The New New Math: Back to Basics

[Hunter]

This newspaper article and "to the editor" letters are interesting.

 

http://www.nytimes.com/2006/11/19/opinion/l19math.html

 

Does anyone here consider themselves to be a "back to basics" math teacher? So many more homeschoolers in the 80's and 90's were "back to basics", but I see a sharp shift from that lately. "Back to Basics" seems to almost be synonymous with child neglect.

Edited September 25, 2012 by Hunter

[regentrude]

This newspaper article and "to the editor" letters are interesting.

 

Does anyone here consider themselves to be a "back to basics" math teacher? So many more homeschoolers in the 80's and 90's were "back to basics", but I see a sharp shift from that lately. "Back to Basics" seems to almost be synonymous with child neglect.

 

Link, please?

[Hunter]

link added :tongue_smilie:

[regentrude]

I am constantly surprised by what is billed as a great new discovery. The article itself was pretty lame, but the comments are quite good. If you just look at the first few pages, many of the suggestions are really just common sense:

 

take all calculators out of the classroom. Students need to understand math concepts. How can they learn if they are allowed to use calculators before mastering the basic concepts.

It is vital that our teachers be better trained to teach math, particularly at the elementary level. Many teachers openly express an outright fear of math, and do not the subject the attention it deserves. The bottom line is that teachers who cannot solve math problems themselves should not be teaching that subject.

Basic arithmetic is essential to gain a feeling for the relationship of numbers. This could never happen if only concepts are taught. Concepts only come with working with the whole array of arithmetic.

The United States curriculum is “a mile wide and an inch deep,” lacking a focus at each grade.

This is simply common sense. Edited September 25, 2012 by regentrude

[crazyforlatin]

This newspaper article and "to the editor" letters are interesting.

 

http://www.nytimes.com/2006/11/19/opinion/l19math.html

 

Does anyone here consider themselves to be a "back to basics" math teacher? So many more homeschoolers in the 80's and 90's were "back to basics", but I see a sharp shift from that lately. "Back to Basics" seems to almost be synonymous with child neglect.

 

What shift have you noticed? I remember that article, but at that time DD was just about year old, so Everyday Math and other math curricula were just names.

 

People who use SM or MM are back to basics, as defined in the article. Since I do use both, and other math books, I must be. :tongue_smilie:

[Hunter]

In the 1980's I attended a church with a lot of homeschoolers. My boys started PS in the early 90's and I knew very few homeschoolers by then. I pulled my 2E 5th grader out in the mid 90's, after doing a couple years of afterschooling.

 

In the mid 90's the PS was just switching over to fuzzy math and the parents were throwing a hissy, but being ignored. It was a disaster in out low income school and just plain bad in the neighboring schools.

 

The few homeschoolers I knew, and what I saw in the catalogs, was all pretty much back-to-basics math, and a few living books and manipulatives mostly sold as ENRICHMENT. Adding in a math journal was trendy :lol:

 

I've been reading a lot of vintage math, How to Tutor, and my new favorite A Guide to Christian Education. I have a bad memory so maybe I've already labeled myself "back-to-basics" in math. I've been seeking out all the 80s math and science I can get my hands on. Some pretty nasty books from the library. And have been adding in 'enrichment' but teaching it as enrichment and not as the core curriculum.

 

I hear so much attention to Asian maths and the conceptual curriculums. I don't remember ever seeing a thread here on back-to-basics math. Even if we talk vintage or oldschool or drill, I don't remember anyone using the term "back-to-basics math" and am not sure I've heard it in a very LONG time. Again, I've got a bad memory from the seizures, so forgive me if anyone remembers me saying who knows what in another thread. :D

 

I just thought it might be fun to throw around the term "back-to-basics" math, and see what came up for conversation. :bigear:

[Spy Car]

People who use SM or MM are back to basics, as defined in the article. Since I do use both, and other math books, I must be. :tongue_smilie:

 

I don't think the rich sort of math education offered by programs like Singapore are what people have in mind when they use the term "back-to-basics." Instead it refers to the shallow algorithm-only style of math education that emphasizes the memorization of "math facts" and de-emphasizes actual understanding of the mathematics.

 

"Back-to-basics" is not a move forward IMO. We need better for the 21st Century.

