Geometry retaught in trig?

[busymama7]

I had another homeschool mom tell me that she had been told that geometry taught as a subject in high school was a complete waste of time as it is all retaught in trig anyways. I was totally blown away as I had never heard such a thing and honestly question her source. But I don't actually know whether or not that is true as I've never taught beyond algebra 2 and I've had all my kids take geometry. In high school, I took geo/trig together as one class.

[Lanny]

My DD just finished Geometry.  I do not believe that was a waste of time. The below is from a web page on the Tech web site (Texas Tech University).  Notice the requirement for 4 Math units:

 

The recommended curriculum includes:

4 units of English
4 units of Math
4 units of Science
2 units of Foreign Language

[kiana]

I had another homeschool mom tell me that she had been told that geometry taught as a subject in high school was a complete waste of time as it is all retaught in trig anyways. I was totally blown away as I had never heard such a thing and honestly question her source. But I don't actually know whether or not that is true as I've never taught beyond algebra 2 and I've had all my kids take geometry. In high school, I took geo/trig together as one class.

 

Absolute rubbish. Lack of geometry knowledge is a common reason for struggling in trig/precalc. Yes, we review and extend, but all but the most highly gifted students without the base of understanding will struggle. It makes as much sense as saying that algebra 1 is a waste of time because we review everything in algebra 2. 

[winterbaby]

When I was in high school trig was a one semester course. No way could they have done the whole geometry course in that time.

 

The real potential waste in public school geometry comes from the tendency to teach it as glorified algebra - given these facts about the diagram, find the value of angle XYZ - rather than proofs. But if you didn't even have that you'd be lost in trig I think.

[justasque]

Most math programs build from year to year - that's normal.  

The first year, you get a little taste of something.  Just a little, "Hey, check this out, interesting, eh?  Let's play around with it for a day or two."

Then the next year, you learn it properly and practice, in some cases in increasing complexity as the year goes on.  (For example, you may learn how to multiply x (x+1), then later have a perimeter word problem to find the area of a rectangle where "the length is one more than the width", which comes out to the same thing.  Or you may learn an algorithm using "easy numbers" then gradually add in fractions and decimals using the same algorithm). 

The third year, you get some review to remember the process, after which you learn new things that build on the prior knowledge and skills.

 

So, yeah, most problems will review some geometry before building on it.  But no so much as to make the entire prior year redundant.  

[regentrude]

No. This is nonsense. Most of geometry is not even revisited in trigonometry.

Trig courses do not spend time on geometric proofs.They require geometry mastery as a prerequisite. 

 

[SparklyUnicorn]

Working through a trig course myself at the moment.  There is some basic geometry review, but not much. 

 

 

[busymama7]

Absolute rubbish. Lack of geometry knowledge is a common reason for struggling in trig/precalc. Yes, we review and extend, but all but the most highly gifted students without the base of understanding will struggle. It makes as much sense as saying that algebra 1 is a waste of time because we review everything in algebra 2.

Thank you. I said as much to her (without using the word rubbish 😂)but I think she was offended.

My other argument was that geometry is really important for non mathy kids who may not get as high as trig/pre calc. I think a blanket statement such as she was told is so dangerous. I only said something because there were many other moms listening in and I thought it very bad advice.

[Mike in SA]

Thank you. I said as much to her (without using the word rubbish 😂)but I think she was offended.

My other argument was that geometry is really important for non mathy kids who may not get as high as trig/pre calc. I think a blanket statement such as she was told is so dangerous. I only said something because there were many other moms listening in and I thought it very bad advice.

 

Good for you - it is absolutely rubbish, and for kids not progressing into higher math, may be the single most important math course they will take.  It's the only one that cannot be executed through rote procedure, and the only one that mandates the development of logical thought.

 

For kids progressing into certain science, engineering, and architecture topics, geometry is absolutely indispensable - and I mean the parts not "covered in trig," which is an almost comical turn of phrase in itself.

[...................]

Yes and no...my son has half a year's Geometry, and the chair of the math department looked at the topics he covered and said they are more than enough for Trig and that the more important factor was that he had a *very* solid foundation in Algebra 2. He accepted the 1/2 credit in lieu of a usual full year Geometry course.

 

Of course depending on your state, cover school or college choice, they will most likely require a full year of Geometry.

 

(Also my son will cover more Geometry at mathnasoum so there's no need to worry about his future as a STEM major, so I would say our situation is unique and not necessarily wise to copy it)

Edited May 27, 2017 by Calming Tea

[Mike in SA]

Yes and no...my son has half a year's Geometry, and the chair of the math department looked at the topics he covered and said they are more than enough for Trig and that the more important factor was that he had a *very* solid foundation in Algebra 2. He accepted the 1/2 credit in lieu of a usual full year Geometry course.

 

Of course depending on your state, cover school or college choice, they will most likely require a full year of Geometry.

 

(Also my son will cover more Geometry at mathnasoum so there's no need to worry about his future as a STEM major, so I would say our situation is unique and not necessarily wise to copy it)

 

I think this is not the point? 

