I suppose they have a good reason but, really, why are they mad? I have never thought about the lives of ants and what might disappoint them or discourage them or disgust them, let alone make them mad. Before I go any farther I better explain what has caused me to contemplate this question.
The National Basketball Association (NBA) has their own minor league group of teams. Fourteen teams across the USA play in something called the NBA Development League, commonly abbreviated as the NBA D-League. This league is designed to give basketball players, who are not quite able to make an NBA roster, a chance to develop their skills and to mature into professional basketball players. Since this league does not have a long history, the teams tend to have fairly original nicknames. Often there is a contest in which members of the community are asked to submit their suggestions for what the team nickname should be. One of the new teams in the league this year is located in Des Moines and plays home games at Wells Fargo Arena. They are called the Iowa Energy. That's a nickname designed to take advantage of Iowa's role in ethanol and other alternative sources of energy (I think). The other nicknames in the league are “Thunderbirds”, “Arsenal”, “Toros”, “Jam”, “14ers”, “Wizards”, “Stampede”, “D-Fenders”, “Vipers”, “Skyforce”, “66ers”, and “Flash”,
Recently on Mediacom (cable television) I saw part of an Iowa Energy game in which they played the Ft. Wayne Mad Ants. That nickname caught my attention right away. The logo they have is probably supposed to represent a “Mad Ant” but it wasn't real clear to me. Anyway, this nickname prompted some questions in my mind: Why are those ants mad? Do they live in a state of perpetual madness? Are all ants mad or just some of them? Are there happy ants? Does “mad” mean crazy insane or is it the type of “mad” that means bitterly upset? Is this madness directed to other ants, to human beings or anybody or anything else? Are there ant psychologists available to help these ants recover from their madness?
I have to admit that about the only contact I have with ants is when I crush them with my foot. They might be crawling over a picnic lunch or just meandering down a sidewalk and I admit that my taking of their life is pretty thoughtless on my part. Come to think of it, that might be one of the reasons why they are so mad. If your life could suddenly and unexpectedly be ended by some thoughtless being, thousands of times larger than you, you might be pretty disillusioned too. How many times might you have had one of your family or friends leave home one day and never come back? Why make any plans for the future? Why have children you might not be able to care for? Why even leave your home “hill” when you might never come back? In fact, why even build that hill when some snotty little human being may come along and gleefully destroy it? Can anybody blame ants for having to attend human picnics to get some food for themselves and their families? It really seems that ants might very well consider themselves, not second class world citizens, but maybe fifty-second class. As far as I can tell, they are the Rodney Dangerfield of the world's living beings. They get no respect.
Well, all frivolity (using the term loosely) aside, I did my homework. I wanted to find out how this basketball team from Ft. Wayne Indiana had decided on this particular nickname. As I mentioned before, the officials of the team had conducted a community contest. The name, “Mad Ants” was an easy winner (“Fire”, “Coyotes”, and “Lightning” were the next three in the voting). It was in reference to General “Mad” Anthony Wayne (1745-1796), a US Army General and statesman whose Revolutionary War triumphs and fiery personality had earned him the title, “Mad Anthony”. The town of Fort Wayne Indiana is named after him, as well as many, many other places across the USA including Wayne State College in Nebraska. So, all in all, I have to say that the team did pick a very creative nickname that does reference its community's past as well as reference triumph in battle. However that last part might be not taking hold right now – the Mad Ants are currently in last place in their division in the D-League (something else to be mad at ?).
One final thing that some people might find maddening. All of these teams have their cheerleader dance teams. In Ft. Wayne it is called the “Madame Ants Dance Team.” Ouch.
Monday, January 28, 2008
Thursday, January 24, 2008
Struggle is Good
STRUGGLE IS GOOD
The above statement might seem a little surprising but allow me to explain. If you know me, you know the explanation will be pretty long! In the January 21, 2008 edition of Sports Illustrated (Brett Favre, in the snow, on the cover), there is an article on basketball coach Rick Majerus. He has been a highly successful college basketball coach over the years, known primarily for taking the University of Utah to the national championship game in 1998 against Kentucky and his great sense of humor. Because of his health and other reasons, Majerus was out of coaching (doing analysis on TV instead) for the past few years. He got back into coaching this season with the Saint Louis University basketball team. The article is an interesting one even if you aren't a sports fan. Here is a link to it.
