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]]>We might not understand all that Einstein discovered, but from the things he has said we can glean some of his thought process and perhaps use that to instruct our students in math.
“It’s better to be amazed than to understand,” he once said. I wondered if he meant. Do we stress out to find the right answer and forget to enjoy the quest? When I was at UCLA I made a short film on antimatter, a physics subject. My advisor was Julian Schwinger, a Nobel prize winner. He assigned two of his post-docs to help me. I remember walking with them through the UCLA sculpture garden to the film building in north campus and how fascinated they were by all the sculptures they saw. They didn’t “understand” them, but they couldn’t stop talking about them. This was new part of campus for them and they were in awe. How do we nurture this same sense of wonder in our students when they encounter a new math problem? Impossible? Maybe not.
Do we, ourselves, go out of the way to encounter new things? Or do we follow the same routines every day? Eat the same foods? Talk to the same people? Watch the same shows on television? Do we see virtual learning an exciting challenge?
As an experiment let’s eat something different for dinner. Introduce yourself to someone new. Read a book instead of watching television.
Yes, we could make a mistake. We might create a tasteless dinner, meet an unappealing person, or read an obnoxious book. But by not making the attempt, we will never discover a great dish, meet someone fascinating, or uncover an idea that could leave us, well, amazed.
Our willingness to embrace new ideas in all aspects of life becomes an example and will help our students to properly approach their math lessons. We let them know that it’s okay to make a mistake and will encourage them to approach a problem differently to find a solution.
Our students will learn that math is more than finding the slope of a line or the volume of a prism. Math teaches a way of thinking. This is not something to learn after we mature and grow up. Actually, when we grow up we must backtrack and learn to become more child-like, to find qualities we had and lost when were very young. Let’s never lose that wonder we see in children’s eyes when given their first balloon or ice cream cone. If our students are amazed when they learn how tessellation works or cherish that “ah hah!” moment when they solve and understand a difficult algebra problem, they will go far in math… and in life.
“I sometimes ask myself,” Einstein once said, “how it came about that I developed the theory of relativity. The reason, I think, is that a normal adult never stops to think about problems of time and space. These are things that he thought of only as a child. But my mental intellectual development was less advanced than others. As a result I began to wonder about space and time only when I had already grown up.”
Einstein was certainly NOT less advanced when he was younger. He just never lost that sense of wonder that he had as a child. We can help our students not lose it either. They might not become the next Albert Einstein, but they can become better at math.
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]]>The post Healing Math Phobia appeared first on Elevatedmath.com.
]]>We hear students say, “I’m not good at math” or “Math isn’t my thing”, especially after receiving a bad test score. These comments are likely subtle signs they are afraid of math. If so, we need to pull the student aside and ask questions that might help shed light on what they are thinking. Are they afraid of failure, or of not understanding, or are they afraid that they are not smart enough?
Then you might offer, “Do you know what helps me when I’m afraid of failing,” or “Do you know what I do when I don’t understand something?” Sharing your own experiences can help.
For instance, I like to explain how I turn scary situations into opportunities. If I have a mountain to climb and start with the premise that the climb will be too hard and I’m not capable of doing it, then I’ve already defeated myself before starting. Working out a math problem is much like working your way up the steep face of a mountain. Sometimes your direction reaches an impasse and you need to backtrack. It’s the same with math problems. The journey can either be fun or tortuous, depending on how you think about it. This reasoning has worked for me when talking with my daughters, and I’m sure it can work for others as well.
Humor helps. It relieves the tension and anxiety that grips us when facing a difficult situation. It could be a math problem or a life and death situation.
When I worked on the CBS Evening News program, West Point Cadets would come to the studio to watch the live recording.
“Why bring them here?” I asked their captain.
“So they can see how a crew acts under stress,” was the answer.
How did this news crew act? They were constantly laughing and telling jokes, especially the director.
I remember the joke-filled speech that President Obama gave at the White House Correspondents’ Dinner the night before the commando raid on bin Laden. It made perfect sense to me. The jokes allayed the anxiety he was feeling from the mission that was about to happen and for which he was responsible. The jokes helped him stay calm and continue to think clearly.
Each Elevated Math lesson has a cartoon introduction. These are not only to reveal the characters, engage the kids and introduce the subject. The cartoons are designed to make kids smile, if not laugh. When we are smiling, we are relaxed. And when we are relaxed, we are free of anxiety and are more open to learn.
