Misconceptions in Math

Gabriellebirchak/ November 25, 2020/ Modern History, Uncategorized

Podcast Transcripts

There are many mis­con­cep­tions about events that hap­pened in his­to­ry. Some of these mis­con­cep­tions have even been stat­ed as fact and cit­ed as such by “experts.” Some­one will cite a source on Wikipedia that is either not accu­rate or is mis­con­strued. Or, when you dig deep­er, you can­not find the source of infor­ma­tion on those mis­con­cep­tions. As a result, that cita­tion becomes the cita­tion of all truth.

Some of these mis­con­cep­tions in his­to­ry include sto­ries that peo­ple from medieval times believed that the earth was flat, or that Ben­jamin Franklin dis­cov­ered elec­tric­i­ty, or that Napoleon Bona­parte was short, or that Roman vom­i­to­ri­ums were used for vomiting.

The truth is, even in medieval times, peo­ple knew that the earth was round, Ben­jamin Franklin exper­i­ment­ed with elec­tric­i­ty, Napoleon Bona­parte was 5’6”, and the Roman vom­i­to­ri­ums were the entrances and exits to sta­di­ums and theaters.

How­ev­er, his­to­ry is not the only place where com­mon mis­con­cep­tions lie. The world of math is full of fal­lac­i­es that ulti­mate­ly hin­der our math­e­mat­i­cal abil­i­ties. I have said it numer­ous times, and I will say it again: every­body is a math­e­mati­cian. We all have math­e­mat­i­cal brains. Sad­ly, many peo­ple let those mis­con­cep­tions become uncon­scious beliefs, which even­tu­al­ly become their truths.

How­ev­er, these fal­lac­i­es do not have to be your truths. So, I will dis­pel my top five mis­con­cep­tions about mathematics.

Math Misconception Number One

Math peo­ple can do math in their heads with rapid speed. The only rea­son why this delu­sion is valid is that math­e­mati­cians do math all of the time. As a result, for lengthy prob­lems, they break it down into small­er por­tions. These small­er por­tions are then solv­able. For exam­ple, every time I am at din­ner or lunch with friends, I am asked to fig­ure out the tip, which most peo­ple cal­cu­late to 15 per­cent. For exam­ple, if our bill came to $49.27, I would first round it up to $50. Then I would cal­cu­late ten per­cent of $50, which is $5. Then, I would take that 10 per­cent val­ue of $5.00 and divide it by two, which is $2.50. So, $5.00 plus $2.50 is $7.50. See! I broke the prob­lem down to solve it quickly.

You can apply this same process in cal­cu­lus, dis­crete math, physics, chem­istry, and any oth­er sub­ject. When math peo­ple are pre­sent­ed with math that they can­not solve in large amounts, they break it down. Then the process goes faster because they can quick­ly do the sim­ple math. When you know it, you can solve it faster. A per­fect exam­ple of this is music. If you are musi­cal­ly inclined, pick a song you know. You can sing it real­ly fast because you know the lyrics and have prob­a­bly sung the song a mil­lion times.

So, start with the lit­tle math and work your way up to the big math, and you will find that you will be able to do math quick­ly too! So to recap Mis­con­cep­tion Num­ber One, any­body can do rapid math in their heads. It just takes practice.

Math Misconception Number Two

Some peo­ple have a mind for math. This belief is false. If you have been lis­ten­ing to my pod­cast, you have prob­a­bly heard me say that our ances­tors had been doing math with­out cal­cu­la­tors for thou­sands of years. Math mind­ed­ness is in our DNA, and it is part of who we are. Our ancient ances­tors were doing the math to deter­mine the sizes and shapes of build­ings and bridges, ana­lyze the amount of land need­ed for mass crops, and cal­cu­late the amount of mon­ey nec­es­sary to buy cat­tle or sheep. They were math­e­mati­cians long before the term math­e­mati­cian was first used around 1500 CE.

We all have a mind for math; we need to engage with math. To turn a blind eye to math is to let this pre­tense con­trol your self-con­fi­dence. Addi­tion­al­ly, the brain is not geared to be stronger on one side or the oth­er. There is a belief that those who are ana­lyt­i­cal and log­i­cal are left-brained, and those who are cre­ative and intu­itive are right-brained. This con­cept, how­ev­er, is a myth. Unless your brain has suf­fered an unfor­tu­nate head injury, it is more than like­ly your mind is healthy in its entire­ty. You are whole-brained!

