Motivating All of Your Students

A #2 pencil and a dream can take you anywhere.
—Joyce Myers, American businesswoman

You are patient, offer encouragement, provide time during and outside of class for students to receive extra help, and differentiate for achievable challenge, yet some students still repeat the same complaints we hear every year, from “Math is my worst subject” to “I already know that. Can’t we learn something new this year?”

Because boring is the most common word students use to describe the reason for their math frustration, it helps to consider what students mean by this. The power of boredom or alienation goes beyond not enjoying a specific course or subject. It leads all the way to dropping out of school.

Nationally, 50 percent of high school students in the largest U.S. cities disengage completely by dropping out. This is the highest dropout rate we’ve ever seen. It is the first time since the institution of public schools in the United States that it is more likely that students’ parents will have graduated from high school than for the students themselves to graduate. The United States is the only industrialized country in the world where this is the case. Many students who don’t drop out nevertheless disengage through inconsistent attendance, disruptive behavior, and inadequate homework and test preparation (Organization for Economic Co-operation and Development, 2004). Another study found that math failure starting in 6th grade and an unsatisfactory behavior mark in at least one class before high school were two of the four greatest predictors of dropping out of high school. In fact, 75 percent of students with these records as early as grade 6 dropped out of high school (Neild, Balfanz, & Herzog, 2007). The association of failure in math and unsatisfactory behavior is a natural consequence of the fight/flight/ freeze reaction of the brain to math negativity.

Surprisingly, it is not the difficulty of academic content that drives students to drop out. In 2006, 81,499 students in grades 9 through 12 from 26 states participated in a survey of student engagement and reasons for dropping out. Only 27 percent said they would consider dropping out because the work was too difficult. The majority of those students suggested that the reason they would consider dropping out was that school was boring. What did the respondents mean by “boring”? The reason 74 percent gave for being bored in class was that the “material wasn’t interesting” and 39 percent stated that the “material wasn’t relevant to me.” Also important is the level of interaction between teacher and student, with 31 percent attributing their boredom to having “no interaction with teachers” (Yazzie-Mintz, 2007).

We strive to motivate students so they are successful in math and develop the extended skills of reasoning and analysis that accompany true conceptual knowledge of mathematics. In addition to keeping them from dropping out, motivation has other benefits. Motivated students are the most responsive and least likely to be “behavior problems” because, as just mentioned, math negativity is associated with the reactive fight/flight/freeze behavior. With your intervention, students’ attention and positive attitude can replace negativity.

The strategies in this chapter start with a focus on capturing your students’ collective imagination and attention—exactly what is needed to get information to the prefrontal cortex instead of being conducted to the fight/flight/freeze area of the lower brain. We will then explore strategies to sustain this attention and construct working memories by lowering stress and increasing positive emotions.

Motivating Students Through Active Engagement

Knowing your students’ interests and background knowledge helps you create lessons with sensory input that is most likely to be selected by the RAS. Because the RAS responds positively to sensory input predicted to increase survival, cause pleasurable feelings, and result in achieving immediately desirable goals, using strategies that stimulate a “here-me-now” response increases the likelihood that this primitive brain filter will select the information you want your students to take into their brains.

The RAS

All information enters the brain as sensory input, and all such input must pass through the reticular activating system (RAS), the brain’s most primitive filter, to enter the information-processing areas. Billions of bits of sensory information are available every second from sound, light, color, smells, touch, position of muscles, and our internal organs. Only a few thousand of these can get through the RAS each second (Lawrence, Ross, Hoffman, Garavan, & Stein, 2003).

If it weren’t for the RAS filter, our nervous systems would be overwhelmed by input. Instead, the RAS—and later, the amygdala—allows the brain to establish priorities and select what is valued enough to admit into our perception. The RAS’s selection determines what the thinking brain has to work with at a conscious level. If the information in your lesson is not selected by this primitive filter, then it doesn’t have any chance of being “learned.”

In animals, including humans, the RAS is attentive to changes in the environment and selectively alerts the brain to new sounds, sights, or smells that may indicate danger or opportunities for pleasure. Those selections allow the animal to survive (food, water, and safe habitats are deemed pleasurable) and the species to be sustained (the sensory input related to a potential mate is selected for its association with pleasurable sexual experiences). Our RAS has not evolved much beyond that of other mammals—it remains alert first for potential danger. Once the RAS establishes that nothing has changed that requires instant protective reactions (fight/flight/freeze), it then selects sensory input about changes that are associated with previously pleasurable experiences.

