When a President Speaks: 6 Reasons to Object to Objectors

I remember President Kennedy urging us kids to be physically fit, and the national president's fitness program that went with it. Anybody else out there earn a Presidential Fitness Award while they were in school? In fact, the program has followed us into adulthood.

Another president is planning to give a speech to school children urging fitness of another kind, educational fitness.

During this special address, the president will speak directly to the nation’s children and youth about persisting and succeeding in school. The president will challenge students to work hard, set educational goals, and take responsibility for their learning.

Why the furor?


Because of the breathtaking opposition.

Unbelievable. Maybe there is no grand tradition, but presidents have addressed remarks to schoolchildren from time to time. Ronald Reagan in 1986, George H.W. Bush in 1991, George W. Bush in 2001.

My problems with all this hullabaloo:

First, the objections are premature. It is silly to object to figments of the imagination. Wait till the president actually says something objectionable in the speech before objecting to it.

Second, the objections break the Golden Rule. In the nutshell, the right is worried that the president may voice a tenet or two of liberalism. I have trouble believing they would object to a Republican president voicing a tenet or two of conservatism. I am not letting the left off easy; they will violate the Good-for-Goose-Good-for-Gander principle when it suits them as often as the right does. As Shakespeare might say, “A pox on both their houses.”

Third, the objections are largely ad hominem. The objections are not criticizing the speech on its merits (probably because the speech has yet to be broadcast). Ad hominem is one of the defining marks of lack of critical thinking. What a lousy role model to set before our kids.

Fourth, the objections are misplaced. Edweek reports that White House efforts to quell the furor have been ineffective.

But the planned 15- to 20-minute noontime speech—and, especially, a menu of classroom activities (for younger and older students) suggested by the White House in connection with it—continued to draw denunciations...

Especially?! I looked at the “menu of classroom activities.” The White House's companion lesson ideas for elementary students and secondary students have no leading questions and emphasize strategies for comprehension. The secondary lesson plans ask students to create a specific action plan for meeting their goals. Maybe it is about time we adults directly ask students what they want, and then find specific ways to help them, instead of creating burdens for students in the name of reform.

Fifth, the objections are politically-motivated disturbance in the guise of concern for our children.

Finally, sixth, and perhaps most importantly, whatever happened to free speech?

Amendment I
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech (bold added) , or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.

What have we come to when a subset of the public maintain foul language is protected speech, and a subset of the public agitate to pre-censure the freedom of the President of the United States to encourage students to study hard and stay in school? Even stranger is that both subsets very likely contain many of the same members.

The White House has a video of the President's speech here.

Place Value Part 4: Geometry of Place Value

So far we have completed three parts of the place value series:

Part 1: The Chocolate Factory which covered the regrouping or trading aspect of place value and explored regrouping in base ten and other bases.

Part 2: Base Ten for Young Students which introduced several games and trading activities to help young children acquire a solid foundation in place value.

Part 3: The Bake Sale demonstrates the role of place value in long division.

Today, Part 4: Geometry of Place Value will explore place value within a quadratic equation. We will further show that each monomial can be modeled geometrically.


Review

The expression, 5x² + 6x + 3, appeared in The Chocolate Factory, as a summary of the chocolate packing activity. Five cases and six boxes were packed with three leftover chocolates. Where x stood for the number of chocolates per box, five cases and six boxes could represent different absolute numbers of chocolates. If x =10, or 10 chocolates per box, then ((5 times 100) + (6 times 10) + 3) chocolates, or 563 chocolates came down the conveyor belt, I Love Lucy style. In fact, this episode of I Love Lucy was the inspiration for the math activity.

If the chocolates are packed in boxes of five then the 563 means ((5 times 25) + (6 times 5) + 3) or 158 chocolates came down the conveyor belt. So a quadratic equation can be thought of as an expression of place value in any base. In fact, a polynomial of any degree can be seen as an expression of place value. Missing terms are represented by zeros. So 2x⁶ + 5x⁵+ 3x² + 7x + 2 would be 2,500,372_{base x}.

Now we can see where the analogy to place value breaks down. If x = 6, then a term like 7x would be “illegal.” Once six “boxes” had been packed, those six boxes would immediately be packed into one “case,” so in base 6 the last three terms would properly be 4x² + x + 2, either way, the last three terms represent 152 “chocolates.” Obviously I have just been speaking to adults initiated into the joys of algebra, not children.

