Brain-based teaching and learning is a necessity to effective teaching and learning. Over the past 25 years, research has exploded with studies that demonstrate the power of teaching to the unique needs, intelligences, strengths, and aptitudes of all students. Brain based teaching intersects, is integrated and is a compatible foundational component for differentiated instruction, assessment, behavior management and an intricate aspect of a holistic education.

When we meet the child or adolescent where they understand “how” they process, retain, and retrieve information, we are creating a successful platform for deeper learning and an extravagant mastery of knowledge. Author and educator Martha Kaufeldt said that neuroscience research may be in its infancy or specific to unique situations, but the new knowledge can provide teachers with insight into the behaviors, learning abilities, skill acquisition, and more importantly the emotional and social development of students. The research is confirming what great teachers know intuitively:

1. Students must feel safe and secure to maximize their ability to engage.
2. Novelty and joyfulness contribute to engagement.
3. Predictable patterns for behaviors and tasks can assist learners to know what to do next.
4. Multisensory experiences in enriched environments can enhance brain growth and development.
5. New concepts are acquired more quickly if they are hooked to prior learning and experiences.

If I had to sum up the dire importance of brain based teaching, in one sentence, it would be: Experiences shape and change the brain. Teaching is the only profession where teachers have the great privilege to reshape the brain, because a child and adolescent’s environment and experiences literally affect the neural connections inside the brain directly impacting the emotional, social, and cognitive functioning of every student.

Learner-centered classrooms are brain-compatible classrooms. Learner-centered classrooms are the seeds that grow, flourish and blossom when watered and cared for with the strategies igniting brain development such as incorporating choices, patterns, novelty, self-reflection, and physical movement inside academic instruction and assignments

Emotions and cognition fit together like a hand and glove. When a child or adolescent is stressed or experiencing a perceived threat, the part of the brain responsible for executive functioning shuts down and learning is a moot point! When positive emotion is emitted, perspectives broaden and there, develops a relaxed alertness and focused attention that create clarity of thought! This is the optimal state of a mind for learning. Cognition and emotions are so intimately intertwined they directly influence each other. Making emotional connections drives attention and memory because when we are emotionally connected to subject matter, it becomes extremely meaningful and relevant.

There are four enemies of the brain that strongly inhibit the connections, processing and integration of prior and new knowledge.  Threat, excessive stress, anxiety, and learned helplessness are states of mind that sometimes as teachers we activate unintentionally with frustrating results. Power struggles commence, hopelessness filters into the classroom and a sense of boredom and apathy loom inside the minds, hearts and instruction of many students.

Relational learning which is defined as: connections created between the heart and head of academic and emotional learning breeds higher test scores, motivated students and teachers, and escalating feelings of self-worth and self-efficacy. We cannot afford NOT to pay attention to the research and developments of brain based teaching and its positive results inside instruction.

Below is an example of a brain based strategy entitled story-chunking. This is a lesson that was developed by one of my graduate students, an inner-city high school algebra teacher who has a student population that struggles with motivation and feeling successful with school in general.  He developed this strategy to engage the interests and in-bred creativity that every individual student embraces. When we engage the brain, we invite a variety of subject matter into the content areas we are teaching. This example below is an excellent portrait of a blend of language arts and math. We will discuss similar strategies during the presentation.

Story Chunking Rational and Irrational Numbers

On a crisp Saturday morning in late November, an unusually dense marine layer gradually blanketed the hillsides of Burbank, then Pasadena on its way towards conquering the skies of Los Angeles. As the invasion of aquatic fog continued its march inland, I stood beneath its imposing shadow of dullish gray. A swift and frigid draft swept across Baldwin Avenue and the sea of spectators packed on the sidewalk all braced their bodies in response to the sudden chill. Not a single muscle on my body moved as I looked towards the sidewalks, and saw the people in the crowd tighten their jackets and windbreakers. My thick uniform jacket and tight-fitting helmet sheltered me from the autumn gusts. To me, the draft felt like a gentle and comforting breeze as it splashed my face, washing away some of the tension and anxiety that had been building up for the last five minutes.

The fatigue of supporting the weight of my 30-pound tenor saxophone solely on my right arm began permeating my thoughts, but I disciplined my mind to ignore it as I continued standing at attention. In just four minutes from now, I will have completed the final performance of a parade I have trained every day after school for since school began in late August. I recall sweeping my peripherals with my eyes, and seeing my fellow band mates lined up in perfect rows and diagonals. The two hundred of us had woken up at 5:00  in the morning and boarded buses that transported us 115 miles from our school in San Diego to the quiet and tranquil L.A. suburb of Arcadia, where we annually compete in the most renown marching band festival in Southern Calif. Our school had won the championship every year for the past four years. Adorned in our school colors as we fielded white jackets with neatly polished buttons, military hats with bleached feathery plumes, and royal blue plants with parallel white stripes streaking vertically down to our white marching shoes, we were poised to bring home the six-foot tall trophy for a fifth consecutive year.