The RAS response to sensory input affects the speed, content, and type of information that enters the higher-thinking regions of the brain. The RAS is key to arousing or “turning on” the brain’s level of receptivity to input. For example, PET scans show increasing activation in the RAS as people change from a relaxed state to an attention-demanding task (Kinomura, Larsson, Gulyas, & Roland, 1996).

Cognitive studies show a correlation between intelligence and the ability of the brain to select which patterns of information pass through the RAS. Students vary in their ability to effectively inhibit task-irrelevant sensory input. In one study, children with high intelligence employed more constructive matching of information to task goals and more effective inhibition of task-irrelevant information compared to a control group of “average” students, suggesting that the “high-intelligence” children’s RAS filters more efficiently select input based on the goal or task at hand (Vigneua, Caissie, & Bors, 2006).

Because the RAS also looks for change in the environment, surprise and novelty can be valuable classroom tools for promoting attentiveness in students. Novelty can be incorporated into lessons through variations in sensory stimuli (tone of voice, volume, or rhythm); visual cues or changes such as color and movement; or other tactile or kinesthetic changes. All of these cues can call attention to what you want your students to see and hear. Your sensory input needs to be selected by the RAS as more potentially pleasurable than the sounds coming from the playground or a conversation with the classmate in the next seat. That’s pretty stiff competition when your job is to teach long division.

Strategy: Engage Students with RAS Grabbers

Novelty, change, and surprise (the unexpected) engage students’ attention and can promote a state of eager motivation (Hunkin et al., 2002). Telling students they must learn math to pass tests—or even because they need the knowledge for future success—is not sensory input valued for selection by the RAS. That information on its own does not have the “here-me-now” qualities that the RAS connects with survival or pleasure.

What will engage the RAS at the start are things that incorporate change or novelty, evoke curiosity, or are associated with pleasure. You can grab your students’ attention with movement, color, music, advertising, discrepant events, or things that don’t behave in expected ways (such as your walking around the classroom backward before starting a lesson about negative numbers).

Knowing that novelty is a big RAS motivator, it is neuro-logical to conclude that if the sensory input is not novel enough to get RAS attention— such as lessons that move too slowly for those who already know the information—it will not engage students’ attention. Individualized instruction that is mindful of different levels of achievable challenge once again becomes important. For example, when some students already know the content and their RAS tunes out, they may miss information that is actually new and important when it comes up. These are lessons that require intermittent short segments of instruction in foundational knowledge (which you know will be “boring” to some students) but that soon include new information these students don’t know. Plan ahead with some agreed-upon cues (e.g., put on a cap, write in a special color) or code words so these students will alert their RAS to refocus attention when you reach the new, important material that comes up in the lesson.

The following are some additional examples of how to build novelty into learning new information.

Speaking Voice. Try speaking in a novel accent or a different cadence of speech.

Suspenseful Pause. Pausing dramatically before saying something important will build anticipation as the students wonder what you will say or do next.

Word Order. Start your sentences with an unusual word order, such as with verbs first, like “Yoda-speak.” For example, to begin a lesson about order
of operations, say, “Think, you will when solving math problems.” Extend the interest by putting up a problem for which students need to know the order of operations to reach a correct solution, such as 80 – 20 x 3 = __. Some students will answer 180, and others will appropriately multiply first and find 20 for the solution. Now students will want to know what you have to teach them because the answers are so different, and it is likely they were all sure their answers were correct.

Color for Novelty and Differentiation. Write key points in priority colors and have students use pencils or pens in the same colors in their notes. If you choose green, yellow, and red to show increased importance, you can have a picture of a traffic light in the classroom to remind students of the system. Not only will the change of color increase RAS attention, the movement in the room as classmates pick up new pencils refocuses the attention of students who have zoned out. Students will also have cues of importance when they study and want to fill in missing information for words they wrote in priority colors.

Font. Changes in fonts (including color) can revitalize focus on tests and assignment sheets.

Thinking Cap. Wear a special cap for important lesson points and rotate it to the side and then backwards to emphasize higher and highest priority.

Play a Song. When students enter the class, play a song that relates to the lesson and challenge them to figure out what the correlation is between the song and the lesson. They will listen to the lesson more carefully and pay attention in order to make the song-lesson correlation.

