Fuzzy Math

Instead of learning addition, subtraction, multiplication, and division, are your kids doing math problems like these?:

A. If math were a color, it would be –, because –.
B. If it were a food, it would be –, because –.
C. If it were weather, it would be –, because –.

If so, they are learning fuzzy math. Read that linked article for how this postmodernist “constructivist” approach to mathematics has become such an educational fiasco. Try solving the above problems for “fuzzy math” (If fuzzy math were a food, it would be ___, because ___.)

About Gene Veith

Professor of Literature at Patrick Henry College, the Director of the Cranach Institute at Concordia Theological Seminary, a columnist for World Magazine and TableTalk, and the author of 18 books on different facets of Christianity & Culture.

  • Carl Vehse

    In the 1960s Tom Lehrer treated a similar educational fad, called New Math in his song parody.

  • Carl Vehse

    In the 1960s Tom Lehrer treated a similar educational fad, called New Math in his song parody.

  • Pingback: EquMath: Math Lessons » Blog Archive » Fuzzy Math

  • Pingback: EquMath: Math Lessons » Blog Archive » Fuzzy Math

  • Joe

    Math (or rather the lack of anything resembling it) was one of the major reasons we began to seriously consider home schooling. It lead us to look critically at the entire curriculum. Once we did that there really was nothing left to do but determine the logistics of home schooling.

  • Joe

    Math (or rather the lack of anything resembling it) was one of the major reasons we began to seriously consider home schooling. It lead us to look critically at the entire curriculum. Once we did that there really was nothing left to do but determine the logistics of home schooling.

  • http://thebookbeast.blogspot.com Darren

    If math were a food, it would be a hamburger. When it’s simple, it’s good. When it gets too complex, it’s inedible.

  • http://thebookbeast.blogspot.com Darren

    If math were a food, it would be a hamburger. When it’s simple, it’s good. When it gets too complex, it’s inedible.

  • http://necessaryroughness.org Dan at Necessary Roughness

    A sad thing is, fuzzy mathematics and fuzzy logic are real and studied phenomenon, where you replace true/false with graduating layers of true-ness and false-ness. It sounds like it would come out of the Colbert Report, but it helped account for bad assumptions in predicting models and helped control systems work more effectively.

    This math without calculations thing is a bit bogus, and I’m wondering how long I have to keep my kids in private school AFTER they would be “ready” for public school.

  • http://necessaryroughness.org Dan at Necessary Roughness

    A sad thing is, fuzzy mathematics and fuzzy logic are real and studied phenomenon, where you replace true/false with graduating layers of true-ness and false-ness. It sounds like it would come out of the Colbert Report, but it helped account for bad assumptions in predicting models and helped control systems work more effectively.

    This math without calculations thing is a bit bogus, and I’m wondering how long I have to keep my kids in private school AFTER they would be “ready” for public school.

  • http://www.faith-filled.com Stephenie

    That’s part of the reason I like the Saxon method so well. Some teachers and parents hate it. It’s dry – they tell me.

    It’s straightforward. I’ve seen huge differences between kids brought up on “pretty math” and those brought up on the basics.

    Pretty math covers all those books that think they have to have glossy pictures and fancy covers. Then, they go on to spend one lesson on math facts. Great priorities!

    I’ve never seen fuzzy math, but it looks like something more appropriate for philosophy class.

  • http://www.faith-filled.com Stephenie

    That’s part of the reason I like the Saxon method so well. Some teachers and parents hate it. It’s dry – they tell me.

    It’s straightforward. I’ve seen huge differences between kids brought up on “pretty math” and those brought up on the basics.

    Pretty math covers all those books that think they have to have glossy pictures and fancy covers. Then, they go on to spend one lesson on math facts. Great priorities!

    I’ve never seen fuzzy math, but it looks like something more appropriate for philosophy class.

  • http://www.faith-filled.com Stephenie

    I just read the article. I’ve got to disagree with the assessment of “spiraling.” How many kids are going to pick up a concept the first time they hear it and use it? Not many. And yet, their skills will build on that skill.

    Effective spiraling is when you work upwards, not just repeat old lessons. My students review their math facts very regularly, while they continue to learn how to do long division. If you don’t know your facts and use them, they diminish.

