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Study Tips for Math & Science

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Study at least 3 times per week

  • You can pick whatever day and time works best for you, but you need at least 3 study dates per week in order to keep the information fresh, catch mistakes, and engrain your understanding of larger concepts and ideas

Always do your practice problems

  • As a student, “practice problems” may seem like nothing more than an annoyance or busy work. As a working adult, I can assure you that most of us would love it if our work came with “practice problems,” opportunities to rehearse what’s coming next and learn from our mistakes before said mistakes actually count against us. Don’t ever let the word “practice” make you feel like something is less important or valuable on your syllabus – the opportunity to practice and prepare/ask questions is a deeply valuable resource built to serve your best interests

Do your chapter reviews!!

  • Like “practice problems,” chapter reviews can seem annoying or uselessly busying. However, these are a key opportunity to not only establish a study routine, but to discover what components of each chapter you ought to focus said study routine on – making your study time all the more efficient, purposeful, and useful. Getting into the habit of reviewing new information soon after you’ve read or encountered it (whether through a lecture, presentation, or other such thing) will serve you well throughout the rest of your life. Nothing impresses more than a keen memory and eye for detail – skills that are flexed and bulked up when you dedicate time to reviewing new information as promptly as possible. Don’t wait till you’ve already forgotten information to review it. Instead, review new information while it’s still fresh in your mind. Keeping it fresh and regularly renewed will help seed it in your mind so that you can begin to puzzle-piece things together in new and more innovative ways later on.

Watch videos and read extracurricular books on the subject

  • Whether your teacher provides you with online materials or you happen upon some useful resources on your own, finding new ways of interacting with and reviewing your study assignments will not only help you learn new things about the materials, but will help you to take that next crucial step beyond memorization and into the realm of invention.
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News Update: Sexism in the Classroom

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This past February, Danielle Kurtzleben’s article, “Grade-school teachers can push girls away from math, with huge consequences,” appeared in Vox, speaking to some very important and, tragically, very widespread misconceptions regarding the gender “math gap” in education. According to Kurtzleben:

“A new working paper from the National Bureau of Economic Research suggests that something else might be at work here shaping the supposed ‘choices’ girls and women make. It shows that young girls’ teachers have biases that push girls away from math and science early on, which could be influencing where they go later in life.

Economists Victor Lavy from the University of Warwick in the United Kingdom and Edith Sand from Israel’s Tel Aviv University looked at Tel Aviv sixth graders’ test scores both on standardized tests and internal tests in Hebrew, English, and math.”

In this research, Lavy and Sand tested to see if there was any difference in test scores if the ones responsible for grading the tests knew or did not know the test-takers’ gender. Their results clearly suggest the existence of a “systematic bias against girls in the marking of math exams.” And as Lavy and Sand followed their sixth-graders through the eighth grade and high school, they found that “those early teacher biases led to significant improvements on the later math exams for boys and negative and significant effects in math for girls.”

Of course, as Kurtzleben also points out, “this is a working paper, meaning its results are preliminary, and it studied students in a different culture and school system, so we can’t assume US students would see the exact same magnitudes of effects” (emphasis added). However, what’s most important about this research now, as Kurtzleben explains, is that it shows how powerfully “socialization takes hold early on” as well as showcases

“the power of biases — discourage a child from pursuing a subject, and she will, years later, later perform worse on that subject (encourage her, meanwhile, and she’ll do better). So when you discourage a whole swath of the population from pursuing high-paying fields, all those people will be much more likely to have lower-paying jobs.”

What does this mean for us in the here and now? What does it mean for us as parents, teachers, and/or fellow students? It means constantly interrogating ourselves and our assumptions. It means asking ourselves hard questions before we hand back that test or agree with our daughters that Yeah, math really is boring or Yeah, math is super hard, when we might be telling our sons, Yeah, but you can do it or Yeah, but you want to be a marine biologist one day, don’t you? The insidious evil of sexism is that you can sometimes be adding to the problem and perpetuating old sins without ever realizing it or meaning to.

This is a trend and social failing that should both greatly concern and anger you, for your sake as well as for the rest of the world’s. After all, as Kurtzleben so well explains:

“This isn’t just a problem for women; it’s a problem for society. This study suggests that girls were just as capable as boys at math at the start of the observation period, but they were slowly pushed away from math. To diminish an entire demographic’s talent at once is to squander their potential productivity, and economic growth.”