Clothing Cues. Wear clothes with geometric prints for lessons on shapes.

Estimation Motivation. Overfill a water glass; assign extreme numbers of homework problems; let students out late for recess. When they question you, respond that you did not estimate before you planned.

Radish. Put a radish on each desk before students enter. Don’t tell them why, but challenge them to write down their ideas about how the radish relates to the lesson as the instruction proceeds. You can relate it to almost any lesson, such as a topic that begins with an R (ratio, rate, or radius) or an activity in addition or subtraction where students in groups combine and remove radishes to get sums or differences.

Strategy: Reinforce Achievable Challenge with “Friendly Numbers”

Most children enjoy the achievable challenge of video games and are intrigued when they see a person do math as quickly as it could be done by a calculator. An example would be a unit about “friendly numbers,” such as mentally adding 23 + 27 by changing the numbers to 20 + 30 to find the sum of 50. You can write the problem on the board while students use calculators to find the sum. While they punch in the numbers, you’d announce the solution before the answer comes up on their calculators. To prove that you didn’t just memorize that one problem, you can give the students a list of friendly number problems, and they can take turns selecting the one for you to do mentally while the class does it on their calculators. After the lesson, they can complete the list for class work or homework.

Students are motivated to learn how you were able to come up with the answer so quickly. Their primitive brains are curious, and this opens the gateway for them to want to learn what you have to teach.

Novelty and Attentive Focus

In an experiment to evaluate the influence of novelty on attention, subjects were shown a variety of photographs followed by a series of words to sort according to meaning. The next day, one group viewed new images and the control group viewed familiar ones. They were all then asked to recall as many words from the previous day’s list as they could. Recall was significantly better in the group that had just viewed new images. In the research team’s opinion, novelty seems to promote attention and memory. To improve memory, they suggested starting lessons with surprising new information before moving on to new instruction (Eriksen & Schultz, 1979).

Strategy: Build Curiosity and Positive anticipation

In addition to opening the RAS to new input, lessons that are punctuated with positive anticipation, curiosity, and evident connections to previous positive experiences also increase dopamine levels for pleasure, focus, and memory. Some approaches that serve this function make use of advertising techniques, discrepant events, and surprising calculation results.

Posters. Build curiosity about an upcoming lesson with posters giving hints about the topic—a form of “teaser” advertising. Students can write down their predictions and will enter the class with curiosity each day to see if you’ve added another clue. For example, a fraction lesson can be advertised with hints conveyed by pictures of an arm in a cast one day, an X-ray of a fractured arm a few days later, followed by sheet music with whole and half notes, and finally desks arranged in a new way (half on one side of the room, a quarter in another section of the room, and two-eighths in another section).

Discrepant Events. Start a class or unit with a demonstration that has an unexpected result or with a statement that is counter to students’ first intuition. This grabs their attention by creating cognitive dissonance, and their minds note a discrepancy between what they see or hear and what seems logical to them. From the students’ desire to clarify the disconnect— between what they think they know and information that doesn’t seem to fit with their prior knowledge—comes eagerness to move to a new, higher level of understanding. The following are some examples of discrepant events with instructional value.

Volume. Have students fill tall, thin containers with water or beans and then predict if all the water will fit if it is poured into a shorter container (which you selected because it has the same volume). Showing that a tall, thin glass tube can contain the same volume of water as a wide, shallow bowl can provoke the curiosity that motivates interest about perceptions of volume. You are providing a puzzling and interesting challenge and motivating focus when you tell students the explanation will come to them as they learn the day’s mathematical procedures and concepts.

Multiples. Pose this question to your students: Would you rather get one cent a week doubled every week starting now, or each week receive one dollar for every year of your age?

Fractions. Have students predict which is larger—half of a quarter of a pizza or a quarter of a half of a pizza. When they are then told the amounts are equal, you can connect their curiosity with a lesson about multiplying fractions.

Size and Mass. How many cotton balls will fit into a glass jar of water filled nearly to the brim before it overflows? Because students don’t realize that the balls are mostly air, many more fit than they predict.

Ratio and Proportion. How are we alike? How will the ratio of your height compared to the circumference of your head compare to the ratio of the same measurements of your classmates? You can use these questions to introduce the concept of the “golden ratio.”