    The least effective math books (IMO) are those who discuss a topic and never come back to it. The children get used to this and think that once they get through a topic (rather than mastering the skill) they don’t have to think about it again (until next year.)

  • http://www.faith-filled.com Stephenie

    I just read the article. I’ve got to disagree with the assessment of “spiraling.” How many kids are going to pick up a concept the first time they hear it and use it? Not many. And yet, their skills will build on that skill.

    Effective spiraling is when you work upwards, not just repeat old lessons. My students review their math facts very regularly, while they continue to learn how to do long division. If you don’t know your facts and use them, they diminish.

    The least effective math books (IMO) are those who discuss a topic and never come back to it. The children get used to this and think that once they get through a topic (rather than mastering the skill) they don’t have to think about it again (until next year.)

  • http://www.brideofchristelc.com Paul A. Siems

    A. If math were a color, it would be black, because it is indelible and because it absorbs energy and gives none back and because it offers no hope, but like the Law, simply states what is.

    B. If it were a food, it would be the fruit of the tree of the knowledge of good and evil, because it is so often misused according to the opposite purposes for which it was given.

    C. If it were weather, it would be cold and still, because it has no life, no motion, no feeling.

    D. If it were a tool (and it is) it would be a combination of a shovel and a sharp cutting instrument because it is can be used to uncover that which is hidden or in some cases to bury what is in plain view, and because it can be used to carve and shape wonderful creations or to strike and to kill and destroy.

  • http://www.brideofchristelc.com Paul A. Siems

    A. If math were a color, it would be black, because it is indelible and because it absorbs energy and gives none back and because it offers no hope, but like the Law, simply states what is.

    B. If it were a food, it would be the fruit of the tree of the knowledge of good and evil, because it is so often misused according to the opposite purposes for which it was given.

    C. If it were weather, it would be cold and still, because it has no life, no motion, no feeling.

    D. If it were a tool (and it is) it would be a combination of a shovel and a sharp cutting instrument because it is can be used to uncover that which is hidden or in some cases to bury what is in plain view, and because it can be used to carve and shape wonderful creations or to strike and to kill and destroy.

  • http://geochristian.wordpress.com Kevin N

    Constructivism is the big fad in science education right now as well, under the name “discovery learning.” The idea is that students will learn science better if they are able to discover the laws of science for themselves. While there is a kernel of truth in this, what usually happens is that students spend two weeks doing activities that they don’t really understand resulting in a reenforcement of the misunderstandings they had in the first place. Then the teacher has to try to undo the misconceptions, which is often impossible by this point. It is an incredibly inefficient way to teach.

    It would be better to teach them how the great scientists of the past came up with their theories and laws than to expect the average student to come up with these scientific concepts by themselves.

  • http://geochristian.wordpress.com Kevin N

    Constructivism is the big fad in science education right now as well, under the name “discovery learning.” The idea is that students will learn science better if they are able to discover the laws of science for themselves. While there is a kernel of truth in this, what usually happens is that students spend two weeks doing activities that they don’t really understand resulting in a reenforcement of the misunderstandings they had in the first place. Then the teacher has to try to undo the misconceptions, which is often impossible by this point. It is an incredibly inefficient way to teach.

    It would be better to teach them how the great scientists of the past came up with their theories and laws than to expect the average student to come up with these scientific concepts by themselves.

  • http://www.brideofchristelc.com Paul A. Siems

    Adam was created with and had the knowledge of what is good. Science is a gift, not a discovery. Adam chose discovery over the gift and lost what he had. Now his knowledge was corrupt and fallible.

    Solomon asked the Lord for wisdom and God gave it. He had knowledge of things that no one else knew about so that people traveled from afar to learn from him what he had been given. But once again, he turned to his own reason and strength and in the end lost everything. He asked for the wisdom to rule God’s people well, and then turned to political machinations such as marriage to daughters of kings and reliance upon fortresses and chariots. This led to his personal downfall, to tyrannical taxation, and the eventual split of the kingdom.

    True Science is one of receiving from the One who knows, not of seeking to know by one’s own discovery. The post on “Destroying the Universe through Scientific Observation” actually hits the mark by this title. Adam did destroy the universe and shorten its life by his anthropocentric scientific observation. If he had continued in the knowledge of the Lord, things would not have changed from the way of everlasting life to the way of death and destruction and decay.

