Think you’re bad at math? You may suffer from ‘math trauma’
Even some teachers suffer from anxiety about math.
I teach people how to teach math, and I've been working in this field for 30 years. Across those decades, I've met many people who suffer from varying degrees of math trauma – a form of debilitating mental shutdown when it comes to doing mathematics.
When people share their stories with me, there are common themes. These include someone telling them they were “not good at math," panicking over timed math tests, or getting stuck on some math topic and struggling to move past it. The topics can be as broad as fractions or an entire class, such as Algebra or Geometry.
One of the biggest challenges U.S. math educators face is helping the large number of elementary teachers who are dealing with math trauma. Imagine being tasked with teaching children mathematics when it is one of your greatest personal fears.
Math trauma manifests as anxiety or dread, a debilitating fear of being wrong. This fear limits access to life paths for many people, including school and career choices.
While math trauma has multiple sources, there are some that parents and teachers have power to influence directly: outdated ideas of what it means to be good at math. These include speed and accuracy, which were important in decades past when humans were actual computers.
But research has confirmed what many people share with me anecdotally: Tying speed with computation debilitates learners. People who struggle to complete a timed test of math facts often experience fear, which shuts down their working memory. This makes it all but impossible to think which reinforces the idea that a person just can't do math – that they are not a math person.
What's more, students who succeed at tests of timed math facts may believe that being good at math means simply being fast and accurate at calculating. This belief can lead to a fragile math identity. Students fear revealing they don't know something or aren't that fast, so may shy away from more challenging work. No one wins.
The myth that fast recall of basic math facts is good for learning has deep and pernicious roots. It comes from the best of intentions – who wouldn't want kids to be good at calculating? But research shows that fact fluency – the ability to easily recall facts, like 3 x 5 = 15 – is best developed from first making sense of arithmetic operations. In other words, the first step in building a mathematical memory is understanding how that math works.
A deeper understanding of the concepts like multiplication and division allow people to see patterns in numbers. For example, 3, 5 and 15 are in a triangular relationship, where 3 x 5 = 15, 5 x 3 = 15, 15 ÷ 5 = 3, and 15 ÷ 3 = 5. Jennifer Ruef, CC BY
Skipping the sensemaking step makes for fragile understanding and cognitively expensive memorization. When someone only memorizes, every new fact is like an island unto itself, and is more readily forgotten. In contrast, understanding patterns in math facts compresses the cognitive load required to recall related facts. Sensemaking promotes deep, robust and flexible understanding, allowing people to apply what they know to new problems.
So what can parents and teachers do to support fact fluency?
First, find the wonder and joy. Games and puzzles that get people playing with numbers, such as Sudoku, KenKen or certain card games, create an intellectual need to use math facts that helps kids develop fact fluency. Asking kids to explain their thinking – using words, pictures or objects – validates the importance of their ideas.
Reframe mistakes as explorations. Not having a correct answer doesn't mean all thinking is incorrect. Asking kids to explain their thinking also helps in understanding what they know now, and what they might learn next. Questions about how a kid got an answer can get them thinking about what does not quite work and is worthy of revision. When you ask these questions, it's good to have a poker face; if you broadcast that an answer is wrong or right, it can reinforce the belief that only right answers count.
Second, do no harm. It's important that parents avoid giving kids messages that they are not math people. This can have a negative impact on kids' beliefs about their own ability to learn. Also, beware claims that kids must suffer to learn mathematics.
For many adults, today's math classes are very different from those we experienced. U.S. schools have moved away from speed and accuracy – sometimes called "drill and kill" – and toward discussing and making sense of mathematics. Mathematics teacher educators are in agreement that these are good things. Look for the deeper meaning in what your child is learning, knowing that deeper understanding comes from connecting multiple ways to solve problems.
If you recognize that you are a survivor of math trauma, take heart. You are not alone, and there are ways to heal. It starts with understanding that mathematics is broad and beautiful – most of us are much more mathematical than we think.
Northwell Health CEO Michael Dowling has an important favor to ask of the American people.
- Michael Dowling is president and CEO of Northwell Health, the largest health care system in New York state. In this PSA, speaking as someone whose company has seen more COVID-19 patients than any other in the country, Dowling implores Americans to wear masks—not only for their own health, but for the health of those around them.
- The CDC reports that there have been close to 7.9 million cases of coronavirus reported in the United States since January. Around 216,000 people have died from the virus so far with hundreds more added to the tally every day. Several labs around the world are working on solutions, but there is currently no vaccine for COVID-19.
- The most basic thing that everyone can do to help slow the spread is to practice social distancing, wash your hands, and to wear a mask. The CDC recommends that everyone ages two and up wear a mask that is two or more layers of material and that covers the nose, mouth, and chin. Gaiters and face shields have been shown to be less effective at blocking droplets. Homemade face coverings are acceptable, but wearers should make sure they are constructed out of the proper materials and that they are washed between uses. Wearing a mask is the most important thing you can do to save lives in your community.
