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Have times changed? (asked seriously) Proofs are the heart of traditional geometry. . . . or, were in my era.

 

TT is much easier than other programs, such as Jacobs. We have used both. Jacobs impressed us as the better program of the two; however, we used TT with a non-math oriented son (who did very well with it).

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I am also looking for Geometry, for a tutoring student. My student will have finished McDougal Littell's Algebra I, which I loved. I want something with proofs, that is rigorous enough for a college-bound honors student. I want something that expects the student to have good critical thinking skills, and with problems that are intellectually interesting/challenging. I also want something with a good teacher's manual, and a worked-out solutions key. He has good math support at home, thus neither of us are interested in a video program. It must have proofs; I'm old school that way.

 

I'm not interested in Saxon.

 

I've taught Jacobs before, back in the day, and enjoyed it, but I understand it has gone through some changes?

 

I know McDougal Littell has a Geometry text, but I know nothing about it.

 

I found Forrester's Algebra tedious, don't know if he has a Geometry.

 

Keys to isn't a full enough program to be an honors high school course.

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ETA: this is meant for Pauline not the OP. These programs are much more proof-heavy than TT.

 

A couple of options:

 

AoPS geometry

The Houghton Mifflin Geometry used by Chalkdust (very proof heavy. I really like it.)

 

I have used the latter and had planned on using it with the rest of my kids b/c I really thought it was a great program. But now I am considering this http://www.tip.duke.edu/node/159 w/ Geometry

by Jurgensen, Ray C.; Brown, Richard G.; Jurgensen, John W.

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AoPS geometry

The Houghton Mifflin Geometry used by Chalkdust (very proof heavy. I really like it.)

 

I have used the latter and had planned on using it with the rest of my kids b/c I really thought it was a great program. But now I am considering this http://www.tip.duke.edu/node/159 w/ Geometry

by Jurgensen, Ray C.; Brown, Richard G.; Jurgensen, John W.

 

Arrggghh!! Looking at the cover of the Jurgensen, I think I actually owned that one at some point, but it's long gone. You just never know what to save and what not to....

ANYWAY, looks like it's cheaper to order the teacher's guide from the publisher than on the used market.

http://www.mcdougallittell.com/store/ProductCatalogController?cmd=Browse&subcmd=LoadDetail&ID=1005500000030773&imprint=hm&frontOrBack=F&division=M01&sortProductsBy=SEQ_TITLE&sortEntriesBy=SEQ_NAME#order

 

Thanks for the info!

Anyone else have any experience using any of these three? Hard to choose when you can't look at any of them...

 

(And OP, sorry for the hijack, but I thought it might be better to put all the geometry chat in one thread...)

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I can recommend Art of Problem Solving's geometry. It's more challenging than some others I've seen, and it isn't the traditional two-column proof approach. My son wasn't a fan of geometry, having already completed Jacobs, until he picked up the AoPS book and voluntarily worked his way through it. He said AoPS "made geometry make sense."

 

I can't speak specifically to the AoPS online geometry class, but we've never had a bad experience with an AoPS class. My son has taken several and plans to take more.

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I'll muddy the waters!! ;)

 

I think if someone had a killer geometry text they could make a fine living!! :) Alas, after checking out all the ones above (acutally did like the McDougal one) I decided to go with Chalkerian and supplementing with Abeka Geometry, I figure if one book does a section poorly perhaps we can reinforce it with a second one...I detest Geometry...give me Calculus any day..I'll integrate to the moon, but can't stand geometry...I'll let you know in 6 months how it went!! :)

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We used Discovering Geometry by Key Curriculum Press this year. It's more hands-on than most Geometry programs. It's also light on proofs.
Then this is the program we will be using! :D

 

 

(Actually, Dn (Dear niece) just finished Geometory using Discovering Geometry this year and she really liked it. She wants to be an architect, and she's very good at math, so between your recommendation, and hers I think we'll just go with it.. And I already know they have it at the resource center. :) )

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  • 1 year later...
Did you ever report how your geometry study went? I'd love to hear.

Here is my review of Discovering Geometry:

 

We used Discovering Geometry by Michael Serra/Key Curriculum Press in 9th grade.

 

Pros:

• Clear and straightforward

• More hands-on than most geometry programs

• Teacher text and Solution manual available

• Algebra review incorporated

• Prepares well for ACT/SAT

 

Pros/Cons:

• Lite on proofs

 

We used the 3rd edition of DG. ISBNs:

student 1-55953-459-1

teacher 1-55953-460-5

solution 1-55953-586-5

 

We also purchased an assessment book and patty paper from Key Curriculum Press. I can no longer find DG at their website however.