    This is why the Scriptures declare that fear of the Lord is the beginning of wisdom. Not fearing the Lord is the end of wisdom, and the beginning of deception. That is why the unbelieving world will continue to resist the teaching of declared facts with the promotion of hypotheses and theories. It is only by the regeneration of the life of faith that people are turned from their own ways to the Lord and the Truth that does not fail.

  • http://www.brideofchristelc.com Paul A. Siems

    Adam was created with and had the knowledge of what is good. Science is a gift, not a discovery. Adam chose discovery over the gift and lost what he had. Now his knowledge was corrupt and fallible.

    Solomon asked the Lord for wisdom and God gave it. He had knowledge of things that no one else knew about so that people traveled from afar to learn from him what he had been given. But once again, he turned to his own reason and strength and in the end lost everything. He asked for the wisdom to rule God’s people well, and then turned to political machinations such as marriage to daughters of kings and reliance upon fortresses and chariots. This led to his personal downfall, to tyrannical taxation, and the eventual split of the kingdom.

    True Science is one of receiving from the One who knows, not of seeking to know by one’s own discovery. The post on “Destroying the Universe through Scientific Observation” actually hits the mark by this title. Adam did destroy the universe and shorten its life by his anthropocentric scientific observation. If he had continued in the knowledge of the Lord, things would not have changed from the way of everlasting life to the way of death and destruction and decay.

    This is why the Scriptures declare that fear of the Lord is the beginning of wisdom. Not fearing the Lord is the end of wisdom, and the beginning of deception. That is why the unbelieving world will continue to resist the teaching of declared facts with the promotion of hypotheses and theories. It is only by the regeneration of the life of faith that people are turned from their own ways to the Lord and the Truth that does not fail.

  • http://diary-of-a-wanna-be-supermom.blogspot.com/ Cate

    Thank goodness some school districts are wising up. Frankly I can’t believe this sham of a math program has gone on as long as it has.

    It’s so frustrating to hear friends of mine defend the program calling it “cool” or “fun.” Shouldn’t the litmus test of a good math program be that the child actually learns how to add, subtract, multiply and divide and not whether it’s “rockin’?”

  • http://diary-of-a-wanna-be-supermom.blogspot.com/ Cate

    Thank goodness some school districts are wising up. Frankly I can’t believe this sham of a math program has gone on as long as it has.

    It’s so frustrating to hear friends of mine defend the program calling it “cool” or “fun.” Shouldn’t the litmus test of a good math program be that the child actually learns how to add, subtract, multiply and divide and not whether it’s “rockin’?”

  • http://castingoutnines.wordpress.com Robert Talbert

    The problem with constructivist pedagogy isn’t so much the pedagogy itself as it is the people who endorse it — or I should say, the core of teachers who believe that constructivism is the way, the truth, and the life, and no student shall come unto mathematical understanding but by discovery learning.

    I’m a college mathematics professor teaching a pretty diverse audience and course load (math majors as well as people who make it into college by grace alone). Do I use constructivism? Sure — when the concept calls for it, when I am sure the students are well-enough grounded to handle it, and when I believe as a content expert that the material is best learned in this way. Otherwise I use a different teaching method.

    This simple philosophy of using the pedagogical method that suits the audience and suits the material best is hopelessly lost on most people who end up designing curricula like these. They’re like people who believe that everything that needs fixing in a house can be fixed with a screwdriver. Screwdrivers work great on screws, but not so much when your toilet is leaking or you need to put up wallpaper. But try telling THEM that.

  • http://castingoutnines.wordpress.com Robert Talbert

    The problem with constructivist pedagogy isn’t so much the pedagogy itself as it is the people who endorse it — or I should say, the core of teachers who believe that constructivism is the way, the truth, and the life, and no student shall come unto mathematical understanding but by discovery learning.

    I’m a college mathematics professor teaching a pretty diverse audience and course load (math majors as well as people who make it into college by grace alone). Do I use constructivism? Sure — when the concept calls for it, when I am sure the students are well-enough grounded to handle it, and when I believe as a content expert that the material is best learned in this way. Otherwise I use a different teaching method.

