Sometimes mathematicians try to tackle a problem head on, and sometimes they come at it sideways. That’s especially true when the mathematical stakes are high, as with the Riemann hypothesis, whose solution comes with a $1 million reward from the Clay Mathematics Institute. Its proof would give mathematicians much deeper certainty about how prime numbers are distributed, while also implying a host of other consequences—making it arguably the most important open question in math.
Mathematicians have no idea how to prove the Riemann hypothesis. But they can still get useful results just by showing that the number of possible exceptions to it is limited. “In many cases, that can be as good as the Riemann hypothesis itself,” said James Maynard of the University of Oxford. “We can get similar results about prime numbers from this.”
In a breakthrough result posted online in May, Maynard and Larry Guth of the Massachusetts Institute of Technology established a new cap on the number of exceptions of a particular type, finally beating a record that had been set more than 80 years earlier. “It’s a sensational result,” said Henryk Iwaniec of Rutgers University. “It’s very, very, very hard. But it’s a gem.”
The new proof automatically leads to better approximations of how many primes exist in short intervals on the number line, and stands to offer many other insights into how primes behave.
A Careful Sidestep
The Riemann hypothesis is a statement about a central formula in number theory called the Riemann zeta function. The zeta (ζ) function is a generalization of a straightforward sum:
1 + 1/2 + 1/3 + 1/4 + 1/5 + ⋯.
This series will become arbitrarily large as more and more terms are added to it—mathematicians say that it diverges. But if instead you were to sum up
you would get π2/6, or about 1.64. Riemann’s surprisingly powerful idea was to turn a series like this into a function, like so:
ζ(s) = 1 + 1/2s + 1/3s + 1/4s + 1/5s + ⋯.
So ζ(1) is infinite, but ζ(2) = π2/6.
Things get really interesting when you let s be a complex number, which has two parts: a “real” part, which is an everyday number, and an “imaginary” part, which is an everyday number multiplied by the square root of −1 (or i, as mathematicians write it). Complex numbers can be plotted on a plane, with the real part on the x-axis and the imaginary part on the y-axis. Here, for example, is 3 + 4i.
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According to the National Math and Science Initiative, STEM education helps students develop critical thinking and problem-solving skills, fosters communication, and bolsters teamwork. In my 25 years of teaching, I have learned that finding and infusing arts into STEM takes the learning even further. I am always on the lookout for STEAM-based resources and tools that engage and inspire my students. In my experience, I have found that using creative, dynamic tools significantly boosts student learning outcomes–but you need to know where to look.
In my current role as a STEAM Specialist, where I teach students from Pre-K all the way to 6th grade, it’s important to use resources that can be tailored to their education level and lesson plans. Having access to STEAM education not only improves classroom outcomes, but better prepares students for the future. The US Bureau of Labor Statistics estimates the total number of STEM careers will increase at twice the rate–and pay more on average–than non-STEM jobs across the next 7 years.
Interacting with STEAM content in the classroom is the first step to inspiring students to explore those career possibilities in the future.
Finding good STEAM tools can feel daunting, so here are some of my favorite resources:
STEM Careers Coalition
The STEM Careers Coalition from Discovery Education is an alliance of industries and nonprofit organizations that provides access to STEM resources and connects students to industry professionals. The free resources are intuitive, easy to use, and tailored to be turnkey. The search features and filters make the career profiles and videos quick to find. There are suggested grade levels for each video and activity, linked questions, and suggested additional resources to follow up to the lesson.
The videos and questions can be embedded into Google Classroom or other learning platforms. This means you can curate content, activities, and lessons for students to complete without jumping to different platforms or tabs. It is a great way to integrate conversations regarding future careers into current STEAM lesson plans, and my students are always excited to connect what they learn in class to a real-life career and STEM professional.
Whether you are encouraging space-obsessed students or inspiring the next generation of engineers, STEM Careers Coalition provides educational materials designed to reflect the diversity of the students watching. Not only is STEM Careers Coalition easy to use, but its commitment to making STEM education equitable and engaging more than earns this resource a spot on this list.
Verizon Innovative Learning HQ
Verizon Innovative Learning HQ offers engaging and cutting-edge resources to support educators and students around the world. This completely free-to-use resource gives you access to 350+ K-12 lessons and activities across all subjects. From stop-motion animation to orbits modeled using augmented reality to in-depth looks at cells and other organisms, there are hundreds of STEAM-focused lessons to choose from.
The search function is very effective, allowing teachers to filter by grade level, subjects, standards, technologies involved, and more. It is easy to find a lesson tailored specifically to your students’ age and interests. The AR and VR apps offered immerse students in the content, making each lesson accessible and engaging. The AR/VR resources remain a student favorite in my classroom.
This database offers a lot of strong, innovative materials that supplement more traditional classroom resources. The emphasis on downloadable apps and creative approaches to standards-based lessons offers news ways to teach STEAM concepts.
Another reason I love Verizon Innovative Learning HQ is because it offers a wide range of professional development modules. These tailored professional development resources helped me sharpen my STEAM teaching skills and support teachers in developing new skills in the ever-changing educational landscape.
STEAM lesson plans for LEGO Education Solutions
With 400+ lessons ranging from Pre-K to 12th grade, these LEGO-based STEAM lesson plans are another versatile classroom tool. Combining coding and LEGOs into interactive stories, students get to investigate a wide variety of STEAM concepts right at their desks as they follow along with the demonstrations.
Each lesson plan includes student worksheets and evaluative materials, write-ups on the relevant STEAM phenomena, and clearly-stated educational standards. The content is easily filtered by subject, grade level, and products needed to complete the lesson. Subjects include a wide range of STEAM topics, including computer science, social emotional development, math, creative exploration, and more.
The lesson plans and building guides are free to access. The LEGO products referenced are extensive and can be used for more than one lesson; the SPIKE Essential Kit, for example, is used in almost 70 different lessons in various ways.
This tool will engage your students in a new and dynamic way, helping them to understand complex topics and concepts through multi-step builds, discussions, and reflections.
If you are looking for comprehensive digital resources, this list is a great place to start. All three of these suggested resources and activities offer ready-to-use, standards-aligned curriculum that are fun and engaging for teachers and students alike. As I prepare for the upcoming school year at the Allegheny Valley School District, I know that I can visit any of these awesome tools and find materials that will get my students excited to learn.
Lisa Gray, Allegheny Valley School District
Lisa Gray is a STEAM Specialist at Acmetonia Elementary School in the Allegheny Valley School District. With 25 years of teaching experience, Lisa Gray loves integrating new and innovative resources into the classroom. During her tenure, Lisa has held roles of Special Education Teacher, Classroom Teacher, STEAM Specialist, and Science Olympiad Coordinator.
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IRVINE, Calif. —MIND Education, an organization dedicated to ensuring that all students are mathematically equipped to solve the world’s most challenging problems, today released the results of its annual ST Math Teacher Survey, conducted by MIND Research Institute, its social impact organization specializing in education and neuroscience research.
Each spring, MIND sends out an annual survey to educators who use ST Math, a program created by MIND Education, to find out how the tool is delivering value, to guide future research and development, and to benchmark the understandings and beliefs of the teachers they serve. ST Math’s evidence-based approach uses visual, interactive play-based learning through problem-solving to deepen students’ understanding of foundational mathematical concepts.
This year’s survey found that ST Math stands out to teachers for its ability to achieve what traditional, language-heavy math instruction cannot. It reaches all types of students, engages them deeply in math lessons they genuinely enjoy, and motivates them to persist, succeed, and grow in confidence, all while enhancing their understanding of mathematics and improving their academic scores.
This year, 5,400 educators from across the U.S. responded to the survey, and the overwhelming majority of them cited the positive impact ST Math has on their students. Some highlights include:
85.8% of respondents agreed or strongly agreed that ST Math increases their students’ engagement in math learning;
81.2% agreed or strongly agreed that ST Math deepens their students’ understanding about how math works;
80.8% said they agreed or strongly agreed that ST Math helps their students of diverse backgrounds and abilities improve their math understanding;
81.9% agreed or strongly agreed that ST Math improves their students’ attitudes about math and math learning; and
81.1% said they agreed or strongly agreed that ST Math improves their students’ confidence in their mathematical abilities.