Some teachers have recommended that we remove the humor within the lessons. We did take out some extraneous, distracting dialogue that had nothing to do with the instruction, but we refused to eliminate all the humor, and we rarely touched the cartoon intro. Humor is important to create a right learning environment – one that is relaxed and free of fear.
Fear and excitement are two emotions that are quite similar to each other. Next time that you feel anxious about a task you need to do, whether it is to give a talk or perform in a show, teach a remote class or cook a dish you’ve never tried making for someone you need to impress, mentally nudge that anxiety you are feeling over to excitement. How cool to try something new! How much you’ll learn if you fail? Pat yourself on the back that you are trying something new and getting closer to a solution or that you even had the courage to try. The task will become easier and not as scary, and maybe even fun! AND, you will have another experience you can share with your students to help them overcome their fears.
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]]>This blogpost was written four years ago, but we are posting it again as it demonstrates how teachers can make huge differences in their students’ lives by adapting to their educational needs. Today, Covid is forcing teachers to teach remotely. The positive and lasting consequences on students by instructors who creatively embrace these challenges is unlimited.
The last year I taught middle school math was over 25 years ago. Years away were NCLB, high-stakes testing, CCSS, RTI Tiers I-III, and teacher accountability. By law, students were allowed in the state to drop out of school once they reached the age of 16, and students who had not passed all subjects in the 8th grade were not allowed to advance into high school. As a result, middle school teachers had a pool of students just biding their time.
That year I had classes of 8th graders who were 14 – 16 years old, mostly boys who had no interest in learning much of anything. These were tough classes. Classes no one wanted. The students who had already turned 16 willingly shared with me that they were there to hang out with friends, eat free breakfast and lunch, and to sleep. Easy to conclude, these students had never been successful in math.
Instructional tools? I remember I had a chalkboard, chalk, a couple of erasers, and an overhead projector that I shared with another teacher. Oh yeah, and I had the adopted textbook for 8th grade that had not been useful in the past, so why should I use it again? But this is all I had… or so I thought.
I asked my classes what they wanted out of math class. They set me straight real fast. They wanted nothing, because once they got out of this stupid school they were going to get a real job making real money.
“Really?” I asked. “What kind of job are you going to get?”
Most of them told me that they would get jobs in the factories around town, drive a fancy car with boom boxes, eat out most of the time, and have a really cool apartment.
“Do you know how much those factory jobs pay?”
Silence.
“Do you know how much it costs to rent an apartment?”
Blank stares.
“Do you know how to make a budget?”
Their expressions made me laugh aloud.
The math curriculum for the year became obvious. I had to make the class real for them. I had to pass on some life skills to get them ready for the real world. How was I going to do that? I went to the students for answers.
“Who knows what minimum wage is?”
No response.
“Have any of you made a grocery list, cut coupons, looked for sales, compared prices, and/or bought groceries?”
No response.
“Do you know how to open a checking and/or savings account, how to write a check, compute interest and sales tax, know when someone is trying to pull one over on you, short change you?”
You should have seen the looks on their faces. Well, that is, until I said the part about short changing. Half the class announced what they would do if someone did that to them.
“Ok, then. Here’s what I can do other than me watching you sleep. I can help you get ready for that job, to rent an apartment, to buy a car. I can help you create a budget for your expenses and teach you to write a check. Like I said, I can help. But you are going to have to work, too.”
Sighs….. feet shuffling.
“But wait a minute…..how would you like not to have a textbook?” Finally, I saw some eyes light up and smiles.
“How ya goin’ do that, Doc? If we don’t got a textbook, what we gonna use?”
“We’re going to use the newspaper.”
“Oh, yeah…” There was some hand slappin’ going on then. They thought this would be a breeze.
I didn’t have a classroom budget for purchasing supplies, so I personally paid to have copies of the local newspaper delivered to my classroom every Wednesday. Why Wednesday? Because that was the day the grocery ads ran. The newspaper became my text, but before we could actually use it, they had a few things to learn, such as how to fill out an application for a job and (sadly ) how to read a newspaper.
I went to a couple of the factories, explained what I was doing, and asked for an application to use in the classroom. My students learned how to put in the important information. None of them had a social security number, so we started the process for getting those, too.
