[Note from Laurie Rogers: On May 1, a Spokane high school student asked if she could interview me for a pre-AP English paper she was writing on mathematics instruction. Below are her questions and my responses. This student received feedback from others on her questions and decided against posting her essay. It's too bad. It is a good essay.]
By Laurie H. Rogers
1) What do you think are the problems which are going to arise from poor math being taught to current students when they grow up and run America?
Most of the students will not be able to run America. I know you’re asking about math, but math is only the most visible problem in our government schools.
Today’s established workers are beginning to retire. There aren’t enough young Americans prepared to take over the reins. It isn’t just Spokane, and it isn’t just the STEM fields. Reform math, a lack of phonics or grammar, extreme constructivism, deceitful data, politically biased materials and approaches (a Spokane teacher openly advocates in his classroom for “revolution”!), obstructed teachers, questionable elective activity and misspent dollars are national problems.
Our public-school graduates don’t know enough math or grammar, how to work individually, how to analyze an argument, how to properly form and support their own argument, or that they should value truth over consensus. Many can’t read cursive writing – and cursive is important. Increasingly, government agencies and businesses hire from other countries. Colleges give seats to foreign students over local students. Who will run our nuclear facilities, fly our airplanes or be our doctors and engineers? Who will stand up for individual rights, the Constitution, the law, a free press or even truth? Who will run the country? Who will lead it? Who will defend it?
Look at Spokane – at the empty buildings, for-lease signs, empty stores in the malls, and failing businesses. Buildings that fall empty in Spokane frequently stay that way. Many are empty for years. The next generation should be starting businesses in them. Everyone blames “this economy.” This economy requires a ready and eager workforce. Too much of our workforce is undereducated, underprepared and uncertain. You can’t grow a city’s economy or run a community on Gonzaga Prep graduates and those few who manage to escape unscathed from SPS.
Public schools could learn from the military, homeschoolers and certain private schools like G-Prep – but they refuse to do it. How many instructional coaches do you suppose G-Prep has? How many teaching days do military instructors miss for “professional development”? How many people in a “Department of Teaching and Learning” – a misnamed department if I ever saw one – does G-Prep have? How much “discovery learning” do military recruits do? How much money per student does it cost the military to teach a high-school graduate basic math? How much time does it take any of these people to teach what the public schools won’t?
In public schools, administrative incompetence doesn’t result in firing; it results in a flood of excuses, blaming of teachers, and more taxpayer dollars for raises, promotions, awards, grants, studies, conferences, professional development and a de facto federal takeover.
Most public-school graduates will never get the academic skills they need. What will the country do with a workforce that lacks basic skills? This grim situation produces discontent, crime, gangs, drug abuse, poverty, social decay, and eventually – left long enough – social upheaval.
It’s ironic that the district blames poverty for many of its failures. As it blames poverty, it contributes to the poverty problem. Poverty is not the cause of the math problem. It’s the excuse, and it’s exacerbated by an administrative refusal to provide students with basic academic skills.
2) Why is the transition to teaching math in a more effective way taking so long?
It’s taking so long because administrators believe that the thing that needs to happen – direct teaching of efficient, effective and sufficient academic material – is wrong-headed. They do everything in their power, going to ridiculous lengths, to keep it out of the classrooms. Public records indicate that much district opposition to traditional math borders on hysteria.
Therefore, the way things are going, the transition will take forever. The current incarnation of reform math has been around since the 1980s, and it’s coming back – although in Spokane it never left.
The colleges of education continue to pump out teachers and administrators who love reform math, whole language instruction (not phonics), political advocacy (in math), and extreme constructivism. In 2010, I attended the 49th Annual Mathematics Conference in Spokane, where graduate students in the College of Education at UW put on several presentations. One presenter said that children who don’t want to learn math in groups fall into one of four categories: “bad apple,” “jerk,” “depressive,” and “slacker.” When I challenged this, she told the group, “We KNOW that children have to learn in groups. We KNOW that.” I asked a presenter for data on his discovery program, and he said: “Our goal here isn’t to prove anything; it’s to say, ‘How do we move teachers in this direction?’” Another asked why I attended if I didn’t agree with them. Another called struggling children “dummies.” As far as I know, I was the only person asking for proof or challenging their underlying premises about math instruction. Over two days of presentations, absolutely no supporting data was offered, and no one but me asked for it.