 

Table of Contents:

http://www.keypress.com/documents/ALookInside/DiscoveringGeometryFourthEd/DG4SE_FM.pdf

 

Student Edition sample:

http://www.keypress.com/documents/ALookInside/DiscoveringGeometryFourthEd/SE%20Sample%20Chapter.pdf

 

Teacher Edition sample:

http://www.keypress.com/documents/ALookInside/DiscoveringGeometryFourthEd/TE%20Sample%20Chapter.pdf

 

ETA:

 

Discovering Geometry has moved to Kendall Hunt:

http://www.kendallhunt.com/discoveringgeometry/

 

Student Edition sample:

http://www.kendallhunt.com/uploadedFiles/Kendall_Hunt/Content/PreK-12/Product_Samples/DG_%20Student_Edition_Sample_Chapter.pdf

 

Teacher Edition Sample:

http://www.kendallhunt.com/uploadedFiles/Kendall_Hunt/Content/PreK-12/Product_Samples/DG_Teachers_Edition_Sample_Chapter.pdf

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Arrggghh!! Looking at the cover of the Jurgensen, I think I actually owned that one at some point, but it's long gone. You just never know what to save and what not to....

ANYWAY, looks like it's cheaper to order the teacher's guide from the publisher than on the used market.

http://www.mcdougallittell.com/store/ProductCatalogController?cmd=Browse&subcmd=LoadDetail&ID=1005500000030773&imprint=hm&frontOrBack=F&division=M01&sortProductsBy=SEQ_TITLE&sortEntriesBy=SEQ_NAME#order

 

Thanks for the info!

Anyone else have any experience using any of these three? Hard to choose when you can't look at any of them...

 

(And OP, sorry for the hijack, but I thought it might be better to put all the geometry chat in one thread...)

 

We used the McDougal Littell text, but I had no idea a teacher's edition was available. That might have helped, but honestly I wouldn't have bought it for that price. It was extremely rigorous and thorough and took a good two hours each day. The "solutions manual" was little more than an answer key and only gave one possible way to do a proof. So having dd redo the proofs to have her match up with theirs was a big part of the time consumption. Poor kid. :tongue_smilie: I also had her do all of the A and B problems and some of the C's as well. Most courses using this text pick and choose - so again, it wouldn't have taken so much time each day. But in hindsight, I'm so glad we used this text! The rigorous proof work has proven valuable in higher math. I highly recommend it for any student (and mom :tongue_smilie:) who's up for the challenge. IMO, if you could get a tutor once or twice a week, that would be ideal - if you're not currently strong on geometric proofs.

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How does Discovering Geometry compare with Jacobs? thanks.

We did not get very far in Jacob's before having to abandon it. I have a degree in math, and I struggled with it. I think it is written for people who are opposite brained from me. I'm very logical. I like clear and concise, so does ds. Jacobs was verbose. From the reviews I have seen, Jacobs is more challenging than DG and more proof heavy. Jacobs has no solutions manual.

 

That's all I know.

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Another perspective, that of a professional geometer.

 

I suggest using whatever the child enjoys enough to stay with. If the book stimulates some interest the child will pursue a deeper understanding at some time.

 

Another point is to determine what are the child's goals. Basic goals are to pass some test like an SAT test, other goals are to understand the ideas behind the subject enough to use them in further study. Other goals are to achieve some mastery, to compete in contests, or go on to an advanced study of geometry.

 

In my opinion, Saxon is a book with only basic academic goals, i.e. pass entrance tests.

 

Serra is basic in another sense, to get an intuitive feel for the topic but not at a precise level. For just introducing geometric thinking without proof, one colleague of mine has also had success structuring his college geometry course, which enrolls many geometry phobes, to begin with experiments using the program Geometer's Sketch Pad. For students who have trouble even visualizing geometric shapes, this program provides many do it yourself constructions that enhance that ability. It may be expensive as our access to it was subsidized. ... Well it isn't so much after all, maybe $69.95 at most, and here is an apparent offer of a student version for $29.95! (from the publishers of Serra's book).

 

http://www.dynamicgeometry.com/

 

Jacobs is a more rigorous book, some proofs not too many, and some nod to the original treatment in Euclid. I liked the entertaining cartoons and amusing news items, chosen also for geometric relevance.

 

AoPS is a better than average text, with challenging problems and mostly rigorous proofs, if not entirely so.

 

For a really strong book, aiming at high level understanding, the original treatment by Euclid is unmatched, but is easier to engage with a companion guide like the first chapter of Hartshorne's Geometry: Euclid and beyond.