Graphing for Prediction. Before a lesson on graphing on X- and Y-axes for prediction of a trend or rate, ask students how many drops of water will fit on top of a penny before water flows off the edge. The number will be larger than they expect because surface tension allows a dome to form. Ask them to see how many drops are held on a nickel and a quarter and graph the results to predict how many will fit on a half-dollar.

Circumference. Using the overhead projector to demonstrate, ask students what will happen if two quarters are placed flat, side by side, face up, and then one is rotated around the circumference of the other. (The quarters should be fairly new so that the edge ridges are not worn to keep them from slipping during the rotation.) Ask these questions: If the portraits on the two coins are facing in the same direction at the start, how will they be aligned at the end of one rotation? How many times will the portrait on the rotated coin go around in one rotation? Logic suggests that the portrait on the rotated quarter should go around once and end up in its original position after the rotation. After doing the activity, most students experience cognitive dissonance because what they thought was logical is not correct. The rotated quarter actually makes two complete rotations around the stationary one.

As these examples suggest, the success of discrepant events is evident when students are surprised and want to know why the event or calculation turned out not to match their expectations. Once you have students involved and interested, they are highly motivated to satisfy their extreme curiosity. Once again, they want to know what you have to teach! The value in all discrepant event activities is not to discover the phenomenon. The goal is to come up with valid reasons for why the event happens. Students do not learn by simply doing activities, but by thinking about what they discover.

In many discrepant-event activities, students can do a quick inquiry in small groups, starting with a plan that will provide evidence for the reason they predict. They then make observations, collect data, analyze results, make adjustments based on the results, and ultimately reach a conclusion that resolves the discrepant event and their previous misconceptions.

Strategy: Avoid Negative Reactions to the Unexpected

Lessons that include surprising phenomena or information can create a stimulating learning environment in which brain states of disequilibrium-prompted curiosity are strong learning motivators. Several considerations will help you avoid negative reactions to discrepant events.

Especially among young children who have unstable lives away from school, the unexpected can signal danger. Students whose common state of mind in math class is bewilderment may be pushed beyond their stress level with the added confusion of cognitive dissonance. If you anticipate these situations, consider preparing these students in advance with assurance that although something unusual or confusing will take place, it will not be bad; their classmates will also be confused and you will help them learn what it means.

Cognitive Dissonance

When students are aroused (but not distressed) by disequilibrium-prompted curiosity (i.e., cognitive dissonance), their RAS is alert for environmental and sensory cues that will restore equilibrium. They are attentive for information to solve problems or to understand the demonstrations that provoked their curiosity. They are motivated to follow the day’s lesson because they can’t evaluate the situation with the information they start with. This reaction is related to the primitive instinct of animals to evaluate change first for survival, then for potential pleasure in response to the unexpected in their environment. (An example would be a fox coming out of its den and seeing and feeling snow for the first time.)

In the brain, the amygdala is positively stimulated so it can transmit data efficiently from the sensory-response centers to the patterning and memory regions. The hippocampus, where relational memories are encoded, is primed to bring up any previously stored information that may potentially connect with the new data to bring a solution and restore equilibrium. In the hippocampus, if incoming sensory information differs from stored knowledge, it sends a pulse of dopamine to dopamine-holding regions of the brain stem. From these regions, nerve fibers extend back to the hippocampus and trigger the release of more dopamine. This feedback loop in response to novelty is why we remember things better when they appear in a novel context.

Plan to avoid quick fixes, such as students who understand the seeming incongruity announcing the explanation for the entire class. Use tools such as whiteboards so students have a way to let you know that they “know.” They can work with peers on an extension of the concept or develop their communication skills by working with students who remain confused even after the class has determined the explanation.

The goal of the cognitive conflict is not only to capture students’ attention, but also to promote critical thinking and build conceptual understanding. Instead of confirming or denying students’ explanations, ask questions or propose “what if ” scenarios to encourage students to arrive at explanations on their own.

Sustaining Motivation Throughout a Lesson and a Unit

Once you’ve grabbed students’ attention and used strategies to promote entry through the RAS of the sensory input related to the math lesson, you still need to sustain motivation for the remainder of the class period (as well as over the course of however many class periods the unit requires); you also need to keep stress down so information continues to get through the amygdala to the prefrontal cortex. Now is the time for strategies that relate lessons to topics and experiences that students find meaningful and relevant (connecting to prior knowledge), offer choices, use “syn-naps,” and incorporate physical movement into lessons.