Many of their attitudes and trends are abusive to the children, and I don’t use the word lightly. Students drop out or graduate exhausted, bored, frustrated, confused, overworked, frightened, underprepared, sure they’re mathematically incompetent, yet filled with fake bravado … Math skills are the tip of the iceberg. For most of them, the damage is forever. They come out of public schools hating and fearing math, and they pass on that hatred and fear to the next generation.
And yet, decision-makers remain willfully ignorant of the students’ reality. (Read the “Betrayed” chapter on the OODA Loop.) People who don’t have children in public schools can afford to remain ignorant, to not stand up for the children and the taxpayers, and to not tell the people the truth. We have little or no leverage to replace them, and there is almost no accountability for the damage. When a $100,000+ administrator (who’s in charge of the math program), says to the school board, “No one knows how to solve the math problem,” why is she not replaced?
Superintendent Nancy Stowell said to me in 2008: “Sometimes I think people don’t want to know because when [you know, you have to] do something about it.” No kidding. She and her administrators have been told repeatedly that their program isn’t working. Instead of fixing it, they tend to “shoot” the messengers. How can we possibly fix a problem the leadership refuses to acknowledge?
On top of that, the Common Core State Standards – adopted unseen, untested, and largely unfunded by districts and states across the country – are leading districts back into reform math. This was my prediction; it is now fact. Districts are using the CCSS to adopt reform math and whole language programs. They call it a “new” way, but it’s the same recycled, reform, “student-centered,” constructivist, “best practices” garbage we’ve been drowning in since the 1980s.
There are slivers of success out there. But too many self-interested decision-makers are motivated to keep things as they are. Many spend taxpayer dollars getting laws passed to stop the public from knowing the truth or from being able to effect any positive change. They’ve also supported laws to blame teachers for dismal outcomes and to give themselves a free pass.
3) What do you think is the biggest problem with the way modern math is being taught?
Biggest problem #1: The most efficient, most effective algorithms are purposefully not being taught. Biggest problem #2: Administrators are convinced reform math and extreme constructivism would work if teachers would just do it right. From my book:
School districts nationwide have adopted “reform” approaches to mathematics. These approaches downplay (or avoid) “traditional” procedures, equations, practice, and memorization. The teacher is supposed to guide, not teach. Reform depends on constructivism (also known as “inquiry” or “discovery learning”), where students work in groups and on their own to “construct” or “discover” their own knowledge and methods for solving problems. Reform math focuses less on accuracy, efficiency, and achievement than on student-constructed strategies. Reform comes under many names: “problem based,” “standards based,” “inquiry based,” “discovery based,” “student centered,” “NSF funded,” and so forth. In addition, Chapter 5 in my book, “Corner 2: The curriculum” provides an overview that argues that mathematics is really quite simple to teach to children. That overview would be good to quote. Also from that chapter: People who are pro-reform say that reform math programs and discovery learning styles get students to “think mathematically.” With discovery, children supposedly explore, create, make connections, communicate, collaborate, build their own strategies for solving problems, and become “math literate,” all while having fun. A traditional approach to teaching mathematics, they say, doesn’t work, doesn’t meet the students’ needs, and isn’t useful in the twenty-first century. It’s bizarre. Traditional math took us to the moon and constructed bridges, railroads, skyscrapers, computers, microscopes, and airplanes. What reformers have been doing has not worked well for the students. Yet, administrators keep pouring time and money into reform math, letting teachers and students swing as they run into the west looking for that elusive sunrise. 4) How will the United States change if math skills with the new generation don’t improve?
I don’t know. It’s no exaggeration to say that the country is at risk. Refer back to my first answer. Who will run our industries and hospitals? Who will protect our nuclear facilities? I began my odyssey because of my daughter. I persevered on behalf of 28,000+ students who aren’t mine. But the deterioration in math skills spans the country. This nationwide educational malpractice puts America in jeopardy. It’s discouraging, but it’s also motivating. I am deeply concerned and worried. I do not want my daughter to live in a country at war with itself.
5) I have always thought there were two main ways to teach math, which were child-centered discovery learning, and traditional, where you do multiple problems and are taught how to do the math. Are there any other ways to teach math?
Some people promote a “balanced” approach, but what does that mean? Some administrators use the term “balanced” to allay concerns while continuing to emphasize reform math.