I gave each student a hypothetical job in one of the factories earning minimum wage working 40 hours a week. They learned to compute their gross pay, calculate withholdings, and figure out net pay. They learned to use a calculator to check their work and how to open a checking and savings account. A minimum of 10% of their wages was put into savings accounts each week to save for their transportation costs. I took one of my personal checks, whited out the address and account numbers, and created personal checkbooks for each student.
Now they were on a payroll with money coming in each week – all hypothetically, of course. So what was the next step? They had to find a place to live and find transportation. The students used the classified ads from the newspaper to find places to possibly rent and, instead of fancy cars, clunkers that could get them to work. Saving for that piece of junk was another task, so finding transportation to work until they had their own “ride” became another thing on the list. No buses, subways, or rails in our rural area.
Another face with reality was when they discovered they couldn’t pay the rent by themselves. Most decided to share a mobile home or an apartment as well as a car with someone else. One group of four decided to split living arrangements, transportation, and expenses. Eat out 4 -5 times a week? Don’t think so. Deposits for water, gas, telephone, and electricity? Uh-oh. Had to beg someone to allow them to “stay” somewhere for a few weeks, long enough to save for those deposits. Problem solving became very important. Sharing the deposits and rent freed up cash for other things… like food! Meals were planned, grocery ads were used to make grocery lists, coupons became important. Groceries were purchased, and checkbooks balanced. Those were important skills.
Are you getting the picture? We learned life skills and in the process, my students learned math skills – how to add, subtract, multiply, and divide whole numbers, integers, decimals, and fractions. They learned about ratio, percent, proportion, how to figure out sales taxes, interest rates (simple and compound), how to balance a budget, write a check, and balance a checkbook. Math became necessary.
I saw learning occur like I had never seen before. I saw hope. Hope for a better future, hope for a better life. I saw students set goals for themselves: personal goals, educational goals, and work goals. Several students even made the decision to stay in school. Maybe they could acquire that fancy car if they finished high school. That last year was quite a year. A lot of hard work, but it was one of the most rewarding of my classroom teaching career.
So much has changed since then; I know that. We have math standards. We have the Common Core. We have NCLB and high-stakes testing. We can now read newspapers digitally, and textbooks are available on eReaders. However, we can make math curriculum relevant for students of all abilities no matter what resources we use. Maybe it’s time to allow real-life situations and problems drive the curriculum.
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]]>The post Don’t Be Afraid of Making a Mistake. Flip Your Classroom. appeared first on Elevatedmath.com.
]]>Articles abound on how traditional teaching methods deny students the chance to learn from their mistakes. But in this pandemic, when teachers are forced to engage in remote learning, they are more than ever scrutinized by parents and staff. Under so much pressure, teachers won’t dare try something new and risk making a mistake. A shame. But is the unwillingness to create a video for a flipped classroom a bigger mistake than failing at such an attempt? Let’s look at this more closely.
A traditional classroom model has the information transfer take place in class with assimilation of that information taking place outside of class. In other words, you lecture to the class and then your class applies what they learn in their homework assignments.
A flipped classroom has the information transfer take place outside of class (often through online videos) and the assimilation and application of this knowledge takes place in class. If implemented correctly, virtual learning can become more robust with an environment where students work together and they have more opportunities to solve challenging problems. What they’ve seen and heard outside of class, now makes sense in class and the instructor is there to guide them.
Let me tell you about a 6th grade class I visited on the East coast. The instructor had flipped his math classroom. He shared with me how he could differentiate his instruction, engage his students, and give meaningful assignments. He told me he now had more time for dynamic classroom activities. I saw how he created videos as screencasts, including himself in them as he intuitively knew that his presence helped keep his students engaged. The more outrageous and funny he could be – with costumes or jokes – the more successful were his assignments. In addition to his screencasts, he would have his students watch Elevated Math videos, especially if one of them had not completely understood his instruction. That was especially nice to see!
Flipping a classroom is much like learning to cook. At first, you will make mistakes. But don’t worry. You’ll still feed your students with needed knowledge and your struggles can actually inject more energy into the class. As you continue, you’ll get better at it. If you are not afraid of making a mistake, you will raise the level of your instruction.
Google “How to make a screencast.” Lots of instruction is available – from using a whiteboard, to setting up a camera, to making a screencast directly on your computer. The worse mistake you can make is not trying to make one.
I’ll end with a quote from Thomas Edison. He writes, “I have not failed. I’ve just found 10,000 ways that won’t work.” The good news is you won’t make that many mistakes when you flip your classroom!