Strategy: Make Connections Relevant to Your Students

Textbooks often start new units with a “real-world application” that may be interesting to a mature brain with neural circuits that have experienced pleasure from knowing the related math, but sometimes students cannot connect to the application. For example, students in math classes may love pizza, but perhaps they haven’t had experiences to establish the networks that directly link learning measurements of pizza ingredients with the pleasure of pizza. Thus, using a description of how to use measurements to make pizza will not be valued at the unconscious level of the RAS. Pizza is pleasurable to eat, but young students may have no pathway in their brains that directly links learning more math with the pleasure of pizza. That connection comes when they are older and the prefrontal cortex has matured to have enough top-down control to “tell” the RAS that the information about measurements involved in making pizza is valuable and will lead to pleasure.

Real-world connections to future jobs are also too remote to signal the RAS that the math knowledge is valuable at the “here-me-now” level at which the RAS works. It is unlikely, for example, that most students’ RAS cares if archeologists use scientific notation for carbon dating.

Your lesson openers will be the most successful when they connect with other parts of the unit and are perceived as invitations for students to enjoy a new, positive, personally valuable experience. Your opening is really a presentation to the RAS. The big picture needs to get through the primitive gatekeeper that gives priority to novelty, threat, and pleasure and that
sustains curiosity.

For young students, relevant real-world connections to estimation might include watching in surprise as you overfill a glass while talking to them. When they tell you that your water is spilling over, this is your chance to say, “Oh, I should have estimated how much water this glass would hold.” Students can then guess how much water different paper or plastic cups will hold before pouring water to check the accuracy of their estimates. After this exercise, have students brainstorm a list of things that are important to estimate, such as doses of medicine or equal shares of water when it is scarce.

Strategy: Use Openings That Sustain Curiosity

Consider big opening questions, surprising facts, media presentations, meaningful current event connections, or guest speakers who can relate the topic to the “here-me-now” level of students’ primitive brain filters. These connections need to be very obvious so the value of the upcoming math is directly linked to the prediction of imminent pleasure. Once students are “hooked” on a topic, they will be motivated to listen, participate, and learn for the duration of the lesson and the unit.

Your own learning outcome or goal for the unit is usually to add to foundational knowledge and help students make new connections and extensions to their core math concepts. This outcome is part of your big picture for the school year. Keep in mind that to succeed at that goal, your opening is the time to prime students’ motivation and build enthusiasm for activities you’ve planned to appeal to their varied learning strengths and interests. Once you have the students engaged, you can build on the positive connections and curiosity you ignite to achieve your goal successfully with your motivated students.

In your planning, consider what you most want students to know and then work backward to develop an opening that promotes sustained interest toward that goal. If possible, represent the unit in several different ways that appeal to different learning strengths and levels of achievable challenge so you can continually engage all students.

Here are some fascinating facts you can use as “big openings” with your students to help them with number sense, specifically with understanding large numbers:

One billion seconds is almost 32 years.
One billion eye blinks (each eye counted separately) occur during an average human lifetime.
One billion grains of salt fill a bathtub.
One billion words are heard and read during a lifetime.
Three billion heartbeats occur during an average lifetime.

The following suggestions are additional strategies to open a lesson in a way that sustains curiosity.

Big-Picture Previews. Initial big-picture connections to a new topic activate prior knowledge, stimulate personal interest, demonstrate real-world “here-me-now” value, and guide students to develop personal goals that will keep them connected to the content. Students will show that they are authentically engaged when they start making personal connections and asking questions.

Before a lesson on negative numbers, bring in different objects that relate to negative numbers, such as a thermometer, a photo of a ship above and below water, a SCUBA tank (or a photo of a SCUBA diver), a checking account register, or stock market quotes. Students begin by considering what the items have in common and move to the idea that things can be “less than one.” This will develop an interest in the topics you’ll teach as students connect with the goal of learning about negative numbers. The multiple big-picture items can then serve as opportunities for students to choose personal reasons why they would consider negative numbers useful.

Engaging Opening Questions. Questions that engage curiosity and interest can be great openers. The best questions for sustaining interest are planned to help students discover the big idea of the unit; they compel students to seek answers as you help guide them in the search. These are questions that can’t be answered without the information you need to teach, but they are interesting enough that students stay alert for clues that bring them closer to an answer as the unit progresses.

