How critical are formal proofs in Geometry for a future engineer?

[steppingstonemomma]

I need to decide whether to stick with Saxon/Saxon Teacher cd combo for my 14yo son for Geometry OR do an online Geometry class. He wants to be an engineer so I want to give him the best preparation possible, but I'm clueless as to how critical "proofs" are in geometry. Honestly, I have NO IDEA what I'm asking. I skipped 3/4ths of my basic level geometry class and learned absolutely nothing and have no clue what a proof even is! I only know about them from reading about a 100 threads today on geometry an proofs! LOL!

 

So how needed are proofs in engineering?

Does Saxon cover proofs (if we use it all the way through Calc)?

 

 

Please, someone put me out of my misery.... I've been researching like a crazy woman for too many hours today on topics I know nothing about! LOL!

 

Tiffany

[regentrude]

He will not need geometric proofs in engineering. However, he will need strong analytical skills and a rigorous math preparation - and IMO that would mean a geometry course that contains proofs.

Proof are a great exercise in logical thinking.

Geometry is a good subject for introducing proofs because they are more visual and a bit less abstract; all higher math courses will involve proofs, but on a more abstract level. Geometry proofs are a good preparation for this type of thinking.

This is also the only occasion for students to see what mathematicians actually do (they prove relationships).

 

I could see skipping geometry proofs with a very weak math student who just needs to satisfy the requirement for some kind of geometry credit.

But for a student interested in engineering who is presumably a strong math student (otherwise engineering would not be a good choice), a high school geometry course should definitely contain proofs.

[steppingstonemomma]

Do you have a suggestion on a text or online class that would give a solid teaching in proofs?

[regentrude]

Do you have a suggestion on a text or online class that would give a solid teaching in proofs?

 

I'd imagine any solid high school geometry would cover proofs.

We have used AoPS, but that is not for everybody.

You might want to search the board for geometry recommendations or wait until somebody else chimes in; I am not familiar with other programs.

[dereksurfs]

I think Jacobs is a well known book with proofs. You can use the Dr. Callahan videos designed for it also: http://www.askdrcall...eometry-bundle/

 

Derek Owens has a good Geometry class online: http://www.derekowens.com/course_info_geometry.php

[Gwen in VA]

I have used and loved Geometry by Jurgensen, Brown, and Jurgensen for years. It does a great job teaching proofs, and its C-level problems are quite challenging, even for REALLY math-inclined kids!

 

It was the the text used by honors students in a highly ranked school district in MA.

[justkeepswimming]

This is from the Saxon website, it might help:

 

http://www.usingsaxon.com/newsletterpage-2012.php

[HS Mom in NC]

Wow. Another Geometry question.

 

Proofs are an exercise in formal logic.

 

My husband used Jacob's textbook along with a beautiful reprint of Euclid's Elements for our girls last semester. They were 14 and 16 at the time. I also had them using Cothran's formal logic books. The oldest was doing the Material Logic (book #3) and the other was doing Traditional Logic (book #1.) Both commented that Geometry and the formal logic books complimented each other very well. They found doing formal logic with Geometry to be very helpful.

[Nscribe]

This is from the Saxon website, it might help:

 

http://www.usingsaxo...erpage-2012.php

 

 

This is actually from Mr. Reed's website, not the "Saxon" official site. However, he explains well the way Saxon's previous editions handle proofs. The key is which ediitons of Saxon you choose to use. We chose to use the editions before the publisher took Geometry out of the Alg 1/Alg2 series (We used Alg 1 3rd edition, Alg. 2 3rd ediiton). If you use these "older" editions and the student completes the first half of Advanced Math, they will have learned and practiced doing proofs as described by Mr. Reed in the excerpt.

 

In very simplistic terms, proofs in Geometry challenge the student to display in an orderly manner the "why" behind a given theorem. It is a form of systematic reasoning. This link http://math.kendallhunt.com/documents/dg4/gp/dg4_gp_02.pdf is helpful in explaining.

 

IMHO, it is at the stage where a student is challenged to consider and express "why" in any field that the student begins to demonstrate their understanding and make the connections that bring the field to life.

[MyThreeSons]

Chiming in here as a current Geometry teacher at our homeschool co-op, and as a former Mechanical Engineer. A student going into an engineering major absolutely ought to have learned how to do proofs.

 

Proofs take a student from "I know A, B, and C" (the given information in the problem) to "I can therefore conclude D" (the 'prove' asked for in the problem). Along the way, there may be a couple of steps, or quite a journey, but each successive step in a proof is laid on the foundation of the truth of the previous steps. If you think about it, a student does the same thing when solving a basic algebra problem. He is given the problem, and by applying the same operation to both sides of the equation at each step, he is making successive true statements based upon the previous statement.