    This simple philosophy of using the pedagogical method that suits the audience and suits the material best is hopelessly lost on most people who end up designing curricula like these. They’re like people who believe that everything that needs fixing in a house can be fixed with a screwdriver. Screwdrivers work great on screws, but not so much when your toilet is leaking or you need to put up wallpaper. But try telling THEM that.

  • http://castingoutnines.wordpress.com Robert Talbert

    I should also mention that constructivism should not be conflated with dopey “What color is math?” kinds of questions. Constructivism, when employed selectively by a skilled teacher with a well-prepared classroom and with well-designed activities, helps students understand not only the mathematical concepts being learned but how it is that mathematicians and scientists order their thinking to come up with those concepts. Frankly, kids today — and Christians today, for that matter — could use more of this.

    But again, it’s just one tool of many, and every kid and every class is different.

  • http://castingoutnines.wordpress.com Robert Talbert

    I should also mention that constructivism should not be conflated with dopey “What color is math?” kinds of questions. Constructivism, when employed selectively by a skilled teacher with a well-prepared classroom and with well-designed activities, helps students understand not only the mathematical concepts being learned but how it is that mathematicians and scientists order their thinking to come up with those concepts. Frankly, kids today — and Christians today, for that matter — could use more of this.

    But again, it’s just one tool of many, and every kid and every class is different.

  • http://www.brideofchristelc.com Paul A. Siems

    Robert,

    You sound like a well grounded professor. It is nice to know some still exist.

    I imagine that your setting is considerably different, however, than those who are teaching grade school children. Even though you may encounter many in college who act like grade schoolers and make you wonder what chance you really have with them, nevertheless, they are at a very different stage of their devolopment of person and mind.

    But then, that’s really what you are saying, isn’t it?

  • http://www.brideofchristelc.com Paul A. Siems

    Robert,

    You sound like a well grounded professor. It is nice to know some still exist.

    I imagine that your setting is considerably different, however, than those who are teaching grade school children. Even though you may encounter many in college who act like grade schoolers and make you wonder what chance you really have with them, nevertheless, they are at a very different stage of their devolopment of person and mind.

    But then, that’s really what you are saying, isn’t it?

  • http://castingoutnines.wordpress.com Robert Talbert

    Paul, you’re certainly right that my setting is different than the K-12 set. The main difference in the setting is the level of bureaucracy. I teach at a private liberal arts college. We have nobody breathing down our necks to make sure x% of students pass the latest standardized test, or whatever. And we profs have a lot of freedom in running our classes the way we want. But as for the public K-12 schools, the teachers who care about teaching tend to get frustrated and burn out at an alarming rate because they KNOW that there are different tools to use in teaching and they KNOW how to teach, but their hands are tied by school boards and other bureaucrats.

    As for the students, you’d be surprised at how many college students I get who not only look and act as if they were still 13-14, but who I believe are actually in a state of arrested maturation (intellectual and moral).

  • http://castingoutnines.wordpress.com Robert Talbert

    Paul, you’re certainly right that my setting is different than the K-12 set. The main difference in the setting is the level of bureaucracy. I teach at a private liberal arts college. We have nobody breathing down our necks to make sure x% of students pass the latest standardized test, or whatever. And we profs have a lot of freedom in running our classes the way we want. But as for the public K-12 schools, the teachers who care about teaching tend to get frustrated and burn out at an alarming rate because they KNOW that there are different tools to use in teaching and they KNOW how to teach, but their hands are tied by school boards and other bureaucrats.

    As for the students, you’d be surprised at how many college students I get who not only look and act as if they were still 13-14, but who I believe are actually in a state of arrested maturation (intellectual and moral).

  • http://www.oldsolar.com/currentblog.php Rick Ritchie

    If math were a color, it would be orange, because that is made by the addition of yellow to red. If it were a food, it would be an orange, because I would rather take it in pieces than swallow it whole. If it were weather, it would be fog, because fog is easy to get lost in. (Aren’t you glad I didn’t say orange?)