In an inter­view with NPR’s Tania Lom­bro­zo, Dr. Kara D. Fed­er­meier, a pro­fes­sor of psy­chol­o­gy affil­i­at­ed with the Neu­ro­sciences Pro­gram and The Beck­man Insti­tute for Advanced Sci­ence, explains that math pro­cess­ing engages a hemi­sphere of the brain called the intra­pari­etal sul­cus, which hap­pens to exist in both sides of the brain. It is true that the left side of the brain allows for mem­o­riz­ing ver­bal infor­ma­tion, thus mak­ing it eas­i­er to recite things like mul­ti­pli­ca­tion tables. It is also true that the right side of the brain allows for the esti­ma­tion of quan­ti­ties. How­ev­er, in most indi­vid­u­als, both of these hemi­spheres are equal­ly strong.¹ Peo­ple are not left-brained or right-brained.

So, to recap mis­con­cep­tion num­ber two: No brain is unique­ly designed for math. We all have a mind for math. To repeat, we all have a mind for math!

Math Misconception Number Three

Some peo­ple can­not over­come math anx­i­ety. Let us talk about anx­i­eties! I have hor­ri­ble anx­i­ety when it comes to spi­ders. If I know that there is a spi­der in the garage, I will run to the oth­er side of the house scream­ing. I am cer­tain my hus­band has video of many of these anx­i­ety attacks because he thinks it is hys­ter­i­cal. I love snakes and lizards. How­ev­er, I have so much anx­i­ety when it comes to spi­ders that I have a pan­ic attack. Accord­ing to Stan­ford Uni­ver­si­ty Pro­fes­sor Jo Boaler, the anx­i­ety that peo­ple have when see­ing spi­ders is the same anx­i­ety peo­ple have when it comes to tak­ing math tests.² It is real. How­ev­er, like my belief that that spi­der will crawl inside my ear in the mid­dle of the night, the assump­tions behind math anx­i­ety are not real.

Hip­pocrates first wrote about anx­i­ety in 400 BCE. He described a man named Nicanor, who was gripped with anx­i­ety every time he went to an evening drink­ing par­ty and heard the flute girl play her music. Nicanor was fine when he heard the music dur­ing the day, but at night, the music gripped him with “mass­es of ter­rors.”³

The con­cept of math anx­i­ety was pop­u­lar­ized around 1957 when the Jour­nal of Edu­ca­tion­al Psy­chol­o­gy pub­lished a study that deter­mined that peo­ple with “num­ber anx­i­ety” did poor­ly on tests. Since then, math anx­i­ety has been a top­ic for dis­cus­sion. So, where does this anx­i­ety come from? The men­tal con­di­tion­ing of stu­dents often comes from par­ents and teach­ers who express their own math anx­i­ety. This anx­i­ety leads to an emo­tion­al response, which results in low­er test scores.

So, how do we com­bat math anx­i­ety? We do it the same way we com­bat any oth­er anx­i­ety: we recon­di­tion the brain. For myself, I am com­mit­ted to find­ing some­thing beau­ti­ful in spi­ders. I am attempt­ing to retrain my brain to see spi­ders as cute as I see my dog.

Math is the same way. Par­ents can approach math with their kids with a “can do” atti­tude when they solve the prob­lems togeth­er. Teach­ers, like­wise, can change the nar­ra­tive and teach their stu­dents that solv­ing math is not about the grade. It is about the dis­cov­ery of math. Addi­tion­al­ly, either the teacher, the par­ent, or even the stu­dent can put a reward sys­tem in place. Tak­ing a math test, regard­less of the out­come, can result in a reward of some kind that might involve a shop­ping trip, favorite din­ner, or a movie. When there is a con­sis­tent reward, the brain asso­ciates the efforts to approach math as a pos­i­tive experience.

Also, self-talk is everything!

• Instead of let­ting our stu­dents say, “I can’t do this,” teach them to trust their own intellect.
• Instead of let­ting them say, “I am real­ly good at math,” remind them that they are get­ting bet­ter and are on the right track of get­ting real­ly good at math.
• Instead of “This is too hard,” teach them that it will not be chal­leng­ing if they take the effort and time to tack­le each problem.
• Instead of “I made a mis­take on this prob­lem,” remind them that the best thing about mis­takes is that we can learn from them.

To recap num­ber three: Math anx­i­ety can be tack­led and dimin­ished with the right mind­set. As for myself, I am ready to hold a taran­tu­la. When the pan­dem­ic is over, I will be post­ing pic­tures on the Ins­ta! So stay tuned!

Math Misconception Number Four

There is only one method for solv­ing math prob­lems. This belief is so wrong! There are many ways to do math! The soon­er that teach­ers come to appre­ci­ate this and pro­vide younger stu­dents with mul­ti­ple ways to solve a prob­lem, the soon­er stu­dents will be able to take own­er­ship of their own math and excel in it. Addi­tion­al­ly, when teach­ers pro­vide stu­dents mul­ti­ple ways to solve math, they empow­er the stu­dents with mul­ti­ple tools that they can use for oth­er problems. 

