rigorous math?

[IATeachingMom]

What's a more rigorous math curric. than Singapore, and what comes after Singapore?

 

I want to "hear" all sequences up through high school if you have them!

[MissKNG]

What grade are you looking for? Horizons K is much more difficult and takes kids farther than Singapore Earlybird. We are moving onto Horizons K after completing EB B before starting 1st grade math.

[abbeyej]

Well, Singapore Primary is *very* rigorous -- if you use all of the parts. So the textbook and workbook, plus Challenging Word Problems, Intensive Practice, and some sort of daily drill.

 

For my family, we've chosen to use Horizons for elementary with Singapore as a secondary program and additional drill and other supplements along the way.

 

I really like the story another WTM poster told years ago about realizing that she had spent all of this time and energy creating a "language-rich environment" for her kids and that they had benefitted from that -- and that they would benefit from her making a similar effort to create a "math-rich" environment. I'm not always successful at doing that, but I do try to remember that "math" is not limited to a single textbook. It's worthwhile for us to have other kinds of math books, board games, card games, hands-on materials (not just manipulatives to use with a book during school time), etc, etc...

 

After Singapore you can go on to any number of middle or high school level programs. My oldest finished Horizons 6 (and had used Singapore and other supplements including the Key To.... Algebra books) and went straight into algebra (Algebra 1: Structure and Method, Brown, Dolciani)... My younger one is less math-oriented, but we're working through Horizons and Singapore with her as well...

 

Some people continue after Singapore Primary to New Elementary Mathematics....

 

I like Horizons because of the breadth of topics and constant review. I like Singapore for its greater depth (especially if you use the Challenging Word Problems and the Intensive Practice) and more thoughtful word problems...

 

(BTW, I'm not a fan of the Singapore Early Bird books. Meh.)

[Laura Corin]

 

I really like the story another WTM poster told years ago about realizing that she had spent all of this time and energy creating a "language-rich environment" for her kids and that they had benefitted from that -- and that they would benefit from her making a similar effort to create a "math-rich" environment.

 

I think it did Calvin a disservice: he was thrown for a loop by maths that arrived from a different angle. FWIW, we now use LOF, Galore Park Maths and two different weekly review programmes.

 

Laura

[8filltheheart]

What's a more rigorous math curric. than Singapore, and what comes after Singapore?

 

I want to "hear" all sequences up through high school if you have them!

 

Rigorous isn't a word I would necessarily equate with elementary level math. Singapore is a completely different approach to math than a traditional approach. It is a bar diagram method of complex problems that we traditionally associate with algebraic solutions. I don't think there is another easily purchased math program that equates with Singapore.

 

For a traditional approach to elementary math, my personal favorite is Horizons. That is the only elementary program I have used for the last 14 yrs, so I don't know much about the others. (I own Singapore, but I don't use it.)

 

As far as high school level math, Foerster and Dolciani are both excellent math programs. Jacobs and Larson (what CD uses) are solid math programs as well. Art of Problem Solving's texts are supposed to be excellent, but I have no experience with their "traditional" math courses, only Counting and Probability and their Art of Problem Solving vols 1 and 2.

 

I am seriously considering their pre-cal course for next yr based on the recommendation of Kathy in Richmond (who has her phD in math and has 2 brilliant math kids.)

 

 

HTH

[stripe]

What does it mean to you for it to be rigorous? Produces a child who is able to answer any arithmetic problem instantly? Material covering lots of ground? Able to apply math to real-world situations? Able to explain one's answer? Clarity? Perception of a "whole" universe of math and concept of how each part is a piece of the puzzle? I think it makes a difference.

[smilesonly]

Interesting question.

 

I have heard people describe Horizons as advanced-yet lacking in conceptual thinking, and test scores reflecting this. :confused:

 

I'm sticking with my math-major dh, with degrees in physics also- he claims there is not a single math curriculum that is *it*. Now combos is another story...:lol:

 

FTR-our oldest dd did Singapore, MUS, Miquon, and CLE-and is heading into Algebra after Christmas break...in 7th grade. I thought I had messed her up when it came to math, as we took a whole year off just doing "living math!" Who knew??;)

 

imho-*nothing* is rigorous if mom can't teach the subject.;):lol:

[8filltheheart]

Interesting question.