Math is what it is. There is a most-efficient way to teach it and myriad less-efficient or inefficient ways. Discovery learning is inefficient. Reform math is ineffective. Together, they don’t lead to proficiency in math. But many administrators do not appear to value efficiency, effectiveness, sufficiency, proficiency, or even right answers. In math, right answers are everything. There is little point to “deeper conceptual understanding” if the end result is incorrect, and I challenge the idea that you can have “deeper conceptual understanding” without procedural skills. Therefore, the best method of teaching math will entail the most efficient, most effective algorithms and approaches. That eliminates extreme constructivism and reform math.
Some pro-reformers have created a harsh caricature of traditional math, which they then criticize. Traditional math can be interesting and fun. In fact, if the teaching is efficient, that leaves more time for interesting activities. Why force students to continually waste time in groups trying to re-invent, for example, the Pythagorean Theorem?
There’s a renewed push for online learning. (Bill Gates is all for it – imagine that.) It’s hard on the eyes, for one thing, and not scientifically proved as being more effective than traditional instruction. Additionally, when I tutor, I see the need for a personal touch, for immediate, hands-on feedback and encouragement. Good teachers modify their instruction to suit their students. I use the same materials to tutor as I did for my daughter, but I pause in different places, choose different practice problems, provide more or less practice, and slightly different explanations … Until you get to Algebra II, the majority of students should receive the same math skills.
Below is a description of how I tutored my daughter. It’s part of an email I sent to an advocate friend who asked me to describe my approach for her legislators:
***
"Our daughter blossomed under Saxon Math, supplemented with older versions of Singapore Math. We sent lessons with her, and she worked quietly and efficiently with them. No calculators until Algebra II. She preferred this approach to the noisy, constructivist classroom. She went at her own pace. When she needed extra time, we paused for extra practice. We tested her regularly to be sure of understanding -- but she didn't view it as testing. She saw it as being sure of herself. Saxon Math is great that way. There is no stress, no confusion, no huge leaps in understanding. It's clear, concise, logical, well ordered, incremental…everything you want in a math program. Well, it's everything PARENTS want in a math program.
"Every evening, I wrote down which questions I wanted her to do, enough for the math period, and she did them the next day. If I knew we wouldn't be able to work on it that night for some reason, I gave her several days' worth. But I never let her get ahead of me. Every night, we went over her work so that I could correct misunderstandings right away. (Compare that to many classrooms, where work sits for a week or more and misunderstandings are allowed to compound.) I added a few drawings for fun. A ghost (me) provided instructions, and a sarcastic kitty (also me) provided humor. It didn't take a lot of time. (Singapore took more time than Saxon, but it was worthwhile. If I had to choose, however, I would choose Saxon over Singapore for the skills and amount of practice in Saxon. But I liked the two together until we hit Algebra I. Then we left Singapore and just stayed with Saxon.) Throughout, Saxon did the heavy lifting.
"In Saxon, the instructions are there. Good process is taught (write the equation, fill in what you know, solve for the variable, answer the question being asked, check your work, do everything vertically so you can see what you're doing, and show the work so you don't have to try to juggle multiple steps in your head). I actually had to reteach this process -- it's one of the problems I have with reform math -- it teaches very bad process that leads to many errors. And it isn't easy to reteach things. It took months to get the bad process out of our daughter. She kept leaping ahead without writing things down, and she's a quick learner, so most times she was right. But she made many errors. Once we got her to do proper process, she settled down and made dramatically fewer mistakes. It's like that with every student I tutor.
"With Saxon Math, there is proper application of concepts, but not foolishness, and no political agenda. Over seven months, our daughter went through Saxon 6/5, 7/6, and Algebra 1/2, plus Singapore Math 5a, 5b, 6a and 6b. It seems like a lot, but there was no loopy group work to slow her down. She just learned it, practiced it, and moved on. Then, over the summer of that year, we finished Algebra 1/2 and began Algebra I. The next year, we let the school handle it. But in 8th grade, faced again with a program we didn't want and a methodology we didn't want, we pulled her out. That year, we finished up Algebra I and began Algebra II. She got about 2/3 of the way through Algebra II by the end of 8th grade. (We probably could have finished it, but we had to deal with Algebra I first. There were important concepts missing from the school's approach to Algebra I. Again, not the teacher's fault -- the district kept dickering with math that year, forcing bad materials on the teachers. The result was almost unintelligible.)