 

Bill

[SorrelZG]

I have a strong focus on mastering the basics which involves knowing them cold as a result of fully grasping them and working with them a lot in many different situations. Being able to compute without comprehension doesn't make sense to me. That's not mastery. Neither is comprehending the idea without being efficient and precise in its use. I don't understand the separation.

[Spy Car]

I have a strong focus on mastering the basics which involves knowing them cold as a result of fully grasping them and working with them a lot in many different situations. Being able to compute without comprehension doesn't make sense to me. That's not mastery. Neither is comprehending the idea without being efficient and precise in its use. I don't understand the separation.

 

Yep. Students need both procedural competence and a deep understanding of the mathematics. But this is not what the "back-to-basics" math movement is about. It is a reactionary movement that believes memorized procedural arithmetics (that is to say the ability to work the standard algorithms without really having a deep grasp of the math, or parroting back "math facts") is an adequate—or even optimal—math education. It is not.

 

"Back-to-basics" also cuts out (or reduces to the minimum) all reasoning, logic, and critical thinking exercises in favor of an approach where student get an almost *no thinking* approach to math.

 

I get that some people have been angered about "fuzzy math" programs like Everyday Mathematics" and—in reaction—have embraced ""back-to-basics" which sounds "good" when children are struggling with basic competence, but in actuality "back-to-basics" is another bad choice.

 

The good news is that there are excellent programs out there that help parents and children learn mathematics as a deep subject. Ones that promote basic skills while teaching the laws of mathematics and promoting *thinking*. This is what students in the 21st Century needs.

 

Bill

Edited September 26, 2012 by Spy Car
Sorry, good not wood

[Farrar]

 

I get that some people have been angered about "fuzzy math" programs like Everyday Mathematics" and—in reaction—have embraced ""back-to-basics" which sounds "good" when children are struggling with basic competence, but in actuality "back-to-basics" is another bad choice.

 

And people present it as if these are the only choices - either things are fuzzy or they're old fashioned. It's just sad that people seem to keep falling for this false dichotomy.

[Hunter]

I don't think that's what they have in mind either. Frankly, I think people who say that just hate math and are looking for an out.

 

I'm sure I'll be flamed for that.

 

What does "say that" mean?

 

I'm mostly just being quiet here, because I'm still trying to get a feel for what has changed, and maybe get some input from people who don't usually post in the math threads.

 

I feel like math here, might be like the proslavery issues. The loudest and most persistent voices might not be indicative of the general thoughts here and elsewhere.

 

I'm wondering if the people who have been teaching for decades teach differently now, and if so why. Catalogs are certainly different. Webpages/blog are different. But I haven't had the chance to observe if families/companies have changed or if different families/companies are broadcasting.

 

I guess I was right that "back-to basics" is a term that is not being used in the homeschool community anymore? I still see it popping up in advertisements for inner city charter schools. The type that use Riggs/Spalding but NOT Asian math.

Edited September 26, 2012 by Hunter

[Spy Car]

I don't think that's what they have in mind either. Frankly, I think people who say that just hate math and are looking for an out.

 

 

The back-to-basics movement believes you can (and should) separate out "arithmetic" from mathematics. They believe that arithmetic can (and should) be taught as a series of procedural steps to be followed, with provided numbers plugged into provided formulas to yeild "correct" answers without teaching the "mathematics" behind operations. It also emphasizes rote-memory of math facts as opposed to learning the axioms behind operations.

 

It strips out (as a negative) the promotion of algebraic thinking and logic.

 

It really isn't what you think it means. "Back-to-basics" is a very shallow approach.

 

Bill

[regentrude]

Yep. Students need both procedural competence and a deep understanding of the mathematics.

 

Absolutely.

 

But this is not what the "back-to-basics" math movement is about. It is a reactionary movement that believes memorized procedural arithmetics (that is to say the ability to work the standard algorithms without really having a deep grasp of the math, or parroting back "math facts") is an adequate—or even optimal—math education. It is not.

"Back-to-basics" also cuts out (or reduces to the minimum) all reasoning, logic, and critical thinking exercises in favor of an approach where student get an almost *no thinking* approach to math.

 

 

:iagree:

[wapiti]

The wood news is that there are excellent programs out there that help parents and children learn mathematics as a deep subject. Ones that promote basic skills while teaching the laws of mathematics and promoting *thinking*. This is what students in the 21st Century needs.