“Tweeeeeeett. Tweet, Tweet, Tweet!” After captivating the audience with his baton twirl, the drum major signaled to band that the stage was ours. The orchestrated cadence of drums and cymbals counted down the final seconds before our performance and then, on a syncopated off-beat, we played our first note of the march and a split second later, our band of 200 stepped off in unison to the low brass opening of “Washington Greys.” Two measures later, the woodwinds joined in, and then, the fanfare of trumpets cut through the air. Down the street we marched to the fast-tempo tune in the key of F-minor. I marveled at how impeccably straight and precise the rows, columns, and diagonals of our parade block remained as we glided down the street, perfectly harmonious in both sound and motion. Just two months earlier, my eyes frequently witnessed the vision of the exact opposite.

When the marching season began, our band seemed years away from the orderly and rationally cohesive performance ensemble we had shaped into by the end of November. Our first few practices were chaotic and confusing. Musicians who had not yet memorized the music kept playing off-beat, often influencing their entire instrument section to play in disagreement with the rest of the band. Our marching was flawed, and I remember the ends of some rows would curve off by an entire yard from the center of the row. On extreme cases, we even had musicians bump into each other and trip then fall down when we were practicing our halftime field shows for football games. At times, the various horn sections of the band were playing two to three seconds apart from where the band was supposed to be during a song… Our band was a disorderly and chaotic mess on some days, unable to perform together rationally as part of a unified ensemble. Our band director held us to a high level of excellence, and had no tolerance for the disorganized display of confused and unorganized musicianship. So, he cracked down hard on us for the irrational mistakes we made, as he increased practice times and frequencies of practices. His hard and uncompromising approach towards subpar and irrational mistakes reminded me the Greek mathematicians Pythagoras and Hippasus.

Thousands of years ago, Pythagoras taught the brightest minds in Ancient Greece on the most advanced topics in math of that era. One of the mathematical ideas that Pythagoras advanced was the idea of rational numbers. Pythagoras believed that all numbers are rational, meaning that they can be written as a ratio of two integers. For example, the number 7.5 is a rational number, because it can expressed as a ratio of the numbers 15, and 2 if we write 15 and two as a fraction: = 7.5. Likewise, the number 2.33333333…, even though it is a repeating decimal, is also a rational number because it can be written as the ratio of two integers. In the case of 2.333333, the two numbers are 7 and 3. If we place 7 on the numerator, and 3 on the denominator, then we come up with the fraction. Dividing 7 by 3, we end up with the answer: 2.3333333…..proving that 2.33333 is a rational number.

However, one of his students named Hippasus started creating disorder, and began disturbing the logical organization that all numbers can be expressed a ratio of two integers. Hippasus said that some numbers, like the square root of 2, cannot be expressed as a ratio of two integers. The value of is 1.414213562373095048801688724209698078569671875 37694 807317667973799…and so it continues without any pattern forever. When Hippasus tried to write the value of as a fraction of two integers, he found there is no solution. He could come close to the answer by solving for 99/70, but the answer was merely a close approximation, not an exact match. Other number values, such as the commonly used Pi, are also irrational. Pi is equal to 3.14159265…and so the numbers continue without any pattern. Thus, Pi cannot be written as a ratio of one integer over another.

Pythagoras was deeply angered and disappointed in his student Hippasus. Just like my band director, Pythagoras would not tolerate a single student who operated out of alignment and in disagreement with the rest of the group. When Hippasus created disharmony within Pythagoras’ teaching by pursuing the idea of irrational numbers, Pythagoras realized that he could not tolerate Hippasus’ disorderly conduct. Since Pythagoras viewed the idea of an irrational number to be illogical and harmful towards his orderly organization of number theory, he knew that Hippasus could no longer be a member of his group. Pythagoras invited Hippasus out a on a sailing trip one afternoon, and threw Hippasus into the sea, drowning his student.

Although our band director was often mean and yelled at us for even the most minor errors in our musical performances, we knew that we were fortunate students because he would work with us on improving our techniques until we could perform as a rationally cohesive group rather than just drown us like Pythagoras did Hippasus when Hippasus discovered the existence of irrational numbers. After all, the ocean was just a few minutes away from our school…

Video link: http://www.youtube.com/watch?v=nuX_6KLyj6Y

Math Lab Assignment (Due Monday, September 20th)

This assignment is worth 20 points in the Labs/Projects category.

Write your own story, relating it to our lesson on rational and irrational numbers. In your story, you must:1) Define what rational and irrational numbers are2) State at least one example of a rational number and one of an irrational number3) State the criteria for rational numbers.

Hint: Use your notes from class. Also, your story can be fictional. Your stories do not have to be tied to a life experience or a historical event like parts of mine are. In fact, I look forward to reading stories that are brilliant works of fiction.

Remember: You have complete creative licensing over this assignment. Your story can be set in outer space, the Triassic period, or a fictional universe. You can personify numbers into characters of your story if you’d like…maybe even create historical satire where one society is depicted as rational numbers, and another society as irrational numbers and explore the differences between the societies… or a league of rational numbered super heroes that is recruiting new members only if they meet the criteria for being a rational number… The possibilities are endless!Be creative, and let your imagination take you to new places!