 

In engineering classes -- beginning with Calculus and Physics and moving up through other math, science, and engineering courses, the student will be following the same method of problem solving. In most of these classes, we don't generally have the student write out his work as a formal two-column proof as we do in Geometry. However, the skills learned by doing Geometry proofs will be invaluable.

 

Any traditional Geometry text will teach proofs. (An aside: I have tutored several students who used Teaching Textbooks Geometry. While they do teach proofs, my experience was that the proofs in the homework were just like the ones in the lesson, with different values for angles, lengths, etc. They did not present an entirely new configuration and ask the student to work through it on his own.)

 

One caution is that proofs are difficult to grade -- there are often multiple legitimate paths to get from the given information to the conclusion. A student's proof may look very different from the solution given in the teacher's manual, yet still be valid.

 

There are books available at Barnes and Noble, and possibly your library, that focus on Geometric proofs. If you find that your current curriculum is light on proofs, perhaps you could supplement with one of them.

 

HTH

[Nscribe]

One other article about Geometry and logical thinking skills....

http://www.educationnews.org/k-12-schools/the-modern-day-high-school-geometry-course-a-lesson-in-illogic/

[FaithManor]

Okay, here is my take on higher maths including geometry.

 

We all know that many adults will never officially "use" proofs, or solve quadratics by completing the square, or factor polynomials, or contemplate vectors, or......

 

Yep, many people will go into jobs in which they do not use that knowledge in their work. They'll probably forget promptly how they ever did that work.

 

But, the maturing of the brain as it wrestles with the formal logic required to complete a proof or factor the quadratic by the most efficient method, etc. is worth it's weight in gold. There are several ways in which brains are "grown", higher maths, sentence diagramming, literary analysis, balancing chemical equations, and the like are all examples of work that requires the student to develop problem solving skills. We need more people who can think logically, not fewer.

 

So, when someone grouses to me that their school wastes their child's time by forcing them to take algebra 1, or write proofs in geometry, or discuss and debate the underlying themes of a Shakespearen play, or read a difficult novel and write a character sketch or.....I tell them that these teachers are their child's best friends because regardless of whether or not they ever feel they've mastered these concepts - the hope is they would, but some just won't since we are all so different from one another- wrestling with the material and striving to understand it IS maturing their brains.

 

Therefore, while there is not a high likelihood that your student will ever need to write proofs, your student does form more neurons or connections through the corpus coloseum of the brain (connective tissue between the two hemispheres) from doing the work, and those connections are vital to higher order thinking. Neurologists have conclusively proven that the students who were most likely to have significant cooperation with both hemispheres of the brain simultaneously are the ones that have thicker corpus coloseums and they've proven - by monitoring MRI's - that the kids with the thickest corpus coloseums have them not due primarily to genetics, but due to the following pursuits - learning to play a musical instrument, becoming fluent in a foreign language, studying higher mathematics and in particular, geometry, developing computer programming skills, woodworking, metalworking, sewing (taking it to the level of being fairly accomplished in apparel sewing or quilting), studying formal logic, debate, and becoming proficient in chemistry and physics. I attended a neurological learning seminar in which the results of long term studies on this through John's Hopkins and a few other teaching universities with 2000+ volunteer students were presented. It was a great seminar! This held true through all economic groups and all ethnicities. It didn't matter what the background was that the student came from - they did eliminate participants whose IQ's were outliers - corpus coloseums grew significantly in the kids that pursued one or more of the above.

 

However, the sad thing is that students from low income families tend to be zoned for school districts in which the offerings are limited and the classroom sizes are so large that getting any additional help needed to gain proficiency in these areas is practically unheard of and of course, lessons on musical instruments, or access to the tools required for woodworking, metalworking, sewing, or lab work is also practically non-existent. So, unfortunately, it's easier for the "haves" to produce children who will "have it". Sigh.....

 

So, the moral of my tale is don't miss an opportunity to grow your child's brain neurons. I've got one child for whom math doesn't come easily - he didn't inherit dh and I's dna...occasionally we laugh quietly to ourselves that the hospital must have switched him at birth with someone else's child :D - and proof writing is hard for him. But, the struggle that he went through to conquer it greatly matured his thinking and it's funny, but other people see it. By the time he completed geometry, my parents and his aunts/uncles were making comments such as, "I just can't believe how much he's matured this semester." Now, it could be coincidental, but I think not. Time and time again my friend at the local PS who teaches geometry and algebra 2 will say that regardless of actual grades earned he sees serious growth in his students who try to learn the material. Even if they end the year with a D, if that D represents their best effort, they grew up a lot. It's the ones that occupy space and refuse to try to learn it that he'd likes to shake and he's got enough of those in his classes that he gets practically depressed about his job - subject for a different thread.