I don't agree or advocate all of the things that Coach Majerus does with his teams (which doesn't mean that those things are wrong for him) but he made an interesting statement in the magazine article. He said, “Parents today want to take all the pain, all the heartache and sadness, out of their kids' lives. All the things that make you a better person.” That particular statement reminded me of one of the philosophical underpinnings of my teaching career. This was something that developed over several years of teaching and seeing how kids react to certain situations and also having former students come back to talk to me after moving on to high school, college, or adulthood. In essence, one of the things they most appreciated about my class was that it was demanding and it caused them to develop better study habits and to have a greater sense of accomplishment when they succeeded. In other words, the students felt more pride in getting a good grade in a demanding course than getting an excellent grade in a less demanding course.
Actually this can be a little more complicated. All kids like to get good grades, and like even more to get excellent grades. Of course part of that happiness is that the good or excellent grade also makes their parents happy. However that is temporary for the student if they conclude that the excellent grade had required little, if any, effort on their part and that almost everyone else in the class – perhaps some who had worked even less than they had – had received the same excellent grade.
As I developed my classes and my expectations I felt it was important to do things the right way, to have my students understand things in ways that would best enable them to learn more in the future, and to encourage them to be detailed and careful with their work. If a student wasn't used to that or couldn't rise to that level of expectation, they would not do well in my class. I would count things wrong, or partially wrong, if they made a slight error. In some cases approximate answers are correct, but in most situations in math, precision in thinking and in answers is necessary. I eventually became much more concerned about how they were thinking about something (being well aware that there wasn't necessarily just one correct way of thinking about something), rather than the answer they eventually got. Sometimes the most trouble I had was with the parents who wanted their kids to do well and didn't always see the value of that attention to detail and precision.
It wasn't unusual that a student in my class would get an average grade (which is a “C”, believe it or not) when they had previously received good or excellent grades. That was not my intention. My intention was to do things the right way, which wasn't always the easiest way. Fortunately I had the backing of the administration who had confidence in me, and eventually I got the backing of my former students who could testify to the effectiveness of what had happened in my class. I did have to fight this battle throughout my teaching career but I felt strongly that I was doing the right thing and enough people agreed with me that it did work out well.
As any teacher knows, middle school students can be pretty simple and direct in how they explain things, Their most frequent explanation of me to their younger siblings who were about to start my class was something to the effect, “He is strict but you will learn a lot.”
Many years ago, I watched the movie, “Wall Street” and the character played by Michael Douglas famously said, “Greed is good.” A few days after that I realized that I had been using a similar philosophy in my teaching - “Struggle is good.” Beyond the learning of mathematical skills and concepts, there was value in requiring students to work to their maximum, or at least to work very hard in order to get the grade they desired. It would bring out the best in them and it would not deceive them (or their parents) into thinking that they really knew more than they did. At first they would resist or be uncomfortable, but I really left them no choice. They had to meet my standards, not the other way around.
Now I need to add something to this philosophy. If the instructor cannot “deliver the goods”, in terms of effective teaching, then the students will not continue to work. They will either conclude that the teacher doesn't know what they are doing or that they themselves don't have the ability to be successful. The teacher has the same responsibility as the student – to work very hard and do their best. I want to stress that setting high expectations for kids requires that we set high expectations for ourselves, whether we be parents or teachers.
What I advocate for teachers and parents is to carefully put struggle into their children's experiences. Don't make the struggle artificial - make it true to the value and importance of what they are doing. Teach them. Don't train them. Set high standards, but not impossible ones. If you are teaching a twelve year old how to pitch and your standard is that they never throw a wild pitch then I would submit that an expectation like that is impossible to reach. If you expect a child (or an adult) to reach an impossible level, they will soon quit and may never be willing to trust your judgment again. The wise teacher or parent can also model the value of struggle by working at something difficult in their own life. Therefore it can be “do as I do” and not just “do as I say.”
Find ways to motivate the kids to want to do what you require because they understand the value of what you want them to learn, but also because you want them to understand the value of struggle and the importance of overcoming the obstacles in their life. Motivation of students was always something that I considered to be a weakness of mine, but I always recognized its importance and I tried to constantly get better at it.
Any adult knows that adversity is a regular part of life and someone who has never had to deal with adversity before, may not be able to overcome it. Effective teaching should not just result in the learning of specific concepts and skills but also result in confidence gained from being required to meet high standards and overcome obstacles and difficulties in their experience. This is done for two reasons – it is the right thing to do (which many would say is enough by itself) and it promotes in kids the confidence and ability in themselves that they can overcome the adversity that will take place in their future.