But what about you? Do you find your­self stuck with math, try­ing to solve it in a way that has always been taught to you? Here is my chal­lenge: the next time you find your­self stumped with math, work through it back­wards, side­ways, or some oth­er way that you have nev­er tried before.

For exam­ple, you have a front yard that you want to install with sod. It is a rec­tan­gu­lar-shaped yard, and you need to fig­ure out how much sod you need. Your yard is 100 feet by 50 feet, so it is 5,000 square feet. Sod at Home Depot costs $ .62 per square foot, and your bud­get for sod caps out at $2,500. Obvi­ous­ly, you will not have enough sod to cov­er your yard, so you are pre­pared to plant flow­ers in the area filled with dirt. How much sod will cov­er your yard, and how will you land­scape it? How do you solve this puzzle?

If you are the kind of per­son who buys what you can afford and then lays it out to see how much you have, you could do that!

If you are the kind of per­son who wants an idea of how much you will get, you could make an edu­cat­ed guess and then eye­ball where you might lay the sod.

If you like draw­ing, you can get grid paper and draw it out, let­ting each grid rep­re­sent a square foot.

If you need to plan it out based on how many flow­ers you have to plant, you could deter­mine where the flow­ers will go and then fig­ure how much sod you need around the flower garden.

Or, you could check the num­bers with math.

For myself, I would round up the cost of the sod to con­sid­er tax­es. In Cal­i­for­nia, sales tax is 7.25 per­cent. I would approx­i­mate it up to 10 per­cent. Then I would add my approx­i­mat­ed val­ue of tax to the cost of the sod, mak­ing it about $0.70 per square foot.

Then I would divide my $2,500 by $0.70 to find out how much sod I can get. 

It comes out to 3,571 square feet, I esti­mate down to 3,500 so I can spend that extra mon­ey at the hot dog stand out front of Home Depot. Now know­ing how much I can get, I map out my land­scap­ing on grid paper.

There is no one way to do math. There is no one way to do sci­ence. As Richard Feyn­man once said, “We must remove the rigid­i­ty of thought… We must leave free­dom for the mind to wan­der about in try­ing to solve the prob­lems. The suc­cess­ful user of math­e­mat­ics is prac­ti­cal­ly an inven­tor of new ways of obtain­ing answers in giv­en sit­u­a­tions. Even if the ways are well known, it is usu­al­ly much eas­i­er for him to invent his own way— a new way or an old way— than it is to try to find it by look­ing it up.”

So, to recap Mis­con­cep­tion Num­ber Four: There is no one way to do math. Math can be cre­ative, and there are mul­ti­ple ways to solve math. Though math is about the des­ti­na­tion, it is also about the adventure!

Finally…

Math Misconception Number Five

One of my favorite math top­ics that I love to dis­pel is this belief that men are bet­ter at math than women are. This con­cept is so incred­i­bly untrue. This con­cept is cre­at­ed out of edu­ca­tors’ assump­tions and their expo­sure to this belief through media and stereotyping.

Accord­ing to Stanford’s Soci­ol­o­gy Pro­fes­sor Shel­ley Car­roll, boys do not attempt math at a high­er rate than girls because they are math­e­mat­i­cal­ly bet­ter; they do so because they think they are bet­ter. Again, this is all about mind­set and self-confidence.

For myself, as a math per­son, I noticed that as I pro­gressed in the more chal­leng­ing math and sci­ence cours­es in col­lege, the more that men began to out­num­ber me in those cours­es. By the time I was close to com­plet­ing my math degree, I was one of two women in a class of sev­en men. I was just one of two because many of my female peers dropped out of the more chal­leng­ing courses.

Some women were vic­tims of dis­crim­i­na­tion. Oth­ers were mar­gin­al­ized and dis­missed by their male pro­fes­sors. Then there were those women who were over­whelmed by the pres­sure to excel with high grades. If they did not receive high scores in their math and sci­ence cours­es, their con­fi­dence fell. These women were hold­ing an emo­tion­al attach­ment to their grades, where­as some of my male peers were not emo­tion­al­ly attached to the out­come. They rec­og­nized where they failed on their tests and attempt­ed to self-cor­rect with every fol­low­ing test.

Dr. Jes­si­ca Cant­lon is a pro­fes­sor of devel­op­men­tal neu­ro­science at Carnegie Mel­lon Uni­ver­si­ty in Pitts­burgh. She and her team did a study using func­tion­al mag­net­ic res­o­nance imag­ing on chil­dren between the ages of three and ten while the chil­dren were watch­ing edu­ca­tion­al videos and doing math prob­lems. Cantlon’s find­ings? She and her team found no gen­der dif­fer­ences in brain pat­terns in the regions in the brain.⁴

So, if women are equal­ly capa­ble at math, why are there more men in STEM-based fields than women?