"Math is a logical ordering of skills. It is what it is. Missing skills lead to missing understanding, which leads to wrong answers, which leads to frustration, confusion, and bad outcomes. It doesn't matter about anyone's feelings, or political agendas, or working in groups to "scaffold understanding," whatever that means. It's about getting right answers. Math is a tool. If you use it properly, you get right answers. If you don't use it properly, you get wrong answers, bad outcomes, frustration, confusion, and straight As from the public-school system, whereupon you try to go to college and wind up in remedial arithmetic (which you are likely to fail).
"I don't make this stuff up. Math is the easiest thing in the world to teach to children. Schools say it's hard. It really isn't, not when it's done properly. Saxon does it properly. And I'm not making any money from Saxon. I have a loaning library at my house. I often recommend people buy the older series secondhand from homeschooling bookstores, or off of eBay or Amazon."
Please note: The information in this post is copyrighted. The proper citation is:
Rogers, L. (May 2012). “America's math problem: What is it, why do we have it, and what will it do to America?" Retrieved (date) from the Betrayed Web site: http://betrayed-whyeducationisfailing.blogspot.com
By Laurie H. Rogers
1) What do you think are the problems which are going to arise from poor math being taught to current students when they grow up and run America?
Most of the students will not be able to run America. I know you’re asking about math, but math is only the most visible problem in our government schools.
Today’s established workers are beginning to retire. There aren’t enough young Americans prepared to take over the reins. It isn’t just Spokane, and it isn’t just the STEM fields. Reform math, a lack of phonics or grammar, extreme constructivism, deceitful data, politically biased materials and approaches (a Spokane teacher openly advocates in his classroom for “revolution”!), obstructed teachers, questionable elective activity and misspent dollars are national problems.
Our public-school graduates don’t know enough math or grammar, how to work individually, how to analyze an argument, how to properly form and support their own argument, or that they should value truth over consensus. Many can’t read cursive writing – and cursive is important. Increasingly, government agencies and businesses hire from other countries. Colleges give seats to foreign students over local students. Who will run our nuclear facilities, fly our airplanes or be our doctors and engineers? Who will stand up for individual rights, the Constitution, the law, a free press or even truth? Who will run the country? Who will lead it? Who will defend it?
Look at Spokane – at the empty buildings, for-lease signs, empty stores in the malls, and failing businesses. Buildings that fall empty in Spokane frequently stay that way. Many are empty for years. The next generation should be starting businesses in them. Everyone blames “this economy.” This economy requires a ready and eager workforce. Too much of our workforce is undereducated, underprepared and uncertain. You can’t grow a city’s economy or run a community on Gonzaga Prep graduates and those few who manage to escape unscathed from SPS.
Public schools could learn from the military, homeschoolers and certain private schools like G-Prep – but they refuse to do it. How many instructional coaches do you suppose G-Prep has? How many teaching days do military instructors miss for “professional development”? How many people in a “Department of Teaching and Learning” – a misnamed department if I ever saw one – does G-Prep have? How much “discovery learning” do military recruits do? How much money per student does it cost the military to teach a high-school graduate basic math? How much time does it take any of these people to teach what the public schools won’t?
In public schools, administrative incompetence doesn’t result in firing; it results in a flood of excuses, blaming of teachers, and more taxpayer dollars for raises, promotions, awards, grants, studies, conferences, professional development and a de facto federal takeover.
Most public-school graduates will never get the academic skills they need. What will the country do with a workforce that lacks basic skills? This grim situation produces discontent, crime, gangs, drug abuse, poverty, social decay, and eventually – left long enough – social upheaval.
It’s ironic that the district blames poverty for many of its failures. As it blames poverty, it contributes to the poverty problem. Poverty is not the cause of the math problem. It’s the excuse, and it’s exacerbated by an administrative refusal to provide students with basic academic skills.
2) Why is the transition to teaching math in a more effective way taking so long?
It’s taking so long because administrators believe that the thing that needs to happen – direct teaching of efficient, effective and sufficient academic material – is wrong-headed. They do everything in their power, going to ridiculous lengths, to keep it out of the classrooms. Public records indicate that much district opposition to traditional math borders on hysteria.
Therefore, the way things are going, the transition will take forever. The current incarnation of reform math has been around since the 1980s, and it’s coming back – although in Spokane it never left.