“I’m very pleased to share our annual spring survey’s results back to teachers and the market for the first time,” said Andrew Coulson, chief data science officer for MIND Research. “Getting a feel for where the vast majority of their fellow teachers are seeing value, validates the confidence of our experienced users. The most satisfactory finding to me in 2024 is the overwhelming agreement that ST Math is helping students of diverse backgrounds and abilities. Our non-conventional approach is designed for every human brain and how it learns. All brains, full stop. It’s very gratifying to see this ST Math value earn the second highest ‘strongly agree’ response, after our hallmark student engagement!”
MIND Education engages, motivates, and challenges students towards mathematical success through its mission to mathematically equip all students to solve the world’s most challenging problems. MIND is the creator of ST Math, a pre-K–8 visual instructional program that leverages the brain’s innate spatial-temporal reasoning ability to solve mathematical problems; and InsightMath, a neuroscience-based K-6 curriculum that transforms student learning by teaching math the way every brain learns so all students are equipped to succeed. During the 2022-23 school year, MIND Education and ST Math reached more than 2.28 million students and 115,000 educators across the country. Visit mindeducation.org
eSchool Media staff cover education technology in all its aspects–from legislation and litigation, to best practices, to lessons learned and new products. First published in March of 1998 as a monthly print and digital newspaper, eSchool Media provides the news and information necessary to help K-20 decision-makers successfully use technology and innovation to transform schools and colleges and achieve their educational goals.
As classrooms close until next fall, talk of the dreaded summer slide increases, particularly as students are still struggling to gain ground lost during the pandemic.
Students’ academic achievement and test scores remain flat or tend to drop during summer break, with greater losses in math than in reading, according to research by Meghan Kuhfeld, PhD, a research scientist for the Collaborative for Student Growth at NWEA and Andrew McEachin, PhD, director of the Collaborative for Student Growth at NWEA.
Their analysis highlights the ongoing debate around just how deeply summer learning loss is felt, if different student groups experience more learning loss than others, and what districts and caregivers can to do keep students’ brains active and learning in fun ways during long school breaks.
Only in the past couple decades have educators and researchers had the tools to measure performance in the spring and fall, leading to the ability to isolate summer in particular.
“The research is a bit mixed, but the consensus is that students stay the same or lose ground in the summer. Different studies have shown different amounts of learning loss–some say it’s a sizable percentage and some say it’s more of a pause in learning versus a real drop,” she added.
The other major aspect of learning loss concerns who is affected—do students from low socioeconomic backgrounds experience more severe summer learning loss? More recent research hasn’t shown losses to a severe degree, Kuhfeld said, but the research is still mixed.
Concerns about summer learning loss can be addressed in two main areas, Kuhfeld said.
Parents and caregivers: Make sure children receive learning opportunities during the summer, such as reading books or visiting museums. Incorporating math into summertime can be a bit more challenging, but can be accomplished if children help with activities such as measuring ingredients during cooking or calculating how far they walk or ride bikes. Weaving learning opportunities into grade-appropriate topics makes learning more fun and engaging.
District level: Many districts offer summer programs, which range in intensity from mandatory summer school to more voluntary programs intended to boost learning for students who fell further behind during the academic year. But districts can’t provide all the summer learning opportunities on their own, and this is why school-community partnerships for camps, internships, and other programs are critical–especially in communities where students lack access to summer enrichment and learning opportunities.
One often-overlooked piece of what schools provide kids is free meals, Kuhfeld added. Pairing summer learning programs with free meals is another way students can keep their brains in shape over the school break, such as free lunches combined with story time and activities at local libraries.
And while summer learning loss is a valid concern, summer does help students build essential skills–durable skills students need for success beyond school, such as creativity, collaboration, and empathy.
“Summer is an opportunity for growth in areas that aren’t academic,” Kuhfeld said. “There’s value in talking about how kids can continue reading and math during the summer, but it’s also a time for building independence and other life skills. Summer shouldn’t look just like school.”
Laura Ascione is the Editorial Director at eSchool Media. She is a graduate of the University of Maryland’s prestigious Philip Merrill College of Journalism.
BEAVERTON, Oregon — Through the companies’ continued partnership, Texas Instruments (TI) and Vernier Science Education are offering a new app-based way for teachers to engage students in real-time, hands-on STEM learning. Students can now use six Vernier Go Direct® sensors in conjunction with the Vernier DataQuest® application on TI-Nspire™ CX II and TI-Nspire CX II CAS graphing calculators to wirelessly collect and analyze scientific data as they explore phenomena and think like real scientists.
“Data collection and graphing helps students visualize and interact with important math concepts, while teaching them the skills needed for success in science,” said Jill Hedrick, CEO of Vernier Science Education. “Vernier has partnered with Texas Instruments for more than 20 years, and shares a commitment to helping teachers easily and efficiently accelerate STEM learning. This most-recent collaboration brings together the latest versions of each of our technologies, which are already being used in classrooms across the country today, to further support high-quality teaching and learning.”
To get started with the data-collection and graphing process, teachers and students can download the latest operating system for free onto their TI-Nspire CX II or TI-Nspire CX II CAS graphing calculators. They can then connect any compatible Go Direct sensor wirelessly to their calculator using the TI-Bluetooth® Adapter or connect the sensor directly through USB. Compatible sensors currently include the Go Direct Motion, Go Direct Temperature, Go Direct Force and Acceleration, Go Direct Light and Color, Go Direct pH, and Go Direct Gas Pressure. Additional Go Direct sensors will be added in the future.
Once connected, students can open the Vernier DataQuest app on their calculator and easily start collecting a range of data, as well as repeat trials quickly to ensure the accuracy of the data. They can additionally view the data in multiple ways on the TI-Nspire CX II suite of applications—including Vernier DataQuest, Lists & Spreadsheets, and Data & Statistics—to deepen their analysis and understanding.
“Providing students with meaningful opportunities to engage in hands-on data collection and analysis is so beneficial in today’s math and science classrooms,” said Peter Balyta, PhD, president of Texas Instruments Education Technology. “This latest collaboration between TI and Vernier Science Education is not only making the data collection and analysis process faster and easier, it is providing students with increased opportunities to make scientific connections and engage in authentic learning.”
To learn more about Vernier Go Direct sensors’ compatibility with TI-Nspire CX II and TI-Nspire CX II CAS graphing calculators, as well as the ongoing partnership between TI and Vernier Science Education, visit https://www.vernier.com/math.
About Texas Instruments
Education Technology, a business of Texas Instruments, provides a wide range of tools connecting the classroom experience with real-world applications, helping students and teachers to explore mathematics and science interactively. TI’s products and services are tested vigorously against recognized third-party research, which shows that the effective use of graphing calculators improves the mathematical skills of students and their attitudes toward mathematics. For more information, visit www.education.ti.com.
Texas Instruments Incorporated (TI) is a global semiconductor design and manufacturing company that develops analog ICs and embedded processors. By employing the world’s brightest minds, TI creates innovations that shape the future of technology. TI is helping more than 100,000 customers transform the future, today. Learn more at www.ti.com.
For more than 40 years, Vernier Science Education has been committed to using our experience, knowledge, and passion to create the best and most reliable solutions for STEM education. Our comprehensive solutions include hardware, software, content, assessment, professional development, and technical support. At the heart of Vernier is our deep commitment to being an authentic and trusted partner to STEM educators. We are dedicated to partnering with educators and communities to build a STEM-literate society where students grow up to become knowledgeable citizens who can solve problems, fully contribute to their communities, and drive innovation. For more information, visit www.vernier.com.
eSchool Media staff cover education technology in all its aspects–from legislation and litigation, to best practices, to lessons learned and new products. First published in March of 1998 as a monthly print and digital newspaper, eSchool Media provides the news and information necessary to help K-20 decision-makers successfully use technology and innovation to transform schools and colleges and achieve their educational goals.
In October, a Falcon Heavy rocket is scheduled to launch from Cape Canaveral in Florida, carrying NASA’s Europa Clipper mission. The $5 billion mission is designed to find out if Europa, Jupiter’s fourth-largest moon, can support life. But because Europa is constantly bombarded by intense radiation created by Jupiter’s magnetic field, the Clipper spacecraft can’t orbit the moon itself. Instead, it will slide into an eccentric orbit around Jupiter and gather data by repeatedly swinging by Europa—53 times in total—before retreating from the worst of the radiation. Every time the spacecraft rounds Jupiter, its path will be slightly different, ensuring that it can take pictures and gather data from Europa’s poles to its equator.