So I say, “Struggle is good.” Now you know why I think that is true. Do you agree?
The above statement might seem a little surprising but allow me to explain. If you know me, you know the explanation will be pretty long! In the January 21, 2008 edition of Sports Illustrated (Brett Favre, in the snow, on the cover), there is an article on basketball coach Rick Majerus. He has been a highly successful college basketball coach over the years, known primarily for taking the University of Utah to the national championship game in 1998 against Kentucky and his great sense of humor. Because of his health and other reasons, Majerus was out of coaching (doing analysis on TV instead) for the past few years. He got back into coaching this season with the Saint Louis University basketball team. The article is an interesting one even if you aren't a sports fan. Here is a link to it.
I don't agree or advocate all of the things that Coach Majerus does with his teams (which doesn't mean that those things are wrong for him) but he made an interesting statement in the magazine article. He said, “Parents today want to take all the pain, all the heartache and sadness, out of their kids' lives. All the things that make you a better person.” That particular statement reminded me of one of the philosophical underpinnings of my teaching career. This was something that developed over several years of teaching and seeing how kids react to certain situations and also having former students come back to talk to me after moving on to high school, college, or adulthood. In essence, one of the things they most appreciated about my class was that it was demanding and it caused them to develop better study habits and to have a greater sense of accomplishment when they succeeded. In other words, the students felt more pride in getting a good grade in a demanding course than getting an excellent grade in a less demanding course.
Actually this can be a little more complicated. All kids like to get good grades, and like even more to get excellent grades. Of course part of that happiness is that the good or excellent grade also makes their parents happy. However that is temporary for the student if they conclude that the excellent grade had required little, if any, effort on their part and that almost everyone else in the class – perhaps some who had worked even less than they had – had received the same excellent grade.
As I developed my classes and my expectations I felt it was important to do things the right way, to have my students understand things in ways that would best enable them to learn more in the future, and to encourage them to be detailed and careful with their work. If a student wasn't used to that or couldn't rise to that level of expectation, they would not do well in my class. I would count things wrong, or partially wrong, if they made a slight error. In some cases approximate answers are correct, but in most situations in math, precision in thinking and in answers is necessary. I eventually became much more concerned about how they were thinking about something (being well aware that there wasn't necessarily just one correct way of thinking about something), rather than the answer they eventually got. Sometimes the most trouble I had was with the parents who wanted their kids to do well and didn't always see the value of that attention to detail and precision.
It wasn't unusual that a student in my class would get an average grade (which is a “C”, believe it or not) when they had previously received good or excellent grades. That was not my intention. My intention was to do things the right way, which wasn't always the easiest way. Fortunately I had the backing of the administration who had confidence in me, and eventually I got the backing of my former students who could testify to the effectiveness of what had happened in my class. I did have to fight this battle throughout my teaching career but I felt strongly that I was doing the right thing and enough people agreed with me that it did work out well.
As any teacher knows, middle school students can be pretty simple and direct in how they explain things, Their most frequent explanation of me to their younger siblings who were about to start my class was something to the effect, “He is strict but you will learn a lot.”
Many years ago, I watched the movie, “Wall Street” and the character played by Michael Douglas famously said, “Greed is good.” A few days after that I realized that I had been using a similar philosophy in my teaching - “Struggle is good.” Beyond the learning of mathematical skills and concepts, there was value in requiring students to work to their maximum, or at least to work very hard in order to get the grade they desired. It would bring out the best in them and it would not deceive them (or their parents) into thinking that they really knew more than they did. At first they would resist or be uncomfortable, but I really left them no choice. They had to meet my standards, not the other way around.
Now I need to add something to this philosophy. If the instructor cannot “deliver the goods”, in terms of effective teaching, then the students will not continue to work. They will either conclude that the teacher doesn't know what they are doing or that they themselves don't have the ability to be successful. The teacher has the same responsibility as the student – to work very hard and do their best. I want to stress that setting high expectations for kids requires that we set high expectations for ourselves, whether we be parents or teachers.
What I advocate for teachers and parents is to carefully put struggle into their children's experiences. Don't make the struggle artificial - make it true to the value and importance of what they are doing. Teach them. Don't train them. Set high standards, but not impossible ones. If you are teaching a twelve year old how to pitch and your standard is that they never throw a wild pitch then I would submit that an expectation like that is impossible to reach. If you expect a child (or an adult) to reach an impossible level, they will soon quit and may never be willing to trust your judgment again. The wise teacher or parent can also model the value of struggle by working at something difficult in their own life. Therefore it can be “do as I do” and not just “do as I say.”