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]]>Math students who begin their math journey into absolute value usually evaluate expressions with absolute value as “always positive.” That is, until they encounter the absolute value of zero, and then their answers become “always positive or zero.”
The formal definition of absolute value is |x| = x if x ≥ 0 or –x if x < 0. The negative x confuses students. They never quite understand that it is the absolute value that is always positive or zero. Unless this misunderstanding is corrected, the situation becomes more problematic when solving inequalities involving absolute value, which can lead to unhappy teachers and muddled students who usually conclude, “we don’t like math.”
In our Elevated Math lessons we make it clear that absolute value is distance, and distance is always positive or zero. We begin lesson M3.1 with instruction and problems on negative numbers. Then we introduce the concept of opposite numbers. Finally we explain absolute value:
Here is how we do it:
Lesson M3.1 continues with an explanation of integers, how they relate on a number line, and how to order integers.
We define absolute value again in lesson A6.1. This is followed by solving basic absolute value equations. Here is a portion of that lesson:
This lesson continues with more problems and instruction that includes solving absolute value equations with one and no solutions.
Lesson A6.2 gives instruction and problems of more advanced absolute value equations. These include two-step linear equations.
Then students reach lessons A6.3 “Inequalities with ‘Absolute Value is Less Than’” and A6.4 “Inequalities with ‘Absolute Value is Greater Than.’” At the end of these lessons they have a firm grasp of the absolute value concept.
The last lesson of this module, A6.5 “Problems with Absolute Value Equations,” have scenarios where we model using an absolute value equation or inequality. Together, all these Elevated Math lessons lead to happy teachers and successful, confident students. These students “like math very much!”
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]]>The post Building Confidence In Math Class appeared first on Elevatedmath.com.
]]>When I ran for school board, one question was asked a number of times, usually by students. “How would I provide more teacher/student interactions?” I assumed the students wanted a more personal experience in their learning until a BBC News article made me realize that this question might include a lot more. In the article I read, “Secondary school pupils are so scared of looking stupid in maths lessons they will not tell their teachers if they do not understand, suggests research.” It continued, “The reasons pupils gave for not asking for help more often were that they were worried about looking foolish, were embarrassed or did not want to draw attention to themselves.” In other words, they lacked confidence.
Besides instructors spending more one-on-one time with their students, are there other ways to build a student’s confidence in math? Yes…
Hiring a good tutor helps. But not every family can afford a tutor, and it takes some effort to find a good one.
Games can make math fun, which in turn can increase skills and build confidence. I read about a mother who believed Khan Academy would make math fun for her son. She thought he would find the points system and accumulation of badges motivating. She was right! “Before he knew it, an hour had passed and he was still interested in the exercises. More importantly, he was not getting frustrated if he got something wrong like he does in class or during homework. He wanted those points and, by golly, he was going to get them.”
Though we don’t have a points system or badges, Elevated Math not only builds math skills, but also solidifies an understanding of critical math concepts. More skills? A better understanding? How can this not increase confidence? And though we love what Elevated Math and Khan Academy are accomplishing, nothing can replace an instructor or parent who recognizes a student or child’s strengths and nurtures him/her through his/her weaknesses. So the question becomes, how do we free up time so we can spend more individual time with students? This is a question we each have to answer on our own.
I talked to a mother who was looking for a school for her daughter. One private girls’ school she visited explained that the school had flipped all their math classes. “Flipped classroom” means that instead of lectures taking place during school time, they are sent home by “screencasts”, where the instructor has pre-recorded the lesson, or by assigning a video to watch, such as from Khan Academy or Elevated Math. “Homework” or problem-solving happens in the classroom. “Flipped classrooms” have proved quite successful since the instructor is available to answer questions and help the students with the problems.
“Of course,” I responded knowingly. “This produces higher achievement.”
“No,” the mother answered. Her answer was a surprise. She explained the school had flipped the math classes because the math teachers found they were not completing their lessons during class time. Why? Because the girls were constantly raising their hands and asking questions. The flipped classroom became a viable solution for this school to get important instruction to the students. So class time was used to solve problems and the teacher answered the students questions.
If you ever visit a typical middle school co-ed classroom, you might notice boys usually are more assertive when it comes to asking and answering questions, and girls more likely refrain from asking questions. This particular girls’ school prided itself in letting their students express themselves in class. As a result, the girls exuded more than enough confidence – if that’s at all possible!