 

I have heard people describe Horizons as advanced-yet lacking in conceptual thinking, and test scores reflecting this. :confused:

 

I'm sticking with my math-major dh, with degrees in physics also- he claims there is not a single math curriculum that is *it*. Now combos is another story...:lol:

 

 

 

Our experience with Horizons is that it is neither advanced nor is it lacking. ;) Singapore wasn't readily available in the US until my oldest was in Horizons 6. I bought all of the Singapore books at that point in time based on the reviews that American children would not be able to solve the problems. He had zero difficulty solving any of the problems with the exception of the rate x time problems b/c he had never been exposed to that formula before. He did, however, solve them in a rudimentary algebraic fashion (not set up in a neat algebraic fashion b/c he had never been exposed to alg before.)

 

I agree with your dh. I think there is far more to math "logic" than typical math curriculums offer. I do believe, however, that there are more ways to achieve that goal than strictly math curriculum.

[8filltheheart]

What does it mean to you for it to be rigorous? Produces a child who is able to answer any arithmetic problem instantly? Material covering lots of ground? Able to apply math to real-world situations? Able to explain one's answer? Clarity? Perception of a "whole" universe of math and concept of how each part is a piece of the puzzle? I think it makes a difference.

 

I wasn't sure if this question was directed toward me or the OP.

 

For me, I have an honest aversion to using the word "rigorous" in regards to any educational topic for young children. Looking at the definition of the word:

 

rigorous [ˈrɪgərəs]

adj

1. characterized by or proceeding from rigour; harsh, strict, or severe rigorous discipline

2. severely accurate; scrupulous rigorous book-keeping

3. (esp of weather) extreme or harsh

4. (Mathematics) (Philosophy / Logic) Maths Logic (of a proof) making the validity of the successive steps completely explicit

 

I do not want to have my young children's education resemble any of the 1st 3 definitions. The 4th definition should be applicable to almost any comprehensive math program that teaches age appropriate material.

 

My POV is that the biggest "switch" in math takes place beyond the elementary yrs. Is the math still "arithmetic" based (which many upper level math programs tend to do. MUS is that way in the upper grades in my experience.) or does the math move toward abstract applications? (The "harder" math texts move beyond the simple factoring/replication type problems into no hand-holding problems.)

 

I agree fully that Singapore that is far more conceptual than any traditional math program. It is definitely mental math. But, I do not necessarily agree that its approach solely always leads to superior long term outcomes than other approaches. Mental manipulations of Singapore's approach are excellent......no question. But they are other ways to give kids mental "logic" manipulation challenges.

[angela in ohio]

imho-*nothing* is rigorous if mom can't teach the subject.;):lol:

 

Yes. It's not necessarily the program you choose, it's how you use it.

[Dinsfamily]

imho-*nothing* is rigorous if mom can't teach the subject.;):lol:

 

Such a true statement!

[siloam]

What's a more rigorous math curric. than Singapore, and what comes after Singapore?

 

I want to "hear" all sequences up through high school if you have them!

 

To me what makes Singapore unique is its focus on understanding concepts vs. memorizing formulas and the critical thinking/problem solving work.

 

I also use Right Start math, which includes the first (understanding concepts) and not as much of the second. Though it is still a really excellent program.

 

When my kids finish the primary levels of Singapore they will move into either Singapore New Elementary Math or Singapore Discovering Mathematics. Both cover Pre-Algebra, Algebra, Geometry, Algebra II and some Pre-Calculus. Most people who finish them move into a Pre-Calculus program. I will be looking at Dolciani and Foerster and anything else that hits my radar as being proof driven demanding.

 

Heather

 

[LlamaMama]

For those of you the have had success in math, I'm curious why you chose not to use Right Start Math or Math-U-See? My oldest child is almost finished with Right Start Math Level A (Kindergarten) and I am at a crossroads with what to purchase after this.

 

I understand the need to provide a math-rich learning environment through games and books, but the bulk of my math teaching will still be driven by the curriculum I choose. Did you find those programs lacking? How so?

[ondreeuh]

Interesting question.

 

I have heard people describe Horizons as advanced-yet lacking in conceptual thinking, and test scores reflecting this. :confused:

 

 

I somewhat agree that Horizons is advanced but weak in conceptual thinking. I've never heard that Horizons is correlated with low math scores; I've just heard the opposite. Do you remember where you heard that?

 

Horizons definitely has a broader scope than traditional classroom math programs. My son just finished Horizons 2 and I think he has met all the state objectives for 3rd grade math and some of 4th. The child's hand is really led through the learning process though so they don't have to be geniuses to make the connections. This makes Horizons accessible for "average" kids.