  • http://www.oldsolar.com/currentblog.php Rick Ritchie

    If math were a color, it would be orange, because that is made by the addition of yellow to red. If it were a food, it would be an orange, because I would rather take it in pieces than swallow it whole. If it were weather, it would be fog, because fog is easy to get lost in. (Aren’t you glad I didn’t say orange?)

  • http://www.cockahoop.com/ tODD

    Largely ignoring the foregoing comments, I just want to say that we’re given absolutely no context (in this entry or in the linked-to entry) for the example question Veith quotes. Does it, in fact, exist “instead of learning addition, subtraction, multiplication, and division,” as Veith states? Or is it something that appears at the front of the book as a soft, friendly introduction to math, perhaps an attempt to disarm many children’s hatred of something they perceive as too difficult?

    I only ask because one of my favorite college electrical engineering textbooks had a very friendly, if humorously irrelevant, introduction that referenced 80s band Devo. I found it charming and quirky (and not at all indicative of the overall seriousness of the book), but someone with an axe to grind might well have cited the Devo bit out of context, complaining that our kids are learning about “rock musicians wearing flower pots” instead of learning about true engineering.

    If I had to guess, I’d say people carry a particularly large amount of baggage with this issue. I had a great public education, and I really don’t bear any animosity towards public education in general.

    But I wonder why it is that everyone feels free to pile on teachers, as if just about anyone could teach, and every opinion was valid. To be fair, my wife’s a (private) high school teacher, so I’m a bit defensive about the profession. I’m certainly not saying there aren’t issues at all levels, nor that there aren’t many silly things in education one could cite. But as a Web developer, I don’t get nearly as many people second-guessing my work.

  • http://www.cockahoop.com/ tODD

    Largely ignoring the foregoing comments, I just want to say that we’re given absolutely no context (in this entry or in the linked-to entry) for the example question Veith quotes. Does it, in fact, exist “instead of learning addition, subtraction, multiplication, and division,” as Veith states? Or is it something that appears at the front of the book as a soft, friendly introduction to math, perhaps an attempt to disarm many children’s hatred of something they perceive as too difficult?

    I only ask because one of my favorite college electrical engineering textbooks had a very friendly, if humorously irrelevant, introduction that referenced 80s band Devo. I found it charming and quirky (and not at all indicative of the overall seriousness of the book), but someone with an axe to grind might well have cited the Devo bit out of context, complaining that our kids are learning about “rock musicians wearing flower pots” instead of learning about true engineering.

    If I had to guess, I’d say people carry a particularly large amount of baggage with this issue. I had a great public education, and I really don’t bear any animosity towards public education in general.

    But I wonder why it is that everyone feels free to pile on teachers, as if just about anyone could teach, and every opinion was valid. To be fair, my wife’s a (private) high school teacher, so I’m a bit defensive about the profession. I’m certainly not saying there aren’t issues at all levels, nor that there aren’t many silly things in education one could cite. But as a Web developer, I don’t get nearly as many people second-guessing my work.

  • http://www.blogger.com/profile/17639370291865261582 Cindy

    If fuzzy math were a color, it would be pink with yellow polka dots, because doesn’t that sound fun and cute?

    If fuzzy math were a food, it would be marshmallows, because it’s nutritionally worthless fluff.

    If fuzzy math were weather, it would be a tornado, because a tornado leaves behind a big mess.

  • http://www.blogger.com/profile/17639370291865261582 Cindy

    If fuzzy math were a color, it would be pink with yellow polka dots, because doesn’t that sound fun and cute?

    If fuzzy math were a food, it would be marshmallows, because it’s nutritionally worthless fluff.

    If fuzzy math were weather, it would be a tornado, because a tornado leaves behind a big mess.

  • http://www.brideofchristelc.com Paul A. Siems

    tODD,

    You say that your wife is a teacher in a private school. As Robert points out, this is VERY different in most cases from government owned school. First, the governmental agenda of globalization is largely missing and instead in most cases the focus is on Biblical morality and in a few cases even God’s grace. This changes the entire mentality.

    Secondly, private schools are not government funded. The families have to make a sacrifice, often a large one, for their children to attend. Thus the parents are devoted to their children’s education. They take charge. They don’t merely participate, but they take charge of their children’s education. This results in much more than parental support or involvement, but the classroom complements the home environment.