Lori Desautels, Ph.D., is a university supervisor for the Indianapolis Teaching Fellows and Teach for America programs. She is an instructor at both the undergraduate and graduate levels at Marian University in Indianapolis.  Before coming to Marian University, Lori taught emotionally handicapped students in the upper elementary grades, worked as a school counselor in Wayne Township, was a private practice counselor through the Indianapolis Counseling Center, and was a behavioral consultant for Methodist Hospital in the adolescent psychiatric unit. She graduated from Butler University with a BS in Special Education, from Indiana University with an MS in counseling, and earned her Ph.D. from The American Institute of Holistic Theology with an emphasis in early adolescence in thought formation. Desaultes’ website is at www.revelationineducation.com

Do you have a brain-based teaching strategy that works well in your classroom? Please share your ideas and suggestions in the comments.

Do you have question for the editor? Do you have a suggestion for a post you would like to read? Are you interested in writing a guest post? Email editor Diane Trim.

Photo credits:
Girl in Marching Band: greenmelinda / Melinda
Wenonah High School Marching Band: ÇP / Curtis Palmer
Game Night: Randy Son Of Robert / Randy Robertson
Big Brass Band!: peasap / Paul Sapiano

StudyBlue provides a free service where students and teachers can create flashcards, notes, and quizzes online. A while back, we created a Facebook application where students could review their StudyBlue flashcards while logged in to Facebook. Our thinking was, “Students are on Facebook… so let’s meet students where they are.” Once we introduced our Facebook app, however, we heard vehement protests from students. Students wanted complete separation between Facebook and studying. Facebook is for online socializing. StudyBlue is for online studying. We quickly scrapped the StudyBlue Facebook app.

This experience taught us some valuable lessons about teaching with technology in the Facebook era. In order for technology to help students learn, it must meet each of what I call the “3 E’s.” It must be Engaging, Effective, and Easy to use.

Engaging Students in the Right Context

When teaching with technology, the learning task must align with the capabilities – and the –context – of said technology. The capabilities part is obvious. It goes without saying we wouldn’t ask students to write a long term paper using their phone as the sole input device. The context piece is less obvious. That is, it’s important to consider what state of mind students are in when they’re using a technology. When students are using Facebook, they’re thinking about socializing, not social studies. They’re getting distracted by pictures of friends and chat messages, not graphs and charts. They’re not thinking about studying, so creating an app for studying on Facebook is difficult.

That said, as Facebook becomes more of a utility, students might find it more and more conducive to studying. Case in point: phones are a utility. Sure, they’re a communications device and people use them for social calls. However, phones have gone beyond just talk and answer. Students use them for texting, but also for studying. As students do more and more things on Facebook – as it becomes more of a utility – there’s a good chance the context of Facebook will change so that it’s more than a social app and more conducive to studying.

Being Effective at Helping Students Learn

Technology must be grounded in the learning research. Students and teachers won’t use a technology if it doesn’t get results. What’s interesting is the research on how we learn has evolved over the past few years. Here’s what the research shows:

• Alternating study environments – studying in both the library and the coffee –shop – can be beneficial
• Our parents told us to turn off the T.V. and radio when we studied, but new research indicates that ambient noise in the background can help students learn
• Other recent research confirms what we’ve known for years: It’s important for students to give themselves time between study sessions
• And students who challenge themselves via “self-testing” retain more

When looking for technologies to assist student learning, check out the latest learning research. Developers should explain how their solutions meet students’ needs and help them learn. Beware of online gimmicks that will entertain or engage students, but not help educate them.

Enhancing What Students Already Do

For technology to get results, it first needs to help people make “baby steps.” Behavior change is hard; technologies that assist users in making baby steps have a better chance of being adopted and, in turn, helping students learn. Also, if teachers are going to implement a technology in their classroom, it needs to help students learn while also fitting easily with what’s already happening in the classroom. This seems self-explanatory, but there are many technologies out there that do not have simple workflows. Both teachers and students are extremely busy and inundated with information; technologies that don’t solve a problem in a simple way won’t get used. When evaluating a technology for use in the classroom, the important question to ask is: How does this technology enhance in an easy way a task I or my students already do? If there isn’t a ready answer to this question, be wary of adopting the technology.

What are your thoughts on how to best teach with technology in the Facebook era? I look forward to seeing your ideas in the comments section.

This is the first of a three-part series by Matt Messinger, Director of Learning at StudyBlue, a free online flashcard and note-taking tool.

Photo credits:
Facebook Like Button: FindYourSearch / SEO
Study Blue Logo: StudyBlue.com
phone LAN: Gustav H / Gustav Holmström

My daughter, a high school freshman, came home from school the other day in a bad mood. She’d worked all weekend on her Social Studies presentation about Cuba, but the speech didn’t go well.

Like millions of Americans, my daughter suffers from a public speaking phobia. The number one phobia among Americans is public speaking. Number two is death.  As comedian Jerry Seinfeld said, at a funeral, most people would rather be in the coffin than delivering the eulogy.