For example, to lead a lesson about fractions, ask younger students, “Are there any numbers that are more than 0 but less than 1?” Older students are naturally curious about questions that seem illogical or impossible. Therefore, you can begin a lesson on fraction multiplication with the question “Can you make numbers smaller by multiplying them?”

Another benefit of curiosity-provoking questions is to build students’ perseverance through longer and more challenging uncertainties. A 3-year-old child doesn’t have the executive function of delay of immediate gratification to wait until the end of his or her birthday party to open the gifts, but as children get older, they usually enjoy the anticipation of seeing the gifts displayed and increase in number because they have experienced the pleasure of positive expectation and the reward of opening all their gifts at once.

Strategy: Create Unit Titles

Instead of using the unit title from the textbook, have your students work in small groups to think of and nominate unit titles every few days. At the end of the unit, they can vote on a class title or select the one they prefer for their own journals. Discussing possible titles activates prior knowledge, reinforces big ideas, and increases the connections between new information and stored memory as neural networks grow.

Near the conclusion of the unit, to further reinforce newly embedded learning, students can choose to keep their identified titles or change them. Then, for the positive motivation that accompanies choice, students can write a paragraph, song, or poem or draw sketches to communicate why the title suits the big idea of the unit. The final unit title, similar to an analogy, builds a connecting bridge for future access to the stored memory when the students want to retrieve the knowledge.

Strategy: Use Syn-naps to Maintain Motivation

We know that synapses are the gaps between neurons in the brain. What I call “syn-naps” are brain breaks that restore neurotransmitters depleted when the same neural circuit is used for extended periods (as few as 5 to 10 minutes for lower-elementary students). They also keep the amygdala from getting overstressed. It is not surprising that students need these syn-naps
more frequently during math than during most other subjects. During these breaks, the newly learned material has the opportunity to go beyond working memory to be consolidated into relational memory in the hippocampus while students replenish their supply of neurotransmitters in one circuit and use another neural pathway for a new activity.

The syn-naps offer an opportunity to regain students’ wandering attention because they involve a change of some sort (type of activity, new partner, movement), but these three- to five-minute brain breaks do not need to disrupt the flow of learning. Sometimes syn-naps can be as simple and brief as singing a math song or hearing a math joke while students stretch or get a drink of water.

Highly Focused Students and ADHD Students

Sometimes stopping for needed breaks is particularly difficult for students who are very intense in their focus or highly interested and invested in an activity. Just as artists in the midst of painting or athletes and actors in the “zone” of peak performance may disregard their bodies’ cues to eat or sleep, students engaged in their cognitive “zones” need your guidance before dopamine and serotonin depletion leads to frustration and even anger.

On the other hand, some students with attention deficit hyperactivity disorder (ADHD) have limited reserves of neurotransmitters to maintain focus and may experience the decreased cognitive efficiency of mental fatigue even sooner than their classmates.

When selecting an activity for longer syn-naps, consider math games that are fun and competitive but safe, so students will feel comfortable playing (lowering amygdala stress) and want to play again (inducing dopamine pleasure). Other kinds of syn-naps activities may continue with the same math topic but use a different neural-processing system, such as providing different sensory input when you go from discussion to manipulatives, from individual to group work, or from a demonstration to a workstation activity. The following are examples of various syn-naps activities.

Buzz. An example of a low-stress, win-win game is Prime Number Buzz. Students stand in a circle or at their desks and go around the room in order, saying either the next sequential number if it is a composite or “buzz” if it is a prime. If they are incorrect, they sit down, but they keep listening and when they catch another student’s error, they stand up and rejoin the game. (The same game format works for Multiples Buzz, using multiples of, for example, 3, 4, and so on.)

Telephone. This is a variation of the perennially popular Whisper Down the Lane. Students line up in two teams and play with a math vocabulary word and definition. The last person in each line recites the words she heard, and the team closest to the correct original definition wins the point.

Commercials. Students work in small groups to create a commercial to advertise a math “product” by showing why it is valuable. For example, if they choose to sell the operation of division, their advertisement would promote the value of division. “Have you ever had 10 cookies to share with 5 friends? If you buy our product called ‘division,’ you’ll be able to figure out how many cookies to give each person so everyone gets a fair share.”