What? No Fourth Dimension

Obviously you can use standard base ten blocks to model quadratic equations. If we assume that x represents base 10, for 4x³ + 3x² + 7x + 2, we would use 4 large cubes, 3 flats, 2 rods, and 2 small cubes to model the expression. However, if all I meant by geometry was geometric solids, I would not have meant much. The geometry is more interesting, and becomes clearer when you look at a set of blocks in a different base, say, base 5, the small cube looks the same as a base ten small cube, but the rod is five cubes long, the flat is a square of 25 cubes, the large cube is 5 flats stacked or 125 cubes.

So the rod of any set of base blocks determines the base of the set. If we look at the large cube of any base, we see that any one of the 12 edges shows x¹, the first dimension, any one of the six faces shows x², the second dimension, and the whole cube shows x³, all three dimensions. Now we run smack into a physical limitation of manipulatives; not one can show more than three dimensions. The power of math is that math is the language of imagination. We can imagine a fourth dimension, x⁴ and beyond, even if we cannot model it. How fun is that?

Interestingly, we can also show x⁰ on the cube. Remember for any x, x⁰ = 1. Cubes of varying bases are all different sizes, or volume. The x¹, x², and x³ is different on each cube. But since x⁰ = 1 for any base, it stands to reason that x⁰ or 1 would have an identical appearance no matter the size of the cube. In fact, it does. You can find x⁰ at any vertex, that is to say, the corner shows 1, the zero-th dimension, if you will. In fact, the vertex is a geometric point, described as having no length, width or height.

Multiplication with Base Ten Blocks

So far we have spent a great deal of time establishing that x² means x times x, and that we can show x times x geometrically, by using a flat from a base block set. The flat has a square shape which we would expect from an expression like x-squared. But let's consider a rectangle shape. Now we are not multiplying the same number by itself, x times x, the very definition of squaring, “the product obtained when a number or quantity is multiplied by itself”.

With a rectangle, we are multiplying two different numbers, x times y (or length times width, the formula for the area of a rectangle). Using the cubes from a base blocks set, we can model 5 x 3.






Math educators call this type of diagram a multiplication array. Now lets try 13 x 11.





To show the factor 13 along the top, I used a rod and three small cubes. The factor 11 is along the side with a rod and one small cube. One rod times one rod equals one flat (square, and you expected a square, right?), one rod times three small cubes equals three rods or three lengths. Then, one small cube times one rod equals one length, and one small cube times three small cubes equals three small cubes.

Combining like terms, that is, similar objects, together, we have one flat (10² or 100), four rods ((3 times 10) + (1 times 10)) or 40, and three small cubes (1 times 3, or 3) for a total of 143 which I could express as(1 x 10²) + (4 x 10) + (3 x 1) .

What if we wanted to multiply (x+3)(x+1). I am using the magenta to stand for x, a number we don't know, also called a variable.




The product is 1x² + 4x +3, and geometrically, the product is the picture of a quadratic equation showing both its factors above and to the left of the crossbars. I recommend manipulatives that elucidate the geometry of quadratic equations, available, for example, the Montessori Binomial Cube and Creative Publications Algebra Lab Gear. Remember we have shown that the magenta rod could stand for any value, that is, for any base.

We can show three factors and therefore three dimensions with the same model by standing a rod and/or stacking small cubes vertically in the corner where the crossbars intersect. If I were to stack four small cubes in that intersection, I would be modeling (4)(x+3)(x+1) or by multiplying the x-factors first, (4)(x² + 4x +3). You could think of it as stacking four layers of the x-factor product. In fact, the formula for volume is height times base, or height layers of the base.

In terms of base blocks, the product would be modeled with 4 flats, 16 rods, and 12 small cubes. If we are working in base ten, we would have 400 + 160 + 12. We can exchange 10 of the rods for a flat, and 10 of the small cubes for a rod, ending up with 5 flats, 7 rods, and 2 small cubes or 572.

If I were to stand a rod in the intersection, I am modeling 10 layers of 143 or 1430. In the upper left hand corner of the product there would be ten flats stacked which I can exchange for a large cube worth 10x10x10. Completing any other exchanges, the product would consist of 1 large cube, 4 flats, 3 rods and 0 small cubes. If I were to stand a magenta rod in that intersection. I would be modeling (x)(x+3)(x+1). The product would have 1 magenta cube, 4 magenta flats, 3 magenta rods and 0 small cubes or x³ + 4x² + 3x.

The Candle Problem: How to Damage Motivation

Herbert Kohl says we are missing the boat, motivation wise, in an open letter to Arne Duncan, Secretary of Education.