If we want to one day live in a better, more just, more equitable, and more peaceful world, then there’s really no better or easier place to start than right at home with the editing, improving, and monitoring of our own attitudes, perspectives, and actions. The hard truth is, we will only have justice and equality for all when we begin treating others justly and equitably.

 

All quotes and facts here were drawn from Danielle Kurtzleben’s Vox article, “Grade-school teachers can push girls away from math, with huge consequences.”

Maker Movement in Classrooms?

First, I’d like to thank My School of Thought for posting such an excellent article on The Maker Movement. As a tutor and “maker” myself, I couldn’t be more thrilled by the take-off of this movement and am very hopeful for the future of our classrooms knowing that more and more teachers are beginning to incorporate more opportunities for students to build, explore, and engage with the materials they’re learning in new ways.

Just take Allen High School’s Blu Bistro, for example. When I was a student of AHS (I can’t believe how many years ago now that was!), cooking classes were basically nonexistent, but were in the works as a possible future extracurricular option for students. And now? Now AHS’ student chefs are not only serving restaurant-quality food of their own making to Allen community residents, but they’re also competing in kitchens across the state of Texas (in both cooking and restaurant management) including in the 2013 Texas Pro-Start Invitational state finals wherein dishes were judged by “members of the Texas Restaurant Association and chefs from culinary schools such as Le Cordon Bleu and The Culinary Institute of America” (Wendy Gragg, Waco Trib). These students are learning to be Makers of a different kind than the Engineering students we’ve started hearing so much about, but they’re Makers just the same. It’s in the art of being a producer that students can often start finding new interests and motivations for themselves to learn and become more active consumers.

As Dale Dougherty, editor of Make Magazine, explains in My School of Thought’s post, “…I want people to see themselves as producers, not just consumers. I’d like to see it become a capability that we use in home life and at work and that we’re proud of it, where we see ourselves as having these powers to do stuff.” I couldn’t agree more. Being a consumer, while fun, challenging, and interesting in its own right, is often today conflated with being more passive whereas being a producer seems to naturally mean being more active and invested in the product itself. But this does not always have to be the case. Rather, by encouraging children and friends to be more active producers, we can help them and ourselves become more active consumers as well.

We often see this in English courses where some students can have trouble getting interested in assigned readings yet leap at the opportunity presented by a creative writing project. Why is this? It isn’t because students are inherently lazy or come out of the womb not enjoying to read or don’t understand the connection between writing and reading — loving reading, loving science, loving learning (loving being a consumer of knowledge) are all things that must be taught and demonstrated for children from an early age. How can you be a creative writer without also learning to love and actively engage in the process of reading — in the process of consuming written materials? How can you be a builder without also learning to love and actively consume the necessary mathematics and scientific principles?

The answer is simply that you cannot — but you can sometimes begin as a producer and so work your way into becoming a more active consumer.

These two identities, these two ways of learning — producing and consuming — feed into each other in a natural cycle. So who’s to say that you need to have one first before the other can follow? Why not let kids try their hand at building or writing or cooking something before they’ve learned all the elemental pieces? — It might just be the kick-in-the-pants they need to start asking questions, to realize what might be out there for them to learn from the cookbooks, mathematicians, and libraries. And the best part is, if the students are the ones asking and seeking answers to their own questions, then they’re also learning to consume knowledge within a useful context and in a more active manner; they’re learning to consume and apply knowledge for a purpose, rather than simply memorizing facts because a school or standardized test demanded it (which can often lead to those facts seeming disjointed and useless). Learning information for a purpose or as part of a larger narrative of questions and exploration can often be key to that information being retained and applied in new ways. Our children learn from us — their mentors, parents, and teachers — what it means to have fun in one’s leisure time. If we spend all of our leisure time watching TV, then that’s what they, our children, will associate with down-time rather than more active and mind-engaging activities like reading, building, writing, or exploring.

And this is why we can’t leave the Maker Movement up solely to our schools and teachers. If we want our children to be more enthusiastic creators and more active consumers, then we must model this behavior for them and become more active and interested ourselves. This can be as simple as swapping out a night of television for a night of reading or puzzle-piecing or fort-building or creative writing or cooking or gardening or scavenger-hunting.

It can be as easy as learning to have fun with each other again.