Pick a Card. This activity uses two identical decks of cards, each containing a number of cards equal to the number of students in the class. Deal out one deck of cards (one card to each student) and keep the other deck. Ask a math question and then pick a card from your deck. The student with the matching card answers the question; if this student doesn’t know the answer, he or she consults a “team member” (another student with a red or black card, or one who has a card of the same suit) who volunteers to help him or her answer. When doing this activity, more students actively think if you ask the question before selecting the card that designates who will give the answer. Selecting the card first might stop others from thinking about the answer because they know they do not have the matching card.

Who’s Who in Math. Students give a short biography of a mathematician or teach a minilesson they prepare and share with the class.

Code Breaking. This activity provides practice in finding patterns. Examples such as “S M T W T F S” (first letter of the days of the week) are available in math activity books.

Strategy: Add Movement to Syn-naps

Dopamine, serotonin, and norepinepherine—neurotransmitters that affect focus, memory, and mood—increase with exercise. Students evaluated on standardized tests taken after moderate exercise were more successful than students who took tests after 20 minutes of sitting still (Hillman et al., 2009). Because movement is another RAS-alerting stimulus, you can incorporate movement in several ways to keep students on track.

Brain Shake-up. Toss a ball (I use a rubber brain ball available through brain-toy Web sites) from student to student for math review. The student who catches the ball says something he or she remembers from the just-concluded discussion or comments about what message he or she got from a guest speaker. Another option is for the student who tosses the ball to ask the receiver an appropriate mental math question. To adapt this to a class with very diverse levels of math students, classmates can play on teams standing on opposite sides of the room. The receiver can have the option of asking a team member for help, but the receiver must ultimately give the answer. Alternatively, each receiver can request a Level 1, 2, or 3 question for a suitable, realistic challenge. You can help the questioner adapt the question so that it is appropriate for the chosen receiver.

Have I Got Something to Tell You! Students are given note cards with math-review information, such as a multiplication fact or, for older students, a procedure to explain, for example, “When subtracting a positive integer, the answer comes from moving to the left on a number line.” Students then walk around the room and share their math facts or explain their procedures to several classmates. If students are unclear about their particular math facts or procedures, give them another card or encourage them to ask for help. The listener repeats the fact or reasoning (in his or her own words) before the students switch roles and repeat the process. The cards can be saved and used another day, with students receiving different cards each time. To keep track of which cards they have had, students can write their initials on the cards they use.

Simon Says. This game is easily adapted for math instruction. For example, you can tell students, “Make an acute angle with your arms” or “Make a semicircle with your fingers.”

And in This Corner… Students move to different corners of the room in response to questions. For example, ask, “What kind of angle is this?” Students would then move to Corner 1 if the angle displayed is acute, Corner 2 for a right angle, Corner 3 for an obtuse angle, and Corner 4 for uncertain. The uncertain students can then walk over to classmates in the other corners and ask for their reasons until they decide which is the correct answer.

We’ve Got Something in Common. Students stand up and meet with two different classmates and try to find something they have in common, such as names with six or more letters, a birthday on a date that is a multiple of 5, or three or more colors in their shirts. Another movement option has students read and explain their “dend-writes” (summary of the previous day’s math lesson), listen to their partners, then add missing information to their own summaries before finding another partner and repeating the process.

I’m No Ordinary Zero. The Human Place Value unit from the Surescore/ MARS Math series of math activities uses a Human Place Value Chart you make by dividing a piece of butcher paper the length of the classroom into 14 sections (or fewer for lower grades). Label each section, starting from the left side: ten billions, billions, hundred millions, and so on, down to tens, ones, tenths, and hundredths. Make sure you include a decimal point between the “ones” and “tenths” sections. After students review place value concepts, such as each section of the chart being equal to ten times the section to its right and one-tenth of the section to its left, have them name each section and discuss patterns they see in the names, such as what they notice about the place value names to the left and right of the decimal.

Students create numbers by standing on the chart to determine if a number is greater than, less than, or equal to another. Give each student an index card and have them all write a number between 0 and 9. Starting with numbers to the left of the decimal point, have four students arrange themselves on the chart in the largest whole number possible using their cards. They return to their seats and another group of four students arrange themselves in the smallest number possible. The whole class should write down the numbers that are formed. Students then write on their whiteboards or hold up fingers in a horizontal V to represent a “greater than” or “less than” sign. You write the correct answer on the board using the appropriate symbols and the comparison of the numbers, such as 4,560 > 1,230.