Find ways to motivate the kids to want to do what you require because they understand the value of what you want them to learn, but also because you want them to understand the value of struggle and the importance of overcoming the obstacles in their life. Motivation of students was always something that I considered to be a weakness of mine, but I always recognized its importance and I tried to constantly get better at it.
Any adult knows that adversity is a regular part of life and someone who has never had to deal with adversity before, may not be able to overcome it. Effective teaching should not just result in the learning of specific concepts and skills but also result in confidence gained from being required to meet high standards and overcome obstacles and difficulties in their experience. This is done for two reasons – it is the right thing to do (which many would say is enough by itself) and it promotes in kids the confidence and ability in themselves that they can overcome the adversity that will take place in their future.
So I say, “Struggle is good.” Now you know why I think that is true. Do you agree?
Wednesday, January 16, 2008
Hair-raising Experience
THE STREAMLINED LOOK
Earlier this year the Spirit Lake boys basketball team beat Sheldon in a home game. As they were preparing to play Sheldon again, this time at Sheldon, I mentioned to (Spirit Lake) Coach Walz that the last time the Spirit Lake boys (varsity) basketball team had won at Sheldon was in 1997. I remember that game well. We had lost 7 games in a row at that point of the season and had lost our best player, Todd Gengerke, to knee surgery the day before the game. The team decided to dedicate the game to him. Sheldon was 14-2 going into the game and was ranked #9 in the state at the time. However our guys played with great purpose and excellent focus throughout the game. It was close all the way. We shot eight for eight from the free throw line in the last minute and a half and ended up winning 55-53. We asked the Sheldon people for the game ball and took it back to Spirit Lake. The team, managers, and coaching staff went out to the hospital that night and presented the game ball, with all of our signatures, to Todd. It was a great moment for all of us, and we asked the photographer and sports reporter for the paper, Mike Early, to take a picture of that presentation. I have that picture framed and in my house.
After I told Coach Walz that story, he asked me to relate that to the current team on the night before they played at Sheldon. I said I would do that and as I thought about it, it seemed to me that I needed to add something that would give the players some extra motivation since they didn't have a teammate in the hospital having knee surgery. I told them that it would be the first time in a long time that we had beaten Sheldon twice which should be motivation enough but, if they did win, I would have my barber cut off my hair – military style. Yes, it was a moment of temporary insanity on my part but I have kept my word. Spirit Lake beat Sheldon on Tuesday night 52-47 in overtime. The morning after the game I went in and got my “induction cut.” I'm not going to be needing my comb for a long time – not that I miss that.
I stopped by Wal Mart and picked up a stocking hat and a baseball hat. Hopefully that will stave off pneumonia during this Iowa winter. After my trip to the barber I stopped by the library and did a little research. I found out that the previous time Spirit Lake had beaten Sheldon twice in the same season was in 1993. Now that they have done it again in 2008, I won't forget what year it took place. Spirit Lake is now 10-3 and is having a very fine season. They have a big game this Friday against LeMars. Spirit Lake is in fourth place right now, just behind LeMars. I am going to see the team this afternoon at their practice and let them see what their win last night accomplished. And I am going to tell them that against LeMars, they are on their own, since I don't have any more hair I am willing to have removed.
Earlier this year the Spirit Lake boys basketball team beat Sheldon in a home game. As they were preparing to play Sheldon again, this time at Sheldon, I mentioned to (Spirit Lake) Coach Walz that the last time the Spirit Lake boys (varsity) basketball team had won at Sheldon was in 1997. I remember that game well. We had lost 7 games in a row at that point of the season and had lost our best player, Todd Gengerke, to knee surgery the day before the game. The team decided to dedicate the game to him. Sheldon was 14-2 going into the game and was ranked #9 in the state at the time. However our guys played with great purpose and excellent focus throughout the game. It was close all the way. We shot eight for eight from the free throw line in the last minute and a half and ended up winning 55-53. We asked the Sheldon people for the game ball and took it back to Spirit Lake. The team, managers, and coaching staff went out to the hospital that night and presented the game ball, with all of our signatures, to Todd. It was a great moment for all of us, and we asked the photographer and sports reporter for the paper, Mike Early, to take a picture of that presentation. I have that picture framed and in my house.