Girls and Women in STEM

“If we’re going to out-innovate and out-educate the rest of the world, we’ve got to open doors for everyone. We need all hands on deck, and that means clearing hurdles for women and girls as they navigate careers in science, technology, engineering, and math.”

— First Lady Michelle Obama, September 26, 2011

While First Lady Obama is perhaps best known for her work to combat childhood obesity, her work to promote STEM (Science, Technology, Engineering, and Mathematics) education for children (and especially for girls) has also been—thankfully—substantial and groundbreaking as well. Improved STEM education is one of the clearest paths to a better future for our world and our children as technological and scientific innovations in medicine, climate change, and energy grow more complex by the day.

STEM education is an investment in everyone’s future.

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According to The Department of Commerce’s (2011) Women in STEM: A Gender Gap to Innovation, “though they represent a mere 24 percent of the STEM workforce, women earn on average 33 percent more when they work in these high-growth fields.” However, even with this boon for entering the STEM fields, and even though “women today currently earn 41% of PhD’s in STEM fields, [they] make up only 28% of tenure-track faculty
in those fields.

Despite this inequality and despite the rampant sexism that is often reported by women studying and working in STEM fields, there are many significant positive steps being taken to encourage and promote more girls and young women to pursue the sciences in their education and careers.

For example, the Department of Education has recently created an “Invest in Innovation” fund that

provides competitive grants to applicants with a record of improving student achievement. The program’s selection criteria prioritizes schools that support women and girls in STEM, emphasizing the need to increase the number of women and girls teaching and studying STEM subjects, and ensuring that both educators and students receive access to rigorous and engaging coursework, high-quality academic preparation, and opportunities for professional development.”

Moreover, NASA has recently gotten in on the game by teaming up with the Girl Scouts of the U.S. to develop a memorandum of understanding uniting the organizations “to achieve common goals: motivating and encouraging girls to do their best.” NASA was present at the Girl Scout’s annual convention and thus created an “opportunity for 17,000 leaders and girls to experience fun, hands-on NASA STEM activities….

In other words, the government is trying to think outside the box for getting young girls more involved and interested in STEM today. But it’s not only the government that’s interested in mining this “new” vein of gold in the American mountain; clubs and organizations are popping up all over the place aimed at supporting young girls’ interests in STEM fields.

Take Kentucky Girls STEM Collaborative Project, for example. The Kentucky Girls Project, led by the University of Kentucky, is focused on “informing and motivating girls to pursue careers in science, technology, engineering, and mathematics…to build a strong, diverse workforce in Kentucky.” Many other states have similar collaboratives supported by various high education institutions including Illinois, Colorado, Missouri, Georgia, New Mexico, and others.

And even our local Texas schools like Lovejoy (Lucas, TX) have started including STEM courses in their elective rotation to support and deepen students’ interest and access to the sciences. Lovejoy now offers several agricultural elective courses to their ninth graders as well as an optional introductory course to design and robotics. Similarly, Ford Middle School (Allen, TX) has begun offering “Career Portals in STEM” as an elective course designed to introduce students to the careers of science and engineering. Of course, given that students begin engaging in the Science Fair as early as 6th grade (in TX) and that children of all ages are often naturally drawn to the splendor and wilds of science, these STEM courses and options ought to be made available to students much earlier.

If you’re a parent, mentor, or student looking to get yourself or someone close to you more involved in STEM fields, here are a few terrific ideas and resources to consider:

 

 

 

Fear No Math, Hate No Math

Given how we’re trained to think about mathematics today, it’s little wonder that so many students begin dreading math early on and regardless of their potential or aptitude for it. Whether it’s parents letting kids off the hook by agreeing that “math is the hardest” or “math is no fun” or “math is pointless” (likely in order to mask their own insecurities regarding mathematics) or television characters fearing mathematics for just such a variety of reasons or even Teen Talk Barbie, we’re constantly told and told again just how “awful” math can be. As TV Tropes explains of much of television today,

Irrational fear of the theorem of Pythagoras is inevitable. Even the most basic of long division is portrayed as mind-bogglingly difficult, especially for parents helping their grade-schoolers do homework. Usually when trying to portray math in this light, writers (particularly in visual media like film) will show a piece of paper/whiteboard/blackboard full of abominably complex equations; use of integral signs,Gratuitous Greekletters (particularly pi and sigma), daemonic occultist geometries, the accursed variables ‘x’ and ‘y’ and such forth are prevalent. Any scene where mathematics is being taught will invariably result in children being bored, falling asleep, or in a few cases, succumbing to gibbering schizophrenia from the Cyclopean confusion of it all (thus the Mad Mathematician).