 

A wonderful book written for the intelligent general public, on non standard topics touching geometry, is Hilbert's Geometry and the Imagination.

 

I recommend to go with whatever works for the student involved at the current time. Anything that gets us into a subject opens the door for us. We all begin by crawling, then walking, then running. Even as a senior professional mathematician, I enjoy sitting in an elementary presentation of a math topic by an expert who is aiming it at absolute beginners. I figure if he does a good job, maybe I too will learn something. And sometimes I do. On this principle, Serra could be a good first choice for someone with little feel for geometry. But one should go further afterwards.

 

I myself did not read Euclid until over age 65, 30 years after my PhD in geometry. Still it is accessible to young children, given the opportunity. Thus I hope to advocate it sooner for younger generations.

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Aspects of geometry: Preferably one does not study geometry as a hurdle to get into a formal school, but to appreciate the shape of our world, and to participate in the intellectual tradition of our human race. Please do not use geometry as a reason to freak out, but as another tool to explore and enjoy life.

 

Geometry studies shapes and their relationships. Elementary plane geometry is about the properties of lines, angles, triangles, quadrilaterals, pentagons, hexagons, and circles and their interrelations. Here are some Euclidean plane geometry “facts”:

 

The three angles of every triangle add up to a straight angle, and if three similarly shaped plane figures (such as squares) are erected on the three sides of a right triangle, then the sum of the areas of the two smaller ones equals the area of the largest one. Two lines which do not meet a third line also do not meet each other.

 

Each triangle has a unique circle that fits inside it with each side of the triangle touching the circle once. Each triangle also has a unique circle that passes through each vertex. Moreover if two triangles have a common base and different upper vertices, then the circle passing through the two common base vertices and through one of the upper vertices, also passes through the other upper vertex if and only if the angles at the 2 upper vertices are equal.

 

If two sides of one triangle are each equal to two sides of another triangle, and if the angles between the two pairs of equal sides are also equal, then the third sides of the two triangles are equal, as are also the other two corresponding angles.

 

If a triangle has all 3 sides of equal length then all three angles are also all equal. However if a quadrilateral has all 4 sides equal then only the opposite angles need be equal. A pentagon with all 5 sides equal can have all 5 angles different, but if it has three equal adjacent angles then all 5 angles are equal.

 

All 3 angle bisectors of a triangle meet in a common point inside the triangle, in fact at the center of the circle that touches each side of the triangle once. The three lines joining each vertex to the midpoint of the opposite side also meet at a common point, the "centroid" of the triangle, a point at which a triangle made of cardboard would balance on a fingertip.

 

If 6 disjoint triangles with all sides equal, are constructed with one vertex common to all, and each edge abutting at that vertex common to 2 triangles, then the regular hexagon they form has all its 6 vertices on a common circle. Thus the “regular” hexagon inscribed in a circle has edge length equal to the radius of that circle.

 

To construct the edge length of a regular decagon inscribed in a given circle with ruler and compass, construct two perpendicular radii and join the midpoint A of one radius to the point B where the perpendicular radius meets the circle. From the segment AB subtract half the radius, and the difference is the edge length sought. After constructing the regular decagon, joining alternate vertices gives a regular pentagon.

 

If two secants meet a circle at A,B and C,D and meet each other inside the circle at X, then the rectangle with sides AX and BX has area equal to that with sides CX and DX.

 

One can appreciate these facts just by making drawings and contemplating them (Serra, SketchPad). The deeper logical side of geometry is to explore which of these facts is forced on us by the others. This is mental practice in the fine art of deduction. Among books offering this practice, some (Jacobs) assume use of “real” numbers while others, especially Euclid, help us build geometric background intuition for appreciating real numbers. I prefer Euclid’s approach as more elementary, and also more helpful intellectually.

 

Here are my free Euclid notes from last summer at epsilon camp.

http://www.math.uga.edu/~roy/camp2011/10.pdf

 

If your child can read these notes profitably, presumably in combination with a copy of Euclid, then he/she is very, very strong.

Edited by mathwonk
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Another perspective, that of a professional geometer.

 

I suggest using whatever the child enjoys enough to stay with. If the book stimulates some interest the child will pursue a deeper understanding at some time.

 

Another point is to determine what are the child's goals. Basic goals are to pass some test like an SAT test, other goals are to understand the ideas behind the subject enough to use them in further study. Other goals are to achieve some mastery, to compete in contests, or go on to an advanced study of geometry.

 

In my opinion, Saxon is a book with only basic academic goals, i.e. pass entrance tests.