After I told Coach Walz that story, he asked me to relate that to the current team on the night before they played at Sheldon. I said I would do that and as I thought about it, it seemed to me that I needed to add something that would give the players some extra motivation since they didn't have a teammate in the hospital having knee surgery. I told them that it would be the first time in a long time that we had beaten Sheldon twice which should be motivation enough but, if they did win, I would have my barber cut off my hair – military style. Yes, it was a moment of temporary insanity on my part but I have kept my word. Spirit Lake beat Sheldon on Tuesday night 52-47 in overtime. The morning after the game I went in and got my “induction cut.” I'm not going to be needing my comb for a long time – not that I miss that.
I stopped by Wal Mart and picked up a stocking hat and a baseball hat. Hopefully that will stave off pneumonia during this Iowa winter. After my trip to the barber I stopped by the library and did a little research. I found out that the previous time Spirit Lake had beaten Sheldon twice in the same season was in 1993. Now that they have done it again in 2008, I won't forget what year it took place. Spirit Lake is now 10-3 and is having a very fine season. They have a big game this Friday against LeMars. Spirit Lake is in fourth place right now, just behind LeMars. I am going to see the team this afternoon at their practice and let them see what their win last night accomplished. And I am going to tell them that against LeMars, they are on their own, since I don't have any more hair I am willing to have removed.
Sunday, January 13, 2008
HALFWAY NUMBERS
Back on Nov. 27, Nov. 29, and Dec. 3rd,on this blog,I posted some information on Mental Math which included philosophy and numerous mental math questions. I would urge you to read that if you have time. The questions represented a wide variety of mental math situations and math content. If time does not permit you to do much mental math, with students or children, but you want to do something rather than nothing, then "halfway" numbers might be the solution. I thought of this by accident but it proved to be a very good concept and a source of good mental computation opportunities. It is something that can be tailored to almost any age group and/or ability. A teacher or parent that does just one or two of these a day can help their students develop some confidence and ability in mental math. Below is an explanation of the concept and techniques.
HALFWAY NUMBERS
Halfway numbers present some very good mental math opportunities for middle school students. Halfway numbers are numbers that are halfway between two other numbers. For example, students could be asked to find the number halfway between 48 and 64. When I first presented this type of question to my students, I had in mind two distinct methods that could be used. Obviously the halfway number would be the average of 48 and 64. (I call this "The Average Method".) So the student would have to add 48 and 64 in their head. A good mental math strategy for that could be to add 40 and 60 (100) and then add 8 and 4 (12) and then add 100 and 12 getting 112. That is called "Front End Addition". (There are other good mental math strategies for adding 48 and 64 but that is not my focus here.) 112 must then be divided by 2. A good mental math strategy is to "distribute" the division. 100/2 is 50. 12/2 is 6. 50 +6=56. Therefore the number halfway between 48 and 64 is 56. The other common strategy for halfway numbers I call "The Difference Method." The (positive) difference between 48 and 64 is found first. The student could mentally subtract 48 from 64 by first subtracting 40 from 64 getting 24 and then subtracting the remaining 8. 24-8 could be done by 24-10+2 (subtracting 8 is the same as subtracting 10 and adding 2.) 24-10+2=14+2=16. So the difference between 64 and 48 is 16. The halfway number is half of that difference (half of 16 is 8) away from 48 and from 64. So the student could add 8 to 48 or subtract 8 from 64. Either way you end up at the halfway number of 56. (By the way, although it is not my focus here, I did want to mention another method for finding the difference between 48 and 64. In general, one of the best ways to subtract in your head is to figure out what you have to add to the smaller number to get to the larger number. In this situation it would be natural to think that you would add 2 to 48 to get to 50 and then add 14 more to 50 to get 64. Thus in total you would add 2+14 or 16 to 48 to get 64 and therefore the difference between 48 and 64 is 16. The concept of “adding on” is a great way for people to do mental math subtraction.)
One class period when I was doing halfway numbers with my students, one of them, named Gary, used a different method. He took half of each number and then added those together. He did get the halfway number. In my example above, that would mean taking half of 48 (24) and half of 64 (32). Then add 24 and 32. You get, of course, 56. I have to admit that at first my reaction was that it was a lucky coincidence. After school that day I looked at it algebraically, and it turns out that "The Gary Method" does work all of the time. You just have to show that a/2 + b/2 = (a+b)/2. As you can see in this example, "The Gary Method" might be the easiest way to find a halfway number between 48 and 64.
