit area in grade 3. The US catches up with the other five in calling for addition algorithms. [3] Japan, Korea, and Taiwan include decimals as fractions n.x = n+(x/10). Japan includes using an abacus and the Japanese names for the powers of ten up to 10,000. Taiwan has “vertical” multiplication of a pair of two digit numbers. The other five have more on angles than the US.

**Grade 4**. The six standards handle fractions and decimals similarly. Some operations are applied to numbers of arbitrary size, with warnings not to overwhelm the kids with huge numbers. Highlighting the main differences: The US standard for adding and subtracting (the standard algorithm) and multiplying (multi-digit times one digit) whole numbers is what the other countries call for in grade 3. The other five give more emphasis to approximation and estimation than does the US. They also mandate areas, as the US did in grade 3. The difference (in treating areas) is that the US explicitly says to ignore units, while the other five call for explaining units of area, such as square meters. In my opinion, the US is wrong to ignore area units. It means treating area as purely geometric (a property of plane figures) rather than physical (a property of things like rugs, roofs, etc.). The US and Japan are better than the others (in my opinion) in calling for placing fractions and decimals on a number line. Korea and Hong Kong call for calculators to check arithmetic.

The contrast in the styles of the standards documents becomes more pronounced in grade 4. The US document treats some topics, such as fractions, in pedagogical detail. Others are left obscure, such as (page 29): “…multiply two two-digit numbers, using *strategies* based on place value and properties …”. By contrast, Taiwan has a whole page (page 139) devoted to illuminating examples of what is and is not mandated for fractions in grade 4. The US call for the standard algorithm makes it less clear, not more, what the methods are intended in grades 2 and 3.

**Grade 5**. The six standards are similar in how they cover arithmetic with fractions and decimals. The US is unique in introducing plane Cartesian coordinates. The US also is uniquely weak in several areas: the greatest common divisor/least common multiple, areas on non-rectangular regions such as triangles, ratios of quantities with units (e.g. miles per gallon, meters per second, kilograms per liter), percentages, and graphical representation of data (pie charts, bar graphs, etc.). Other countries are doing more to prepare students for algebra. Hong Kong has what I consider a great topic, understanding large numbers such as 10,000,000.

There is a fundamental difference in the treatment of geometry in grade 5. The other five discuss interesting (my opinion) topics like tilings, similarities, and polygons. The US standard is what I consider rote memorization of properties of figures. You can appreciate the difference by thinking how you would test the material. One might be: “Give a way to divide a 1 X 3 rectangle into a collection of four triangles?” The other might be: “In what way is a square different from a rectangle?”

The US standards document continues to puzzle me. After paying little attention to estimation in grades 3 and 4 (while the other five standards constantly emphasize it), now estimation returns. The description of Cartesian coordinates seems to imply that people might be unfamiliar with the concept: “Use a pair of perpendicular number lines, called axes, to define a coordinate system …” Cartesian coordinates are great (opinion), but they should be described in a way that will make sense to fifth graders. The document suggests measuring volumes by counting cubes, including cubic cm, cubic ft (will classrooms have piles of foot sized cubes?), and *improvised units* (cubic cubits?).

**Grade 6**. All six standards finish arithmetic, including multiplication and division of fractions and decimals, factoring of integers, and LCM/GCD for manipulating fractions. All discuss ratios, percentages, constant speed, and general proportionality expressed symbolically (e.g. d = 5t, where d is distance and t is time). All standards advance algebra using variables and abstract manipulation, but to different degrees. But the standards are much more different in grade six than for earlier grades. I take these differences by topic.

In pre-Cartesian (non-coordinate) geometry, the US catches up by doing areas of triangles, while the others pull ahead by doing areas and circumferences involving p. [4] Japan discusses making scaled copies of figures.

Only the US and Singapore have coordinate geometry. The US calls for determining distance between points whose x or y coordinates are identical (not very interesting in my opinion). Singapore graphs linear functions, connects this to the algebraic idea of proportionate change, and discusses the slope of a line (more interesting).

Only the US discusses negative numbers. Other countries do negatives in grade 7. Much time is devoted to arithmetic with whole numbers and fractions of arbitrary sign, distances between signed quantities, absolute value, and the “rational number line” (see pet peeves below). In the examples of naturally occurring negative numbers (negative temperatures, owing money) there is “negative electrical charge”. I highly doubt (my opinion) that any sixth grader will be able to appreciate the difference between positive and negative charge.

The US standard has much more on statistics than the others, including multiple measures of center (mean and median) and variation (quantile differences, mean absolute value deviation). Korea has some probability, but that part of their standard is vague. Japan and Hong Kong have mean, but not median or measures of variation. Taiwan, Singapore, and Korea stop at data representation without doing summary statistics. The US has less practice in graphical data presentation than the other five.