 

:iagree: This is so important.

 

And people present it as if these are the only choices - either things are fuzzy or they're old fashioned. It's just sad that people seem to keep falling for this false dichotomy.

:iagree:

 

FWIW, I'm guessing "back to basics" is simply "traditional" math - the pendulum swinging way back to the other side again, away from the "new new math" ("new new math" = fuzzy math). I wish the pendulum would stop in the middle ;).

[Spy Car]

And people present it as if these are the only choices - either things are fuzzy or they're old fashioned. It's just sad that people seem to keep falling for this false dichotomy.

 

Yep. It is a trap between thinking the only alternatives are between two bad choices. When that is not the case.

 

There is a third choice.

 

Bill

[regentrude]

I feel like math here, might be like the proslavery issues. The loudest and most persistent voices might not be indicative of the general thoughts here and elsewhere.

 

 

I am not sure why one would want to look for the "general" thoughts on math education - I would look for the thoughts of people who use math every day and know what the shortcomings of students are.

This is precisely one of the problem with math educators: they do not use math, they have not the slightest idea of what math skills people need who actually use it - they are dreaming up concepts and ideas in their ivory towers (and come up with stuff like Everyday Math... the actual mathematicians involved the developing the curriculum have long been alienated from it)

 

I'm wondering if the people who have been teaching for decades teach differently now, and if so why.

 

What people? Teachers at school have no choice how to teach; the school board chooses the curriculum (typically without any subject expertise) and forces the teacher to use whatever they have picked.

Homeschooling parents very often choose what everybody else is picking - because most people do not have the math background to carefully select a good curriculum. You have to know the material before you can choose what to teach it with. So just because there are trends, it does not mean that there is an actual paradigm shift. It means things go in and out of fashion, like skirt lengths.

[Hunter]

I agree that "back-to-basics" is reactionary and any reaction can be as bad as what is being reacted to, if it is taken too far.

 

Reactions get us started, and then we need to level out quickly to the middle ground.

[regentrude]

That is what I thought back to basics meant. Like the way I was taught. I was never taught concepts such as place value. I recall the first mention of the commutative and associate properties in high school geometry while learning about proofs. My 7 year old understands these concepts without any trouble. There is nothing fuzzy about it. It's almost painful to learn about the basics without these concepts.

 

And it is also much harder and more time consuming.

A student with understanding will never forget - because he will always able to reconstruct the relationship.

Unfortunately, some curricula that emphasize conceptual understanding are neglecting the actual proficiency in execution; as SpyCar said before, all conceptual understanding is not good enough if the student can not quickly and efficiently compute.

 

I do not see where this either-or approach comes from. When I attended school (in communist East Germany), our math program was strong in both conceptual understanding and computational speed and accuracy; it is perfectly possible to have BOTH.

[Hunter]

I am not sure why one would want to look for the "general" thoughts on math education

 

I just got curious. :tongue_smilie: :bigear:

[Hunter]

I think one of the biggest problems is that elementary school teachers aren't generally specialized as math educators. It's hard to be strong in every subject and math too often seems to be the subject many are especially weak in.

 

I think many homeschools have this same issue to work through.

[regentrude]

I think one of the biggest problems is that elementary school teachers aren't generally specialized as math educators. It's hard to be strong in every subject and math too often seems to be the subject many are especially weak in.

:iagree:

Yep. (My son had a 2nd grade teacher who did not understand percent.)

Unfortunately, this is not even restricted to elementary math teachers.

In order to teach a subject well, it is necessary to know not just the material one will be teaching, but to have expertise several levels above the level one is teaching. You can't teach effectively if you are close to the limit of your knowledge; you need more, to have the necessary perspective.

[regentrude]

I think many homeschools have this same issue to work through.

 

Yes. And I know that my opinion will be very unpopular and get flames: but a parent who does not herself understand fractions or negative numbers can not possibly teach her children to understand fractions or negative numbers. Some of the questions posed by parents on these boards occasionally have me scratch my head why these people think they can, and should, teach math.

Now you can all hate me.

[Spy Car]

I agree that "back-to-basics" is reactionary and any reaction can be as bad as what is being reacted to, if it is taken too far.