Finally, one day, when I was explaining "The Difference Method" I used a number line diagram. I drew a number line putting a tick mark on the left labeled 48 and a tick mark on the right, labeled 64. I put a tick mark halfway between 48 and 64 and said we needed to find what that number was. I drew a little arc from 48 toward 64. The arc represented a jump of two to 50. Then I drew a similar arc from 64 to 62. So now the halfway number is halfway between 50 and 62. Some students can see right then that the halfway number has to be 56. If others don't see that you can continue moving toward the halfway number equal amounts until the halfway number is obvious. I ended up calling this "The Number Line Method." They do need to be able to do it in their head, of course. Some students really like this method. They "see" what is going on a little better.
Give them some easy examples at first and let them try to find the answer their own way. Students will naturally gravitate to one or two of the above methods. You can gradually introduce the other methods and then show how each method could be the best way to do certain halfway number questions. Who knows? One of your students may discover an altogether different method that also works.
By the way, when students are first asked to do any type of mental math question, they will tend to try to do the paper and pencil method in their head. I do everything I can to discourage that. Pencil and paper methods are good when you use pencil and paper. When doing mental math we want to use strategies that are appropriate for mental math. Thinking this way and using the strategies of mental math can be very empowering to students who previously assumed that they were not good at math. They may realize that they are good at math when they are taught and allowed to use their brain in a natural way.
HALFWAY NUMBERS
Halfway numbers present some very good mental math opportunities for middle school students. Halfway numbers are numbers that are halfway between two other numbers. For example, students could be asked to find the number halfway between 48 and 64. When I first presented this type of question to my students, I had in mind two distinct methods that could be used. Obviously the halfway number would be the average of 48 and 64. (I call this "The Average Method".) So the student would have to add 48 and 64 in their head. A good mental math strategy for that could be to add 40 and 60 (100) and then add 8 and 4 (12) and then add 100 and 12 getting 112. That is called "Front End Addition". (There are other good mental math strategies for adding 48 and 64 but that is not my focus here.) 112 must then be divided by 2. A good mental math strategy is to "distribute" the division. 100/2 is 50. 12/2 is 6. 50 +6=56. Therefore the number halfway between 48 and 64 is 56. The other common strategy for halfway numbers I call "The Difference Method." The (positive) difference between 48 and 64 is found first. The student could mentally subtract 48 from 64 by first subtracting 40 from 64 getting 24 and then subtracting the remaining 8. 24-8 could be done by 24-10+2 (subtracting 8 is the same as subtracting 10 and adding 2.) 24-10+2=14+2=16. So the difference between 64 and 48 is 16. The halfway number is half of that difference (half of 16 is 8) away from 48 and from 64. So the student could add 8 to 48 or subtract 8 from 64. Either way you end up at the halfway number of 56. (By the way, although it is not my focus here, I did want to mention another method for finding the difference between 48 and 64. In general, one of the best ways to subtract in your head is to figure out what you have to add to the smaller number to get to the larger number. In this situation it would be natural to think that you would add 2 to 48 to get to 50 and then add 14 more to 50 to get 64. Thus in total you would add 2+14 or 16 to 48 to get 64 and therefore the difference between 48 and 64 is 16. The concept of “adding on” is a great way for people to do mental math subtraction.)
One class period when I was doing halfway numbers with my students, one of them, named Gary, used a different method. He took half of each number and then added those together. He did get the halfway number. In my example above, that would mean taking half of 48 (24) and half of 64 (32). Then add 24 and 32. You get, of course, 56. I have to admit that at first my reaction was that it was a lucky coincidence. After school that day I looked at it algebraically, and it turns out that "The Gary Method" does work all of the time. You just have to show that a/2 + b/2 = (a+b)/2. As you can see in this example, "The Gary Method" might be the easiest way to find a halfway number between 48 and 64.
Finally, one day, when I was explaining "The Difference Method" I used a number line diagram. I drew a number line putting a tick mark on the left labeled 48 and a tick mark on the right, labeled 64. I put a tick mark halfway between 48 and 64 and said we needed to find what that number was. I drew a little arc from 48 toward 64. The arc represented a jump of two to 50. Then I drew a similar arc from 64 to 62. So now the halfway number is halfway between 50 and 62. Some students can see right then that the halfway number has to be 56. If others don't see that you can continue moving toward the halfway number equal amounts until the halfway number is obvious. I ended up calling this "The Number Line Method." They do need to be able to do it in their head, of course. Some students really like this method. They "see" what is going on a little better.
Give them some easy examples at first and let them try to find the answer their own way. Students will naturally gravitate to one or two of the above methods. You can gradually introduce the other methods and then show how each method could be the best way to do certain halfway number questions. Who knows? One of your students may discover an altogether different method that also works.