The other five countries all have less material in sixth grade than they had in fifth grade or the US has in sixth. I can only guess that this is considered a consolidation year for them, with much time spent honing skills.

The US standard for sixth grade is (in my opinion) careless and vague.

– (page 39): “…*that a data distribution may not have a definite center and* that different ways to measure center yield different values.” The italicized part is incorrect whatever center means, a data set has one by that definition. If it were deleted, the rest would be simpler and more correct.

– The standard calls for formulas involving powers, but powers (squares, cubes, etc.) have not been discussed yet. Is this their first introduction?

– There are many references to “real world examples” but no examples. I wonder what they have in mind for real world examples of distances between points in the plane with the same x coordinate.

– (page 45): “Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.” As a mathematician conducting research in computational statistics, I wonder what this could refer to. Maybe it refers to questions of robustness in which fat tailed distributions call for using the median rather than the mean. If it is a *standard*, people should know what it means.

**Grade 7**. I leave out Hong Kong because combines grades 7-9. The standards from Japan for grades 7 and 8 are less complete than for earlier grades. All five countries now use coordinate geometry at least to place points and graph lines. All have some algebraic manipulation, though the US has the least. All have a more thorough discussion of rates and proportionality with a variety of practical examples and graphical implications. All expect a full mastery of the rational number system (ratios of signed integers) that the US specified in grade 6 (and repeats in grade 7). The US catches up in geometry, including p, for example. Beyond this, the US differs from the others.

Korea has the least algebra, somewhat more than the US, particularly functional notation and exponents. It has much more geometry than the US, both in breadth (lots about polyhedra) and depth (systematic reasoning bordering on Euclid style theorem proving). It is unique in covering binary representations of numbers.

Taiwan and Singapore have a most of a full “Algebra I” class, with much practice in general algebraic manipulation, including rational expressions and solution of two linear equations in two unknowns. Taiwan discusses exponents, particularly for representing powers of ten and scientific notation, which I strongly endorse (an opinion). Singapore has the Pythagorean theorem, probably without proof. Singapore also has basic probability and mean and median of a data set, but without measures of variability. Taiwan has no statistics or probability this year.

The US standard is distinguished from the others by its breadth and depth in statistics and basic probability. I have reservations about many of the specifics. The US standards document continues to be problematic. The grade 7 standard contains many helpful examples, which makes the many remaining vague items without examples less explicable. Here are some sample quibbles:

– I recommend removing the hydrogen atom as an example of charge cancellation. The background knowledge for this is missing: electrons, protons, atoms, charge, electric attraction (holding the atom together), …

– (page 50) suggests drawing “with technology”. Does this mean a computer drawing program that students would have to learn to use? If so, it would be a very large investment of student time for not very much educational gain. This kind of thing should not be ambiguous in a standards document.

– (page 50) states that someone (teacher, student?) should “give an informal derivation of the relationship between the circumference and area of a circle.” I imagine this might have to do with the area difference between circles of slightly different radius. Is that right?

– (page 51) Students are to choose words at random from a book. How? They are to use random digits to simulate a random process. Where do the digits come from?

– Most seriously, the standard calls for drawing “informal comparative inferences about two populations”. This amounts to testing the hypothesis of equality among sample means. The method suggested, comparing the difference between the means to twice the mean absolute deviation, has no basis in statistics. Any real test would depend on the sample sizes. This is an admirable topic, but the contents proposed are disinformation (a judgment).

– The notion of “probability sample space” is, in my opinion, not very helpful in this very elementary setting. I prefer the approach of Taiwan — discussing events as sets without taking time to define the whole space.

**Grade 8**. I am dropping Singapore because they combine grades 8 and 9. I compare the remaining standards (US, Korea, Taiwan, Japan) area by area.

Roots and irrational numbers: All have square roots, with the possible exception of Japan. Taiwan has more general rational exponents, but lightly. The US asks students to “know that the square root of 2 is not rational”. Does this mean being able to repeat that sentence or understanding the proof? The US standard asks students to tell that the square root of 2 is between 1.4 and 1.5 by truncating its decimal expansion. But where does the decimal expansion come from, a calculator?

Algebra: Both Korea and Taiwan call for generic operations of algebra such as factoring, multiplying polynomials, polynomial division (not in all cases), completing the square, etc. The US standard by contrast, supports a tightly circumscribed list of algebraic tasks centered on pairs of linear equations in two unknowns. The US catches up with exponents. It includes the mathematicians’ definition of function (set of ordered pairs so that …) but with an uncertain range of application. Included are general linear functions, at least one quadratic (with a proof that quadratics are not linear, as though a glance at the graph would not suffice), and possibly others that can be increasing and decreasing over different intervals of their argument (as functions are in calculus).