 

Horizons does begin algebra in 2nd grade (just of the type n - 6 = 15) and teaches the child to perform the same action on each side to solve for n. We do some of these problems the Singapore way and some the Horizons way. I think Singapore complements Horizons very well.

 

Horizons doesn't spend as much time on concrete teaching (although the TG does say things like "demonstrate with base-10 blocks" which is at least a nod towards it). Even though the TG isn't scripted, the way the problems are presented do show the steps you go through and not just a formula. For example, while working on fractions the child first learns to color 2/5 (two out of five). Then later there will be a group of ten, and the child will ring groups of five and color 2 from each group. Then later they will be asked the question 2/5 of 15 is ____? with the pictures still there for them to ring and color. My MIL was floored when I showed her those problems in the Grade 2 book, and she's a gifted/talented teacher!

 

Like *any* math program, it is really up to the parent to make sure the child's understanding is solid. I could see Horizons not being successful if the child works independently. A workbook just cannot replace direct instruction.

[angela in ohio]

For those of you the have had success in math, I'm curious why you chose not to use Right Start Math or Math-U-See? My oldest child is almost finished with Right Start Math Level A (Kindergarten) and I am at a crossroads with what to purchase after this.

 

I understand the need to provide a math-rich learning environment through games and books, but the bulk of my math teaching will still be driven by the curriculum I choose. Did you find those programs lacking? How so?

 

We use an abacus, math games, and all manner of manipulatives, but they are supplements to a rigorous standard program.

 

I have used a good standards-based program (Horizons, Exploring Mathematics, BJU, any of them work, I go with what I can acquire inexpensively for the year) along with some Singapore and with a side of manipulatives, Montessori materials, and Miquon for the early years. My girls score in the 99th percentile in math, and oldest was well-prepared for Algebra.

[siloam]

For those of you the have had success in math, I'm curious why you chose not to use Right Start Math or Math-U-See? My oldest child is almost finished with Right Start Math Level A (Kindergarten) and I am at a crossroads with what to purchase after this.

 

I understand the need to provide a math-rich learning environment through games and books, but the bulk of my math teaching will still be driven by the curriculum I choose. Did you find those programs lacking? How so?

 

I use both. Singapore was my first love in math (still is), but my kids are visual spacial learners that need hands on. At first I use Miquon but by kids hated the rods (which is why MUS was never a consideration), so after trying to do Singapore alone for a while (note: without the HIG's which do have some hands on stuff-I don't know if it would have been enough), which worked but took a lot of time to teach and go through things with the child, I found RS.

 

Let me back up and say my oldest hated math, Miquon and Singapore both. It was her least favorite subject. We started RS and she actually enjoyed math. Once more it gave her a fluency (for lack of a better term) in math that wasn't there before. Now after doing RS B-E she would tell you that she doesn't really like math, but she is good at it. It is no longer her least favorite subject, despite still doing Singapore. My 2nd dd absolutely couldn't do Singapore alone she is so hands on, I doubt the HIG work would have been enough for her. My oldest is auditory/hands on, while my 2nd dd is hands on/visual.

 

While RS is more teacher intensive for my kids it ends up being the same. I spent so much extra time in Singapore working with them because they didn't get it right away (Singapore makes logical leaps that RS goes through step by step-those leaps would have me working with the kids more) that it was the same as doing RS. Now that I do RS they can pick up and do Singapore with almost no teaching. I was not teaching it but once in a while they totally missed the point of a page and did the whole thing wrong, so now I go over it enough to make sure they know what is expected of them. If a child had a different learning style (are not so hands on) the results might be different.

 

For kids that are mathy Singapore is probably the best choice, especially if they are visual or audio learners. If they are hands on and are average to LD in math RS would probably work better.

 

Heather

 

p.s. I do both because I want to use upper level Singapore math, I also consider Singapore our critical thinking program, and we do have a distinct math focus here. My oldest two want to be vets (at the moment) so that means lots of math in their future.

 

[8filltheheart]

For those of you the have had success in math, I'm curious why you chose not to use Right Start Math or Math-U-See? My oldest child is almost finished with Right Start Math Level A (Kindergarten) and I am at a crossroads with what to purchase after this.

 

I understand the need to provide a math-rich learning environment through games and books, but the bulk of my math teaching will still be driven by the curriculum I choose. Did you find those programs lacking? How so?