    The curriculum is generally different because the expectations are different, too.

    The entire agenda of government schools has changed in America during my lifetime, but it was already changing when I was in school, too.

    As a pastor, I have taught many children, especially in Catechism classes. It is appalling to encounter the weaknesses of those who attend government schools, especially on matters of faith. But even basic reading skills suffer terribly, especially when families do not push the children to higher expectations.

    In one Catechism setting, in a class of about a dozen, three of the students were convinced that they were stupid. They could barely read. They had very low comprehension. Their attention spans were terribly short. They had no clue how to memorize. They continually responded, “I can’t do this. I’m stupid.” I responded, “No. You are not stupid. Yes, you can do this. Yes, you will do this, and I will help you.” After a couple of months with them, the same students were volunteering to read and were excitedly reciting their memory work. They were reporting that their grades were improving drastically in school and their teachers and families were surprised. My time with them was a weekly time of an hour and a half.

    What Robert indicated about the value of demonstrating the applicability of a subject is invaluable in helping students to see the value of what they are being asked to learn. This is especially true regarding teaching the doctrine of the Bible. When the students are not merely learning about Jesus but are meeting Him and encountering His grace and learning how the means of grace really work, they become truly hungry. In another Catechism class one of the mothers repeatedly came to me bewildered, saying, “I don’t remember ever being exited about Catechism like my son is. He comes home saying, “Mom, Catechism is awesome, just awesome.””

    For a pastor it is much easier than for teachers of other subjects. Pastors don’t really have to be all that good, they only have to know Jesus and be truly living in the Holy Communion. Teachers cannot give what they themselves do not have. But the true faith is so easy to share because the Gospel is the power. When it is taught purely and in true faith, those who receive it are changed by it.

    But the Truth is powerful in all aspects of life. Any aspect of the Truth is exciting. This is because all articles of the Truth are from the One who is the Truth, and even encountering Him in Analytical Geometry or Micro Biology or Organic Chemistry is exciting. This is why even nonbelievers experience excitement in learning, because the power of the Truth is encountered.

    Even as a Web developer you have experienced the thrill of exposing people to a new article of the Truth. When you present a new understanding to people and they truly understand it, they become exited about it. That’s teaching! That is discipling. When the discipling is in the fullness of the glory of God, Christ, that’s heavenly! Ultimately, that is what is missing in government schools (and nearly all churches) today.

  • http://www.brideofchristelc.com Paul A. Siems

    tODD,

    You say that your wife is a teacher in a private school. As Robert points out, this is VERY different in most cases from government owned school. First, the governmental agenda of globalization is largely missing and instead in most cases the focus is on Biblical morality and in a few cases even God’s grace. This changes the entire mentality.

    Secondly, private schools are not government funded. The families have to make a sacrifice, often a large one, for their children to attend. Thus the parents are devoted to their children’s education. They take charge. They don’t merely participate, but they take charge of their children’s education. This results in much more than parental support or involvement, but the classroom complements the home environment.

    The curriculum is generally different because the expectations are different, too.

    The entire agenda of government schools has changed in America during my lifetime, but it was already changing when I was in school, too.

    As a pastor, I have taught many children, especially in Catechism classes. It is appalling to encounter the weaknesses of those who attend government schools, especially on matters of faith. But even basic reading skills suffer terribly, especially when families do not push the children to higher expectations.

    In one Catechism setting, in a class of about a dozen, three of the students were convinced that they were stupid. They could barely read. They had very low comprehension. Their attention spans were terribly short. They had no clue how to memorize. They continually responded, “I can’t do this. I’m stupid.” I responded, “No. You are not stupid. Yes, you can do this. Yes, you will do this, and I will help you.” After a couple of months with them, the same students were volunteering to read and were excitedly reciting their memory work. They were reporting that their grades were improving drastically in school and their teachers and families were surprised. My time with them was a weekly time of an hour and a half.

    What Robert indicated about the value of demonstrating the applicability of a subject is invaluable in helping students to see the value of what they are being asked to learn. This is especially true regarding teaching the doctrine of the Bible. When the students are not merely learning about Jesus but are meeting Him and encountering His grace and learning how the means of grace really work, they become truly hungry. In another Catechism class one of the mothers repeatedly came to me bewildered, saying, “I don’t remember ever being exited about Catechism like my son is. He comes home saying, “Mom, Catechism is awesome, just awesome.””