 

Reactions get us started, and then we need to level out quickly to the middle ground.

 

With due respect, we do not need "middle ground" we need to find "new ground." A synthesis between two failed approaches will not yield success. We need to move on along a different a pole, rather than swing back and sort between failed approaches and thinking "common ground" between might be the answer.

 

Bill

Edited September 26, 2012 by Spy Car

[kiana]

:iagree:

Yep. (My son had a 2nd grade teacher who did not understand percent.)

Unfortunately, this is not even restricted to elementary math teachers.

In order to teach a subject well, it is necessary to know not just the material one will be teaching, but to have expertise several levels above the level one is teaching. You can't teach effectively if you are close to the limit of your knowledge; you need more, to have the necessary perspective.

 

And yet, when teaching math for elementary teachers, the comment of 'But why do I have to learn fractions? I'm just going to teach kindergarten!' is frequently heard.

 

:banghead:

[mommymilkies]

I'm not sure what "back to basics" math is. I was a student in the 80s. We learned how to add, subtract, multiply, and divide whole numbers. We had a few brief topics in fractions, percents, and decimals. Then I was dropped into the middle of the ocean that was algebra in the 7th grade. I felt so lost I hated math and pretty much gave up.

 

Fast forward to now and using SM with my kids I feel like someone flicked a switch and a lot of stuff makes sense. There is nothing "new math" or fuzzy about it. What it doesn't really do is ONLY teach memorizing facts. That's all I was taught. I remember just calculating with my crayons. I asked my parents to buy me a REALLY big box of crayons. I never knew how to calculate other than memorize the facts or count my box of crayons. I certainly had no idea what any of it was good for. Even my 7 year old math hating son already has it figured out better. And that's even despite me!

 

Edited to add, we did not learn how to do those things....we memorized math facts.

 

:iagree: it took me reading Knowing and Teaching...by Liping Ma and doing SM with my kids to understand even basic math. And I was pre-med! I could memorize it, but understanding came relatively recently.

[mommymilkies]

I honestly have no idea how I passed math in high school. I was so disgusted I didn't even do my homework.

 

I homeschool in huge part because I don't want my kids to have that same experience.

 

Exactly! I expect understanding, not guessing by my kids. The sad thing is that I'm not even bad at math. I just was never really taught to understand it. Just to plug in numbers to get it over with!

[birchbark]

I'm not sure it is correct to say all "old-fashioned" or "back to basics" math is shallow and without critical thinking or logic. Take a look at old, reprinted math books such as Ray's or Strayer-Upton or this old text. I think the back-to-basics math I used in the 80's may fit that categorization better.

 

Here also are some brief thoughts by an older math teacher.

[Spy Car]

I'm not sure it is correct to say all "old-fashioned" or "back to basics" math is shallow and without critical thinking or logic. Take a look at old, reprinted math books such as Ray's or Strayer-Upton or this old text. I think the back-to-basics math I used in the 80's may fit that categorization better.

 

Here also are some brief thoughts by an older math teacher.

 

The linked text is a critique of the algorithm-only style of education which gives emphasis to procedural written work at the expense of more efficient mental math techniques. It is a critique of the model supported by the "back-to-basics" proponents.

 

Bill

[Tanikit]

This reminds me of the phonics vs whole word approach to reading. Why, oh why can't we all just use BOTH? Back-to-basics is sort of like using whole words to teach initial reading - it gets people going without the whole break down being understood - the algorithms and the rote memorization are there to speed things up and to enable people to do problems in what would be considered a reasonable length of time. The "fluffy" math is there to work creatively to solve problems and is the type needed most in math olympiads or even in many word problems. The aim of "fluffy" math was that in order to get an answer without rote memorization some understanding of the problem needed to be there.

 

So let them try to solve it, get them to say their ways of figuring it out and then ask them which method was fastest and most efficient and if they didn't give the fastest method then teach them the algorithm. They need BOTH - they need to be able to try problems without an algorithm which they might not understand but once they understand it they need to know the fastest way to solve it since time is money.

 

Basically though math is closely related to language and unless someone understands what is being asked they will not be able to solve it (which is why word problems can be so challenging) Algebra is often seen as very difficult, but really it is where langauge and math meet and so it makes sense.