To plan convoluted tours like this one, trajectory planners use computer models that meticulously calculate the trajectory one step at a time. The planning takes hundreds of mission requirements into account, and it’s bolstered by decades of mathematical research into orbits and how to join them into complicated tours. Mathematicians are now developing tools which they hope can be used to create a more systematic understanding of how orbits relate to one another.
“What we have is the previous computations that we’ve done, that guide us as we do the current computations. But it’s not a complete picture of all the options that we have,” said Daniel Scheeres, an aerospace engineer at the University of Colorado, Boulder.
“I think that was my biggest frustration when I was a student,” said Dayung Koh, an engineer at NASA’s Jet Propulsion Laboratory. “I know these orbits are there, but I don’t know why.” Given the expense and complexity of missions to the moons of Jupiter and Saturn, not knowing why orbits are where they are is a problem. What if there is a completely different orbit that could get the job done with fewer resources? As Koh said: “Did I find them all? Are there more? I can’t tell that.”
After getting her doctorate from the University of Southern California in 2016, Koh grew interested in how orbits can be cataloged into families. Jovian orbits that are far from Europa form such a family; so do orbits close to Europa. But other families are less obvious. For instance, for any two bodies, like Jupiter and Europa, there is an intermediate point where the two bodies’ gravitational effects balance to create stable points. Spacecraft can orbit this point, even though there is nothing at the center of the orbit. These orbits form a family called Lyapunov orbits. Add a little energy to such an orbit by firing a spacecraft engine, and at first you’ll stay in the same family. But add enough, and you’ll cross over into another family—say, one that includes Jupiter inside its orbits. Some orbit families might require less fuel than others, remain in sunlight at all times, or have other useful features.
Dayung Koh, an engineer at NASA’s Jet Propulsion Laboratory, is trying to come to a systematic understanding of how orbits in a planetary system relate to one another.
Step closer to summer with new resources from Discovery Education! Find engaging content for your May lessons to keep your students excited about learning through the end of the school year. Pop of Professional Learning What’s New Trending Topics Magic Moment Pop of Professional Learning Educators, administrators, and corporate leaders all agree: we need to […]
BETHESDA, Md./PRNewswire-PRWeb/ —EPS Learning, the leading provider of PreK-12 literacy solutions, announced that four of its programs have been recommended by the Virginia Board of Education for evidence-based literacy instruction that’s aligned to science-based reading research. The recognition supports Virginia schools in a multi-year effort to improve early learning outcomes for students who are below proficiency levels in reading.
According to the 2022–2023 Virginia Assessment Results, which demonstrate significant and persistent learning loss in reading and math, more than half of students in grades 3-8 either failed or were at risk of failing their reading SOL exam. To remedy reading proficiency beginning in the 2024–2025 school year, the Virginia Literacy Act (VLA) will mandate core literacy and research-grounded instruction for K–5 students. The enacted legislation provides tools, resources, technical assistance and funding to schools within the state.
EPS Learning programs meet the required parameters to be recommended as top literacy intervention solutions, including alignment with evidence-based literacy instruction, comprehensive and intensive intervention, support that is accessible and can be easily implemented into any curriculum, inclusivity and representation. The EPS Learning programs included in the recommendation are:
SPIRE Family (Specialized Program Individualizing Reading Excellence): Provides explicit, systematic, multisensory instruction through an easy-to-implement intensive program.
Reading Assistant for SPIRE: Offers assessment, including a dyslexia screener, highly personalized reading practice for students and real time performance data for teachers through an AI-powered virtual “tutor.”
Megawords: Teaches the reading, spelling and contextual uses of multisyllabic words through multisensory instruction and a systematic progression of skills.
Wordly Wise 3000: Provides direct academic vocabulary instruction to develop the critical link between vocabulary and reading comprehension.
SPIRE Next™: Provides skills-based, genre-specific instruction and practice that uses close reading to build comprehension.
Additionally, EPS Learning offers several sets of decodable readers and other materials not subject to VLA approval that complement these programs:
Readfetti – full-color fiction and non-fiction decodable readers and read aloud cards that align with many popular phonics programs
Mac & Tab – decodable readers featuring an adorable cat and rat, made popular through the Primary Phonics program
Alphabet Series – decodable readers including charming stories, made popular through the Recipe for Reading program
“The recognition of EPS Learning solutions by the Virginia Department of Education further validates our framework for literacy instruction that’s backed by nearly 70 years of experience,” said Steven Guttentag, Chief Executive Officer at EPS Learning. “We champion Virginia’s significant efforts to ensure that all students in the state can access literacy as the springboard to lifelong learning and opportunity.”
About EPS Learning EPS Learning has partnered with educators for more than 70 years to advance literacy as the springboard for lifelong learning and opportunity. The 20+ literacy solutions included in the EPS Literacy Framework are based on the science of reading and support grades PreK through 12, all tiers of instruction, and every pillar of reading. EPS Learning offers evidence-based intervention and customized professional learning to help move students toward growth, mastery, and success. Visit http://www.epslearning.com to learn more.
eSchool Media staff cover education technology in all its aspects–from legislation and litigation, to best practices, to lessons learned and new products. First published in March of 1998 as a monthly print and digital newspaper, eSchool Media provides the news and information necessary to help K-20 decision-makers successfully use technology and innovation to transform schools and colleges and achieve their educational goals.
The STEM pipeline – a metaphor for the development of future scientists, engineers and other high tech workers – likely starts with a narrower funnel in the post-pandemic era. Credit: CSA Images via Getty Images
Universities, philanthropies, and even the U.S. government are all trying to encourage more young Americans to pursue careers in STEM, an acronym for science, technology, engineering and mathematics. Many business sectors, from high tech to manufacturing, are plagued with shortages of workers with technical skills. In New York City, where I live, the subway is frequently plastered with advertisements carrying the message that STEM fields pay well. But studying STEM requires more than an interest in science or a desire to make good money. Students also need adequate training, even in elementary and middle school.
That’s why it’s concerning that high-achieving students, who’ve received less public attention than lower achieving students, were also set back by remote learning and pandemic uncertainty. Fewer students with math skills shrinks the pool of people who are likely to cultivate an expertise in science, engineering and technology a decade from now. In other words, the STEM pipeline – a metaphor for the development of future scientists, engineers and other high tech workers – likely starts with a narrower funnel in the post-pandemic era.
The stakes are high not only for Gen Z, as they age out of school and enter the workforce, but also for the future of the U.S. economy, which needs skilled scientists and engineers to grow.
The leading indicators of STEM troubles ahead are apparent within the 2022 scores from a national test called the National Assessment of Educational Progress (NAEP). The immediate headlines from that first post-pandemic test focused on the fact that two decades of academic progress had been suddenly erased. Low-achieving children, who tend to be poor, had lost the most ground. An alarming number of American children – as high as 38 percent of eighth graders – were functioning below the “basic” level in math, meaning that they didn’t have even the most rudimentary math skills.
Statisticians at the National Center for Education Statistics (NCES) have continued to dig into the 2022 data, and they’ve been also turning their attention to students at the top. These children are on grade level, but the eighth grade NAEP assessment shows that far fewer of them are hitting an advanced performance level, or even a proficient one. Math scores among top performers dropped as steeply as scores did among low performers. Even the scores of students at Catholic schools, who otherwise weathered the pandemic well, plummeted in eighth grade math.
We don’t have data for other private schools because they have refused to participate in NAEP testing, but the eighth grade math declines among both high-achieving public school and Catholic school students are not good signs.
NAEP tests reading and math in both fourth and eighth grades every two years in order to track educational progress. It’s one of the only tests that can be used for comparisons across states and generations. More than 400,000 students are specially selected to represent the regions and demographic characteristics of the nation.
Among the four NAEP tests, eighth grade math showed the sharpest pandemic drop. Math took a bigger hit than reading because kids can still read at home, while math is something that students primarily learn at school. If you didn’t read “The Hobbit” in your seventh grade English class because you were out sick with Covid, you can still be a good lifelong reader But not getting enough practice with rates, ratios and percentages in middle school can derail someone who might have otherwise excelled.
Why eighth grade math was hit harder than fourth grade math is a bit less obvious. One explanation is that the concepts that students need to learn are more difficult. Square roots and exponents are possibly more challenging to master than multiplication and division. And fewer parents are able to assist with homework as the math increases in complexity.