Actually, no. In her book “Inferior,” (published last month), Angela Saini writes, “In every case, except for throwing distance and vertical jumping, females are less than one standard deviation apart from males.
On many measures, they are less than a tenth apart of a standard deviation, which is indistinguishable in everyday life.” For example, “mathematics problem solving” for men showed an increase of only a 0.08 standard deviation. Interestingly, with “mathematics concepts” women out-performed men by 0.03 standard deviations. Men had more self-esteem by a range of 0.04 to 0.21 standard deviations, which increased through adolescence. However, the likelihood of men making more “intrusive interruptions” measured 0.33 standard deviations.
The differences may be interesting, but they are also very small.
Flipped classrooms will help build confidence, but it has nothing to do with gender. If students don’t get the instructional video with the first viewing, they can review the video again. Or they can ask a friend to explain it. Or show the video to their parents for help. If none of these steps explain the concept, students can confidently go back into class the next day knowing that the problem lies not in their lack of understanding but in their teacher’s explanation.
These days are difficult for parents and math instructors. With virtual or online learning shoved into many homes, and teacher job satisfaction and wages low (which they have always been), our educational system is in crisis mode. Yet, more than ever, instructors and parents need to project their own confidence onto their students, which means they have to find confidence in themselves. This requires work – is a struggle. We need to embrace this situation, be willing to make mistakes, try new ways, and aggressively fight our fear. It’s not enough to just stay positive. We need to acknowledge the progress – even if a little – that we see in our students.
This all comes back to the need to work as much as possible one-on-one with students. More teacher/parent/student interaction is a solution that will certainly help.
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]]>Instructors should read the Teacher Notes before playing the lesson, and explain the “Get Started” ideas to the student.
Elevated Math provides all the tools for teaching two years of math, pre-algebra and algebra. To use these tools takes work. Watching the videos is not enough. Find worksheets for the Guided Notes and Practice Problems of each lesson below the videos on the website. Instructors should print these out and give them to the student so he/she can work out each problem when the video pauses.
Take a short break between chapters while watching the video. This is a good time to explain the Common Errors students might encounter in the math lesson they are watching. (These Common Errors are also listed in the Teacher Notes.)
When the video ends give students the Independent Practice problems for solving. Check their answers with the provided Keys. The results let you to see required review. Play a chapter again if necessary. Need more problems? Find them in the Additional Practice Problems.
All print material is on the lesson’s video page. The exceptions are the module tests, which are at the end of each Unit. Have the students take one of these tests after they have completed a module (4-7 lessons). Based on the result of the module test, a student might need to review part of a lesson. Should you need to give the test again, a second module test is provided.
No need to subscribe to see a sample lesson. One is on the homepage of ElevatedMath.com. Check it out. And remember when you subscribe you have 172 more lessons just like it.
Learning requires effort – more than most people think. Unless you have highly motivated and self-driven students (which is rare), parents and teachers need to direct their study. Why you might ask, didn’t we make more interactive tools as other online programs have, where a student can answer a question online and then if the answer is correct he/she gets a harder problem? Or if the answer is incorrect, an easier one? Wouldn’t this make it easier for the instructor? Yes, it would make it easier, but it doesn’t help the student learn better. In fact, keeping everything on a computer screen impairs comprehension.
Studies show that most students favor using a mixture of paper and computers as this Scientific American article explains. Also, students taking notes exclusively on laptops perform worse on conceptual questions than students who take notes longhand. It stands to reason the same holds true for solving math problems. They need to solve the problems on paper.
A 2016 Dartmouth study found “when learning, it may be in your best interests to digest the information from multiple media forms.” The results of this study show that computer screens impact abstract thinking. Therefore, students can understand abstract math concepts better if they work out problems on paper rather than on a computer or tablet.
Finally – and we have no studies to support this next conclusion, only personal experience – the more students see their parents and instructors working hard to further their education, the more students learn. For years, I served on PTA’s and then on a school board where I could clearly watch the students of parents who took an active role in their kid’s education. These students got better grades, good colleges admitted them, and they succeeded in life. Why was this, I wondered? Then the answer dawned on me. These students saw the importance of their education, and school, and studying because their parents demonstrated its importance. They were working hard for them.