 

This article was written in 2006 - where have things come since then? Are they still using fluffy math or is it basic algorithms and rote memorization or have they put both together to make a more balanced approach?

[kiana]

Estimating is actually a very useful skill in any sort of real-life application and in error-checking. For example, if I take the average (arithmetic mean, for any pedants out there) of a set of ten single-digit numbers, I should not get a double-digit answer. If I'm calculating funds needed for gas for a trip, I don't need to calculate to the last penny; I estimate and then add 10%. To toss this sort of skill out as 'It's just guessing' is ridiculous.

[Hunter]

Grube's Method is old and is conceptual.

 

The vintage Eclectic teacher's manual teacher concepts in math and geography, and warns about drilling without understanding.

[Hunter]

I'm not sure it is correct to say all "old-fashioned" or "back to basics" math is shallow and without critical thinking or logic. Take a look at old, reprinted math books such as Ray's or Strayer-Upton or this old text. I think the back-to-basics math I used in the 80's may fit that categorization better.

 

Here also are some brief thoughts by an older math teacher.

 

Thanks for the links! I love math links :D Especially vintage and controversial ones!

[Spy Car]

What is fluffy math?

 

I think she meant to say "fuzzy math," which is the pergorative term for programs like Everyday Mathematics and TERC Investigations.

 

Bil

Edited September 26, 2012 by Spy Car

[Spy Car]

Oh...

 

:D

 

You knew that...didn't ya? :D

 

Bill

[Hunter]

In my son's 4th grade class, fuzzy math meant only 3 students were able to do short division by the end of the year. All 3 were taught by their parents. My son was the only one able to do long division by the end of the year. The burly construction worker dad who was teaching his little daughter was a hoot. He was DISGUSTED and so underprepared and didn't know what else to do but try. The only thing funnier would have been watching him try and change a diaper.

 

The school principal said I trained my son like a monkey. Yeh, well...at least he could divide at all. :tongue_smilie: Yes I hadn't taught him concepts, because I was a dumb, sick, low-income housewife, only a few years out of my teens, who had nothing to use other than a library book.

 

The next year, I yanked him out of school and using nothing but scraps from yard sales and the library and Saxon Algebra 1, he managed to score the highest scores in our entire very large town.

 

I try to continue to study as much about math as I can, and listen to all sides. Then afford what I can, and look at the realities of the students I am teaching, and my own current health and time to teach. All we can do is our best right?

 

I appreciate all the math chat. Math chat has changed over the years. I mean SERIOUSLY changed. More money is being spent. More time is being spent. I'm not at all sure that students are learning more math though. Parent sure feel prouder or worse about THEMSELVES though. :001_huh:

[Hunter]

:001_huh: Oh brother. What kind of principal says stuff like that!

 

One who believes fuzzy math is the ONLY way. :tongue_smilie:

 

I kinda wish it was the construction worker who had been the sucessful one and that the principal had told HIM that he had trained his DAUGHTER like a monkey. :lol:

[Violet Crown]

The back-to-basics movement believes you can (and should) separate out "arithmetic" from mathematics.

 

Well now, I was agreeing with you up to this point, but we've always separated "arithmetic" from "math" in our household, and it's very successful. Arithmetic here means increasing speed and accuracy in computation through practice problems of gradually increasing difficulty. So for instance learning how to divide, how division relates to multiplication, fractions, and slope, etc. are part of the math lesson; and while math moves onward, the arithmetic lessons provide practice in division problems, eventually including techniques for division with multiple-digit divisors.

 

It neatly solves the problem, we find, of children being able to grasp mathematical concepts but not yet having the stamina for large or complex problems involving those concepts. But then, we are guilty of loving New Math and Back to Basics and any kind of number fun we can lay our hands on around here. Our math is even fuzzy when the cat plops down on the paper.

[Spy Car]

Well now, I was agreeing with you up to this point, but we've always separated "arithmetic" from "math" in our household, and it's very successful. Arithmetic here means increasing speed and accuracy in computation through practice problems of gradually increasing difficulty. So for instance learning how to divide, how division relates to multiplication, fractions, and slope, etc. are part of the math lesson; and while math moves onward, the arithmetic lessons provide practice in division problems, eventually including techniques for division with multiple-digit divisors.