Two massive clouds of dust in orbit around the Earth have been discussed for years and finally proven to exist.
- Hungarian astronomers have proven the existence of two "pseudo-satellites" in orbit around the earth.
- These dust clouds were first discovered in the sixties, but are so difficult to spot that scientists have debated their existence since then.
- The findings may be used to decide where to put satellites in the future and will have to be considered when interplanetary space missions are undertaken.
What are they?<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xODgyMDA0NC9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYzNTM1ODc0Mn0.NH33LuauIo__sUBi4tvhwxDcsvhflDFD-Nhx9FjlSNk/img.jpg?width=1245&coordinates=148%2C0%2C149%2C0&height=700" id="cec96" class="rm-shortcode" data-rm-shortcode-id="acb78abe2ab46a17e419ad30906751d6" data-rm-shortcode-name="rebelmouse-image" />
Artist's impression of the Kordylewski cloud in the night sky (with its brightness greatly enhanced) at the time of the observations.
G. Horváth<p>The<a href="https://en.wikipedia.org/wiki/Kordylewski_cloud" target="_blank"> Kordylewski clouds</a> are two dust clouds first observed by Polish astronomer Kazimierz Kordylewski in 1961. They are situated at two of the <a href="https://www.space.com/30302-lagrange-points.html" target="_blank">Lagrange points</a> in Earth's orbit. These points are locations where the gravity of two objects, such as the Earth and the Moon or a planet and the Sun, equals the centripetal required to orbit the objects while staying in the same relative position. There are five of these spots between the Earth and Moon. The clouds rest at what are called points four and five, forming a triangle with the clouds and the Earth at the three corners.</p><p>The clouds are enormous, taking up the same space in the night sky as twenty lunar discs; covering an area of 45,000 miles. They are roughly 250,000 miles away, about the same distance from us as the Moon. They are entirely comprised of specks of dust which reflect the light of the sun so faintly most astronomers that looked for them were unable to see them at all. </p><p>The clouds themselves are probably ancient, but the model that the scientists created to learn about them suggests that the individual dust particles that comprise them can be blown away by solar wind and replaced by the dust from other cosmic sources like comet tails. This means that the clouds hardly move but are <a href="https://www.nationalgeographic.com/science/2018/11/news-earth-moon-dust-clouds-satellites-planets-space/" target="_blank">eternally changing</a>. </p>
How did they discover this?<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xODgyMDAzNi9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY1Nzc4MjQ4MX0.7uU9OqmQcWw5Ll1UXAav0PCu4nTg-GdJdAWADHanC7c/img.jpg?width=1245&coordinates=0%2C180%2C0%2C181&height=700" id="952fb" class="rm-shortcode" data-rm-shortcode-id="a778280a20f1c54cd2c14c8313224be2" data-rm-shortcode-name="rebelmouse-image" />
"In this picture the central region of the Kordylewski dust cloud is visible (bright red pixels). The straight tilted lines are traces of satellites."
J. Slíz-Balogh<p>In their study published in the <a href="https://academic.oup.com/mnras" target="_blank">Monthly Notices of the Royal Astronomical Society</a>, Hungarian astronomers Judit Slíz-Balogh, András Barta, and Gábor Horváth described how they were able to find the dust clouds using polarized lenses.</p><p>Since the clouds were expected to polarize the light that bounces off of them, by configuring the telescopes to look for this kind of light the clouds were much easier to spot. What the scientists observed, polarized light in patterns that extended outside the view of the telescope lens, was in line with the predictions of their mathematical model and ruled out other possible sources. </p>
Why are we just learning this now?<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8xODgyMDAzOS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY2MjUyNDMyMH0.Zl8GmQ_rJHiL4b7hN0r_YBmgb6_ZqIRvqOVuko2ubpw/img.jpg?width=1245&coordinates=0%2C141%2C0%2C185&height=700" id="87afe" class="rm-shortcode" data-rm-shortcode-id="dd4c0b5088e601d7279cc5eb226f8b7b" data-rm-shortcode-name="rebelmouse-image" />
"Mosaic pattern of the angle of polarization around the L5 point (white dot) of the Earth-Moon system. The five rectangular windows correspond to the imaging telescope with which the patterns of the Kordylewski cloud were measured."
