geometry - is it better to be heavy in proofs or light?

[Parrothead]

I was reading a thread about geometry yesterday and there were a couple mentions of particular programs being either heavy in proof or light in proofs. How and why does it matter if one is using a proof heavy program as opposed to one light on proofs?

 

Is there any way to tell how a particular program handles proofs other than to search each curriculum for a review?

 

Are their any more geared for middle of the road? Say, something for a college bound kid who wants to be a dance instructor but will be of use if she changes majors in college.

[regentrude]

Define "better". I would, of course, argue that the more rigorous course that focuses heavily on proofs is better, because it teaches more.

Another person might find it better to do geometry "light" and include little proofs because they do not consider math learning as important and find the course that teaches less better for their student.

 

Geometric proofs introduce the students to a way of reasoning about mathematics they have not encountered before, and gives them for the first time a glimpse of what mathematicians actually do. Studying proofs in great for logical thinking and illuminates how math is constructed. There are, of course, proofs in all areas of mathematics, but geometry proofs are particularly accessible to students and serve as a good introduction. Understanding proofs will be important in higher math, because more and more math will focus on deriving and proving relationships before applying them to problems.

 

This said, no, I do not think a student who wants to be a dance instructor needs a rigorous math curriculum. I think however, a student who could possibly change her mind about her major in college should attempt at least a middle-of-the-road program in order not to close any doors and keep all options. you won't need the specific geometry proofs in the higher classes, but you will need the logical thinking and techniques developed in geometry.

[Parrothead]

Define "better". I would, of course, argue that the more rigorous course that focuses heavily on proofs is better, because it teaches more.

Another person might find it better to do geometry "light" and include little proofs because they do not consider math learning as important and find the course that teaches less better for their student.

 

Geometric proofs introduce the students to a way of reasoning about mathematics they have not encountered before, and gives them for the first time a glimpse of what mathematicians actually do. Studying proofs in great for logical thinking and illuminates how math is constructed. There are, of course, proofs in all areas of mathematics, but geometry proofs are particularly accessible to students and serve as a good introduction. Understanding proofs will be important in higher math, because more and more math will focus on deriving and proving relationships before applying them to problems.

 

This said, no, I do not think a student who wants to be a dance instructor needs a rigorous math curriculum. I think however, a student who could possibly change her mind about her major in college should attempt at least a middle-of-the-road program in order not to close any doors and keep all options. you won't need the specific geometry proofs in the higher classes, but you will need the logical thinking and techniques developed in geometry.

 

Okay, thanks. I appreciate and respect your thoughts.

 

By chance is there a comparison chart somewhere for homeschool geometry texts?

[Lolly]

Area to note: For a proof heavy geometry, you are going to need a teacher who can grade and/or help the student. The answers in the teacher's manual are not the only way to work to the solution. The teacher's manual will only give one answer/approach. There are multiple, just as correct, ways to arrive at the same conclusion.

[swimmermom3]

<snip>

Geometric proofs introduce the students to a way of reasoning about mathematics they have not encountered before, and gives them for the first time a glimpse of what mathematicians actually do. Studying proofs in great for logical thinking and illuminates how math is constructed. There are, of course, proofs in all areas of mathematics, but geometry proofs are particularly accessible to students and serve as a good introduction. Understanding proofs will be important in higher math, because more and more math will focus on deriving and proving relationships before applying them to problems.

 

This said, no, I do not think a student who wants to be a dance instructor needs a rigorous math curriculum. I think however, a student who could possibly change her mind about her major in college should attempt at least a middle-of-the-road program in order not to close any doors and keep all options. you won't need the specific geometry proofs in the higher classes, but you will need the logical thinking and techniques developed in geometry.

 

 

I believe that in an indirect way, the patterning that is used in the development of proofs is similar to that used in writing a good essay with a solid argument. Even with my most math-phobic student, we worked some proofs outside of her regular geometry class and with practice she was able to sometimes even enjoy the challenge of the process. It became a game.

 

I also second Regentrude's suggestion that you go with at least a middle-of-the-road program in order to keep all options. Personally, I cringe when I see someone (not OP) write that their child will probably not need a basic discipline because they'll never do something in a particular field as an adult. I was the journalism major who later decided to back back to school for an MBA. I took four years of math in high school not because I ever thought I would really need it, but because I did not want to close any doors. I am so glad I did or reading financial statements or deciphering statistics would have been difficult, not to mention passing the GMAT in the first place.