 

It neatly solves the problem, we find, of children being able to grasp mathematical concepts but not yet having the stamina for large or complex problems involving those concepts. But then, we are guilty of loving New Math and Back to Basics and any kind of number fun we can lay our hands on around here. Our math is even fuzzy when the cat plops down on the paper.

 

The difference being they don't believe in teaching "mathematics" to children. You do. I'm all for developing strong procedural competency in arithmetic. But we both know that is not the end of the story.

 

Bill

[SunnyDays]

One who believes fuzzy math is the ONLY way. :tongue_smilie:

 

I kinda wish it was the construction worker who had been the sucessful one and that the principal had told HIM that he had trained his DAUGHTER like a monkey. :lol:

 

That would have been fun to watch. :D

 

As for believing fuzzy math is the only way... unfortunately I think that line of thought is all too prevalent around here. The districts in all directions around us are now using Everyday Math... some *just* switched over this year and are touting how successful the program has been and how they look forward to using it. Not sure what studies they're reading...

[WishboneDawn]

Yes. And I know that my opinion will be very unpopular and get flames: but a parent who does not herself understand fractions or negative numbers can not possibly teach her children to understand fractions or negative numbers. Some of the questions posed by parents on these boards occasionally have me scratch my head why these people think they can, and should, teach math.

Now you can all hate me.

 

 

:lol: No hate here.

 

I have the same issue when folks are teaching their kids English but can't seem to capitalize the first letter in sentences.

[WishboneDawn]

:iagree:

Yep. (My son had a 2nd grade teacher who did not understand percent.)

Unfortunately, this is not even restricted to elementary math teachers.

In order to teach a subject well, it is necessary to know not just the material one will be teaching, but to have expertise several levels above the level one is teaching. You can't teach effectively if you are close to the limit of your knowledge; you need more, to have the necessary perspective.

 

I agree even though for much of our math homeschooling and even now, I'm learning along with my daughter. I'm very lucky in that she's exceedingly quick, and very much a self-directed learner but if my son had come first I would have been up S**t Creek without a paddle. As it is I'm still sending her off to the DH quite often and may have to search for a tutor for grades 11 and 12.

 

I didn't get that for many years, I thought learning along with my child was fine but now that I can look back on arithmetic and pre-algebra and see many of the connections and concepts I'm a little put out that I couldn't offer that to my daughter. But it worked out okay and when you know better, you do better. I hope. :)

[shinyhappypeople]

The back-to-basics movement believes you can (and should) separate out "arithmetic" from mathematics. They believe that arithmetic can (and should) be taught as a series of procedural steps to be followed, with provided numbers plugged into provided formulas to yeild "correct" answers without teaching the "mathematics" behind operations. It also emphasizes rote-memory of math facts as opposed to learning the axioms behind operations.

 

It strips out (as a negative) the promotion of algebraic thinking and logic.

 

It really isn't what you think it means. "Back-to-basics" is a very shallow approach.

 

Bill

 

I guess it depends on how you define "back to basics."

 

I have 2 daughters. I'm taking a "back to basics" approach with my 9 year old. What that means is that we prioritize arithmetic over math, and yes, algebra will be given a back seat until she's older and more ready to deal with abstractions. Our approach is concrete, visual, and practical. It is not rote. It is definitely not drill and kill. My goal is that she have rock solid understanding of the 4 operations, decimals/fractions before we move to algebra topics. This is what she needs. We use a traditional math program with tons of manipulatives (definitely feeling the c-rod love at our house).

 

Back to basics doesn't mean that she isn't developing a deeper understanding of arithmetic. We were just covering the x4 multiplication facts. Day 1 she looked at the first problem (7x4) and she smiled and said, "That's 14+14." She then used her x2 facts to figure out all of her x4 facts. I'm starting to see her have these little light bulb moments all the time now. So, I guess traditional "back to basics" math hasn't been an utter failure for her.

 

My 7 yo daughter is a whole 'nother story. She's talented in math, intuitively understands abstract concepts, plays with negative numbers and can easily make connections that her older sister can't (yet). I use very little formal curricula with her beyond recently re-subbing to Dreambox. She dances with math, plays with it like a toy.

 

Two kids, two approaches. That's the beauty of home schooling.