J. Slíz-Balogh<p>The objects, being dust clouds, are very faint and hard to see. While Kordylewski observed them in 1961, other astronomers have looked there and given mixed reports over the following decades. This discouraged many astronomers from joining the search, as study co-author Judit Slíz-Balogh <a href="https://ras.ac.uk/news-and-press/research-highlights/earths-dust-cloud-satellites-confirmed" target="_blank">explained</a>, <em>"The Kordylewski clouds are two of the toughest objects to find, and though they are as close to Earth as the Moon are largely overlooked by researchers in astronomy. It is intriguing to confirm that our planet has dusty pseudo-satellites in orbit alongside our lunar neighbor."</em></p>
Will this have any impact on space travel?<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="c3d797fff5430c64afcb5a49bddc3616"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/Ou8N3v9SFPE?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span><p>Lagrange points have been put forward as excellent locations for a space station or satellites like the <a href="https://jwst.nasa.gov/about.html" target="_blank">James Webb Telescope</a> to be put into orbit, as they would require little fuel to stay in place. Knowing about a massive dust cloud that could damage sensitive equipment already being there could save money and lives in the future. While we only know about the clouds at Lagrange points four and five right now, the study's authors suggest there could be more at the other points.</p><p>While the discovery of a couple of dust clouds might not seem all that impressive, it is the result of a half-century of astronomical and mathematical work and reminds us that wonders are still hidden in our cosmic backyard. While you might never need to worry about these clouds again, there is nothing wrong with looking at the sky with wonder at the strange and fantastic things we can discover. </p>
Instead of looking forward, we should be consulting the past.
When will the pandemic end? All these months in, with over 37 million COVID-19 cases and more than 1 million deaths globally, you may be wondering, with increasing exasperation, how long this will continue.
New cancer-scanning technology reveals a previously unknown detail of human anatomy.
- Scientists using new scanning technology and hunting for prostate tumors get a surprise.
- Behind the nasopharynx is a set of salivary glands that no one knew about.
- Finding the glands may allow for more complication-free radiation therapies.
PSMA PET/CT technology<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="676e611b970c9b516cace0870447b325"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/RHAyoQF09X4?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span><p>PSMA PET/CT is a new combination of <a href="https://www.mayoclinic.org/tests-procedures/pet-scan/about/pac-20385078" target="_blank">PET scans</a> and <a href="https://www.mayoclinic.org/tests-procedures/ct-scan/about/pac-20393675" target="_blank">CT scans</a> that is believed to offer a more reliable means of locating prostate cancer metastasis. A <a href="https://www.cancer.gov/news-events/cancer-currents-blog/2020/prostate-cancer-psma-pet-ct-metastasis" target="_blank" rel="noopener noreferrer">study</a> published last spring suggests it may be the most accurate way to diagnose prostate cancer metastasis than any method previously available.</p><p>Prior to PSMA PET/CT, the primary way to look for metastatic prostate cancer was to image the body using x-ray-based CT scans and to perform bone scans, since bone is where prostate cancer often spreads. CT scans, however, often miss small tumors, and bone scans can generate false positives as a result of other damage or abnormalities that have nothing to do with prostate cancer.</p><p>PSMA PET/CT scans track the travels of an intravenously administered radioactive glucose tracer throughout the body. For hunting down prostate cancer, this tracer contains a molecule that binds to the <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1472940/" target="_blank">PSMA</a> protein that's present in large amounts in prostate tumors. The molecule is linked to a radioisotope, <a href="https://netrf.org/2018/11/13/gallium-68-scan-for-neuroendocrine-tumors/" target="_blank" rel="noopener noreferrer">gallium-68</a> (Ga-68).</p><p>In last spring's research, PSAM PET/CT was shown to be 27 percent more accurate than previous methods at finding metastases (92 percent accuracy as opposed to 65 percent). In addition, it was found to be much less likely to produce false positives, and it was particularly good at detecting tumors far removed from the prostate.</p>
A good kind of avoidance behavior<p>"Radiation therapy can damage the salivary glands," says Vogel, "which may lead to complications. Patients may have trouble eating, swallowing, or speaking, which can be a real burden."</p><p>The researchers looked back through the cases of 723 patients who had undergone radiation treatment, interested in seeing if inadvertent radiation of the tubarial glands was associated with the complications experienced by the patients. It turned out that this <em>was</em> the case: In cases where more radiation had been delivered to this area, patients did indeed report more in the way of complications of the type one would expect when salivary glands are radiated.</p><p>Now that we know the tubarial salivary glands exist, therapists can stay out of their way. Vogel says, "For most patients, it should technically be possible to avoid delivering radiation to this newly discovered location of the salivary gland system in the same way we try to spare known glands."</p><p>He's hopeful that that things may be about to get at least a bit better for cancer patients: "Our next step is to find out how we can best spare these new glands and in which patients. If we can do this, patients may experience less side effects which will benefit their overall quality of life after treatment."</p>
A new survey found that 27 percent of millennials are saving more money due to the pandemic, but most can't stay within their budgets.