So, if you intend not to devote time and effort to helping your student learn basic math, geometry and algebra concepts found in the Elevated Math lessons – lessons that lead to success in higher math classes, achieve good scores on SAT/ACT tests, admission to better colleges and success in life – do NOT subscribe to ElevatedMath.com. You are wasting your money.
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]]>The post WHY I ALWAYS HATED THE “B” GRADE appeared first on Elevatedmath.com.
]]>An article in The Atlantic entitled “Letter Grades Deserve an F” by Jessica Lahey struck a cord and inspired this post. Ms. Lahey writes, “points-based grading undermines learning and creativity, rewards cheating, damages students’ peer relationships and trust in their teachers, encourages students to avoid challenging work, and teaches students to value grades over knowledge.” As I read the article I wished I could recapture the hours of anguish I suffered in school for all the “B”s I received. You see, I hated “B”s, more than “C”s or “D”s. Getting a “C” or “D” meant that I hadn’t understood the material, which was fair and acceptable, but a “B”? On an essay it meant the writing was good, but not really great, and on a test it was a reminder that I was okay but not perfect. A “B” was like a bullet fired at my self-esteem.
This problem persisted until the beginning of my junior year at UCLA when I realized that because I was striving for an “A”, maybe that’s why I wasn’t getting as many as I wanted. I decided to experiment and try something different. I told each of my instructors that they could write as many comments as they wanted on a paper of mine, but not to put a letter grade on it. If they put one in their grade books, fine, but don’t tell me what it was.
Suddenly I felt free. I wrote what I wanted to write. If I was inspired to write a paper in the style of a church sermon, I did. If I had to compare two films (I was a motion picture major), I could pick two unlikely films I liked and not care if the essay turned out well or not.
But a curious thing happened. My instructors would hand back my papers, shake their heads, and say they didn’t understand why I didn’t want a grade. Some even exclaimed that I had written the best paper in the class!
Fast forward a number of years later when I was I teaching a senior class at an art college. In design there is never a “right” answer, and I found myself spending an inordinate amount of time breaking students’ habits that came from years of schooling. I found them striving for that great idea or right answer, or even the elusive “A”. I broke them of this habit by making them generate a lot of ideas, not caring if they were good or bad, and if they found these ideas in the allotted time – a very short period – they got an “A.”
If you strive to find one great idea, you rarely find it. But if you generate a lot of ideas first, you might just discover one that is great. And that is what these students discovered.
A few years later, I was on a school board where our innovative district staff inserted a S.T.E.M. (Science, Technology, Engineering, Mathematics) class into the curriculum of the 6th grade classes. Brilliant. These S.T.E.M. classes taught that the “right answer” was not as important as the process – asking the right questions, experimenting, and being willing to try new ideas. This, I realized, was an answer to the letter grade dilemma.
We will never get rid of letter grades. They are engrained in our school system, and it’s what college admissions want to see. But we can teach our students that what’s important is to do their best, to experiment with ideas, and to work hard. Middle school is the best place to teach this. In middle school you can even fail a student and use that failure to teach him/her how to recover. Remember a “F” in middle school never shows up on high school transcripts sent to college.
But I’m not advocating that we fail students in middle school. On the contrary, we need to build their confidence. They need to learn how to recover from failure, to focus on innovation and hard work, not the grade. A middle school classroom and the online math and algebra lessons of ElevatedMath.com provide an opportunity to help students gain a mastery of the grading system, and not feel subservient to it. This can happen if the focus remains on understanding concepts and not just getting right answers.
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]]>The post DAYDREAMING IS GOOD appeared first on Elevatedmath.com.
]]>I came across a Wall Street Journal article with the headline that read, “Wandering Mind Heads Straight Toward Insight,” and the sub headline read, “Researchers Map the Anatomy of the Brain’s Breakthrough Moments and Reveal the Payoff of Daydreaming.”
Here’s the question we need to ask: Are we giving students enough time to daydream?
One of my design students once said that “getting a good idea is like catching a fly.” I’ve caught flies out of the air, which requires concentration and an ability to relax and go with your intuition. Consider this example in the WSJ article. Rene Descartes who, while lying in bed watching flies, realized that he could describe a fly’s position by coordinate geometry. The point the article made is that finding a good idea requires putting the problem in front of you and then letting your mind wander.
In the WSJ article we read, “our brain may be most actively engaged when our mind is wandering and we’ve actually lost track of our thoughts…” One researcher suspects that, “the flypaper of an unfocused mind may trap new ideas and unexpected associations more effectively than methodical reasoning.”