 

Serra is basic in another sense, to get an intuitive feel for the topic but not at a precise level. For just introducing geometric thinking without proof, one colleague of mine has also had success structuring his college geometry course, which enrolls many geometry phobes, to begin with experiments using the program Geometer's Sketch Pad. For students who have trouble even visualizing geometric shapes, this program provides many do it yourself constructions that enhance that ability. It may be expensive as our access to it was subsidized. ... Well it isn't so much after all, maybe $69.95 at most, and here is an apparent offer of a student version for $29.95! (from the publishers of Serra's book).

 

http://www.dynamicgeometry.com/

 

Jacobs is a more rigorous book, some proofs not too many, and some nod to the original treatment in Euclid. I liked the entertaining cartoons and amusing news items, chosen also for geometric relevance.

 

AoPS is a better than average text, with challenging problems and mostly rigorous proofs, if not entirely so.

 

For a really strong book, aiming at high level understanding, the original treatment by Euclid is unmatched, but is easier to engage with a companion guide like the first chapter of Hartshorne's Geometry: Euclid and beyond.

 

A wonderful book written for the intelligent general public, on non standard topics touching geometry, is Hilbert's Geometry and the Imagination.

 

I recommend to go with whatever works for the student involved at the current time. Anything that gets us into a subject opens the door for us. We all begin by crawling, then walking, then running. Even as a senior professional mathematician, I enjoy sitting in an elementary presentation of a math topic by an expert who is aiming it at absolute beginners. I figure if he does a good job, maybe I too will learn something. And sometimes I do. On this principle, Serra could be a good first choice for someone with little feel for geometry. But one should go further afterwards.

 

I myself did not read Euclid until over age 65, 30 years after my PhD in geometry. Still it is accessible to young children, given the opportunity. Thus I hope to advocate it sooner for younger generations.

 

Thank you for that post. I've got to plan Geometry for my daughter next year it that was a big help.

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Thank you! And please consider also the last paragraph of the previous boring post #19.

 

Not boring at all! I'm printing that one off so I can point out (or prefferably, find a way to let them discover) those things. Thank you again.

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Aspects of geometry: Preferably one does not study geometry as a hurdle to get into a formal school, but to appreciate the shape of our world, and to participate in the intellectual tradition of our human race. Please do not use geometry as a reason to freak out, but as another tool to explore and enjoy life.

 

Geometry studies shapes and their relationships. Elementary plane geometry is about the properties of lines, angles, triangles, quadrilaterals, pentagons, hexagons, and circles and their interrelations. Here are some Euclidean plane geometry “factsâ€:

 

The three angles of every triangle add up to a straight angle, and if three similarly shaped plane figures (such as squares) are erected on the three sides of a right triangle, then the sum of the areas of the two smaller ones equals the area of the largest one. Two lines which do not meet a third line also do not meet each other.

 

Each triangle has a unique circle that fits inside it with each side of the triangle touching the circle once. Each triangle also has a unique circle that passes through each vertex. Moreover if two triangles have a common base and different upper vertices, then the circle passing through the two common base vertices and through one of the upper vertices, also passes through the other upper vertex if and only if the angles at the 2 upper vertices are equal.

 

If two sides of one triangle are each equal to two sides of another triangle, and if the angles between the two pairs of equal sides are also equal, then the third sides of the two triangles are equal, as are also the other two corresponding angles.

 

If a triangle has all 3 sides of equal length then all three angles are also all equal. However if a quadrilateral has all 4 sides equal then only the opposite angles need be equal. A pentagon with all 5 sides equal can have all 5 angles different, but if it has three equal adjacent angles then all 5 angles are equal.

 

All 3 angle bisectors of a triangle meet in a common point inside the triangle, as do the three lines joining each vertex to the midpoint of the opposite side.

 

If 6 disjoint triangles with all sides equal, are constructed with one vertex common to all, and each edge abutting at that vertex common to 2 triangles, then the regular hexagon they form has all its 6 vertices on a common circle. Thus the “regular†hexagon inscribed in a circle has edge length equal to the radius of that circle.

 

To construct the edge length of a regular decagon inscribed in a given circle with ruler and compass, construct two perpendicular radii and join the midpoint A of one radius to the point B where the perpendicular radius meets the circle. From the segment AB subtract half the radius, and the difference is the edge length sought. After constructing the regular decagon, joining alternate vertices gives a regular pentagon.

 

If two secants meet a circle at A,B and C,D and meet each other inside the circle at X, then the rectangle with sides AX and BX has area equal to that with sides CX and DX.