 

Yes, some states don't even require it, and yes, you can get through trig without much geometry - the question seemed to be whether geometry was relevant and "covered" in trig...

[Julie of KY]

Yes and no...my son has half a year's Geometry, and the chair of the math department looked at the topics he covered and said they are more than enough for Trig and that the more important factor was that he had a *very* solid foundation in Algebra 2. He accepted the 1/2 credit in lieu of a usual full year Geometry course.

 

 

To be able to do trig, you do not need to know most of geometry. The basic geometry required for trig is usually reviewed, but there is much more to geometry that is not needed in trig.

 

A good geometry course teaches way more than simply the prerequisite geometry for trig. Can you do geometry light and move on in math? Sure. but you certainly haven't covered all of geometry.

[EKS]

I had another homeschool mom tell me that she had been told that geometry taught as a subject in high school was a complete waste of time as it is all retaught in trig anyways. I was totally blown away as I had never heard such a thing and honestly question her source. But I don't actually know whether or not that is true as I've never taught beyond algebra 2 and I've had all my kids take geometry. In high school, I took geo/trig together as one class.

 

Geometry is not retaught in trig.  The only part of geometry that is retaught in trig is the right triangle trig stuff (SOH CAH TOA).  That's like one chapter out of 12.

[daijobu]

I had a mom tell me that students don't learn anything in middle school anyway.  Apparently the students just bide their time until high school.

 

I just nod and smile and back away slowly.  

[regentrude]

I had a mom tell me that students don't learn anything in middle school anyway.  Apparently the students just bide their time until high school.

 

That was exactly my experience in the public middle school, and one of the reason I pulled my kids out.

 

If kids finish 4th grade having learned arithmetic with positive integers and do not progress to algebra until 9th grade, i.e. spend the entire four years of middle school on arithmetic with fractions, the above is pretty much correct.

In math, this seems to be a fairly standard situation. 

Edited May 28, 2017 by regentrude

[RootAnn]

I think you can do a surface-light amount of trig without a full year of geometry (as Calming Tea pointed out) because while there is some geo in trig, the coverage isn't the same at all. I think that was CT's point, maybe? (I could tell a similar story about not having completed a full geo program before starting trig and not having a problem.)

 

IMO, you should have the geo coverage no matter what. It'll help with trig, but trig in no way covers what a geometry course covers other than they both deal with some of the same things (angles, for instance).

[...................]

I think you can do a surface-light amount of trig without a full year of geometry (as Calming Tea pointed out) because while there is some geo in trig, the coverage isn't the same at all. I think that was CT's point, maybe? (I could tell a similar story about not having completed a full geo program before starting trig and not having a problem.)

 

IMO, you should have the geo coverage no matter what. It'll help with trig, but trig in no way covers what a geometry course covers other than they both deal with some of the same things (angles, for instance).

 

yeah I am sorry I rambled there, but my point was that if you want to do a light Geometry course with some basic proofs (such as what's included in Saxon Algebra 2 if you finish teh ENTIRE book), or maybe a light course that isn't as "academic"  (I'm thinking TT, paradigm accelerated), or a Self Paced course like Kahn Academy, it seems, according to this dean of the math department at our local college, that you will have no problem in future maths.

 

But, as far as I understand it, you cannot SKIP Geometry, as it is really NOT repeated in Trig. 

 

So, all in all, just agreeing with the others here.

[quark]

I had another homeschool mom tell me that she had been told that geometry taught as a subject in high school was a complete waste of time as it is all retaught in trig anyways. I was totally blown away as I had never heard such a thing and honestly question her source. But I don't actually know whether or not that is true as I've never taught beyond algebra 2 and I've had all my kids take geometry. In high school, I took geo/trig together as one class.

I wonder if she might have her math course names mixed up or might be referring to the very (too) light emphasis some schools place on proofs and therefore, mixing up geometry in high school with what students learn in middle school? There was SO much in geometry for my kid to learn that was accessible at that age that we even opted to add another 6 months of advanced topics to keep the fire for geometry burning. I wish I had had this opportunity in school. The effect on my logical thinking skills would have been enormous.

 

In our experience, a very thorough exposure to geometry and algebra 2 with trig, led to skipping an official precalculus with trig class. Switching the emphasis around would have been a poor choice indeed.

[quark]

I had a mom tell me that students don't learn anything in middle school anyway. Apparently the students just bide their time until high school.

 

I just nod and smile and back away slowly.

Oh no, was it me? I would have completely agreed with that mom. 😊 It does depend on the kid though. From what I have observed, highly social kids appreciate having that time in school. Academically though, many of the kids I know would have benefitted from a different social experience in addition to being given the chance to learn outside school at their own pace.

[EKS]

I had a mom tell me that students don't learn anything in middle school anyway.  Apparently the students just bide their time until high school.

 

I just nod and smile and back away slowly.  

 

I heard this same thing from a principal of one of the local schools.  It was weird because usually she was a pretty knowledgeable person.