The weekend before her Social Studies presentation, I sat with my daughter as she prepared her speech and she looked for praise after she finished every PowerPoint slide. I was her audience as she practiced. I made my husband, my brother-in-law, and our dog listen to the speech. We all learned more about Cuba than we’d ever known before, even the dog. My daughter felt confident the night before class.

However the morning of the speech, my daughter was a mess. She had a stomach ache, she had a head ache, she might have even had the plague. I tossed her backpack in the van and insisted that she buckle up. I dropped her off at school and she walked through the double doors like a teen condemned to the gallows.

When she came home that evening, I asked her how her speech went. O.K., she said and angrily tossed notebooks and textbooks out of her backpack. I sensed that it wasn’t O.K., and I pressed her for details. She said that the teacher kept interrupting her. The teacher stopped her and asked that she speak louder. She interrupted her to ask her questions. She interrupted her to redirect another student who wasn’t paying attention. By the time my daughter ended her speech, she was flustered and wanted to hide in the rest room.

Hand signals. We become so relaxed in our own classrooms that sometimes we forget that the students don’t feel the level of ease with one another and the material that we do. However, the teacher could have communicated all of the things during my daughter’s speech with nonverbal gestures.

A hand signal or nonverbal gesture is a great way to communicate with students when you don’t want to lose the flow of your lesson. If a student isn’t following along in the textbook, there’s no need to take a break from instruction. Keep talking and wander over to the student’s desk. If your presence isn’t enough to redirect the student, keep up your instructional flow, but quietly find the right page and the right passage and put your finger on it. Then walk away. My daughter’s teacher could have redirected the student who was off-task during the Cuba presentation without interrupting.

She could have also shown my daughter the universal signal for speak louder, which is a hand cupped to her ear. She could have saved her question about Cuba for the end of the presentation.

I’m sure that the teacher meant well. I’m confident that she didn’t wake up that morning and think to herself: I’m going to reinforce a student’s fear of public speaking today.

Signposts. Another nonverbal way to communicate with students is to post common questions and answers on the walls. If a student raises a hand to ask permission to use the restroom, don’t answer the question. Continue instruction and point to the poster on the wall that outlines your restroom pass procedures. If a student forgets what an adjective is, point to the poster on the wall that shows six of Snow White’s seven dwarfs. When a student responds in English in your French classroom, point to the poster that lists common responses in French.

Taking it to the extreme. Like anything an adult uses with teens, nonverbal cues can go from effective to spectacularly ineffective very quickly. Overuse a teaching technique and the teens in your room will turn it into the next big joke. I remember a well meaning assistant principal who was overwhelmed with lunch duty. The students in the cafeteria were loud and goofy. The assistant principal was prim and proper. The students had a ball teasing the poor woman and misbehaving behind her back.

In response, the assistant principal started carrying a sign with her, sometimes several signs. Instead of approaching the students about their loud voices, she’d show them a sign: Keep your voice down. If students began to chase one another, she had another sign: Remain seated. When students left a mess at their tables, she’d find them and hold the sign: Pick up your trash.

You can imagine how the teens used the assistant principal’s signs as the next big joke. They made their own signs. They posted signs in the hallways and on their lockers. They created signs to wave at basketball games. They tried bringing their signs into classes. Students chanted the words on the assistant principal’s signs to one another and used the words as punchlines. The assistant principal was not a person to give up, though, and she stuck with her lunch room signs until school let out in May, months after I would have abandoned them in the recycle bin.

Nonverbal cues are beneficial. Even though teens can corrupt them, the benefit of using hand signals, signs, and other nonverbal cues outweighs the risk that they’ll become the next hallway joke. With nonverbal cues, no one interrupts instruction to ask or answer a simple question. Redirection occurs quietly and at the lowest level of conflict. Often redirection occurs so smoothly and quietly that students around the off-task student don’t even realize that the teacher has intervened at all. Pointing to a sign in the classroom to remind students about a rule or an important concept reminds students of the basics without embarrassing them in front of the group.

So, instead of interrupting my daughter during her speech, her Social Studies teacher had options that wouldn’t have increased my daughter’s fear of pubic speaking. We all have options to communicate at the lowest level of conflict to maintain student dignity and keep the lesson flowing. It’s not always possible to use these hand gestures and signs and sometimes it takes a little extra time to do so, but I think that it’s good practice.

Do you have a question for the editor? Would you like to suggest a topic for a post you’d like to read? Are you interested in writing a guest post? E-mail editor Diane Trim.

Photo credits:
I can’t hear you [teacher]: munickat
Talk Shows On Mute: Katie Tegtmeyer
i can’t hear you!: velkr0
Signs of Philadelphia: Bogart Handsome Devil
Shh … 10 inch voice: Enokson

“Limit pop quizzes. Pop quizzes contribute unnecessarily to anxiety and rarely lead to increased competence. In fact, the sudden wave of fear that an unexpected test elicits can quickly shut down learning and memory, leading to poorer performance. Tell your students that you won’t play games with them. You will let them know of all upcoming tests well in advance so that they can allocate sufficient time for study and seek help if needed.”