Yet another explanation is a psychological one. These eighth graders were in sixth grade when the pandemic erupted in the spring of 2020. This is a critical time in adolescent development when children are figuring out who they are and where they belong. A lot of this development occurs through social interaction. The isolation may have stunted psychological development and that ultimately affected motivation, study skills and the ability to delay gratification – all necessary to excel in math.
Let’s walk through the numbers together.
Highest achieving students lost ground in eighth grade math
Source: NAEP Report Card Mathematics 2022
This chart shows that the highest performing students, those at the top 10 percent and the top 25 percent, lost as much as low-achieving students at the bottom in eighth grade math. These eighth graders were in the spring of sixth grade when the pandemic hit in 2020, and it’s possible that they didn’t master important prerequisite skills, such as rates and ratios. These kids at the top are performing at grade level, but not as high performing as past eighth graders.
Fewer eighth grade students hit advanced and proficient levels
Source: NAEP Report Card Mathematics 2022
This bar chart shows that before the pandemic 10 percent of the nation’s eighth graders were performing at an advanced level in math. That fell to 7 percent. And the number of students deemed proficient in eighth grade math fell even more, from 24 percent to 20 percent. Before the pandemic, arguably, 34 percent of the eighth grade population was on track to pursue advanced math in high school and a future STEM career if they wanted one. After the pandemic in 2022, only 27 percent were well prepared.
Students at Catholic schools are generally much higher performing than students at public schools. In large part, that’s because of family income; wealthier students tend to have higher test scores than poorer students. Catholic school students tend to be wealthier; their families can afford private school tuition. In recent years, the Catholic Church has closed hundreds of schools that catered to low-income families, leaving a higher income population in its remaining classrooms.
Catholic schools outperformed public schools but also dropped
Source: NAEP Report Card Mathematics 2022
This chart shows that Catholic school students, depicted by the diamonds, outperformed public school students, depicted by the circles, in eighth grade math. But it was still a sharp five-point decline in eighth grade math performance for Catholic school students, almost as large as the eight-point decline for public school students. Scores of white students at Catholic schools declined five points; scores of students at Catholic schools in the suburbs declined seven points. Almost a quarter of Catholic school students are now functioning below a basic level in math for their grade.
Despite the good academic reputation of Catholic schools and the praise Catholic schools received for resuming in-person instruction sooner, math scores suggest a problem. And it’s a problem that potentially extends to the whole private school universe, where 9 percent of students are enrolled, according to the most recently available data from 2019.
I talked with Ron Reynolds, the executive director of the California Association of Private School Organizations, who explained that not just Catholic schools, but also many other private schools suffered even if they hadn’t been closed for long. Reynolds said that private schools were still hit by illnesses, deaths and absences and that might have affected instruction.
“Private schools are tightly knit communities in which teachers tend to be more intertwined in the lives of the children and families they serve,” he said. “When you have a crisis, and so many people experiencing stress and loss, that can certainly impact the teacher in some significant ways.”
Unfortunately, we don’t know exactly how other private schools fared during the pandemic because they have refused to participate in the NAEP tests for the past decade. Reynolds, who serves on the governing board that oversees the NAEP exam, has been trying to lobby more private schools to participate, but so far, to no avail.
Together private schools, selective public schools and affluent suburban schools have been important training grounds for the nation’s future scientists and engineers. Of course, it is possible that these high achieving students, now 10th graders, will catch up. Many of them are from wealthier families who can afford tutors, or attend well-resourced schools. But I am not seeing much evidence that schools have had the ability to think about the pipeline of advanced students when many students are so needy. And with post-pandemic grade inflation, students and parents may not be getting the signals they need to seek extra help independently.
The administration of the 2024 NAEP test wrapped up in March, but results won’t be known for many months. I’ll be keeping an eye on eighth grade math and on SAT, ACT and Advanced Placement scores in the years to come.
This story aboutmath scores was written by Jill Barshay and produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Proof Points newsletter.
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Say what you will about the universality of numbers and symbols; I’d politely argue that it does not follow that mathematics is a universal language. The problem for many struggling math students is that often those “universal” numbers and symbols hide in surrounding contexts of unfamiliar vocabulary, settings, and narratives.
As math educators, we can help those students by finding ways to relate their classroom learning to more recognizable cultural frames of reference that are authentic to the range of experiences in the room. In the process, math can actually become a universal thread to connect many types of content and learners. Number sense and quantities are some of the very few things that tie us together in a common experience.
Through my own work in the classroom with students and educators, I’ve discovered a few key ways to change the narrative around math.
Math is joyful!
Math should be an exciting space to be in, one that’s connected to experiences outside of the textbook or classroom. It should be joyful. But for multilingual students like me whose native language is not English, the math classroom can be a daunting place.
I’m a first-generation Dominican American. My mother’s emphasis on speaking Spanish in our home was one of the best things to happen to me—because of her decision, I’m bilingual today. But although I was a stellar student academically, I struggled in math. The linguistic supports I received in other content areas were not as present during math, in large part because of the assumption that math is a universal language.
Despite these experiences, I found my love for math as I became an elementary teacher after earning a master’s degree in education. My years as a classroom teacher and instructional math coach showed me that math not only is fun, and can be found everywhere, but every single person is capable of learning and excelling in the subject.
Through my years in the classroom, I saw many students who reminded me of my early learning self–cautious and or apprehensive of math and their abilities to learn it. While educators provide many scaffolds to help our students learn math, we need to make sure that we integrate content and language into those frameworks. We should teach—and students should learn—them simultaneously.
Every student can be a math person
As a society we’ve considered math a gatekeeper to opportunities. Excel in math and you can pursue a wealth of STEM and other rewarding careers.
Unfortunately, we’ve also conveyed the idea that “some people are not innately math people.” This mindset and belief system could not be further from the truth. In many cases, struggling students simply have not had equitable access to math due to language barriers, underperforming schools, socio-economic issues, or other challenges. But we now have a wealth of resources and proven methodologies to ensure that every student knows and believes from the beginning that they are, in fact, a math person.
Instead of being an opportunity-killing gatekeeper, math can be the bridge builder, a pathway to choice and opportunity, and the thread that connects students to richer learning and life experiences.
Relate math to your students’ cultural frameworks
Educators can start by employing a culturally sustaining pedagogy, tapping into the unique experiences that each learner brings into the classroom. We must invite our students into the learning process as their whole selves, complete with their individuality, differences, and cultural diversity. Then we need to relate the math to each student’s cultural frame of reference, encouraging them to develop (and sustain) their own cultural and mathematical identities while seeing themselves as capable learners.
Utilizing digital learning tools to help improve and support meaningful student participation in math discussions is a key way to bridge this gap. Incorporating translanguaging during class can also encourage students to use their full linguistic repertoire to navigate the content. Language is complex, and we know that navigating it doesn’t always adhere to the silos of one or two. Students may know more or need more help than they’re able to express in any single language.
Math connects content and learners
All students benefit from storytelling and other integrating techniques; relevant and thought-provoking conversations elevate student voices and engage learners. Using storytelling during math instruction can:
Provide context and make numbers on a page come to life. Math isn’t just 2 + 2 = 4. It’s two baskets for a four-point lead at halftime.
Bridge mathematical learning to a world beyond the classroom. Teachers can help students see how math animates science, history, music, social studies, art, and sports.
Restore, affirm, and sustain positive mathematical identities.
In teaching math, we also can’t lose sight of early numeracy. We need to be aware of unfinished learning–not every student comes into class at grade level; taking the time to learn about the whole child and their unique points of view will go a long way in nurturing their joy for learning and, in particular, mathematics.
Odalis Amparo
Odalis Amparo is a former elementary school teacher and instructional math coach. She is currently a professional learning specialist at Illustrative Mathematics where she continues her passion for spreading the love of math to all students.
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This extreme fragility might make quantum computing sound hopeless. But in 1995, the applied mathematician Peter Shor discovered a clever way to store quantum information. His encoding had two key properties. First, it could tolerate errors that only affected individual qubits. Second, it came with a procedure for correcting errors as they occurred, preventing them from piling up and derailing a computation. Shor’s discovery was the first example of a quantum error-correcting code, and its two key properties are the defining features of all such codes.
The first property stems from a simple principle: Secret information is less vulnerable when it’s divided up. Spy networks employ a similar strategy. Each spy knows very little about the network as a whole, so the organization remains safe even if any individual is captured. But quantum error-correcting codes take this logic to the extreme. In a quantum spy network, no single spy would know anything at all, yet together they’d know a lot.