Geometry: Korea, Taiwan, and Japan call for significant work in the direction of traditional high school Euclidean geometric proof, but not as much as US high school geometry from the 1960s. This includes ruler and compass constructions (perpendiculars, bisections, congruences) and some of the easier proofs. The US calls for students to “understand” congruence of plane figures, but it is unclear what this means beyond the definition. US students are asked to know the Pythagorean theorem and its proof, but I question the wisdom of asking students to memorize something they do not have the background to appreciate. The US makes more of the geometric interpretation of pairs of linear equations than the other countries to.

Statistics: Only the US discusses statistical modeling and hypothesis testing. In grade 8, it discusses linear regression models and hypothesis testing on categorical data. But students have no systematic way to do either task. Linear fits are to be made “informally” from scatterplots. Goodness of fit is to be judged by eye. Categorical data decisions are made on (as far as I can tell) no basis whatsoever. If 60% of boys and 70% of girls pass math, is that a significant difference? How would one decide? In my opinion, this is negative education — giving kids the incorrect idea that they know something about regression and categorical data analysis. There is an AP statistics class in many high schools (both my kids took it). This has, for example, the ideas behind hypothesis testing, the role of statistical models, and the central limit theorem (informally). Making statistical inferences with less than this is dangerous.

**Algebra**. There are two styles of algebra, with the US on one side and most of the other countries on the other. Japan is in the middle. All ask students to understand abstract variables, such as *x* and *y*, and to know how to solve pairs of linear equations. All ask students to have seen manipulations such as dividing both sides of an equation by the same number to preserve the equality. The US (up to grade basically stops here. Japan includes multiplication and division of polynomials. The other countries go further to for example completing the square (solving general quadratics), manipulating rational functions, etc.

An item from the Japanese standard captures the difference: “Transform algebraic expressions depending on purpose.” General algebraic manipulation requires the student constantly to recall the mathematical principles and to plan strategy. Suppose, for example, a students wants to isolate a variable on one side of the equation. He or she must develop a strategy consisting of a sequence of operations. The strategy will be different from problem to problem. If manipulations are limited to pairs of linear equations, the student will simply memorize the operations required to solve them.

**Pet peeves**:

**–****Problem solving, rote, and patterns**. Most people believe that math education should involve some serious independent creative problem solving. It also is a sad fact that students want to be told how to do things, and teachers like to tell them. Items introduced into the curriculum as problem solving can evolve into rote. This is nowhere more clear than in looking for patterns in sequences of numbers. The sequences offered tend to be arithmetic, and students are trained to look for common differences. The grade 4 patterns of the six curricula are all arithmetic progressions. But students could be presented with a wider range of patterns. For example, 1,2,1,2,1,2,… (easy but not arithmetic), 1,2,1,1,2,1,1,1,2,1,1,1,2,… (slightly harder), 1,1,2,3,5,8,13,23,… (a real challenge, but probably some kids would get it).

**–****Mathematical exactitude**. Mathematicians have a bad reputation in the K-12 math ed world partly because of the “new math” disaster we helped create in the 1960s. My sixth grade math book from that period (found much later in my parents’ closet) had a discussion of sets that included (approximately) the sentence: “For any set and any property, you can form the subset of all members of the set that satisfy the property.” This probably was followed by an example such as picking out the apples from a set of pieces of fruit. As a recent math PhD, I recognized the *aussonderung* axiom of Zermelo Fraenkel set theory. I knew that this axiom has the purpose of ruling out Russell’s paradox. But how could it have helped a sixth grader? Mathematicians (in K-12 math ed discussions) must get used to things that are well enough understood even if not absolutely precise. We should avoid concepts that require more maturity than kids of a certain age have. We need not describe the coordinate plane in detail for fifth graders, or expect sixth graders to appreciate the distinction between a finite and infinite set of solutions. At the same time, we can prevent flatly incorrect statements such as (US, page 45): “Recognize a statistical question as one that anticipates variability in the data related to the question …”, which confuses a statistician’s model of random data variation with the fact of a single unchanging data set. Also (Taiwan, page 175): “For example, even though both 14 and 16 are composite numbers, they are coprime.” (Should have been 14 and 15?)

**Notes**

[1] The US is unique in having a standard for Kindergarten. I have combined the US kindergarten and grade 1 standards when comparing to grade 1 standards from the other countries.

[2] This opinion is stated as a judgment because I expect few to disagree.

[3] I do not know whether the plural is significant. The Everyday Mathematics curriculum adopted by the New York City Department of Education includes several variants of each of the algorithms of arithmetic. In my opinion, teaching multiple algorithms is a confusing waste of the students’ time.

[4] Hong Kong has a charming learning objective (page 44): “Tell the stories of ancient Chinese mathematicians discovering p.” I think this is time well spent.

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