 

Chemistry was a nightmare for my dd, but now that she is applying for her cosmetology license, she is quite glad to have a basic understanding of how chemical bonding works.

[bugs]

I only have experience with 2 Geometry programs: BJU and TT. I feel that the BJU is very heavy in proofs and TT is about middle of the road. BJU assignments could easil have 5 proofs in them where the TT have 2 each lesson. To me, two proof problems for most assignments provides enough practice to get the hang of solving them.

[Parrothead]

I only have experience with 2 Geometry programs: BJU and TT. I feel that the BJU is very heavy in proofs and TT is about middle of the road. BJU assignments could easil have 5 proofs in them where the TT have 2 each lesson. To me, two proof problems for most assignments provides enough practice to get the hang of solving them.

Thanks for the suggestions. I can't use BJU. Do you (or anyone else) know if MUS is satisfactory for a middle of the road choice? Also I found something called Key to Geometry. And Jacobs geometry. It seems good based on the reviews at Amazon, but the look inside feature is no available for Jacobs.

 

Funny thing. I thought I had this all figured out this time last year.

[at the beach]

Thanks for the suggestions. I can't use BJU. Do you (or anyone else) know if MUS is satisfactory for a middle of the road choice? Also I found something called Key to Geometry. And Jacobs geometry. It seems good based on the reviews at Amazon, but the look inside feature is no available for Jacobs.

 

Funny thing. I thought I had this all figured out this time last year.

 

 

My daughter used MUS Geometry. I feel it's a satisfactory choice. She did all the worksheets, including honors. Because folks are often concerned about testing, I will add that when she took the PSAT, she got every geometry question correct with no prep.

[Parrothead]

 

 

My daughter used MUS Geometry. I feel it's a satisfactory choice. She did all the worksheets, including honors. Because folks are often concerned about testing, I will add that when she took the PSAT, she got every geometry question correct with no prep.

 

Thank you.

[shanvan]

If you are considering Jacob's read some threads here. There are differences b/t the 2nd and 3rd editions and people seem to feel strongly about using one or the other. Also some kids just don't seem to get what some have called Jacob's 'intuitive' type of learning. It's not a hold your hand type of curriculum. I've know several kids/parents that had trouble with Jacob's and did well using a different curriculum.

[Parrothead]

If you are considering Jacob's read some threads here. There are differences b/t the 2nd and 3rd editions and people seem to feel strongly about using one or the other. Also some kids just don't seem to get what some have called Jacob's 'intuitive' type of learning. It's not a hold your hand type of curriculum. I've know several kids/parents that had trouble with Jacob's and did well using a different curriculum.

Thanks for the info. I suppose I'll cross it off the list. I think I've narrowed it down to TT or MUS. We are used to MUS style since that is what dd used up until she got stuck on Algebra. So I'm leaning toward MUS - the evil you know and all that. And it is $100 cheaper than TT.

[bugs]

Thanks for the suggestions. I can't use BJU. Do you (or anyone else) know if MUS is satisfactory for a middle of the road choice? Also I found something called Key to Geometry. And Jacobs geometry. It seems good based on the reviews at Amazon, but the look inside feature is no available for Jacobs.

 

Funny thing. I thought I had this all figured out this time last year.

 

 

I haven't looked at MUS Geometry. I have quickly perused through Key to Geometry and what I remember it was a lot of construction (angles, bisecting angles, etc.).

[Mom22ns]

Thanks for the info. I suppose I'll cross it off the list. I think I've narrowed it down to TT or MUS. We are used to MUS style since that is what dd used up until she got stuck on Algebra. So I'm leaning toward MUS - the evil you know and all that. And it is $100 cheaper than TT.

 

I really like MUS Geometry, but it is definitely proof light. When ds took the Plan test (ACT prep for Sophomores) he got every geometry question right and he was just about 3/4 of the way through MUS Geometry. If your goal is to train a future mathematician, I would skip MUS. If you just want the geometry needed for ACT/SAT testing, it fits the bill.

 

I haven't used TT, but my understanding is that it has more proofs than MUS.