 

My kids tend to be math intuitive. Manipulatives frustrate them in most cases.

 

The repetition in MUS would push them to the brink. :tongue_smilie: In the higher grades, MUS is a very weak curriculum. (I know there are MUS advocates that love MUS and will argue that is not the case. However, having taught MUS and Foerster I have absolutely no qualms stating emphatically that they are not in any way equivalent programs.)

 

I know nothing about Right Start.

 

I love Horizons b/c it provides a very solid foundation for upper level math.

 

We are a game oriented family and spend hours every week playing logic/strategy type games. My kids all excel in math and upper level math, while challenging, is not something that "stumps" them. It is an approach that has worked very well for our family.

 

However, as another poster pointed out, it isn't necessarily the curriculum, but maybe how it is taught. I don't teach according the TE. I simply teach. How things are taught does make a difference and that is something that is different in every household.

[forty-two]

rigorous [ˈrɪgərəs]

adj

...

4. (Mathematics) (Philosophy / Logic) Maths Logic (of a proof) making the validity of the successive steps completely explicit

...

The 4th definition should be applicable to almost any comprehensive math program that teaches age appropriate material.

 

It *should* be, but I'm not sure that is actually true of most programs, unfortunately. I've been reading several papers by Professor Wu, a math professor at Berkeley who is interested in math education, many of which discuss where our current math programs fall short. He discusses five basic characteristics of mathematics - precision, definitions, reasoning, coherence, and purposefulness - and shows how much of current K-12 math education lacks these characteristics in their approach. Fractions, in particular, are presented exceptionally badly.

 

So as far as "making the validity of the successive steps completely explicit" goes, while most curricula might show each step in working out a problem, and teach kids to do the same, in far too many cases those steps are never shown to have a valid mathematical basis. If you haven't precisely defined what you are working with, nothing from that point will be valid - you can't reason properly from improperly established premises.

[8filltheheart]

It *should* be, but I'm not sure that is actually true of most programs, unfortunately. I've been reading several papers by Professor Wu, a math professor at Berkeley who is interested in math education, many of which discuss where our current math programs fall short. He discusses five basic characteristics of mathematics - precision, definitions, reasoning, coherence, and purposefulness - and shows how much of current K-12 math education lacks these characteristics in their approach. Fractions, in particular, are presented exceptionally badly.

 

So as far as "making the validity of the successive steps completely explicit" goes, while most curricula might show each step in working out a problem, and teach kids to do the same, in far too many cases those steps are never shown to have a valid mathematical basis. If you haven't precisely defined what you are working with, nothing from that point will be valid - you can't reason properly from improperly established premises.

 

Good point. You are correct. Horizons does use correct terminology from the very beginning and expects the kids to know it. This makes transition to programs like Foerster which expect proofs based on properties easy b/c they have been learning those principles for yrs.

 

You reminded me of a post on the high school board where an algebra program asked the student to "undo" a problem. I have never heard of "undo" as a mathematical term.

Edited November 2, 2009 by 8FillTheHeart

[IATeachingMom]

Wow, such great responses. I've never actually thought about making math more "well rounded" like I do with other subjects. I think I'm on the search for a supplementary math program.....

[Dinsfamily]

Wow, such great responses. I've never actually thought about making math more "well rounded" like I do with other subjects. I think I'm on the search for a supplementary math program.....

 

:iagree:and thanks for asking the question! This is a great thread! I am glad that I've found a great combo for math and will be sticking with it. You ladies have redefined my idea of "rigorous math." I'm not sure how my program will change with the differences in my dc's learning styles, but you all have given me a lot to think about.

 

I still don't have a clear picture of what to do once we're done with elementary math yet, but thankfully, I have a few years to figure that out.

[Spy Car]

Wow, such great responses. I've never actually thought about making math more "well rounded" like I do with other subjects. I think I'm on the search for a supplementary math program.....

 

You might want to look at the "Mathematics Enhancement Programme" aka "MEP."

 

This is a British program based on a Hungarian model that, to my mind, is a wonderful compliment to Singapore. The methods are similar, yet different enough to "round out" a math program. There are wonderful lesson plans and activities that while aimed at "classrooms" can be very valuable for home use, and thought provoking workbooks.

 

MEP challenges children to really think, and is, as a consequence, a program most children find "fun."

 

It is available without cost (other than printing) as PDFs.