Each quantum error-correcting code is a specific recipe for distributing quantum information across many qubits in a collective superposition state. This procedure effectively transforms a cluster of physical qubits into a single virtual qubit. Repeat the process many times with a large array of qubits, and you’ll get many virtual qubits that you can use to perform computations.
The physical qubits that make up each virtual qubit are like those oblivious quantum spies. Measure any one of them and you’ll learn nothing about the state of the virtual qubit it’s a part of—a property called local indistinguishability. Since each physical qubit encodes no information, errors in single qubits won’t ruin a computation. The information that matters is somehow everywhere, yet nowhere in particular.
“You can’t pin it down to any individual qubit,” Cubitt said.
All quantum error-correcting codes can absorb at least one error without any effect on the encoded information, but they will all eventually succumb as errors accumulate. That’s where the second property of quantum error-correcting codes kicks in—the actual error correction. This is closely related to local indistinguishability: Because errors in individual qubits don’t destroy any information, it’s always possible to reverse any error using established procedures specific to each code.
Taken for a Ride
Zhi Li, a postdoc at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, was well versed in the theory of quantum error correction. But the subject was far from his mind when he struck up a conversation with his colleague Latham Boyle. It was the fall of 2022, and the two physicists were on an evening shuttle from Waterloo to Toronto. Boyle, an expert in aperiodic tilings who lived in Toronto at the time and is now at the University of Edinburgh, was a familiar face on those shuttle rides, which often got stuck in heavy traffic.
“Normally they could be very miserable,” Boyle said. “This was like the greatest one of all time.”
Before that fateful evening, Li and Boyle knew of each other’s work, but their research areas didn’t directly overlap, and they’d never had a one-on-one conversation. But like countless researchers in unrelated fields, Li was curious about aperiodic tilings. “It’s very hard to be not interested,” he said.
Editor’s note: This story led off this week’s Future of Learning newsletter, which is delivered free to subscribers’ inboxes every other Wednesday with trends and top stories about education innovation. Subscribe today!
Last year, I began reporting on the growing interest in teaching young people about data science amid calls that Algebra II and other higher-level math classes are being taught in outdated ways and need to be modernized. Experts were already raising concerns about falling math scores before the pandemic, and those scores nationwide have only continued to worsen.
There’s no easy answer – math experts, STEM professors, high school educators, parents, advocates and even students have vastly different opinions on what math knowledge and courses should be required for students to succeed in college and careers.
Nowhere has this been clearer than in California. As I wrote in my latest story, co-published with The Washington Post, the state’s public higher education system has gone back and forth on whether data science (an interdisciplinary field that combines computer programming, math and statistics) and other statistics-based courses fit into existing math pathways and can serve as an alternative to Algebra II in admissions.
But missing from these debates was the voices of students and educators – those most affected by any decisions made by the state’s public university system. I wanted to see for myself what students were learning in high school data science classes, why they were signing up for the course and how decisions about which math classes to take were being determined.
In December, I visited Oxnard Union High School District, which launched a data science pathway in 2020. The class targeted students who didn’t plan to major in STEM fields in college, as well as those who planned to attend a community college or go straight into the workforce or military. A “math class for poets” was how the district’s superintendent, Tom McCoy, had jokingly described it.
From my visits to the district’s high school data science classes and my conversations with teachers and students, two things became clear: The course’s structure is very different than a traditional math class – it’s an applied, project-based learning course in which students collaborate closely as they learn the material. And the way different teachers and schools approach the class differs greatly, even within a single district. Some teachers emphasize data literacy (teaching students how to read and analyze data); others incorporate math concepts from algebra and statistics; and still others may inject more computer programming or coding.
That variation — both in how the classes are taught and their content – has added to concerns that data science courses are low quality and insufficiently rigorous. And it’s in part why there’s an emerging push to develop standards around the course, and tackle the question of what an effective data science course should look like.
Much of the concern around data science in California centers around three programs — Introduction to Data Science, Youcubed and CourseKata — that make up the majority of data science courses available there. According to a recent report from University of California committee that sets admissions standards, none of the courses “even come close to meeting the required standard to be a ‘more advanced’ course,” and are more similar to data literacy courses than advanced mathematics. (Oxnard Union uses a different curricula, one developed by ed tech vendor Bootstrap.)
Mahmoud Harding is the instructional design director at Data Science 4 Everyone, a national initiative based at the University of Chicago. He co-developed a high school data science program at the North Carolina School of Science and Mathematics and teaches a course at North Carolina State’s Data Science Academy. He said a high school data science course should help students find more real-world applications for concepts they learn in algebra.
In addition, the class should build conceptual knowledge of statistical topics through computation, visualizations and simulations, and help students understand bias within data and ethical concerns in using flawed data. Data science courses also need to be substantively different from statistics or computer programing courses, he said, noting that data science is “inherently interdisciplinary.”
“I don’t think a data science course is the same as an Algebra II course,” Harding said. “But it doesn’t mean that a data science course isn’t rigorous, or it doesn’t mean that you can’t matriculate into higher forms of algebra because you’ve taken data science.”
Harding’s group, Data Science 4 Everyone, is helping to lead the new effort to develop standards for data science. Zarek Drozda, the group’s executive director, said this year it will convene a working group of experts, K-12 educators, STEM professors, curriculum providers, state and district leaders, students and industry and workforce professionals including those with tech companies, to help create a list of recommendations of baseline data science standards.
As career opportunities involving AI, computing and data increase, Drozda said it is “critical” that we think about the foundational knowledge students need by the time they graduate from college. The group is engaging people from all sides of the data science debate to look critically at the courses currently offered and identify how to create classes that will better meet the needs of students.
Drozda said he also hopes the working group will consider how exposure to data science classes can help more students get excited about STEM fields that don’t necessarily require a four-year degree.
“I think there’s a false perception that we are trying to replace fundamental mathematics,” Drozda said. “In reality, we are trying to modernize, add options and enhance the relevance of mathematics and prove to students that math matters in the 21st century.”
The Hechinger Report provides in-depth, fact-based, unbiased reporting on education that is free to all readers. But that doesn’t mean it’s free to produce. Our work keeps educators and the public informed about pressing issues at schools and on campuses throughout the country. We tell the whole story, even when the details are inconvenient. Help us keep doing that.
A growing chorus of education researchers, pundits and “science of reading” advocates are calling for young children to be taught more about the world around them. It’s an indirect way of teaching reading comprehension. The theory is that what we grasp from what we read depends on whether we can hook it to concepts and topics that we already know. Natalie Wexler’s 2019 best-selling book, The Knowledge Gap, championed knowledge-building curricula and more schools around the country, from Baltimore to Michigan to Colorado, are adopting these content-filled lesson plans to teach geography, astronomy and even art history.
Makers of knowledge-building curricula say their lessons are based on research, but the truth is that there is scant classroom evidence that building knowledge first increases future reading comprehension.
More importantly, the students at these charter schools were largely from middle and upper middle class families. And what we really want to know is whether knowledge building at school helps poorer children, who are less likely to be exposed to the world through travel, live performances, and other experiences that money can buy.
A new study, published online on Feb. 26, 2024, in the peer-reviewed journal Developmental Psychology, now provides stronger causal evidence that building background knowledge can translate into higher reading achievement for low-income children. The study took place in an unnamed, large urban school district in North Carolinawhere most of the students are Black and Hispanic and 40 percent are from low-income families.
In 2019, a group of researchers, led by James Kim, a professor at Harvard University’s Graduate School of Education, randomly selected 15 of the district’s 30 elementary schools to teach first graders special knowledge-building lessons for three years, through third grade. Kim, a reading specialist, and other researchers had developed two sets of multi-year lesson plans, one for science and one for social studies. Students were also given related books to read during the summer. (This research was funded by the Chan Zuckerberg Initiative, which is among the many funders of The Hechinger Report.)
The remaining 15 elementary schools in the district continued to teach their students as usual, still delivering some social studies and science instruction, but not these special lessons. Regular reading class was untouched in the experiment. All 30 schools were using the same reading curriculum, Expeditionary Learning, which follows science of reading principles and teaches phonics.