[Parrothead]

 

 

I really like MUS Geometry, but it is definitely proof light. When ds took the Plan test (ACT prep for Sophomores) he got every geometry question right and he was just about 3/4 of the way through MUS Geometry. If your goal is to train a future mathematician, I would skip MUS. If you just want the geometry needed for ACT/SAT testing, it fits the bill.

 

I haven't used TT, but my understanding is that it has more proofs than MUS.

Nope, not training a mathematician. She, for the past 5 years, has said she wants to teach dance.

[mom31257]

I only have experience with 2 Geometry programs: BJU and TT. I feel that the BJU is very heavy in proofs and TT is about middle of the road. BJU assignments could easil have 5 proofs in them where the TT have 2 each lesson. To me, two proof problems for most assignments provides enough practice to get the hang of solving them.

 

 

Yes, BJU is heavy on proofs. I'm using it because it was given to me, and dh is laid off work this year. I had wanted to use TT, but I just couldn't see investing the money when I had a perfectly good program for free. I am cutting down the number of proofs and giving dd some partially filled in. She says she used to not like math, now she hates it. She seemed to be getting bogged down in which theorem, postulate, or definition was the reason more than the steps on the left side of a proof. I'm staggering them for her and trying to see if she can fill in the missing blanks. She's doing well as of now.

[Candid]

Ummm, I don't think how many proofs are in a program is a good predictor of whether that program is strong if by strong you mean a rigorous demanding program. Singapore's NEM program does ZERO formal proofs, they do on occasion show students why something is so. Nevertheless it is a strong a rigorous program covering a lot of math.

 

I am not sure if AoPS does formal proofs either (and I'm hoping someone will chime in).

 

Further, according to one mathematician the proofs you find in a high school geometry text are not those real mathematician's use: http://www.maa.org/devlin/lockhartslament.pdf

[regentrude]

Ummm, I don't think how many proofs are in a program is a good predictor of whether that program is strong if by strong you mean a rigorous demanding program. Singapore's NEM program does ZERO formal proofs, they do on occasion show students why something is so. Nevertheless it is a strong a rigorous program covering a lot of math.

 

 

Mathematically rigorous means that every relationship is proved, not just explained in a hand-waving manner. Given reasons why something is so "on occasion" is not mathematically rigorous. It may have lots of problems and be challenging to the student - but rigorous in a mathematical sense it is not.

 

 

I am not sure if AoPS does formal proofs either (and I'm hoping someone will chime in).

 

 

Oh absolutely- AoPS proves EVERYTHING. Not just in geometry, but in the other texts as well.

They do, however, write their proofs like mathematicians do and do not follow the artificial "two-column format" used in schools. There are plenty of proofs in problems and exercises.

 

Thanks for posting Lockhardt's Lament. It should be required reading for everybody who is teaching mathematics.

[Parrothead]

Ummm, I don't think how many proofs are in a program is a good predictor of whether that program is strong if by strong you mean a rigorous demanding program. Singapore's NEM program does ZERO formal proofs, they do on occasion show students why something is so. Nevertheless it is a strong a rigorous program covering a lot of math.

 

I am not sure if AoPS does formal proofs either (and I'm hoping someone will chime in).

 

Further, according to one mathematician the proofs you find in a high school geometry text are not those real mathematician's use: http://www.maa.org/d...hartslament.pdf

 

Interesting, that.

 

Thanks for linking it.

[Candid]

Mathematically rigorous means that every relationship is proved, not just explained in a hand-waving manner. Given reasons why something is so "on occasion" is not mathematically rigorous. It may have lots of problems and be challenging to the student - but rigorous in a mathematical sense it is not.

 

 

 

 

Oh absolutely- AoPS proves EVERYTHING. Not just in geometry, but in the other texts as well.

They do, however, write their proofs like mathematicians do and do not follow the artificial "two-column format" used in schools. There are plenty of proofs in problems and exercises.

 

Thanks for posting Lockhardt's Lament. It should be required reading for everybody who is teaching mathematics.

 

 

Two thoughts here, first I don't know what real mathematicians do so it is quite possible NEM does what AoPS does. My oldest has now switched to AoPS because he finished NEM and Additional Mathematics in 9th grade. The proofs in the AoPS book we are using look similar to what NEM does.

 

BUT that leads to my following point: when parents ask about proofs in geometry text what I take that they mean is two column ones not real ones. So if we define terms in this question then the answer is definitely what I said, NO, two column proofs are not an indicator of a rigorous program.