When students are ready to progress, explain that they will make numbers starting from the tens place and lining up to the right, so they will make a number with a decimal point. The first four students make the largest number they can using the two decimal places, and the next students assemble themselves to represent the smallest possible number following the same placement rule. Again, students write their answers and compare them to the correct answer you write on the board.

For an additional level of challenge, instruct each group to stand to the right of the decimal point, extending the line beyond the hundredths place. Help the class read the new decimal number. Make numbers with more and more places to the right of the decimal, name them, and continue to play the game with students lining up at the designated starting point and forming themselves into the largest and smallest arrangements while the class determines which number is “greater than” another, using the place value chart.

Larger numbers can be done by including more students standing on the number line and making numbers in the billions place as the remaining class members write the number numerically and in word form.

A challenge extension is to ask students if (and why) someone holding a zero in one place on the line has a different value than someone holding a zero in another place on the line. What about zeros after the last number
following the decimal?

A Matter of Perspective. Change the location of teaching to refresh students’ learning perspective. Move to a different side of the room to teach; when you walk around the class, have students turn their heads and torsos to see you. They now have a changed visual background—they see behind you for added input that will alert the RAS.

Alternatively, go outdoors for a math lesson if possible. Use chalk to draw giant graphs of coordinate planes and have students walk to the spot you assign them by giving them the coordinates of the point. Take students on a walk to study from a different point of view. Look for geometric shapes in buildings, nature, sidewalks, and signs. Challenge older students to use their heights and the lengths of their shadows to calculate the height of a tree or flagpole based on its shadow.

Maintaining Motivation

As should be clear by now, motivation is an ongoing concern. Student attention needs to be grabbed from the outset, sustained throughout a lesson, and maintained throughout a unit. To stay motivated, students need continual reinforcement. Here are a few more ideas for keeping your students motivated:

Periodically remind students that their mental effort is relevant to pleasure in the near future. The younger the children, the less tolerant their brains are to activities that are not pleasurable now or expected to be so in the very near future. Fortunately, the dopamine-reward network releases motivating dopamine in expectation of pleasure. Let students know which of their enjoyable math activities will be coming up during the lesson and how what they are practicing now connects to the desirable activity. The dopamine release gives you the time you need to work with students on procedures and facts that must be understood for them to build a math foundation, such as multiplication tables or place-value names.
Periodically ask questions and encourage opinions and predictions related to the big picture, the big question, or the discrepant event that started the lesson to renew students’ curiosity. Start with questions that are within all students’ achievable-challenge range so they experience the pleasure of success. Ask questions that don’t call for a specific answer, such as, “How can you find the sum of…?” or “Who can explain why 6 + 7 = 13?” or “What would you do to figure out how many students there are in all three 5th grade classes?”
Use frequent informal assessment with whiteboards and active participation such as gesture responses that are fun to signify yes or no (e.g., pat your head and rub your tummy, spin to the right or left, make a butterfly or bunny ears with your hands). These activities maintain attention and can help correct misconceptions.
Purposely make a mistake to see if students are paying attention. As you count aloud by ones or multiples, have students make a thumbs-up when they hear you repeat or skip one (this activity increases listening skills and reduces mistake negativity). Make an obvious mistake during a lesson to see if students are paying attention.
Use a magic word of the day. Your students are too young to know the Groucho Marx quiz show, but a recurring gag was Groucho’s secret word of the day. If one of the contestants said the word in conversation, they would win an extra prize. In some of my lessons, I tell (auditory) and write (visual) the magic word of the day. Instead of saying it to win, the person who first puts a finger on his or her nose when I use the word during class is the winner.

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Over time, you’ll add to these suggestions with many of your own ideas for motivating students. The results you’ll see in terms of attentive students who are eager to learn will, in turn, motivate you. It’s a win-win situation.

When students come to your class with math negativity, expressed as boredom, disruptive behavior, low effort, or resistance to applying effort, you have the opportunity to change much more than their math success. Because such a high premium is placed on math achievement, students understandably correlate their low performance with their academic abilities in general. If you help them connect to math through their interests, curiosity, and appropriate level of achievable challenge, and if you help them recognize that their efforts to reach achievable goals are bringing them closer to success, then you plant the seeds of hope.

This is when you see the gradual change from the stress of hopelessness and helplessness to the mind-set of the possible. These are the students you successfully set back on paths where they once joyfully counted aloud to all who would listen!