Now the mantra is high expectations and high standards. Yet, with all that zeal to produce measurable learning outcomes we have lost sight of the essential motivations to learn that moved my students. Recently I asked a number of elementary school students what they were learning about and the reactions were consistently, “We are learning how to do good on the tests.” They did not say they were learning to read.

Mr. Kohl sees a fundamental contradiction between what we say we want and what we are doing to get it.

It is hard for me to understand how educators can claim that they are creating high standards when the substance and content of learning is reduced to the mechanical task of getting a correct answer on a manufactured test.

What, for Mr. Kohl, motivates learning, at least for learning to read?

...reading is a tool, an instrument that is used for pleasure and for the acquisition of knowledge and information about the way the world works. The mastery of complex reading skills develops as students grapple with ideas, learn to understand plot and character, and develop and articulate opinions on literature.

Nowhere does Mr. Kohl mention extrinsic rewards. Teachers have observed, and Robert Slavin's research has confirmed the dissipating effect of extrinsic rewards.

Robert Slavin's position--that extrinsic rewards promote student motivation and learning--may be valid within the context of a "facts-and-skills" curriculum. However, extrinsic rewards are unnecessary when schools offer engaging learning activities; programs addressing social, ethical, and cognitive development; and a supportive environment.

Not only do extrinsic rewards fail to motivate, except in limited cases, but research has also found that extrinsic rewards actually sabotage motivation.



So what's with the ubiquitous classroom token economies? Why must teachers have jars ofmarbleson their desks? Are we deliberately sacrificing long-term learning benefits for short-term classroom management? How about pay-for-performance or merit pay? First. And foundationally, EVERYONE deserves to be paid FAIRLY. “Getting the issue of money off the table,” as Dan Pink says.

If our society want to motivate the highest performance from teachers, then give them:

Autonomy
Mastery
Purpose

NOT merit pay.

Merit pay is inherently unfair. The bug-a-boo with merit pay is that teachers have so little control over the factors that impact student achievement. What do we say, for example, about the student who actually scored worse after his first year with me only to leapfrog three grades the second year with me.  Should I have lost pay the first year?  I was still the same great teacher.  I had no idea his alcoholic uncle moved in with him and his mom that first year. What do you do if you are a great teacher in an environment where just about everything seems to be conspiring against the kids? And what if you are lucky enough to teach in a school where kids have all kinds of advantages and their scores show it regardless of who is their teacher? Policy-makers have not figured out any equitable mechanism for awarding merit pay.

Western Education has the Wrong Mindset

Science educators know full well that school textbooks lag at least a generation behind the times. Teachers who do not take the initiative to independently keep up and supplement the textbook with current information are teaching possibly out-of-date stuff. Sad to say, the vast majority of teachers teach the book, especially at the lower grades where the lifetime foundations for critical thinking are laid.

Hans Rosling, a professor of public health, in a presentation to the US State Department, marvels that the Western world is a generation behind in its understanding of the global situation, especially regarding the developing world.

My problem is that the worldview of my students corresponds to the reality in the world the year their teachers were born.

In Dr. Rosling's words, “Their mindset does not match the data set.”

We have a world that cannot be looked upon as divided.
...snip...
The world is converging.

We have completely misunderstood the HIV “epidemic.”

There is no such thing as an HIV epidemic in Africa...It's not war...It's not economy...Don't make it Africa. Don't make it a race issue. Make it a local issue and do (appropriate) preventative approaches.

Dr. Rosling has made his data presentation software available for free at Gapminder.

I Love Eureka! Physics

Here is a complete episode guide.

It is pretty expensive to purchase the entire series. Here is one source.

Here are a handful of the first episodes:

Episode 1-Inertia




Episode 2-Mass



Episode 3-Speed



Episode 4-Acceleration Part 1



Episode 5-Acceleration Part 2



Here is a video player.

Enjoy.

The New School House Rock

Give a listen to Georgia teacher, Crystal Huau Mills, her students and friends performing their version of Grammar: the Musical, entitled Grammar Jammer, available on DVD.
Crustal Huau Mills wrote the lyrics and her friend, Bryan Shaw, put them to music. When they were all done, they had thirteen songs.

The teacher, who is played by Crystal, falls into a dream world where her class and some of her co-workers are transformed. Many of the normal classroom objects come to life to help her reinforce the underlying lesson behind each song. The clock, the flag, the globe, a crayon, the computer, the ruler, her class pet, a goldfish as well as the dictionary all spring to life to help her teach the class.