Covid hit in the middle of the experiment. When schools shut down in the spring of 2020, the researchers scrapped the planned social studies units for second graders. In 2021, students were still not attending school in person. The researchers revised their science curriculum and decided to give an abridged online version to all 30 schools instead of just half. In the end, children in the original 15 schools received one year of social studies lessons and three years of science lessons compared to only one year of science in the comparison group.
Still, approximately 1,000 students who had received the special science and social studies lessons in first and second grades outperformed the 1,000 students who got only the abbreviated online science in third grade. Their reading and math scores on the North Carolina state tests were higher not only in third grade, but also in fourth grade, more than a year after the knowledge-building experiment ended.
It wasn’t a huge boost to reading achievement, but it was significant and long-lasting. It cost about $400 per student in instructional materials and teacher training.
Timothy Shanahan, a literacy expert and a professor emeritus at the University of Illinois at Chicago who was not involved in this research or the development of these science lessons, praised the study. “The study makes it very clear (as have a few others recently) that it is possible to combine reading with social studies and science curriculum in powerful ways that can improve both literacy and content knowledge,” he said by email.
Connecting background knowledge to reading comprehension is not a new idea. A famous 1987 experiment documented that children who were weaker readers but knowledgeable about baseball understood a reading passage about baseball better than children who were stronger readers but didn’t know much about the sport.
Obviously, it’s not realistic for schools to attempt to familiarize students with every topic they might encounter in a book. And there is disagreement among researchers about how general knowledge of the world translates into higher reading performance.
Kim thinks that a knowledge-building curriculum doesn’t need to teach many topics. Random facts, he says, are not important. He argues for depth instead of breadth. He says it’s important to construct a thoughtful sequence of lessons over the years, allowing students to see how the same patterns crop up in different ways. He calls these patterns “schemas.” In this experiment, for example, students learned about animal survival in first grade and dinosaur extinction in second grade. In third grade, that evolved into a more general understanding of how living systems function. By the end of third grade, many students were able to see how the idea of functioning systems can apply to inanimate objects, such as skyscrapers.
It’s the patterns that can be analogized to new circumstances, Kim explained. Once a student is familiar with the template, a new text on an unfamiliar topic can be easier to grasp.
Kim and his team also paired the science lessons with clusters of vocabulary words that were likely to come up again in the future – almost like wine pairings with a meal.
The full benefits of this kind of knowledge building didn’t materialize until after several years of coordinated instruction. In the first years, students were only able to transfer their ability to comprehend text on one topic to another if the topics were very similar. This study indicates that as their content knowledge deepened, their ability to generalize increased as well.
There’s a lot going on here: a spiraling curriculum that revisits and builds upon themes year after year; an explicit teaching of underlying patterns; new vocabulary words, and a progression from the simple to the complex.
There are many versions of knowledge-rich curricula and this one isn’t about exposing students to a classical canon. It remains unclear if all knowledge-building curricula work as well. Other programs sometimes replace the main reading class with knowledge-building lessons. This one didn’t tinker with regular reading class.
The biggest challenge with the approach used in the North Carolina experiment is that it requires schools to coordinate lessons across grades. That’s hard. Some teachers may want to keep their favorite units on, say, growing a bean plant, and may bristle at the idea of throwing away their old lesson plans.
It’s also worth noting that students’ math scores improved as much as their reading scores did in this North Carolina experiment. It might seem surprising that a literacy intervention would also boost math. But math also requires a lot of reading; the state’s math tests were full of word problems. Any successful effort to boost reading skills is also likely to have positive spillovers into math, researchers explained.
School leaders are under great pressure to boost test scores. To do that, they’ve often doubled time spent on reading and cut science and social studies classes. Studies like this one suggest that those cuts may have been costly, further undermining reading achievement instead of improving it. As researchers discover more about the science of reading, it may well turn out to be that more time on science itself is what kids need to become good readers.
This story about background knowledge was written by Jill Barshay and produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Proof Points newsletter.
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The Hechinger Report provides in-depth, fact-based, unbiased reporting on education that is free to all readers. But that doesn’t mean it’s free to produce. Our work keeps educators and the public informed about pressing issues at schools and on campuses throughout the country. We tell the whole story, even when the details are inconvenient. Help us keep doing that.
COLORADO SPRINGS, Colo./PRNewswire-PRWeb/ —TouchMath, a multisensory math program that makes learning crucial mathematical concepts accessible and clear for students who struggle to understand grade-level content, announces the launch of TouchMath Extend and Dyscalculia Extension. These groundbreaking solutions aim to bridge mathematical gaps and advance dyscalculia advocacy. Coinciding with two significant milestones, International Dyscalculia Day (March 3rd) and the 50th anniversary of the term ‘Developmental Dyscalculia,’ coined in March 1974, TouchMath reaffirms its commitment to providing essential resources and support to students experiencing mathematical barriers.
“Considering TouchMath’s unwavering commitment to educational equity over nearly five decades, the launch of TouchMath Extend and Dyscalculia Extension signifies a pivotal moment in our mission,” stated Dr. Sandra Elliott, Chief Academic Officer at TouchMath. “Recognizing that approximately 75% of students with dyscalculia also experience dyslexia, it’s clear that both conditions warrant equal recognition and support. Through these innovative solutions, we aim to not only raise awareness but also provide concrete assistance, empowering students to overcome mathematical challenges. As we celebrate the 50th anniversary of Ladislav Kosc’s pioneering work, it’s time to dispel misconceptions, deepen understanding, and champion inclusive education where every learner, regardless of their challenges, can thrive.”
Dyscalculia, estimated to affect 3-7% of the population, is a learning disability with profound impacts on academic performance and daily life. Challenges include struggles with basic math operations and understanding mathematical concepts. However, only about 15% of students have been screened for dyscalculia, while 40% of math teachers report students performing below grade level. Unlike dyslexia, dyscalculia lacks systematic tracking in the U.S. despite the urgent need for skilled STEM professionals. While more than 45 U.S. states have enacted dyslexia-related legislation, fewer than ten states have passed laws addressing math intervention and instruction since 2021.
“While dyslexia-related legislation has seen significant progress, there’s a notable gap in addressing math intervention and instruction,” notes Dr. Chelsi Brosh, Vice President, Product Innovation at TouchMath. “TouchMath Extend and Dyscalculia Extension fill this void, offering comprehensive solutions to support students struggling with math.”
Dyscalculia Extension Overview: Dyscalculia Extension offers tailored support through a multisensory program, providing comprehensive resources like 60 math games/tasks and 180 downloadable activity sheets. Aligned with Standards Edition curricula, it ensures adherence to educational standards and includes supporting tools such as graphic organizers and dyscalculia-specific strategies. With diverse activities catering to various learning styles, Dyscalculia Extension is versatile, aligns with DSM-5 standards, and integrates seamlessly into special and general education classrooms.
In addition to dyscalculia advocacy, TouchMath acknowledges the diverse challenges faced by students with autism spectrum disorder (ASD) in mathematics education and other STEM subjects. Research supports the effectiveness of multisensory approaches in enhancing mathematical learning for students with disabilities, and TouchMath Extend aligns with these findings, offering tailored solutions to address the diverse learning needs of all students.
TouchMath Extend Overview: TouchMath Extend is an innovative multisensory extended school year, summer school, and ongoing math intervention solution designed to transform math learning. It offers a tailored 12-week curriculum focusing on skill remediation and teacher support through on-demand video training. The program combines traditional workbooks with digital math games to enhance comprehension and provides long-term value through the TouchMath digital platform. TouchMath Extend prepares students for future success while embodying TouchMath’s commitment to comprehensive math education.
“Reflecting on our founding mission nearly 50 years ago, TouchMath remains dedicated to creating intentional learning experiences for students, especially those facing vulnerabilities,” said Sean Lockwood, Chief Executive Officer at TouchMath. “We will continue championing accessibility and inclusivity in mathematics education, paving the way for a brighter future for all learners.”
TouchMath’s commitment to dyscalculia advocacy goes beyond its latest product launches. In the last year, TouchMath released the free DySc screener and an extensive whitepaper to increase awareness and understanding of dyscalculia and promote efforts to ensure that all children have access to the support they need.
To learn more about TouchMath and its research-proven solutions, visit https://touchmath.com/.