Insight favors a prepared mind, which means that we still need to work out a solution. But then, after we have looked at different options, perhaps writing them down, we should forget about the problem and let our minds wander.
If we want our math classes to succeed, we should encourage students to approach problems insightfully – with discipline, of course – but also with the freedom to nurture questions, and let the questions swirl around in their thoughts and even daydream about them a little.
Oh, one more thing, researchers have found that “People in a positive mood are more likely to experience an insight.” What we are thinking beforehand affects how we handle a problem. This is a reason why a cartoon precedes each math and algebra lesson in Elevated Math. The cartoons help relax students, putting them in a positive mood to solve problems.
http://online.wsj.com/article/SB124535297048828601.html
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]]>After I was elected on the school board, a principal introduced me to a middle school math teacher whose students had averaged 98% advanced or proficiency in Algebra 1 over the past three years.
“Wow! How did you do that?” I exclaimed. “Is there something special in your teaching technique?” Obviously, this teacher knew her subject. So do many teachers, but without achieving these results.
“I care for my students,” she responded.
Okay. Yes, caring does have a lot to do with a teacher’s success. We wrote a blog about it called We MUST Engage Our Kids. Caring was one of four ways that we suggested. But 98% advanced? Can “caring” account for that kind of success? After I pressed for more information, this teacher finally revealed that somehow she is can tell if her students understand her instruction or not. For instance, she will see a student sitting in the back row and know he has not done his homework simply by his facial expressions and body language. Her students were always amazed how she knew them so well.
I realized that this math teacher had a natural skill of observation. Is this something we learn or is it a talent that some of us have?
I think it’s both. I’m convinced that becoming better at observation is something we can learn. Here’s why:
Years ago, when riding in the car with my six-year-old daughter, we played a game. We counted Volkswagen Beetles. Whenever we saw one, we would call out its color. The prize came from a black VW, which would earn us a cookie when we arrived at our destination. (a black VW bug was my first car, btw) At first, every week or so, we would spot a black VW, but then, gradually, they became more frequent to the point where I would spot one every day. Even now, I will notice them quite frequently. From this experience I realized that we are capable of training ourselves to become more observant. But what is the best way of doing this?
I taught a class on creativity at a design college and researched how creative people work. More often than not, they kept journals. Andy Warhol kept one. So did Leonardo da Vinci. The Atlantic reported in 1995 that 3500 notebooks of Thomas Edison’s were discovered. “The notebooks are filled with fascinating observations and insights–many pertaining to unrelated projects, in a seeming free flow of associations.”
I met a historian who was reading the journals of Christopher Columbus. He told me that Columbus would write down every minute detail of what he saw and felt when he was at sea – the way the waves moved, the debris found in the water, the kind of birds and the direction they were flying, even how the air made his bones feel. It makes sense that Columbus, through his observations, had a hunch that if he sailed far enough west he wouldn’t fall off the earth, he would find land.
I required my students to keep a journal and write in it, and I encourage teachers to do the same. As I told my students, it doesn’t matter what you write as long as you do it consistently. I usually required at least two pages a day.
Use the pages to record things you see or have seen. It doesn’t matter what it is. Describe the ceiling in a coffee shop, the way your dog looks at you, the color and style of the shoes the person across the room is wearing, the clutter on your desk. Gradually, you’ll find yourself becoming more observant. Continue doing this, but turn your attention to your students: describe what they are wearing (tennis shoes, loafers, ironed or wrinkled shirts), how they sit at their desks (straight, slouching), their personality characteristics (outgoing, shy, teasing, cautious), how they speak up in class (confidently, timidly, arrogantly), and most important, their knowledge of the material and if and how they falter.
I suspect that you will start picking up subtle nuances in your students’ behavior and know intuitively if they are learning the material properly. If they don’t understand something, you’ll catch it right away and make the correction in your teaching.
I urge you to try it. Go to a stationary store and buy a nice notebook. Writing in it will take some discipline, and starting will be the first hurdle, but if you write every day, it will become a habit. Isn’t this what you require of your students – to study everyday?
If you do give this a try, please let us know how it goes. There is no science behind this idea – not that I know of – but I strongly believe that nurturing our skills in observation can increase our creativity and make us a better teachers.
The post A KEY TO EFFECTIVE TEACHING: OBSERVATION appeared first on Elevatedmath.com.
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