-Dr. Allen Mendler, Connecting with Students, p. 56.

The punitive pop quiz. In my own teaching practice, I’ve given my share of pop quizzes, but they were mostly at the beginning of my teaching career. In fact, I had a cooperating teacher during my student teaching experience who recommended pop quizzes and had a large stash of them prepared for any occasion. She was kind of a funny gal who didn’t know the names of her students. She sat them alphabetically on the first day of class and marked her attendance sheets based on empty desks. She expected her students (mostly freshmen and sophomores) to enter class quietly, take their seats, and begin on the warm-up, but she never communicated this to the students. Her method was the punitive pop quiz. If they didn’t comply with her unwritten expectations, she’d quietly hand out the pop quiz. Never did she explain what she was doing or hold it out as a threat. She just silently passed it out and collected it. One day, when the kids were preparing for the inevitable pop quiz, she didn’t give it to them. They were already quiet, seated, and ready for work. She was a quirky gal, that cooperating teacher.

And I hearby confess that I had a store of pop quizzes that I’d created my first year just for my nightmare seventh period class (ugh!). Unlike those of my cooperating teacher, my pop quizzes never had the calming effect on my classes that hers did. I knew, even back then, that learning shouldn’t be punitive and my heart wasn’t really into the pop quiz.

I will say that I often gave reading quizzes to students after I assigned a short story or book chapters. I never looked on those as pop quizzes, though, because students knew in advance that I’d be asking questions to verify their reading comprehension so we could have a meaningful literature discussion.

Student anxiety. As the parent of a high school student with AD/HD, I can tell you that pop quizzes generate anxiety. Well, not the first one. The first pop quiz in a class doesn’t generate the anxiety that subsequent pop quizzes create. My daughter wouldn’t have the time to work herself into a frenzy about the first unannounced quiz. However, every class period after the pop quiz, she’d work herself up about the potential of a pop quiz, even if the teacher didn’t give any quizzes after the first one.

For students like my daughter, that anxiety is enough to shut her down from learning in the period that precedes the pop quiz class. She’ll fidget and stew about the next class and won’t be able to focus on conjugations or cosines. When she arrives in the next class, she’ll experience a moment of relief when there isn’t a pop quiz, and then worry the rest of the class period about what might be on the one for the next day.

Sure, my daughter might be an extreme case, and yes, she’s on medication. However, as a 10-year classroom veteran, I know that I didn’t employ the pop quiz beyond my first year of teaching. Instead I used formative assessments that didn’t cause a student to fidget and worry. I asked for exit slips at the end of class, engaged the students in meaningful class discussions, and monitored their homework for knowledge gaps. When we had a test or quiz in class, students knew what to expect and how to achieve on it. They understood that questions were linked to lesson objectives and that the test was to illustrate mastery, not a cool head under pressure.

I know that many of my colleagues, good teachers with great teaching methods and loyal students, still give out pop quizzes. But for me, other measures of student learning worked better.

Reference:
Mendler, Allen N. (2001.) Connecting with Students. Alexandria, Va.: ASCD

Interested in more from Dr. Allen Mendler? Check out Teaching Impulsive, Inattentive and Oppositional Students in the Differentiated Classroom

How about you? Have you ever given a pop quiz? What results were you hoping to achieve with the pop quiz? Do you think pop quizzes create too much anxiety among students, or do you think that they’re a valuable teaching tool? What kinds of formative assessments do you prefer? Please share your thoughts in the comments.

I think that those appreciations helped me to get to know my fellow teachers better and they went a long way to creating good will among us throughout the school year. I liked the idea so much that I implemented it with my own students.

After a group work session, I asked students to give the person on their right or the person sitting across from them an appreciation. The appreciation had to have something to do with the discussion the group just had. Comments like, “You look good in blue,” were funny and appreciative, but not allowed.

At first the appreciations were awkward and tongue-in-cheek. I nearly abandoned them with my students, but when I tried to skip it, the students began to remind me that we hadn’t done the appreciation yet.  It turns out they really liked it.

As the year went on, the appreciations became less goofy and more sincere. I don’t want to say that the appreciations transformed my classes; that’s giving the technique too much power. However, I do think that hearing something nice from a classmate is powerful. Those small words of genuine thanks built bridges among students who had very little contact with one another. At the end of the year, my classes had a feeling of community.

I also think that the appreciations helped students who were reluctant to participate in a group want to join in. Sometimes students hold back in a group or say funny things because they don’t want the rest of the students to think they’re not smart. However, each group member wanted an appreciation and knew it was coming at the end of the activity. Kids wanted to hear something besides, “You take good notes,” or “Your comment was funny.”

Out of all the things that you can do to encourage a learning community in your classroom, this one is pretty easy, requires no advance planning, and pays off in student good will. Give the appreciation strategy a try next time your students have a group activity to complete. Let me know how it goes.