    For a pastor it is much easier than for teachers of other subjects. Pastors don’t really have to be all that good, they only have to know Jesus and be truly living in the Holy Communion. Teachers cannot give what they themselves do not have. But the true faith is so easy to share because the Gospel is the power. When it is taught purely and in true faith, those who receive it are changed by it.

    But the Truth is powerful in all aspects of life. Any aspect of the Truth is exciting. This is because all articles of the Truth are from the One who is the Truth, and even encountering Him in Analytical Geometry or Micro Biology or Organic Chemistry is exciting. This is why even nonbelievers experience excitement in learning, because the power of the Truth is encountered.

    Even as a Web developer you have experienced the thrill of exposing people to a new article of the Truth. When you present a new understanding to people and they truly understand it, they become exited about it. That’s teaching! That is discipling. When the discipling is in the fullness of the glory of God, Christ, that’s heavenly! Ultimately, that is what is missing in government schools (and nearly all churches) today.

  • Joe

    tODD,

    I don’ t think anyone here was piling on teachers – we were piling on the schools and the manner teachers are forced to teach. When my wife and I were deciding if we should home school our daughter one of our major reservations was the fact that she had had terrific teachers. If they would have been allowed to teach with effective tools our decision would have been much harder to make. I thnk we probably would have ended up home school anyway but it would have been so much more difficult.

  • Joe

    tODD,

    I don’ t think anyone here was piling on teachers – we were piling on the schools and the manner teachers are forced to teach. When my wife and I were deciding if we should home school our daughter one of our major reservations was the fact that she had had terrific teachers. If they would have been allowed to teach with effective tools our decision would have been much harder to make. I thnk we probably would have ended up home school anyway but it would have been so much more difficult.

  • Jill

    Most people who speak against traditional math like Saxon have never looked at it. Saxon math discusses a topic thoroughly, and has many ‘revisits’ throughout the year. Also, the skill taught is revisited indirectly when it comes up in a more complicated lesson…the building block approach. A skill is taught, and then built upon…not left behind never to be seen again as reform/constructivist/integrated fans claim. And Saxon provides plenty of practice problems with each skill or topic, rather than an introduction and several options for discovery learning and almost no practice as in reform/integrated/fuzzy math.

    The spiraling that Everyday math (and other reform approaches) use has been devastating to my daughter because each topic is “touched on” or “introduced” with the promise of it returning but never is it drilled on or practiced enough for a child not strong in math to ever remember.

    Reform math did a great job making my daughter feel like she was good at math because she always got As, but then in 4th grade it was finally exposed that she really hadn’t learned or remembered a thing. All those years at teacher conferences where my husband and I mentioned that she really didn’t seem to know how to do math, often cried when trying to complete simple computations, etc, teachers would say “don’t worry, we don’t expect they will know how to do that yet, the students will gain more mastery they next time it comes around…”. In 4th grade her grades fell to Ds and I had her tested by a nationally normed test called the Peabody. She tested in 2nd grade at best and had holes in her knowledge. I bet that 2nd grade level was gained at our kitchen table when my husband or I would sometimes make up our own lessons to teach her skills she really should know. For instance, Everyday Math offered her several ways to compute addition and subtraction problems, de-emphasizing the standard algorithm, which sent our daughter to tears. She needed someone to teach her the ONE method that worked every time so she could find the correct answers. Trying to make her understand the “why” was confusing her as her brain was not ready for the why yet. It still isn’t, and neither was mine until I was in my late twenties. Embedding conceptual understanding into all math lessons by way of constructivist methods left my daughter in the dust…and since roughly a third of students struggle with it I fail to see why reform math has been allowed to stay in so many schools. Though I can tell from experience that parents have NO power in the math debate in my state and the School boards just do what the teachers want. (see my letter on this blog: http://mnedreform.blogspot.com/2007/06/was-choice-of-everyday-math.html)

    Reform math introduces far too many topics each year for any of them to be learned well…and then it relies on this spiraling to help kids to learn all of them over a number of years. Traditional math covers far less topics each year, and each topic is much more thoroughly taught, explored, practiced, and learned so that the building block method begins right away.