The colleges of education continue to pump out teachers and administrators who love reform math, whole language instruction (not phonics), political advocacy (in math), and extreme constructivism. In 2010, I attended the 49th Annual Mathematics Conference in Spokane, where graduate students in the College of Education at UW put on several presentations. One presenter said that children who don’t want to learn math in groups fall into one of four categories: “bad apple,” “jerk,” “depressive,” and “slacker.” When I challenged this, she told the group, “We KNOW that children have to learn in groups. We KNOW that.” I asked a presenter for data on his discovery program, and he said: “Our goal here isn’t to prove anything; it’s to say, ‘How do we move teachers in this direction?’” Another asked why I attended if I didn’t agree with them. Another called struggling children “dummies.” As far as I know, I was the only person asking for proof or challenging their underlying premises about math instruction. Over two days of presentations, absolutely no supporting data was offered, and no one but me asked for it.
Many of their attitudes and trends are abusive to the children, and I don’t use the word lightly. Students drop out or graduate exhausted, bored, frustrated, confused, overworked, frightened, underprepared, sure they’re mathematically incompetent, yet filled with fake bravado … Math skills are the tip of the iceberg. For most of them, the damage is forever. They come out of public schools hating and fearing math, and they pass on that hatred and fear to the next generation.
And yet, decision-makers remain willfully ignorant of the students’ reality. (Read the “Betrayed” chapter on the OODA Loop.) People who don’t have children in public schools can afford to remain ignorant, to not stand up for the children and the taxpayers, and to not tell the people the truth. We have little or no leverage to replace them, and there is almost no accountability for the damage. When a $100,000+ administrator (who’s in charge of the math program), says to the school board, “No one knows how to solve the math problem,” why is she not replaced?
Superintendent Nancy Stowell said to me in 2008: “Sometimes I think people don’t want to know because when [you know, you have to] do something about it.” No kidding. She and her administrators have been told repeatedly that their program isn’t working. Instead of fixing it, they tend to “shoot” the messengers. How can we possibly fix a problem the leadership refuses to acknowledge?
On top of that, the Common Core State Standards – adopted unseen, untested, and largely unfunded by districts and states across the country – are leading districts back into reform math. This was my prediction; it is now fact. Districts are using the CCSS to adopt reform math and whole language programs. They call it a “new” way, but it’s the same recycled, reform, “student-centered,” constructivist, “best practices” garbage we’ve been drowning in since the 1980s.
There are slivers of success out there. But too many self-interested decision-makers are motivated to keep things as they are. Many spend taxpayer dollars getting laws passed to stop the public from knowing the truth or from being able to effect any positive change. They’ve also supported laws to blame teachers for dismal outcomes and to give themselves a free pass.
3) What do you think is the biggest problem with the way modern math is being taught?
Biggest problem #1: The most efficient, most effective algorithms are purposefully not being taught. Biggest problem #2: Administrators are convinced reform math and extreme constructivism would work if teachers would just do it right. From my book:
I don’t know. It’s no exaggeration to say that the country is at risk. Refer back to my first answer. Who will run our industries and hospitals? Who will protect our nuclear facilities? I began my odyssey because of my daughter. I persevered on behalf of 28,000+ students who aren’t mine. But the deterioration in math skills spans the country. This nationwide educational malpractice puts America in jeopardy. It’s discouraging, but it’s also motivating. I am deeply concerned and worried. I do not want my daughter to live in a country at war with itself.
5) I have always thought there were two main ways to teach math, which were child-centered discovery learning, and traditional, where you do multiple problems and are taught how to do the math. Are there any other ways to teach math?
Some people promote a “balanced” approach, but what does that mean? Some administrators use the term “balanced” to allay concerns while continuing to emphasize reform math.
Math is what it is. There is a most-efficient way to teach it and myriad less-efficient or inefficient ways. Discovery learning is inefficient. Reform math is ineffective. Together, they don’t lead to proficiency in math. But many administrators do not appear to value efficiency, effectiveness, sufficiency, proficiency, or even right answers. In math, right answers are everything. There is little point to “deeper conceptual understanding” if the end result is incorrect, and I challenge the idea that you can have “deeper conceptual understanding” without procedural skills. Therefore, the best method of teaching math will entail the most efficient, most effective algorithms and approaches. That eliminates extreme constructivism and reform math.
Some pro-reformers have created a harsh caricature of traditional math, which they then criticize. Traditional math can be interesting and fun. In fact, if the teaching is efficient, that leaves more time for interesting activities. Why force students to continually waste time in groups trying to re-invent, for example, the Pythagorean Theorem?