Have you used the appreciation technique with your students in group work? Are you thinking of trying it? Do you have other simple ways to encourage students to work well with one another? Please share in the comments.

Math doesn’t have to be hard. It is a tool: the tool of science and economics; the tool of problem solving and the algorithmic approach to issues. One of the many beauties of the tool is, it has been around for thousands of years, and although we find and develop new aspects, it is largely unchanged. I approach teaching math by trying to show the students that what they are learning is all within their current knowledge.

Number Sets
When I discuss number sets with the students I like to use a few analogies. I use a story about how numbers developed to discuss the natural progression of natural numbers to irrational. As I discuss each level, I like to the layer the discussion with geography: everyone in your neighborhood lives in your city, but not everyone in your city lives in your neighborhood. When I get to the final rational, irrational, real story, I link rational to the state we live in and irrational to the neighboring state. That leaves real to be the US.., no land of its own, but joining all of the states.

Adding and Subtracting Numbers or Like Terms
This seems like it should be easy; we all know our basic arithmetic, but this piece can leave more students dumbfounded and convinced that they cannot be successful in math. One big piece I highly emphasize is the idea of stacking like terms, or numbers that are being combined. When we are first introduced to math computation, we learn vertically, but once we get into algebra, not only do we add variables, we also include a horizontal approach. When the numbers are stacked, I put a rectangle around the sign. When I teach older students, especially when I taught in an urban setting, I would tell them that the rectangle was an ally. There are two rivals, the positives and the negatives. I ask them, “Are they going to party or are they going fight?” If they are the same sign, they party and we figure out how many are partying. If they end up in a battle, I ask, “Who is going to win and how many will survive?”

This topic is expanded with I discuss polynomials and multiplying them. Anyone who has survived an algebra class has heard FOIL – first, outer, inner, last. I have tried to avoid this acronym.  It is VERY limiting. It only discusses what to do if you multiply two terms to two terms, but what if there are more? It also emphasizes the horizontal approach to math versus a vertical approach, which is much more comfortable to students.

So what is the alternative? I like to reinforce the distributive property, which is what the acronym is reinforcing. I tell my students to use the “distributive property with stacking.” Distribute each term from the first parenthesis to every term in the second parenthesis and stack the like terms. It allows for easy completion of this type of problem. It also allows for flexibility of multiplying any number of terms to any number, making any problem approachable.

Math isn’t hard
Math is math. I remember my mother telling me that she could never understand Spanish; and consequently, I believed I could never learn the language. I made it through the high school requirements, and was relieved it was over with. In college I thought I would try it again, and give it a new chance. As it turned out, when I didn’t believe learning Spanish was impossible, the class became easy.

In other countries math isn’t hard because people don’t talk about it being hard. The brainwashing isn’t there. If we step back and give math a real chance, see it as a way to break problems down systematically to find a solution, it may not be the great stressor so many student see it to be.

Huckleberry Rahr taught high school mathematics for nine years throughout the Midwest and one year in Papua New Guinea. During that time, Rahr earned a Masters of Education from Cardinal Stritch University. She spent two years working in the private sector before returning to education as a full-time instructor for ITT Technical Institute in Madison, Wis. Rahr is a member of Inside the School’s editorial board.

Photo credits:
Math Class: attercop311 / Lauren on Flickr.com Creative Commons
Math Finals: ensign_beedrill / Rough Tough, Real Stuff on Flickr.com Creative Commons
for my math girl: crd! / Craig Dugas on Flickr.com Creative Commons

I’ll give you five possible spoon feeding scenarios. Let me know in the comments which one(s) are spoon feeding and which one(s) represent good teaching.

Scenario 1: One test hint

Lindsay is new teacher who passes out Test Hint coupons like extra credit points. During a test or a quiz, a student may use one coupon for a free teacher hint on a question. Students ask the teacher a question and she gives them a hint. She doesn’t accept the question, “Is this right?” but the rest are fair game.

Scenario 2: Testing from homework

Matt, the math teacher, encourages his students to complete their homework and ask questions about problems they can’t solve. He gives homework a completion grades only and doesn’t grade at all on correct answers. Matt told me that he wants students to attempt the homework and to figure out a method for solving the problems that worked for them. As a reward for the students who complete homework every day, Matt creates his tests and quizzes from the homework questions. Students who keep up with the math class’s daily work tend to perform well on Matt’s assessments.

Scenario 3: The review game

A popular history teacher always plays a review game with his students before a test. The questions he uses are right off the test sheet. Students may use notes, books, or one another to answer questions. When the class finishes the game, the students take the test.

Scenario 4: The cheat sheet

Our physics teacher believes her students have a difficult time memorizing all the formulas and measurements they need to answer physics questions. The day before a test, she distributes a 3 x 5” index card to her classes. Students fill up the card – in ink only, no printed material – with formulas, definitions, and facts they think they’ll need for the next day’s test. The physics teacher claims that creating the “cheat sheet” actually helps them study. She also says that her testing objectives aren’t at the understanding level of Bloom’s Taxonomy. She aims for the higher levels of analyzing, applying, and evaluating.