    We now homeschool, and it’s a good thing because my 2nd grade son is a whiz at math and can move at his own pace. All the while his sister can fill in the holes, go at her own pace, and isn’t stressed anymore. She will get the why for each topic when she is ready…and her brother will probably be the one to explain it to her because he gets it with no effort. That’s just how they are made.

    http://mnedreform.blogspot.com/2007/06/was-choice-of-everyday-math.html

  • Jill

    Most people who speak against traditional math like Saxon have never looked at it. Saxon math discusses a topic thoroughly, and has many ‘revisits’ throughout the year. Also, the skill taught is revisited indirectly when it comes up in a more complicated lesson…the building block approach. A skill is taught, and then built upon…not left behind never to be seen again as reform/constructivist/integrated fans claim. And Saxon provides plenty of practice problems with each skill or topic, rather than an introduction and several options for discovery learning and almost no practice as in reform/integrated/fuzzy math.

    The spiraling that Everyday math (and other reform approaches) use has been devastating to my daughter because each topic is “touched on” or “introduced” with the promise of it returning but never is it drilled on or practiced enough for a child not strong in math to ever remember.

    Reform math did a great job making my daughter feel like she was good at math because she always got As, but then in 4th grade it was finally exposed that she really hadn’t learned or remembered a thing. All those years at teacher conferences where my husband and I mentioned that she really didn’t seem to know how to do math, often cried when trying to complete simple computations, etc, teachers would say “don’t worry, we don’t expect they will know how to do that yet, the students will gain more mastery they next time it comes around…”. In 4th grade her grades fell to Ds and I had her tested by a nationally normed test called the Peabody. She tested in 2nd grade at best and had holes in her knowledge. I bet that 2nd grade level was gained at our kitchen table when my husband or I would sometimes make up our own lessons to teach her skills she really should know. For instance, Everyday Math offered her several ways to compute addition and subtraction problems, de-emphasizing the standard algorithm, which sent our daughter to tears. She needed someone to teach her the ONE method that worked every time so she could find the correct answers. Trying to make her understand the “why” was confusing her as her brain was not ready for the why yet. It still isn’t, and neither was mine until I was in my late twenties. Embedding conceptual understanding into all math lessons by way of constructivist methods left my daughter in the dust…and since roughly a third of students struggle with it I fail to see why reform math has been allowed to stay in so many schools. Though I can tell from experience that parents have NO power in the math debate in my state and the School boards just do what the teachers want. (see my letter on this blog: http://mnedreform.blogspot.com/2007/06/was-choice-of-everyday-math.html)

    Reform math introduces far too many topics each year for any of them to be learned well…and then it relies on this spiraling to help kids to learn all of them over a number of years. Traditional math covers far less topics each year, and each topic is much more thoroughly taught, explored, practiced, and learned so that the building block method begins right away.

    We now homeschool, and it’s a good thing because my 2nd grade son is a whiz at math and can move at his own pace. All the while his sister can fill in the holes, go at her own pace, and isn’t stressed anymore. She will get the why for each topic when she is ready…and her brother will probably be the one to explain it to her because he gets it with no effort. That’s just how they are made.

    http://mnedreform.blogspot.com/2007/06/was-choice-of-everyday-math.html

  • http://blog.faith-filled.com/ Stephenie

    Jill, you e-mailed me privately about this, but I don’t think you understood my post.

    I was saying I DO like Saxon for the same reasons you just mentioned.

    Saxon does refer to its method as spiraling (check the teacher’s manual.)

    Re-read both my comments, and I think you’ll see that I wasn’t slamming Saxon at all.

    Stephenie
    http://blog.faith-filled.com/

  • http://blog.faith-filled.com/ Stephenie

    Jill, you e-mailed me privately about this, but I don’t think you understood my post.

    I was saying I DO like Saxon for the same reasons you just mentioned.

    Saxon does refer to its method as spiraling (check the teacher’s manual.)

    Re-read both my comments, and I think you’ll see that I wasn’t slamming Saxon at all.

    Stephenie
    http://blog.faith-filled.com/


CLOSE | X

HIDE | X