Edited May 28, 2017 by EKS

[daijobu]

Oh no, was it me? I would have completely agreed with that mom. 😊 It does depend on the kid though. From what I have observed, highly social kids appreciate having that time in school. Academically though, many of the kids I know would have benefitted from a different social experience in addition to being given the chance to learn outside school at their own pace.

 

Lol, not you, but a mom of a kid in regular school.  I think she was rationalizing that her son indeed wasn't really learning anything, but giving herself permission to not do anything about it.  

 

My thought was well maybe her son won't learn anything for 3 years, but I intend for my dd's to grow at least a bit academically in middle school.  

[Arcadia]

Geometry isn't retaught in trigonometry. Trigonometry modules are in algebra 2 and/or precalculus depending on which textbooks the public school opt for.

 

However if I look at the old 1997 California standards that are now replaced by common core standards, there is some overlap.

 

"Geometry

 

Grades Eight Through Twelve - Mathematics Content Standards

 

The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills and concepts, students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems.

 

1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.

 

2.0 Students write geometric proofs, including proofs by contradiction.

 

3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.

 

4.0 Students prove basic theorems involving congruence and similarity.

 

5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.

 

6.0 Students know and are able to use the triangle inequality theorem.

 

7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.

 

8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.

 

9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.

 

10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.

 

11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.

 

12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems.

 

13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.

 

14.0 Students prove the Pythagorean theorem.

 

15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.

 

16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.

 

17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.

 

18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))2 + (cos(x)) 2 = 1.

 

19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.

 

20.0 Students know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles.

 

21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.

 

22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections."

 

"Trigonometry

 

Grades Eight Through Twelve - Mathematics Content Standards

 

Trigonometry uses the techniques that students have previously learned from the study of algebra and geometry. The trigonometric functions studied are defined geometrically rather than in terms of algebraic equations. Facility with these functions as well as the ability to prove basic identities regarding them is especially important for students intending to study calculus, more advanced mathematics, physics and other sciences, and engineering in college.

 

1.0 Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians.

 

2.0 Students know the definition of sine and cosine as y-and x-coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.

 

3.0 Students know the identity cos2 (x) + sin2 (x) = 1:

 

3.1 Students prove that this identity is equivalent to the Pythagorean theorem (i.e., students can prove this identity by using the Pythagorean theorem and, conversely, they can prove the Pythagorean theorem as a consequence of this identity).

 

3.2 Students prove other trigonometric identities and simplify others by using the identity cos2 (x) + sin2 (x) = 1. For example, students use this identity to prove that sec2 (x) = tan2 (x) + 1.

 

4.0 Students graph functions of the form f(t) = A sin (Bt + C) or f(t) = A cos (Bt + C) and interpret A, B, and C in terms of amplitude, frequency, period, and phase shift.

 

5.0 Students know the definitions of the tangent and cotangent functions and can graph them.

 

6.0 Students know the definitions of the secant and cosecant functions and can graph them.

 

7.0 Students know that the tangent of the angle that a line makes with the x-axis is equal to the slope of the line.

 

8.0 Students know the definitions of the inverse trigonometric functions and can graph the functions.

 

9.0 Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.

 

10.0 Students demonstrate an understanding of the addition formulas for sines and cosines and their proofs and can use those formulas to prove and/or simplify other trigonometric identities.

 

11.0 Students demonstrate an understanding of half-angle and double-angle formulas for sines and cosines and can use those formulas to prove and/or simplify other trigonometric identities.

 

12.0 Students use trigonometry to determine unknown sides or angles in right triangles.

 

13.0 Students know the law of sines and the law of cosines and apply those laws to solve problems.

 

14.0 Students determine the area of a triangle, given one angle and the two adjacent sides.

 

15.0 Students are familiar with polar coordinates. In particular, they can determine polar coordinates of a point given in rectangular coordinates and vice versa.

 

16.0 Students represent equations given in rectangular coordinates in terms of polar coordinates.

 

17.0 Students are familiar with complex numbers. They can represent a complex number in polar form and know how to multiply complex numbers in their polar form.

 

18.0 Students know DeMoivre’s theorem and can give nth roots of a complex number given in polar form.

 

19.0 Students are adept at using trigonometry in a variety of applications and word problems." http://www.cde.ca.gov/be/st/ss/documents/mathstandards.doc

 

 

I heard this same thing from a principal of one of the local schools.  It was weird because usually she was a pretty knowledgeable person.

  

Lol, not you, but a mom of a kid in regular school.  I think she was rationalizing that her son indeed wasn't really learning anything, but giving herself permission to not do anything about it.  

 

The kids that were kicked out of my nearest library for breaking rules such as eating dorito chips in the library and being too noisy were the 5th-8th graders usually.

I heard quite a few who complain that their kids didn't retain much from middle school. Isn't those years the heaviest teenage brain fog years?

[...................]

I was going to talk about Middle School but then I realized it's totally off topic :)

Edited May 28, 2017 by Calming Tea