In other words, we’re all being told to fear math as something that’s impossible to understand or something that’s only for the socially inept (consider, for example, The Big Bang Theory’s Sheldon character) or something that we simply don’t need to know (consider, for example, The Big Bang Theory’s maddeningly slow and dull-witted Penny character). All of this social reinforcement that “math is simply too hard,” can convince students who would otherwise enjoy math or who face challenges with math early on that it’s not worth their time and that it’s normal to hate and misunderstand mathematics. As PBS explains, there are a number of core skills that students can struggle with for a variety of reasons over the course of their K-12 educational careers, which can end up negatively coloring their opinions, feelings, and success with math if they aren’t encouraged to enjoy or pursue mathematics. According to PBS, these core skills include: “incomplete mastery of number facts,” “computational weakness,” “difficulty transferring knowledge, making connections,” “incomplete understanding of the language of math,” and “difficulty comprehending the visual and spatial aspects and perceptual difficulties.”

And, while each of these challenges come with their own unique signs and degrees of intensity, each of these also have their own set of creative solutions. Mathematics, after all, isn’t something we can simply give up on. It isn’t something to be feared or relegated into the spheres of the antisocial or the hopelessly mysterious or pointless. Mathematics is a unique and beautiful language that can give us hope of a new, better, healthier, and richer world. So, if math is something you’re struggling with, regardless of your age, regardless of whether or not you’re a parent or student, seek out tutoring services and mathematics courses near you to help you practice and enhance your mathematical skills. These are important not only for various careers (ranging from businesspersons to scientists to electricians to veterinarians to computer programmers), but can also be useful for boosting your self-confidence and even in protecting yourself against Of course, we’re still learning more day by day regarding how we learn and perceive mathematics. Just take this recent Stanford study of why some children seem to learn math more easily than others:

In a study of third-graders’ responses to math tutoring, Stanford scientists found that the size and wiring of specific brain structures predicted how much an individual child would benefit from math tutoring. … The research is the first to use brain scans to look for a link between math-learning abilities and brain structure or function, and also the first to compare neural and cognitive predictors of kids’ responses to tutoring. In addition, it provides information on the differences between how children and adults learn math, and could help researchers understand the origins of math-learning disabilities.

However, regardless of ability, here are a few quick tips to help students of all ages and levels combat some of core skill challenges to learning and excelling in mathematics:

  • Improve your handwriting: this may seem to be a silly, unimportant thing, but it’s actually a common problem that many people face — they’ll be keeping notes or writing out different components of a problem, only to misread something due to poor or unclear handwriting and lead themselves astray
  • Improve your note-taking: make certain to keep clear and complete notes throughout the entirety of your equations. You won’t always have to do this, but, for a certain amount of time while learning and practicing new types and branches of mathematics, keeping thorough and complete notes of each new step will not only help you reach more precise conclusions, but will also help you better identify any specific areas or components of the problem that you may be struggling with. Keeping such complete notes will also provide you with a study guide to refer back to as you move forward.
  • Always have a stress ball handy: sometimes it can be easy to become overwhelmed and fidgety when faced with whole sheets of math problems. Having something like a stress ball ready at hand can go a long way to calming and refocusing you by providing an outlet for some of that distracting adrenaline.
  • Rewrite and/or breakdown word problems until you’ve isolated and understood each different component of the puzzle. Word problems are occasionally written in such a way as to trick or mask some component of a mathematical problem, but it is often the case that word problems are laid out in hopes of being as clear and straightforward as possible. Either way, they can often pose unique challenges to students of all ages as word problems force students to tackle two very different challenges at once: mathematics and critical reading. So, read each problem thoroughly and rewrite each sentence however necessary in order to assure that you’ve understood and taken account of each aspect.  
  • But, mostly, don’t forget to take some comfort in the straightforwardness of mathematics. In a world wherein relationships, socializing, and politics can be a constant wave of stress and uncertainty, don’t forget that mathematics can provide you with a simpler, creative, and elegant way of viewing and exploring the world — one with clear and often inarguable answers.