By the way, when students are first asked to do any type of mental math question, they will tend to try to do the paper and pencil method in their head. I do everything I can to discourage that. Pencil and paper methods are good when you use pencil and paper. When doing mental math we want to use strategies that are appropriate for mental math. Thinking this way and using the strategies of mental math can be very empowering to students who previously assumed that they were not good at math. They may realize that they are good at math when they are taught and allowed to use their brain in a natural way.
Tuesday, January 8, 2008
One-on-One With Obama
Recently I read an interesting article in Sports Illustrated in the "Point After" section, the last page of the magazine. That section used to be written by Rick Riley, who I really liked, but he has moved on to another position. Anyway this column is written by S. L. Price and talks about a one-on-one basketball game he had with Barack Obama, during a campaign trip at the Spencer, Iowa, YMCA. I have played basketball at that "Y", years ago, and I have become an Obama supporter. You can also find out what basketball had to do with the budding relationship between Barack and his future wife, Michelle. It's a good "read."
Here is the link.
Here is the link.
Friday, January 4, 2008
Caucus Night and Math
On Thursday night I attended my first caucus. It was a fairly interesting experience.
First I will tell you who I supported and why. I consider myself an independent although I tend to favor the Democrats. I have voted for some Republicans over the years, like Senator Grassley, and various other candidates in more local elections.
As I looked at this year's slate of Presidential candidates, both Republican and Democrat, I saw several good choices. I am old enough, or should I say experienced enough, to know that no one is going to be perfect. There is no candidate that I agree with on everything but my first priority was to look for someone who might be able to unite the country. Unless that happens we are going to continue to have gridlock. For example I agree with Hillary Clinton on a lot of issues but she is easily the most polarizing candidate that has a reasonable chance to win. If she were to win the Presidency, her best intentions and best programs would never come to fruition because of the intense hatred so many of her enemies have for her and her husband. Her ideas would be rejected by many just because they came from her, not necessarily because they were bad ideas.
Of the remaining "viable" candidates, I felt that Obama, McCain, Richardson, Huckabee, and Edwards (in that order) were the most likely to be able to work with the other party in a constructive way and unite the country. That is the most important thing in my opinion because the challenges we face, both foreign and domestic, are going to require a united effort. Immigration and health care are good examples. There is basically unanimous agreement that these are problems that need to be addressed but nothing has happened in the last seven years because of gridlock.
Barack Obama does lack experience in certain areas but I feel he has the most unifying message (which he first outlined at the Democratic convention in 2004)and I think he has the potential to be a great President. He has brought a lot of young people back into the political process and seems to give the most hope for uniting the country and starting a groundswell of momentum to make things better WITHOUT denigrating the other side. I also have the feeling that if Obama became President that it would be a positive in the eyes of most of the rest of the world. That would help us in defeating the actual threats to the freedom of our country and our allies.
Now on to the caucus on Thursday night. My precinct in Dickinson County had 121 people that showed up to express their preference. We were told that for a candidate to be "viable" that they would need to have at least 15 percent of that total. A little mental math on my part (move the decimal point one place to the left, take half and add it on) told me that would be 18 people. We then moved to our separate groups. We in the Obama group had way more than 18; Clinton and Edwards also had more than 18. Biden had about six or seven and Richardson had three. Those people had to reorganize and they received "pitches" from the other three groups. Some went to Edwards, but most came to Obama. In the end, Obama had 60 voters, Clinton had 32 and Edwards had 29.
Our particular precinct, based on population, had been assigned seven delegates to the state convention, so those seven had to be divided among the three viable candidates. So of course they took the number of voters in each group divided by the total number of voters (121) and then multiplied by seven. Edwards got about 1.68, Clinton about 1.85 and Obama about 3.47. By the rules they had to round to the nearest whole number (no partial delegates!) so Edwards and Clinton received two delegates each and Obama got three delegates. Those were the three numbers reported to the state Democratic party and those are the numbers used in determining the percentages that are reported on television and in the newspaper.
As an Obama supporter, I was a little disappointed since we had almost twice as many votes as each of the other two but only got one more delegate.
From what I had heard I was expecting the process to last from one to two hours but it was actually over for the voters in about half an hour. I'm glad I participated and it was interesting to see some of the people I know and who they favored. I especially respect the people who originally stood up for Biden and Richardson, knowing that they would be unlikely to reach that 15% level. (Early on, a few months ago, I had favored Richardson but I ended up feeling that Obama would be more likely to unite and inspire the country as a whole. Their policy differences are slight.)