About TouchMath TouchMath provides a wide range of curriculum and tools for educators and their students who struggle to understand grade-level content. TouchMath is committed to maximizing student potential through its worldwide delivery of hands-on math programs, cultivating success with individuals of all abilities. Since 1975, TouchMath has delivered the only multi-sensory math program that uses the numeral as a manipulative, bringing students along the evidence-based Concrete-Representational-Abstract continuum for mathematics. Visit touchmath.com to learn more.
eSchool Media staff cover education technology in all its aspects–from legislation and litigation, to best practices, to lessons learned and new products. First published in March of 1998 as a monthly print and digital newspaper, eSchool Media provides the news and information necessary to help K-20 decision-makers successfully use technology and innovation to transform schools and colleges and achieve their educational goals.
Because of the skill-based nature of mathematics in general, math resources pair especially well with digital tools like apps and websites. On these kinds of platforms, accounts can be created, progress can be visualized, mastery can be documented, complexity can be adjusted to individual needs, and achievements can even be given as a kind of motivation mechanic.
Year to year, the best math resources tend to stay the same, with large platforms like the Kahn Academy being supplemented by well-designed apps like Quizlet and Math Agent. (Many of these are covered in our best math apps for kids.)
But each year, a handful of new math apps, websites, and other resources emerge to be useful for elementary school, middle school, high school, homeschooling, and college-prep practice. Below, we’ve gathered 25 of the best math resources–a mix of established and all-new tools to support the building of math skills and the grasp of important mathematical concepts.
Math Resources For Elementary School Students
Wolfram Alpha
Renowned for its computational power, Wolfram Alpha is a go-to tool for students needing instant solutions, step-by-step explanations, and interactive visualizations across various mathematical domains, including calculus, linear algebra, and statistics.
Coursera
Partnering with universities worldwide, Coursera offers many math courses delivered by esteemed professors, covering diverse topics like mathematical modeling, graph theory, and differential equations, with self-paced and instructor-led learning options.
MIT OpenCourseWare
Providing free access to lecture notes, assignments, and exams from actual MIT courses, MIT OpenCourseWare is an invaluable resource for students seeking in-depth understanding and rigorous study materials in discrete mathematics, probability, and mathematical logic.
Paul’s Online Math Notes
Created by Professor Paul Dawkins, this website offers clear and concise explanations, extensive examples, and practice problems, covering topics ranging from pre-algebra to advanced calculus. It is an excellent supplementary resource for students seeking additional clarity.
Desmos
Known for its interactive graphing calculator, Desmos offers a user-friendly platform for visualizing mathematical concepts, exploring functions, and creating dynamic graphs, suitable for students at various levels of mathematical proficiency.
Art of Problem Solving (AoPS)
Focused on developing problem-solving skills and mathematical creativity, AoPS provides online courses, textbooks, and a vibrant community where students can engage in challenging problems, competitions, and discussions, fostering a deep appreciation for mathematics beyond the classroom curriculum.
Developer Description: The K-3 math movies teach educational topics like time, money, number sense, geometry, measurement, addition, subtraction, and fractions.
IXL provides personalized learning, along with a real-time math diagnostic test. The diagnostic designs a recommendations list based around areas you struggle.
Developer Description: A mobile application which utilizes a phone’s camera to recognize mathematical equations, and to display the step-by-step solution onscreen.
Silence may be golden, but when it comes to learning with a tutor, talking is pure gold. It’s audible proof that a student is paying attention and not drifting off, research suggests. More importantly, the more a student articulates his or her reasoning, the easier it is for a tutor to correct misunderstandings or praise a breakthrough. Those are the moments when learning happens.
One India-based tutoring company, Cuemath, trains its tutors to encourage students to talk more. Its tutors are in India, but many of its clients are American families with elementary school children. The tutoring takes place at home via online video, like a Zoom meeting with a whiteboard, where both tutor and student can work on math problems together.
The company wanted to see if it could boost student participation so it collaborated with researchers at Stanford University to develop a “talk meter,” sort of a Fitbit for the voice, for its tutoring site. Thanks to advances in artificial intelligence, the researchers could separate the audio of the tutors from that of the students and calculate the ratio of tutor-to-student speech.
In initial pilot tests, the talk meter was posted on the tutor’s video screen for the entire one-hour tutoring session, but tutors found that too distracting. The study was revised so that the meter pops up every 20 minutes or three times during the session. When the student is talking less than 25 percent of the time, the meter goes red, indicating that improvement is needed. When the student is talking more than half the time, the meter turns green. In between, it’s yellow.
More than 700 tutors and 1,200 of their students were randomly assigned to one of three groups: one where the tutors were shown the talk meter, another where both tutors and students were shown the talk meter, and a third “control” group which wasn’t shown the talk meter at all for comparison.
When just the tutors saw the talk meter, they tended to curtail their explanations and talk much less. But despite their efforts to prod their tutees to talk more, students increased their talking only by 7 percent.
When students were also shown the talk meter, the dynamic changed. Students increased their talking by 18 percent. Introverts especially started speaking up, according to interviews with the tutors.
The results show how teaching and learning is a two-way street. It’s not just about coaching teachers to be better at their craft. We also need to coach students to be better learners.
“It’s not all the teacher’s responsibility to change student behavior,” said Dorottya Demszky, an assistant professor in education data science at Stanford University and lead author of the study. “I think it’s genuinely, super transformative to think of the student as part of it as well.”
In analyzing the sound files, Demszky noticed that students tended to work on their practice problems with the tutor more silently in both the control and tutor-only talk meter groups. But students started to verbalize their steps aloud once they saw the talk meter. Students were filling more of the silences.
In interviews with the researchers, students said the meter made the tutoring session feel like a game. One student said, “It’s like a competition. So if you talk more, it’s like, I think you’re better at it.” Another noted: “When I see that it’s red, I get a little bit sad and then I keep on talking, then I see it yellow, and then I keep on talking more. Then I see it green and then I’m super happy.”
Some students found the meter distracting. “It can get annoying because sometimes when I’m trying to look at a question, it just appears, and then sometimes I can’t get rid of it,” one said.
Tutors had mixed reactions, too. For many, the talk meter was a helpful reminder not to be long-winded in their explanations and to ask more probing, open-ended questions. Some tutors said they felt pressured to reach a 50-50 ratio and that they were unnaturally holding back from speaking. One tutor pointed out that it’s not always desirable for a student to talk so much. When you’re introducing a new concept or the student is really lost and struggling, it may be better for the teacher to speak more.
Surprisingly, kids didn’t just fill the air with silly talk to move the gauge. Demszky’s team analyzed the transcripts in a subset of the tutoring sessions and found that students were genuinely talking about their math work and expressing their reasoning. The use of math terms increased by 42 percent.
Unfortunately, there are several drawbacks to the study design. We don’t know if students’ math achievement improved from the talk meter. The problem was that students of different ages were learning different things in different grades and different countries and there was no single, standardized test to give them all.
Another confounding factor is that students who saw the talk meter were also given extra information sessions and worksheets about the benefits of talking more. So we can’t tell from this experiment if the talk meter made the difference or if the information on the value of talking aloud would have been enough to get them to talk more.
Demszky is working on developing a talk meter app that can be used in traditional classrooms to encourage more student participation. She hopes teachers will share talk meter results with their students. “I think you could involve the students a little more: ‘It seems like some of you weren’t participating. Or it seems like my questions were very closed ended? How can we work on this together?’”
But she said she’s treading carefully because she is aware that there can be unintended consequences with measurement apps. She wants to give feedback not only on how much students are talking but also on the quality of what they are talking about. And natural language processing still has trouble with English in foreign accents and background noise. Beyond the technological hurdles, there are psychological ones too.
“Not everyone wants a Fitbit or a tool that gives them metrics and feedback,” Demszky acknowledges.
This story about student participationwas written by Jill Barshay and produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Proof Points newsletter.
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The Hechinger Report provides in-depth, fact-based, unbiased reporting on education that is free to all readers. But that doesn’t mean it’s free to produce. Our work keeps educators and the public informed about pressing issues at schools and on campuses throughout the country. We tell the whole story, even when the details are inconvenient. Help us keep doing that.
Welcome back! As you jump into January, Discovery Education has new resources and ideas to help you spark students’ curiosity in potential careers, meaningful moments in history, and STEM! Pop of Professional Learning What’s New Trending Topics Magic Moment Pop of Professional Learning Is one of your New Years Resolutions to plan cross-curricular lessons? Two […]
Back in early 2020, educators and students nationwide were living in a fast-paced world full of choices, adjustments, and constant changes. But in March of that year, everything changed. Our district, like so many across the country, was forced to re-imagine what learning looked like. Under the great leadership of Dr. Shawn Foster, the Orangeburg County School District Superintendent, my school district had an active plan of action to ensure continuity of learning for all students.