There’s a renewed push for online learning. (Bill Gates is all for it – imagine that.) It’s hard on the eyes, for one thing, and not scientifically proved as being more effective than traditional instruction. Additionally, when I tutor, I see the need for a personal touch, for immediate, hands-on feedback and encouragement. Good teachers modify their instruction to suit their students. I use the same materials to tutor as I did for my daughter, but I pause in different places, choose different practice problems, provide more or less practice, and slightly different explanations … Until you get to Algebra II, the majority of students should receive the same math skills.
Below is a description of how I tutored my daughter. It’s part of an email I sent to an advocate friend who asked me to describe my approach for her legislators:
***
"Our daughter blossomed under Saxon Math, supplemented with older versions of Singapore Math. We sent lessons with her, and she worked quietly and efficiently with them. No calculators until Algebra II. She preferred this approach to the noisy, constructivist classroom. She went at her own pace. When she needed extra time, we paused for extra practice. We tested her regularly to be sure of understanding -- but she didn't view it as testing. She saw it as being sure of herself. Saxon Math is great that way. There is no stress, no confusion, no huge leaps in understanding. It's clear, concise, logical, well ordered, incremental…everything you want in a math program. Well, it's everything PARENTS want in a math program.
"Every evening, I wrote down which questions I wanted her to do, enough for the math period, and she did them the next day. If I knew we wouldn't be able to work on it that night for some reason, I gave her several days' worth. But I never let her get ahead of me. Every night, we went over her work so that I could correct misunderstandings right away. (Compare that to many classrooms, where work sits for a week or more and misunderstandings are allowed to compound.) I added a few drawings for fun. A ghost (me) provided instructions, and a sarcastic kitty (also me) provided humor. It didn't take a lot of time. (Singapore took more time than Saxon, but it was worthwhile. If I had to choose, however, I would choose Saxon over Singapore for the skills and amount of practice in Saxon. But I liked the two together until we hit Algebra I. Then we left Singapore and just stayed with Saxon.) Throughout, Saxon did the heavy lifting.
"In Saxon, the instructions are there. Good process is taught (write the equation, fill in what you know, solve for the variable, answer the question being asked, check your work, do everything vertically so you can see what you're doing, and show the work so you don't have to try to juggle multiple steps in your head). I actually had to reteach this process -- it's one of the problems I have with reform math -- it teaches very bad process that leads to many errors. And it isn't easy to reteach things. It took months to get the bad process out of our daughter. She kept leaping ahead without writing things down, and she's a quick learner, so most times she was right. But she made many errors. Once we got her to do proper process, she settled down and made dramatically fewer mistakes. It's like that with every student I tutor.
"With Saxon Math, there is proper application of concepts, but not foolishness, and no political agenda. Over seven months, our daughter went through Saxon 6/5, 7/6, and Algebra 1/2, plus Singapore Math 5a, 5b, 6a and 6b. It seems like a lot, but there was no loopy group work to slow her down. She just learned it, practiced it, and moved on. Then, over the summer of that year, we finished Algebra 1/2 and began Algebra I. The next year, we let the school handle it. But in 8th grade, faced again with a program we didn't want and a methodology we didn't want, we pulled her out. That year, we finished up Algebra I and began Algebra II. She got about 2/3 of the way through Algebra II by the end of 8th grade. (We probably could have finished it, but we had to deal with Algebra I first. There were important concepts missing from the school's approach to Algebra I. Again, not the teacher's fault -- the district kept dickering with math that year, forcing bad materials on the teachers. The result was almost unintelligible.)
"Math is a logical ordering of skills. It is what it is. Missing skills lead to missing understanding, which leads to wrong answers, which leads to frustration, confusion, and bad outcomes. It doesn't matter about anyone's feelings, or political agendas, or working in groups to "scaffold understanding," whatever that means. It's about getting right answers. Math is a tool. If you use it properly, you get right answers. If you don't use it properly, you get wrong answers, bad outcomes, frustration, confusion, and straight As from the public-school system, whereupon you try to go to college and wind up in remedial arithmetic (which you are likely to fail).
"I don't make this stuff up. Math is the easiest thing in the world to teach to children. Schools say it's hard. It really isn't, not when it's done properly. Saxon does it properly. And I'm not making any money from Saxon. I have a loaning library at my house. I often recommend people buy the older series secondhand from homeschooling bookstores, or off of eBay or Amazon."
Please note: The information in this post is copyrighted. The proper citation is:
Rogers, L. (May 2012). “America's math problem: What is it, why do we have it, and what will it do to America?" Retrieved (date) from the Betrayed Web site: http://betrayed-whyeducationisfailing.blogspot.com