Barack Obama does remind me a little of John Kennedy (once again showing my age). He is young, an inspiring speaker, relativley inexperienced on the national stage, has to overcome a possible prejudice (Kennedy as a Catholic and Obama as an African-American) and overall gives people hope for a new era in politics and a new era for America. Ladies and gentlemen, I think we are about to experience a significant historical moment in American history.
First I will tell you who I supported and why. I consider myself an independent although I tend to favor the Democrats. I have voted for some Republicans over the years, like Senator Grassley, and various other candidates in more local elections.
As I looked at this year's slate of Presidential candidates, both Republican and Democrat, I saw several good choices. I am old enough, or should I say experienced enough, to know that no one is going to be perfect. There is no candidate that I agree with on everything but my first priority was to look for someone who might be able to unite the country. Unless that happens we are going to continue to have gridlock. For example I agree with Hillary Clinton on a lot of issues but she is easily the most polarizing candidate that has a reasonable chance to win. If she were to win the Presidency, her best intentions and best programs would never come to fruition because of the intense hatred so many of her enemies have for her and her husband. Her ideas would be rejected by many just because they came from her, not necessarily because they were bad ideas.
Of the remaining "viable" candidates, I felt that Obama, McCain, Richardson, Huckabee, and Edwards (in that order) were the most likely to be able to work with the other party in a constructive way and unite the country. That is the most important thing in my opinion because the challenges we face, both foreign and domestic, are going to require a united effort. Immigration and health care are good examples. There is basically unanimous agreement that these are problems that need to be addressed but nothing has happened in the last seven years because of gridlock.
Barack Obama does lack experience in certain areas but I feel he has the most unifying message (which he first outlined at the Democratic convention in 2004)and I think he has the potential to be a great President. He has brought a lot of young people back into the political process and seems to give the most hope for uniting the country and starting a groundswell of momentum to make things better WITHOUT denigrating the other side. I also have the feeling that if Obama became President that it would be a positive in the eyes of most of the rest of the world. That would help us in defeating the actual threats to the freedom of our country and our allies.
Now on to the caucus on Thursday night. My precinct in Dickinson County had 121 people that showed up to express their preference. We were told that for a candidate to be "viable" that they would need to have at least 15 percent of that total. A little mental math on my part (move the decimal point one place to the left, take half and add it on) told me that would be 18 people. We then moved to our separate groups. We in the Obama group had way more than 18; Clinton and Edwards also had more than 18. Biden had about six or seven and Richardson had three. Those people had to reorganize and they received "pitches" from the other three groups. Some went to Edwards, but most came to Obama. In the end, Obama had 60 voters, Clinton had 32 and Edwards had 29.
Our particular precinct, based on population, had been assigned seven delegates to the state convention, so those seven had to be divided among the three viable candidates. So of course they took the number of voters in each group divided by the total number of voters (121) and then multiplied by seven. Edwards got about 1.68, Clinton about 1.85 and Obama about 3.47. By the rules they had to round to the nearest whole number (no partial delegates!) so Edwards and Clinton received two delegates each and Obama got three delegates. Those were the three numbers reported to the state Democratic party and those are the numbers used in determining the percentages that are reported on television and in the newspaper.
As an Obama supporter, I was a little disappointed since we had almost twice as many votes as each of the other two but only got one more delegate.
From what I had heard I was expecting the process to last from one to two hours but it was actually over for the voters in about half an hour. I'm glad I participated and it was interesting to see some of the people I know and who they favored. I especially respect the people who originally stood up for Biden and Richardson, knowing that they would be unlikely to reach that 15% level. (Early on, a few months ago, I had favored Richardson but I ended up feeling that Obama would be more likely to unite and inspire the country as a whole. Their policy differences are slight.)
Barack Obama does remind me a little of John Kennedy (once again showing my age). He is young, an inspiring speaker, relativley inexperienced on the national stage, has to overcome a possible prejudice (Kennedy as a Catholic and Obama as an African-American) and overall gives people hope for a new era in politics and a new era for America. Ladies and gentlemen, I think we are about to experience a significant historical moment in American history.
Wednesday, January 2, 2008
Helping the Boys
For anyone who has taught and/or parented a middle school/high school boy, you know that organization, planning, and logical thinking are often in short supply. I came across an article that relates to that with some suggestions for ways to help.
Here is the link.
Here is the link.
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