While we move further away from day-to-day impacts of the COVID pandemic, in some ways it is still with us. Although all members of the team worked hard to maintain continuity of learning during the pandemic, COVID has left our students’ reading and math skills in a state of emergency. Today, our challenge is to empower, encourage, equip, and support our teachers and students as they recover the learning lost during the pandemic.
To support the success of all students in the post pandemic world and to address the state of emergency in our students’ reading and math skills, our district has reviewed its edtech resources. We’ve decided to keep those that are proven effective in helping our students regain lost learning. Here are the tools we kept:
Waterford.org provides parents and educators with a variety of resources supporting young learners. From its powerful PK-2 early literacy curriculum to its math literacy tools to their many professional learning opportunities, Waterford.org offers helps teachers and parents’ partner on supporting the developing literacy and math skills of elementary school students.
Through the South Carolina Department of Education’s Instructional Hub, my school system and school systems across the state have no-cost access to Discovery Education Experience. The wide array of digital resources now available to me help me better differentiate instruction and provide learners of all levels the appropriate resources for improving their math and literacy scores. The high-quality resources offered by Discovery Education also nurture my students’ natural curiosity, making it the perfect tool for improving student engagement.
Eureka Math is also an important component in our efforts to boost student success in math. It features a spiraled curriculum that builds upon each lesson daily. As Eureka Math focuses on key concepts that layer over time, students gain an enduring body of math knowledge, not just a discrete set of skills. Plus, because students use the same models and problem-solving methods from grade to grade, math concepts stay with them, year after year.
Alongside Eureka Math, we use i-Ready. A connected system of assessments and learning resources, i-Ready provides educators like me not only a deeper understand of what my students know and do not know, but also a host of resources that help me remediate where needed and provide student enrich for students operating above grade level.
To provide teachers even more insight into our students’ understanding of core concepts, my school system is now combining i-Ready and Mastery Connect to implement mini-assessments that allow us to target support in identified areas even faster than before. The insights gleaned from these mini assessments help identify areas needing additional help very quickly, allowing me to adjust teaching and provide students more individual support.
Augmenting all these resources are resources from a number of nonprofit providers, such as the Save the Children Foundation and the 21st Century After School Program. This content provides after-school caregivers with additional tools to help students continue learning after the last bell.
As much as we’d like to think we’ve moved on from the COVID pandemic, the fact is that we will be grappling with its aftermath for a long time. Thankfully, the district I am proud to serve in—Orangeburg School District in South Carolina—is dedicated to ensuring all students discover and develop their person, purpose, and platform through high-quality educational experiences. They are putting their money where their mouth is by making sure educators have the tools needed to overcome our current state of emergency. I believe these resources, when in the hands of my innovative colleagues, will get the job done!
Dr. Vickel Darby, Coordinator of Early Learning and Instructional Technology, Orangeburg County School District
Dr. Vickel Darby is the Coordinator of Early Learning and Instructional Technology in South Carolina’s Orangeburg County School District.
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Dr. Vickel Darby, Coordinator of Early Learning and Instructional Technology, Orangeburg County School District
BALTIMORE, Maryland — IXL Learning, developer of personalized learning products used by millions of people globally, has unveiled the findings of a Johns Hopkins University study that affirms IXL Math’s effectiveness in boosting student achievement. The evaluation of IXL Math’s impact meets the required rigor of Every Student Succeeds Act (ESSA) Tier 1 and What Works Clearinghouse standards for evidence-based interventions.
The Center for Research and Reform in Education (CRRE) at Johns Hopkins University conducted an independent, randomized control trial in Spring 2023 at Holland Public Schools in Michigan. The goal of the study was to determine IXL Math’s efficacy on students in grades 3-5. Half of the classrooms were assigned to the treatment group and used IXL Math to supplement instruction, while the remaining students continued learning as usual.
Students in IXL classrooms surpassed their control group peers: IXL Math students significantly outperformed the control group by an average of 10 points on the Star Math assessment.
Underserved students achieved larger gains: Improved math performance was particularly pronounced among Hispanic, Special Education, English Language Learner, and FARMS (Free and Reduced Meal Program) student populations, with gains ranging from 13 to 17 points.
A positive correlation between usage and achievement: IXL Math usage was significantly correlated with student performance on the Star Math and M-STEP assessments.
Teachers overwhelmingly praised their IXL implementation: Approximately 90% of teachers reported that their implementation of IXL was successful and had a meaningful impact on instruction. The initial professional development provided by IXL was particularly valuable, according to teachers.
“We are proud that this expert-led study clearly confirms IXL’s positive impact on math achievement and places it within ESSA’s highest tier of efficacy,” said Bo Bashkov, Manager of Research at IXL Learning. “A compelling body of evidence from previous studies spanning 70,000 schools throughout the United States shows a remarkable pattern: Schools utilizing IXL consistently outperform those using other solutions. This new report corroborates existing findings and further underscores that IXL empowers students and teachers to achieve greater success.”
Visit our research page for more information about IXL’s studies.
How IXL helps students succeed in math
IXL Math is an adaptive program that is proven to help students master essential skills. In fact, studies show that schools using IXL Math consistently outperform others, ranking as much as 15 percentile points higher on state assessments. In addition to helping schools and students succeed academically, IXL can uncover hidden obstacles to learning, increase teacher engagement, develop students’ intrinsic motivation to learn, and more.
Comprehensive curriculum for deeper learning
With more than 4,900 standards-aligned skills, IXL Math’s K-12 curriculum promotes rigor by helping students develop a conceptual understanding of math, build procedural fluency, and tackle challenging problems that have real-world applications. Each skill is adaptive, adjusting in difficulty to ensure students are perfectly challenged. Based on students’ previous work, IXL generates personalized recommendations in real time that guide learners to skills that will help them make the most progress.
IXL now also provides a groundbreaking curriculum, Takeoff by IXL Math™, to deliver core instruction and help teachers differentiate a full year of daily math learning without any prior planning. The Takeoff curriculum equips teachers with everything they need to provide tailored math instruction, including lesson plans, dynamic recommendations for support and enrichment, and ready-made unit assessments. Seamlessly integrated into IXL’s personalized learning platform, these resources give students the support they need and show teachers instant insights into their progress.
Accurately assess knowledge in real time
IXL’s first-of-its-kind assessment suite, which includes the Real-Time Diagnostic and universal screener, works in concert with its math curriculum to give educators real-time insight into performance, pinpoint gaps in knowledge, and provide specific next steps to help each student grow. Additionally, IXL’s comprehensive diagnostic reports allow administrators to easily identify students across their district who are working below grade level and may need additional support.
Support and empower students at every step
Built-in instructional resources, including more than 2,700 video tutorials for Grade 2 through Precalculus skills, support students when they’re working independently and ensure they have the guidance to learn with confidence.
Provide teachers the insights that they need
IXL Analytics provides teachers with real-time insights that pinpoint trouble spots and monitor performance, allowing them to respond to student needs more quickly and facilitate meaningful growth. Administrators can use IXL District Analytics and IXL School Analytics to track student progress and teacher engagement, enabling them to improve IXL’s impact on their school or district.
About IXL
Currently used by 15 million students and in 95 of the top 100 U.S. school districts, IXL is an all-inclusive educational platform that provides a comprehensive PK-12 curriculum and instructional resources, actionable analytics and a state-of-the-art assessment suite. IXL’s end-to-end teaching and learning solution supports personalized instruction in math, English language arts, science, social studies and Spanish. With more than 130 billion questions asked and answered around the world, IXL is helping schools and parents successfully boost student achievement. The IXL Learning family of products also includes Rosetta Stone, TPT, SpanishDictionary.com, inglés.com, Wyzant, Vocabulary.com, ABCya, Education.com and Emmersion. To learn more about IXL, visit www.ixl.com, facebook.com/IXL and twitter.com/IXLLearning.
eSchool Media staff cover education technology in all its aspects–from legislation and litigation, to best practices, to lessons learned and new products. First published in March of 1998 as a monthly print and digital newspaper, eSchool Media provides the news and information necessary to help K-20 decision-makers successfully use technology and innovation to transform schools and colleges and achieve their educational goals.
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