Scenario 5: Start me out

Michelle, the English teacher, often takes modeling essay writing one step further for students who aren’t strong writers. She sits with a small group and begins a sentence for them. She asks her students to finish the sentence with their own words. She and her students draft a paragraph together and she models the essay writing process with them. Before the students return to their seats, Michelle makes sure each kid has at least an introduction, a thesis statement, topic sentences, a clincher, and an outline for the rest of the essay.

What do you think? Are any of these scenarios examples of spoon feeding students information? How much assistance is too much? Where do you draw the line in your own classroom?

Over the years, my students have taught me how much lecture they can tolerate and what holds their attention the best.

1. Keep it short. My goal is to lecture for 15 minutes, tops. I try very hard to stick to one topic. If I need more time to cover more topics, I’ll spread out the lectures. When I taught on the block schedule with 84-minute class periods, I might have two 15-minute lectures in a class period, spaced out with out-of-the seat activities or small group discussions. The shorter the lecture was, the more I was able to keep my students’ attention. Some people might look at students’ short attention spans as a shortcoming, but I know that when I’m in a meeting, 15 minutes seems long to me, too.
2. Keep it focused. One of my lectures might be about how the Globe Theatre differed structurally from modern theaters. I don’t branch out into the Elizabethan world view or Shakespeare’s sources. Those are topics for another lecture. Have a clear plan for the lecture and let your students know what that plan is early on. It’s effective to use a graphic organizer as both the lecture’s outline and a student handout with blanks for guided note taking. Vary the shapes and configurations of graphic organizers for each lecture. Some students will remember the material on the organizer with arrows or the organizer with bubbles. Of course, using an outline with blanks helps reinforce outlining as a concept, too.
3. Make it personal. Even if the lecture is about polynomials, finding a connection between your students’ interests and your curriculum will make the lecture more relevant to their lives. Sure, sometimes it’s hard to make the learning personal, but the more you help your students connect the content to their prior knowledge, experience, or interests, the more they’ll retain.
4. Allow for interaction. It’s tough for a kid to nod off while you’re talking about the Civil War if you’re always asking your students for feedback or asking them quick questions. You can have them predict what the answer might be, ask them to hold fingers up in front of their shirts to vote on a response, or throw out a quick review question from a previous lesson. It’s also useful to ask students to turn to a partner and offer a 15-second (timed) summary of an important fact. If you don’t have a question to ask, just mention students by name as you lecture to increase and maintain. While you talk about eukaryotes, address a student. You might say, “So, Tyra, a eukaryote cell has complex structures within it. Those structures, Matt, are enclosed with membranes.”
5. Use visuals. People love to look at something while they listen. It’s normal and it gives the brain another pathway to remember the lecture’s information. When I lectured about Edgar Alan Poe’s “The Cask of Amontillado,” I brought in my photos of Paris’ catacombs for students to view. When we read Eugenia Collier’s short story “Sweet Potato Pie,” I brought some in for my students who had never tried it. If I were lecturing about the Scottsboro Boys and the trial’s influence on To Kill a Mockingbird, I brought in transparencies of political cartoons and photos of the men on trial. An obvious visual is the PowerPoint presentation, which can be over used. If the PowerPoint is used as a visual aid, with many photos and illustrations, but few words, students will find the slides more engaging and listen to the lecture rather than tune it out.
6. Wander the room. Free yourself from the lectern, the projector, and the front of the classroom and allow yourself to conduct your lecture while circulating among your students. If you need to write on the overhead, the chalkboard, or the interactive whiteboard, ask a student volunteer to write for you. Circulating among the students encourages them to remain on task and it makes redirection easy. Stand beside the desk of a student who wants to chat to a neighbor, silently offer a loaner pencil to a student who isn’t taking notes, and scan the crowd for covert texting. Students will become used to the idea that you can be next to them at any moment and will be more likely to pay attention to the lecture. They’re also more likely to ask you a question when you’re nearby rather than further away.

These aren’t the only ways to make a classroom lecture more interesting for students, but it’s a start. I’d love for you to share your lecture methods in the comments.

Despite the fact that Dr. Goldacre doesn’t believe in the amazing health benefits and antioxidant powers of chocolate, I think that his conclusions are sound, especially those about the mind’s incredible response to belief.

The post is called “Superstition,” and is about the results of a German study of good luck. Even if you’re a skeptic, you might want to look at this like Pascal’s Wager and keep a lucky penny in your pocket. Of all the things that might not raise test scores, this one is pretty harmless and has some science behind it, too. Here’s what the researchers found and how we can apply it in the classroom.

Experiment One

The researchers took 28 test subjects to a putting green. The researchers gave the subjects a golf ball and 10 chances to putt. For half of the subjects, the experimenter told them, “Here is your ball. So far it has turned out to be a lucky ball.” For the other half, the experimenter said, “This is the ball everyone has used so far.”

Test subjects who had the “lucky ball” did better than those who had the plain ol’ golf ball, and not just a little bit. Lucky ball average: 6.42, plain ol’ golf ball: 4.75.