 

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

 

Bill

Edited November 2, 2009 by Spy Car

[angela in ohio]

You reminded me of a post on the high school board where an algebra program asked the student to "undo" a problem. I have never heard of "undo" as a mathematical term.

 

That seriously bugged me, but I didn't want to be accused of "bashing" that program. ;)

[TeaTotaler]

Abbey,

Can you tell me more about your use of Dolciani. What edition are you using? Where did you purchase your materials. What made you decide on that program?

I don't want to hijack this thread so do you mind posting in a thread I just wrote on needing help with math progression.

Thanks.

 

Well, Singapore Primary is *very* rigorous -- if you use all of the parts. So the textbook and workbook, plus Challenging Word Problems, Intensive Practice, and some sort of daily drill.

 

For my family, we've chosen to use Horizons for elementary with Singapore as a secondary program and additional drill and other supplements along the way.

 

I really like the story another WTM poster told years ago about realizing that she had spent all of this time and energy creating a "language-rich environment" for her kids and that they had benefitted from that -- and that they would benefit from her making a similar effort to create a "math-rich" environment. I'm not always successful at doing that, but I do try to remember that "math" is not limited to a single textbook. It's worthwhile for us to have other kinds of math books, board games, card games, hands-on materials (not just manipulatives to use with a book during school time), etc, etc...

 

After Singapore you can go on to any number of middle or high school level programs. My oldest finished Horizons 6 (and had used Singapore and other supplements including the Key To.... Algebra books) and went straight into algebra (Algebra 1: Structure and Method, Brown, Dolciani)... My younger one is less math-oriented, but we're working through Horizons and Singapore with her as well...

 

Some people continue after Singapore Primary to New Elementary Mathematics....

 

I like Horizons because of the breadth of topics and constant review. I like Singapore for its greater depth (especially if you use the Challenging Word Problems and the Intensive Practice) and more thoughtful word problems...

 

(BTW, I'm not a fan of the Singapore Early Bird books. Meh.)

[KJB]

As resources, I've found these two books thought provoking and helpful:

 

 

Knowing and Teaching Elementary Mathematics

http://www.singaporemath.com/Knowing_and_Teaching_Elem_Math_by_Liping_Ma_p/ktem.htm

 

and

 

Providing a Foundation for Teaching Mathematics in the Middle Grades

http://www.amazon.com/gp/product/0791425347/ref=ox_ya_os_product

 

I think becoming the best teacher I can be is much more effective than finding the magic bullet math program.

[Jen in PA]

You might want to look at the "Mathematics Enhancement Programme" aka "MEP."

 

This is a British program based on a Hungarian model that, to my mind, is a wonderful compliment to Singapore. The methods are similar, yet different enough to "round out" a math program. There are wonderful lesson plans and activities that while aimed at "classrooms" can be very valuable for home use, and thought provoking workbooks.

 

MEP challenges children to really think, and is, as a consequence, a program most children find "fun."

 

It is available without cost (other than printing) as PDFs.

 

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

 

Bill

:iagree:

MEP is a really wonderful program and the price is unbeatable. I use it very loosely to supplement Singapore.

[WTMindy]

That seriously bugged me, but I didn't want to be accused of "bashing" that program. ;)

 

I wouldn't consider that a mathematical term, but it is a concept that I teach my math students to help them know why you subtract 5 from both sides of an equation or divide both sides by 3 when you are solving for x. So, I don't think it is out of the realm of reasonable in a math book if the presentation has been made as to WHY you are undoing something. Of course, I didn't read the original thread.

 

In my opinion, as a math teacher, I would agree that MUS is not a rigorous program, however the one thing it has going for it, is that it is very accessible to homeschooling families. For students who struggle in math and parents who struggle teaching it, it is filling a niche that was missing. They have made it a bit stronger by adding in the honors materials into each lesson. I'm glad they did this.

 

My daughter is using NEM 2 right now, and I think that this is a RIGOROUS program. It has LOTS of problems (we don't do them all), very high level thinking problems (which is part of what defines rigor to me), and good sound mathematical teaching. However, I have many students (I teach at a homeschool co-op) that would absolutely fail if I gave them that book and asked them to complete assignments. So, I use MUS with my co-op kids and NEM with my own kids. This is the first year I am only using one curriculum, we have always used two.