[regentrude]

Two thoughts here, first I don't know what real mathematicians do so it is quite possible NEM does what AoPS does. My oldest has now switched to AoPS because he finished NEM and Additional Mathematics in 9th grade. The proofs in the AoPS book we are using look similar to what NEM does.

 

BUT that leads to my following point: when parents ask about proofs in geometry text what I take that they mean is two column ones not real ones. So if we define terms in this question then the answer is definitely what I said, NO, two column proofs are not an indicator of a rigorous program.

 

I do not really think it matters at all in which form the proofs are given. The two column format is artificial, but may be a good learning tool (just like the five paragraph essay is an abomination, but a good practice recipe for learners).

To judge rigor and quality of a math program, I would not discern between two column proofs or narrative proofs since the form is not really important - I would simply look at the extent to which proofs are incorporated, irrespective of format.

[FourOaks]

I have a question. I always hear that proofs are important and need to be studied because they take logic and students learn to use logical thinking.

 

If a student has had quite a bit of logic and seems to do well with logic, would said student have a better (or at least seemingly better) ability to solve proofs? Is said student did not use a "proof heavy" geometry curriculum, but did great and has excelled in all other math (up through Alg 2), would it be safe to say that the student could pick up some type of book on geometry proofs and without much difficulty work through it if needed?

 

Maybe this doesn't even make sense. I am ANYTHING but a mathematician, so I am quite clueless as to how this all really fits together.

 

Thanks for any insight!

[TravelingChris]

WEll after reading Lambert's Lament, I could see how my first and third child would like to have less traditional math but I can also see how my second child is much happier with the cut and dried math.

 

I did think it was interesting to hear his ideas about what we use in real life. I have used fractions in my real life- both in cooking/baking and in measurements for things I was making (now I know I wouldn't have used them if I was using metric but I am here in the USA and most things are still in the old system and use fractions). I have even used trigonometry once to make a window seat and I have used algebra many times in all types of situations.

 

I did like his annoyance at the nomenclature distinctions between identical numbers like mixed fractions and uneven fractions. I have been tremendously unimpressed when some program we were using wanted fractions and we were doing decimals or opposite or multiplying fractions versus dividing by the denominator. You should use what you want and if it turns out to be too cumbersome, you can always switch back to another way that uses a new name for the same number.

[quark]

I am learning much from this thread and thanks to the OP for starting it.

 

I searched for more info on how mathematicians write proofs, or at least how to start formulating proofs outside the standard two-column format and found clearly-written information here, at the Math Camp website. Thought it might benefit others too.

[Evergreen State Sue]

If you are considering Jacob's read some threads here. There are differences b/t the 2nd and 3rd editions and people seem to feel strongly about using one or the other. Also some kids just don't seem to get what some have called Jacob's 'intuitive' type of learning. It's not a hold your hand type of curriculum. I've know several kids/parents that had trouble with Jacob's and did well using a different curriculum.

 

I have two different math learners and Jacob's "intuitive" type learning is why we have finally decided to jump ship with one of my students. My ds has learned to hate math more than he even did before. Wish I had made the change sooner.

 

I really like MUS Geometry, but it is definitely proof light. When ds took the Plan test (ACT prep for Sophomores) he got every geometry question right and he was just about 3/4 of the way through MUS Geometry. If your goal is to train a future mathematician, I would skip MUS. If you just want the geometry needed for ACT/SAT testing, it fits the bill.

 

This is good news. We've decided to go with MUS Geometry. The books should arrive this week!

[Parrothead]

I have two different math learners and Jacob's "intuitive" type learning is why we have finally decided to jump ship with one of my students. My ds has learned to hate math more than he even did before. Wish I had made the change sooner.

 

 

 

This is good news. We've decided to go with MUS Geometry. The books should arrive this week!

 

Mine arrived today. As odd as it seems to say, it looks like it will be fun. Or at least but the fun back in math.

[Evergreen State Sue]

Mine arrived today. As odd as it seems to say, it looks like it will be fun. Or at least but the fun back in math.

 

 

UPS delivered our MUS Geometry today! We've committed to taking one last test in the old book and then will start back to the beginning in MUS. I'm hoping since we've suffered through 10 lessons of the old book we can double up on lessons in MUS and finish by the end of June. I hope it goes well for you and yours.