The New School Year: My Top Ten To-do

Number 10. Go through your closet and get your own school clothes ready to go. Update or accessorize your outfits. I know I did not like wasting time trying to figure out what to wear, or discovering at the last moment I had forgotten to dryclean or mend something.

Number 9. Get to know those important unsung heroes, the backbone, of the school. The janitor, school secretary, librarian, the cafeteria ladies, the recess monitors, the school nurse.

Number 8. Figure out your rules and consequences for violation. Have a behavior management system in place. Make sure your rules and consequences are compatible with school policies and the general practices of other teachers. Talk to other teachers early to shut down efforts by students to play teachers off each other before it has a chance to begin.

Number 7. Rehearse routines with students every day until following the routines is automatic. Think about: how do I want students to enter the room and record their tardies? Do I want a student monitor to help me with roll, leading the pledge of allegiance, lunch money collection, other? What is the procedure for turning in homework? How should they set up their desks for start of class. When are pencils to be sharpened? Bathroom procedures? Papers for absent students? What kind of behavior do I expect when there is a substitute? Make sure EVERYTHING is spelled out so that they know exactly what to expect.

“Design some method to manage and keep track of daily paperwork -- especially for absent students. If you have all of your students regularly asking you for their work, you’ll lose your mind. There are so many options out there. My favorite is to have a hanging folder for each student in every class. If I pass out papers, the student at the front of the row is responsible for filing the handouts for every absent student in the appropriate folder. When the student returns they know they can look in their folder for all their work.”

Number 6. Communicate with parents before school starts.

“You can start communication with parents before the first day of school. Teachers can call home to welcome students and talk to the parents before school starts. I like to send postcards to new students introducing myself. Other teachers hold special class events such as class picnics in the park or an ice cream social before the first day. An opening letter from you on the first day of school is a wonderful way to introduce yourself to the families you will work with. Along with the letter, I also send home a family survey. The data gathered provides insight and invaluable information about my students and families right from the start. Here are some things I include in my family survey:

• What languages are spoken at home?
• Is there someone to help your child with homework?
• Emergency phone numbers, emails, updated address
• Food allergies/Health issues/Diet
• Celebrations and Cultural Awareness
• Child’s Strengths
• Special Needs
• Interests and Talents (parents love this)
• Areas of Concerns, if any
• Expectations for the year
• Questions”

I also plan for open house. I like the custom of Japanese teachers who visit the homes of every student. Take a little gift with you, maybe something the students can use in your class. Oriental Trading has tons of ideas. I like these crayon-shaped erasers.

Number 5. Write a week's worth of lesson plans for the substitute teacher BEFORE you are so sick you cannot even lift your head. I like to base my substitute teacher plans on that last “optional” chapter of the textbook, the one no one ever gets to. As a hands-on science teacher, I preferred to interrupt my regular lessons over burdening a substitute with overseeing an experiment.

Number 4. Plan your first day of class. Start out with an engaging activity that also provides students with a chance to learn and practice something to help them be successful during the year. I had my students to a simple experiment on the first day as a vehicle for teaching them lab rules and procedures in an interesting way.

Number 3. Find another teacher, whether in your grade level or field or not, to partner with, peer mentor each other, and integrate materials. You may want to integrate with more than one teacher at your grade level and with teachers in other grades.

Examples of multi-grade integration suitable for k-8 schools:
Have students create some sort of science teaching aid, like paper models of body systems, and use their teaching aid to teach younger students in another grade. Or invite a younger class to be lab partners with middle school students for a class period.

Examples of within-grade integration suitable for a middle or high school:
Coordinate spelling words with the English teacher. In my case, a word like “hypothesis” might be an extra credit word. Or combine assignments, so that a lab report written in my class get graded for data analysis and conclusions, but the same report gets graded in English class for English mechanics. Or coordinate with the math teacher to teach the metric system in math class at the same time the science teacher is teaching the metric system for gathering quantitative data.

Number 2. Get your supplemental materials together for the first unit, and make a list of the supplemental materials for subsequent units. Put a note on your calendar about a week or so before the end of a unit to remind yourself to gather the listed materials together for the next unit.

Number 1. Know your material, Read over your curriculum several times. Write out a scope and sequence for the entire year. Invariably you will make adjustments as the year progresses, but you will be able to prevent becoming bogged down if you keep an eye on the destination.

Finally, do something nice for yourself.