One rea­son is the ear­ly con­di­tion­ing. Stud­ies show that in Kinder­garten through high school, edu­ca­tors spend more time help­ing the boys with their prob­lems, give more praise to boys for their results, and encour­age them to ask ques­tions more so than the girls. 

Soci­ety, cul­ture, and stereo­typ­ing are oth­er rea­sons why women begin to drop off the STEM map. Since the enter­tain­ment industry’s incep­tion, more movies, shows, and adver­tise­ments show white men as sci­en­tists and doc­tors. It is not just gen­der stereo­typ­ing; it is also race stereo­typ­ing. This stereo­typ­ing leads to cre­at­ing self-doubt among mar­gin­al­ized stu­dents.⁵

These stereo­types car­ry over into our soci­ety and our edu­ca­tors. There are numer­ous sto­ries of women being told that they do not belong in their math or sci­ence cours­es. I con­sid­er myself lucky that I nev­er expe­ri­enced such stereo­typ­ing. How­ev­er, it hap­pens, and it affects the self-con­fi­dence of girls and women.

So, to recap mis­con­cep­tion num­ber five: Boys and men are bet­ter at math than girls and women. Math and sci­ence are not gen­der-spe­cif­ic sub­jects. Girls and women are as smart and capa­ble at math and sci­ence as their male peers. They can achieve a lev­el of aca­d­e­mics and accom­plish­ments as much as any oth­er man. Unfor­tu­nate­ly, our com­mu­ni­ties, edu­ca­tion­al sys­tems, and soci­ety need to rec­og­nize this and make sig­nif­i­cant changes. Through mak­ing these changes, we can allow the mar­gin­al­ized to stand on equal foot­ing with boys and men.

Many oth­er mis­con­cep­tions in math­e­mat­ics, unfor­tu­nate­ly, hold so many peo­ple back. More­over, because these dis­tort­ed beliefs have become com­mon, peo­ple begin to take these notions for truths. These beliefs are dam­ag­ing and need to be removed. Math and sci­ence deserve bet­ter. Math is a beau­ti­ful world of dis­cov­ery. Unfor­tu­nate­ly, these fal­lac­i­es have kept so many peo­ple from expe­ri­enc­ing the joy of math. Once we destroy these unfound­ed opin­ions and embrace the extra­or­di­nary world of math, we will be able to grow our math com­mu­ni­ties and obtain sig­nif­i­cant innovations!

Math is a won­der­ful thing! If you are intrigued, this is my invi­ta­tion to you to join this world of dis­cov­ery! Even if it is just to learn how to fig­ure out how to cal­cu­late a tip, or cal­cu­late the amount of paint to buy for a room, or to do your tax­es, you got this! You are a math per­son! You are a math­e­mati­cian! Go with it and see what kind of new world awaits your hid­den genius!

---

1. Tania Lom­bro­zo, “The Truth About The Left Brain / Right Brain Rela­tion­ship,” NPR.org, last mod­i­fied Decem­ber 2, 2013, https://www.npr.org/sections/13.7/2013/12/02/248089436/the-truth-about-the-left-brain-right-brain-relationship.
2. Christi­na B. Young, Sarah S. Wu, and Vin­od Menon, “The Neu­rode­vel­op­men­tal Basis of Math Anx­i­ety,” Psy­cho­log­i­cal Sci­ence 23, no. 5 (2012): 492–501, doi:10.1177/0956797611429134.
3. Hip­pocrates. Vol VII. Epi­demics 2, 4–7. Trans: Smith WD. Loeb Clas­si­cal Library. Cam­bridge, MA: Har­vard Uni­ver­si­ty Press; 1994
4. Sta­cy Kish, “Study Finds Brains of Girls and Boys Are Sim­i­lar, Pro­duc­ing Equal Math Abil­i­ty — News — Carnegie Mel­lon Uni­ver­si­ty,” CMU — Carnegie Mel­lon Uni­ver­si­ty, last mod­i­fied Novem­ber 8, 2019, https://www.cmu.edu/news/stories/archives/2019/november/girls-boys-brains-produce-equal-math-ability.html.
5. Diane Halpern, Camil­la Ben­bow, and Mor­ton A. Gerns­bach­er, “The Sci­ence of Sex Dif­fer­ences in Sci­ence and Math­e­mat­ics,” PubMed Cen­tral (PMC), last mod­i­fied August 2007, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4270278.