[8filltheheart]

It really bugged me, too. I was also bothered by how the students were taught to solve the problem. But, I must say, I was not surprised.;)

[8filltheheart]

I wouldn't consider that a mathematical term, but it is a concept that I teach my math students to help them know why you subtract 5 from both sides of an equation or divide both sides by 3 when you are solving for x. So, I don't think it is out of the realm of reasonable in a math book if the presentation has been made as to WHY you are undoing something. Of course, I didn't read the original thread.

 

 

 

My personal opinion is that it should be explained in authentic mathematical terms. It is as simple as explaining that equations must remain balanced and that if you perform an operation on one side of an equation, it must also be performed on the other side or you have altered the numerical value of only one side. My kids learn that concept as early as 3rd grade. I believe that a high school algebra program should be able to request that a problem is solved according to mathematical terms, not lingo.

[abbeyej]

Abbey,

Can you tell me more about your use of Dolciani. What edition are you using? Where did you purchase your materials. What made you decide on that program?

I don't want to hijack this thread so do you mind posting in a thread I just wrote on needing help with math progression.

Thanks.

 

Well, I'm maybe a half step ahead of you, lol, so I may not be the one to ask. ;)

 

I started to panic last winter, after Christmas, and I ordered a whole stack of used pre-algebra and algebra texts based on various recommendations here and elsewhere... I found that I liked the Dolciani text (mine is a 1997 printing of the 1990 edition), and I was also swayed towards it because there's a local math teacher (he also does online distance courses) who gets very high marks from all sorts of people, and this is the algebra 1 text he uses (the 2000 ed, I think). Since I think it extremely likely that we'll be turning to him for geometry and algebra 2, I thought it made sense to go ahead and use the text he uses for algebra 1 as well... He even has syllabi for his classes available on the website, so we're following it to get a rough idea what the pacing in his classes will be like before we dive in.

 

We're about 1/3 of the way in and so far I'm really liking the text. I've had a couple of questions and frustrations along the way, but I think that's inevitable given that we're moving into some math that has gotten a bit rusty for me. ;) Today though, T was *cackling* through part of the lesson because he found it so much fun. Weirdo. :)

[ELaurie]

but I use Professor B Math with my dc. You might want to check it out

here.

 

You'll find some reviews linked here.

 

HTH!

 

PS. If you have questions, I'll try to make time to answer them later :001_smile:

[Nan in Mass]

His sequence was:

Chicago Everyday Math K-4th public school (when I pulled him out his mathematical thinking was a mess)

Saxon 56 (did not work for this child - chopped up into too small pieces for this child to put back together again - he got the problems right but couldn't apply his math to real life - it did help him to memorize the standard algorithms for basic arithmetic, which was good)

Singapore Primary Math 3-6 (this "fixed" his thinking)

NEM1-3 with Keys to Algebra 1-3 partway thorugh NEM1, just for more practice with all those "little rules" (his words)

Community collge pre-calculus

 

Considering how messed up he was to begin with, we think he did very well to get through pre-calculus his senior year. Now he is taking technical calculus in college and says that although he doesn't always get the calculus, he "rocks at algebra compared to the other kids in my class". He can't believe what they can't do. He also isn't calculator dependent.

 

I'm not pushing this particular sequence, which has its problems. You asked to see sequences, though, so I thought you might like to see one from beginning to end.

-Nan

[TeaTotaler]

Thanks Abbey. I had come across that website some time ago and thought I had saved it but could not find it again. My favorites on my computer need some serious cleaning up!! I will poke around the site some more. Did you buy the teacher's edition for the book you listed below? If not, would the ISBN be listed inside the cover of your student book? I did see that edition when I was looking around last year but wasn't sure if the teacher's edition would match exactly.

 

Imagining "T" cackling through a math lesson brought a smile to my face:D

He's one smart cookie! I'm glad you mentioned the syllabi because that was very helpful in seeing how the class was paced. Handling these huge textbooks compared to the SM books makes setting a pace a little daunting.

 

Thanks again for your help.

 

 

Well, I'm maybe a half step ahead of you, lol, so I may not be the one to ask. ;)

 

I started to panic last winter, after Christmas, and I ordered a whole stack of used pre-algebra and algebra texts based on various recommendations here and elsewhere... I found that I liked the Dolciani text (mine is a 1997 printing of the 1990 edition), and I was also swayed towards it because there's a local math teacher (he also does online distance courses) who gets very high marks from all sorts of people, and this is the algebra 1 text he uses (the 2000 ed, I think). Since I think it extremely likely that we'll be turning to him for geometry and algebra 2, I thought it made sense to go ahead and use the text he uses for algebra 1 as well... He even has syllabi for his classes available on the website, so we're following it to get a rough idea what the pacing in his classes will be like before we dive in.