[lorisuewho]

 

I appreciate all the math chat. Math chat has changed over the years. I mean SERIOUSLY changed. More money is being spent. More time is being spent. I'm not at all sure that students are learning more math though. Parent sure feel prouder or worse about THEMSELVES though. :001_huh:

 

Interesting observation.

What do the experts (who are the experts?) tell us? Are children better at mathematics today than 20 or 50 or 100 years ago?

[regentrude]

Interesting observation.

What do the experts (who are the experts?) tell us? Are children better at mathematics today than 20 or 50 or 100 years ago?

 

I am not an expert on math education, but every physics professor I ever talked to will tell you that the math skills of incoming college freshmen are at a much lower level than decades ago, and steadily getting worse. The biggest issues are:

1. Calculator dependence.

Many students can not perform simple mental math at elementary school level.

They are unfamiliar with the shape and properties of basic functions (sine, cosine) because they use the calculator to compute and do not bother to simplify their expressions like they would have decades ago when it was a pain to look values up in a table.

They are unable to graph unknown functions qualitatively by looking at the mathematical expression and evaluating limits and special cases; they rely on graphing calculators.

I am not anti technology; it has its place- but only after the student is proficient in the concept, not instead of thinking.

 

2. Lack of conceptual understanding

They can plug and chug - but don't know where the quadratic formula comes from. If they can do math at all, they have been drilled procedures without a strong background in the underlying concepts.

 

I am not sure to what degree this second aspect was better decades ago in this country; about the calculator dependence I am perfectly certain - because there simply were none several decades ago, and the methods used back then required a much better understanding than punching buttons does.

[nmoira]

2. Lack of conceptual understanding

They can plug and chug - but don't know where the quadratic formula comes from. If they can do math at all, they have been drilled procedures without a strong background in the underlying concepts.

.

Deriving the quadratic formula is trivial given a handful of basic algebraic techniques, and IMHO, nobody should get out of Algebra I without being able to do so at the drop of a hat; not to pay their dues or as a brain strengthening exercise, but because it's fundamental.

 

There are other reasons, but I'm glad we homeschool if only for the math.

Edited September 29, 2012 by nmoira

[Violet Crown]

Agreeing with regentrude; but I had gathered the "more math chat" etc. was referring to homeschoolers particularly, not to American math education in general. My apologies if I have misunderstood.

[momtoamiracle]

This may be a silly question, but after all the talk, will Math Mammoth give my son the math background he needs?

 

 

 

 

I grew up in the 70's, graduated in 1985. I had no problem with algebra in high school, I absolutely loved it, but up to that time I despised math. I understood it fine, but it was boring, I guess. Algebra, especially my second year, was like play to me.

 

 

Can someone tell me why that is? I have never been able to figure it out.

 

 

 

 

 

I just don't know enough about new math to give an opinion about it. I've been out of school a long time and my son just turned six...

[Spy Car]

This may be a silly question, but after all the talk, will Math Mammoth give my son the math background he needs?

 

 

 

 

I grew up in the 70's, graduated in 1985. I had no problem with algebra in high school, I absolutely loved it, but up to that time I despised math. I understood it fine, but it was boring, I guess. Algebra, especially my second year, was like play to me.

 

 

Can someone tell me why that is? I have never been able to figure it out.

 

 

 

My guess is that when you got to algebra you started getting questions that involved creative problem solving instead of boring "procedurally" based problems that really didn't require you to think beyond very low levels of congnition. But when problems make ones mind light up, then math is fun.

 

Bill

[momtoamiracle]

Bill-probably that is it.i liked the long procedures to get the answers. I loved the problems that would take a whole page. I do love mysteries and crossword puzzles, and sewing as well. Same concept I guess.

 

 

 

I think my son may be the same way.

[Spy Car]

Bill-probably that is it.i liked the long procedures to get the answers. I loved the problems that would take a whole page. I do love mysteries and crossword puzzles, and sewing as well. Same concept I guess.

 

 

 

I think my son may be the same way.

 

Are you familiar with the Mathematics Enhancement Programme (aka MEP)?

 

It is a British/Hungarian math program with a lot of *thinking* and puzzely type problems. The materials are free to download here:

 

http://www.cimt.plymouth.ac.uk/projects/mep/default.htm

 

Bill