What does this mean in the classroom? Well, with this knowledge, every pen I loaned out would be a lucky pen. Any test sheet would be a lucky test sheet. Sure, it can be overdone, but that’s part of the appeal for me. Best of all, insisting that this quiz is a lucky quiz because other classes did well on it is free. And, it just might improve scores.

Experiment Two

The researchers asked a group of 51 test subjects to do one of those tilt board games where a player tilts a maze to roll balls into holes. Test subjects were in three different groups. Before a subject in the first group began the task, the researcher said, “I press the thumbs for you,” which is a German saying that means, “I’m keeping my fingers crossed.” The second group heard, “I press the watch for you,” which is a German expression that offers encouragement. The final group heard, “On you go.”

The test subjects who heard the fingers crossed suggestion finished the game faster than the other two groups.

What does this mean in the classroom? Before a test or a quiz, just say that you’re crossing your fingers for your students. It doesn’t cost anything to say it and your students might complete the task faster than you’d expected.

Experiment Three

The experimenters rounded up 41 test subjects who had a lucky charm and they asked the subject to bring the lucky object with them to the lab. Half of the subjects were allowed to keep their lucky charm with them in the testing room. The other lucky charms were taken away “to be photographed.” Researchers gave the test subjects a memory game and a post-game questionnaire about how confident they felt about their performance on the memory game.

Not only did the test subjects who had their good luck charm with them do better on the memory task, but also they reported higher levels of “self-efficacy,” which means they felt more confident about their work.

What does this mean for the classroom? It means that I’m going to talk about lucky charms from day one. I’m going to bring in a necklace or four-leaf clover and ask my students to do the same. I’m going to encourage them to bring their lucky charms (within reason) to class every day and refer to them often. “Does everyone have a lucky pencil?” If a little piece of luck makes my students perform better and feel more confident, I’ll start growing four-leaf clovers myself.

Experiment Four

The luck researchers invited 31 test subjects to bring their lucky charms to the lab. Again, only half of the subjects were able to take their good luck objects with them into the testing room. This time, the subjects had an anagram to play with: how many words can you create out of a certain word? Before the test, though, the researchers asked the test subjects to set a goal: what percentage of the words did the participant think she could find?

As you might expect now, the test subjects who were able to keep their lucky objects with them did better than their luck-deprived counterparts and they reported more “self-efficacy” or confidence. Even better, those with their good luck charms set higher goals and stuck with the task longer than the unlucky subjects.

What does this mean for the classroom? Again, I’m going to encourage good luck charms, but I’m also going to ask students to write a goal score in the bottom corner of the test or quiz page. Maybe if they give themselves a target to shoot for, they’ll try to hit it.

Bottom Line

Do I believe in luck? Well, I believe in the power of belief. I think that often what someone believes about herself becomes true. If she believes she’s lucky, she will be. If a student believes he’ll be successful, it becomes self-fulfilling. If I, as a teacher, express my belief in my students, that’s a powerful form of belief, too. Call it luck, I don’t care. It’s powerful and I’m going to use it in the name of good teaching and higher test scores.

How about you? Is this luck thing nonsense or will you, like me, exploit it to the point that every sheet of paper sparkles with fairy dust? Have you had experience with the power of luck or belief? Please share in the comments!

My husband asks me why I don’t just throw it all away.

Well, some catalogs I might be able to cut up to use as conversation starters or metaphors in class. Some flyers I might be able to use in my mass media class to teach a persuasive print advertising technique.

And let’s face it: I like the pieces that call me by name.

I know it’s a trap before I open the envelope, but I respond better to the junk mail with my name on it rather than resident or valued customer.

Students are the same way.

When I taught, I tried hard not to lecture for most of the class period. But, we all know that the lecture, even a short lecture, is inevitable. Here’s how I ran mine:

Guided note taking. I gave students an outline for their notes so they could anticipate what was important and what topics we’d cover.

Student involvement. I had a designated note taker at the board or overhead projector who wrote the notes for the class. That freed me up to circulate among the students and make sure they were on task and that I was available for questions. I also had the designated name picker choose volunteers to answer questions from a deck of name cards.

Name dropping. This is the smartest thing I’ve done to help kids pay attention during a lecture. As I mentioned, it’s inspired from my junk mail. As often as possible, I tried to incorporate a student’s name into an example during my lecture. I didn’t choose someone who was nodding off or doodling instead of listening. I spread the joy around and tried to name each kid in the class during the lecture at least once.

If the student name didn’t work well in an example, I worked it in like I was having a one-on-one conversation with individual students. It went like this:

“So, Jonah, we’re not really sure if it was Shakespeare who wrote these plays or if someone else did it. But that’s not really important, right Jenny? The words by any pen would still be terrific, don’t you think, Lisa?”

That example might be overdoing it, but just saying those student names at random during the lecture and making eye contact with each kid really helped them pay attention. We all love it when someone calls us by name.

It’s just like how those colorful mailers get my attention when they print my name on the envelope: Diane Trim, you could be our next winner!

Name dropping like that is hard to ignore.