 

We're about 1/3 of the way in and so far I'm really liking the text. I've had a couple of questions and frustrations along the way, but I think that's inevitable given that we're moving into some math that has gotten a bit rusty for me. ;) Today though, T was *cackling* through part of the lesson because he found it so much fun. Weirdo. :)

[abbeyej]

T...Did you buy the teacher's edition for the book you listed below? If not, would the ISBN be listed inside the cover of your student book? I did see that edition when I was looking around last year but wasn't sure if the teacher's edition would match exactly...

 

I don't have the TM, and I just checked my copy and couldn't find an ISBN for the TM. I know I've seen the TM on Amazon... The book does have the answers for the odds in the back, and for the most part that plus the explanations in the book have been adequate. That said, the TM might be nice to have! :)

[TeaTotaler]

Thanks. One more quick question. About how much time do you allocate for Math each day including your teaching time?

 

I don't have the TM, and I just checked my copy and couldn't find an ISBN for the TM. I know I've seen the TM on Amazon... The book does have the answers for the odds in the back, and for the most part that plus the explanations in the book have been adequate. That said, the TM might be nice to have! :)

[missmoe]

What makes a math rigorous? For me, making math rigorous is more than the book one chooses. I haven't used exactly the same sequence for any of my five kids. I believe one has to include math in everyday life just as one incorporates reading into everyday life. Teach math so that it can be used. Teach it all different ways. Take the time to think and talk about it throughout your day. Talk about all the different ways one can work out the same problem. Along with reading together as a family, work out logic and math problems together as a family.

[sleepymommy]

His sequence was:

Chicago Everyday Math K-4th public school (when I pulled him out his mathematical thinking was a mess)

Saxon 56 (did not work for this child - chopped up into too small pieces for this child to put back together again - he got the problems right but couldn't apply his math to real life - it did help him to memorize the standard algorithms for basic arithmetic, which was good)

Singapore Primary Math 3-6 (this "fixed" his thinking)

NEM1-3 with Keys to Algebra 1-3 partway thorugh NEM1, just for more practice with all those "little rules" (his words)

Community collge pre-calculus

 

Considering how messed up he was to begin with, we think he did very well to get through pre-calculus his senior year. Now he is taking technical calculus in college and says that although he doesn't always get the calculus, he "rocks at algebra compared to the other kids in my class". He can't believe what they can't do. He also isn't calculator dependent.

 

I'm not pushing this particular sequence, which has its problems. You asked to see sequences, though, so I thought you might like to see one from beginning to end.

-Nan

 

Thanks for sharing your son's sequence, it does help to see how one progresses until college.

[abbeyej]

Thanks. One more quick question. About how much time do you allocate for Math each day including your teaching time?

 

Honestly it's about 60-90 minutes. On the one hand, that seems like a lot. On the other, if I think about kids in school with classroom work (and I do think there are good teachers at that level who make use of their whole 50 minutes!) plus homework... Then it doesn't seem so far off.

[TeaTotaler]

Thanks.

 

Honestly it's about 60-90 minutes. On the one hand, that seems like a lot. On the other, if I think about kids in school with classroom work (and I do think there are good teachers at that level who make use of their whole 50 minutes!) plus homework... Then it doesn't seem so far off.

[WTMindy]

My personal opinion is that it should be explained in authentic mathematical terms. It is as simple as explaining that equations must remain balanced and that if you perform an operation on one side of an equation, it must also be performed on the other side or you have altered the numerical value of only one side. My kids learn that concept as early as 3rd grade. I believe that a high school algebra program should be able to request that a problem is solved according to mathematical terms, not lingo.

 

I share that personal opinion with you. And, I must start by saying that I don't know what text you are referring to, and I don't even really know the context of the quote!! But, does that stop me from offering my opinion? Apparently not! :-)

 

I also agree that it is as simple as balancing an equation and if you perform an operation on one side, you must do that to the other side. But, where I might use the word "undo" is to help them visualize *WHICH* operation to perform. For example in x+2=5 you are adding the 2, so you will have to "undo" the addition by subtracting. If you are multiplying 3x=9, you have to "undo" the multiplication by dividing. I always use the technical terms with my students as well, but sometimes a more common word sticks the idea better to their brains. So, I use both.