 

Embrace the proofs, love the proofs, get excited about the proofs, make your kids think you've lost your mind and if necessary, break out the M & M's...ds's attitude towards math always improves greatly when there is a little pile of M & M's at his elbow to munch on while he works. I'm all for bribing with chocolate!!!!! I used to do this at the Lutheran school when I taught science. If we had a heady topic coming up, I used to grease the wheels with a fun size hershey's bar for each student, or I'd put out a platter of fruit, etc. Sometimes I made mini sandwiches and the kids, as long as they were quiet and respectful, could get out of their seats and get a snack whenever they wanted to while I lectured or they worked on their assignments. You'd be surprised how well this worked. I'm convinced that many teens experience a blood sugar drop while doing schoolwork and if it happens when their brains are really being challenged, it's brutal. Make sure they've recently eaten before starting in on a proof.

 

Break out the food, bribe them, and if necessary hold their hands through every step until "the light bulb goes on"! You won't regret it regardless of whether or not your student becomes the next Pythagorus!

 

Faith

[EKS]

An aside: I have tutored several students who used Teaching Textbooks Geometry. While they do teach proofs, my experience was that the proofs in the homework were just like the ones in the lesson, with different values for angles, lengths, etc. They did not present an entirely new configuration and ask the student to work through it on his own.

 

Having used TT Geometry, I wanted to say that some proofs are like this, but there are plenty of others that ask more of the student.

[Nscribe]

Okay, here is my take on higher maths including geometry.

 

Faith

:wub: What She Said!!!!

[Jane in NC]

Faith,

 

I will argue that learning how to do proofs can also help one become a better writer as well as a more logical thinker. A good essay will flow logically from one idea to the next. Same for a proof. Unfortunately the two column proofs in many high school texts are long winded compared to "real" mathematical proofs, but the idea of connected flow remains.

[wapiti]

I will argue that learning how to do proofs can also help one become a better writer as well as a more logical thinker. A good essay will flow logically from one idea to the next. Same for a proof. Unfortunately the two column proofs in many high school texts are long winded compared to "real" mathematical proofs, but the idea of connected flow remains.

 

 

This. Understanding proofs provided a critical basis for my writing when I was a lawyer.

[Tullia]

It will depend on his math requirements. My son who is a computer science major with minor in math is very grateful this semester for his years of logic (Memoria Press) and having slogged through a year's worth of geometry proofs in high school. He's still being challenged by his math courses this semester; a few of his classmates who don't have the background are in serious trouble.

[Lang Syne Boardie]

We were happy with TT Geometry. My son brought his own curiosity and talent to the proofs, rarely doing it exactly according to the book. DH enjoyed discussing Geometry with him after supper every night; it's the most involved DH has ever been in the actual homeschooling. :)

 

My son also studied Memoria Press Traditional Logic I and II and Material Logic before doing Geometry. He's also a Latin student and good at English grammar...I do think it all fits together. A Well-Trained Mind.

[MyThreeSons]

This. Understanding proofs provided a critical basis for my writing when I was a lawyer.

 

 

And you're in good company. Abraham Lincoln spent considerable time working through Geometry proofs to help him sharpen his reasoning, logic, and argumentation skills.

[wapiti]

And you're in good company. Abraham Lincoln spent considerable time working through Geometry proofs to help him sharpen his reasoning, logic, and argumentation skills.

 

 

I did not know that. That's so interesting that I had to look it up! Apparently he studied Euclid quite extensively.

 

IME, it's much easier to write directly, and therefore persuasively, by visualizing an argument as a proof rather than the vague "writing" that I learned (or failed to learn) in high school. I didn't realize the connection until one day I had the urge to end a brief with "Q.E.D." :)

[mathwonk]

I used to point out to my classes that if you do your own taxes and try to get a deduction for something, you have to write a proof that you deserve the deduction. I.e. a proof is merely a convincing logical argument proceeding from accepted meanings of the terms used. E.g. if the deduction is available to persons over 65 but not earning more than $50,000/year, and having paid some taxes the year before, but not on social security, then you have a few conditions you have to "prove" that you meet, in order to get the deduction. I.e. you could state it as: Theorem: I deserve this deduction. Proof: I satisfy all criteria...because...

 

Remark: Harold Jacobs revised his geometry book in the third edition and weakened the treatment of proof significantly over the first edition.