 

One can appreciate these facts just by making drawings and contemplating them (Serra, SketchPad). The deeper logical side of geometry is to explore which of these facts is forced on us by the others. This is mental practice in the fine art of deduction. Among books offering this practice, some (Jacobs) assume use of “real†numbers while others, especially Euclid, help us build geometric background intuition for appreciating real numbers. I prefer Euclid’s approach as more elementary, and also more helpful intellectually.

 

Here are my free Euclid notes from last summer at epsilon camp.

http://www.math.uga.edu/~roy/camp2011/10.pdf

 

If your child can read these notes profitably, presumably in combination with a copy of Euclid, then he/she is very, very strong.

 

Thank you for both of your posts actually, but this one in particular. We use Chalkdust Geometry with the Houghton Mifflin text and the lectures taught on DVD by Dana Mosely so I am not looking for another text but your posts are enhancing what we already use. Looking forward to reading your notes.

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We used Discovering Geometry by Key Curriculum Press this year. It's more hands-on than most Geometry programs. It's also light on proofs. Teacher manuals and solution manuals can be purchased.

 

Sue,

 

I'm curious...

 

Would completing Discovering Geometry by Key Curriculum Press count as 1 credit?

 

What about Algebra by Key Curr. Press?

 

Thanks!

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We used Discovering Geometry by Key Curriculum Press this year. It's more hands-on than most Geometry programs. It's also light on proofs. Teacher manuals and solution manuals can be purchased.

 

 

Sue,

 

Is this the Discovering Geometry you are talking about?

 

 

Pic: (below)

 

 

Table of Contents:

 

0-Geometric Arty

1- Inductive Reasoning

2-Introducing Geometry

3-Geometric Construction

4-Discovering Geometry

5-Congruence

6-Circles

7-Transformations and Tessellations

8-Area

9-Pythagorean Theorem

10-Volume

11-Similarity

12-Trigonometry

13-Deductive Reasoning

14-Geometric Proof

15-Geometric Proof II

 

 

Also, would I only need the:

text 0-913684-08-2

resource book- 0-9138-684-09-0

TE guide/key 0-913684-68-6

 

 

Is there anything else I would need with it? What about Sketchpad on their site?

 

Thank you!

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Here are some $1 used copies of Discovering Geometry, I think. How many books does he have? One says "investigative approach" and one says "inductive approach", and one says neither. Well they are all available here for cheap. For some reason the supply of used books suggests a lot of school systems, or students, have dumped this one. That of course is a plus for the used book market.

 

http://www.abebooks.com/servlet/SearchResults?an=serra&sts=t&tn=discovering+geometry

 

 

Here for instance is a famous standard calculus book also for a dollar:

 

http://www.abebooks.com/servlet/SearchResults?an=george+thomas&sts=t&tn=calculus

 

 

So I guess the low price suggests that at some point it has been very popular. Old Beatles records are cheap too.

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Is this the Discovering Geometry you are talking about?

That does not look like the book I have. Here is a link to the Kendall Hunt site for it.

 

Here are the ISBNs we used again:

We used the 3rd edition of DG. ISBNs:

student 1-55953-459-1

teacher 1-55953-460-5

solution 1-55953-586-5

 

We also purchased an assessment book and patty paper from Key Curriculum Press.

 

HTH!

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I think Michael Serra has been selling that book for quite a while now, so it has gone through several editions. In such cases there is seldom any advantage to using the newer editions which are written either to simplify the presentation and attract more buyers, or just to keep the price artificially high. I cannot be sure without seeing the insides of the books, but i would guess those $1 copies on the abebooks link are as good as the new ones for sale by the publisher.

 

I looked at a sample chapter of the one on display at the Kendall Hunt site and that did not look like a high school level book to me. I am not sure what age it is aimed at but it seems more of a grammar school level book. I could only see one sample chapter (5), but I would be wary of going off to college with only that level of preparation, unless one was confident of not taking any more math. Maybe it gets more serious in later chapters, but I am skeptical.

 

It may well be appropriate as a gentle introduction to geometric thinking, but I believe it needs to be followed by a stronger treatment like that of Harold Jacobs, to give a reasonable preparation for further study.

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Kinetics Books has the first seven chapters of their geometry program available for preview. We signed up for the trial and so far dd likes it better than Jacobs. I think once the full fledged program comes out, we will go with this rather than continue with Jacobs which seemed dry to her. My $0.02.

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  • 2 months later...

 

Kinetics Books has the first seven chapters of their geometry program available for preview. We signed up for the trial and so far dd likes it better than Jacobs. I think once the full fledged program comes out, we will go with this rather than continue with Jacobs which seemed dry to her. My $0.02.
When is it set to be done and available for purchase?
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