Veterans: What is Your Favorite Math to Teach?

[Gil]

What is your favorite math--by grade, subject and text to teach?

 

 

[regentrude]

Art of Problem Solving.

All books Intro to Algebra and up i.e. for us 6th grade through 12th grade.

I have no experience with the prealgebra text.

[MiMi 4under3]

My favorite is Saxon, and I think grade 3 is the best one of the lower levels. That was a fun math year to teach because dc went from baby math like adding 1+1, to square roots and graphing on a coordinate plane.

 

 

[EKS]

Algebra I using Jacobs.

[FaithManor]

Geometry using Harold Jacobs, I have the third edition, and Algebra 2 with Lial' s. But, I am using Sullivan for the first time for pre_calc, and getting along nicely. Dh taught pre_calc to dd and he hated whatever he was using.

[FloridaLisa]

The one I know -- Saxon

 

We've also used Life of Fred for geometry but I found after trying to switch to Singapore last year that I was just very comfortable teaching Saxon and it works for us. 

 

Lisa

[Melissa B]

Saxon - all the way through.

 

 

We are also enjoying Beast Academy for an elementary supplement, but it is only our second year using it.

[Lori D.]

Algebra 1 and Geometry (2nd ed.) by Harold Jacobs. Great real-world examples for every lesson, a sense of humor, incremental/mastery based with steps that build from one concept to the next at just the right pace. Includes review, but not so much as to overkill. The lessons were so clear that not a lot of additional teacher support was needed. (And, a good thing, as it is a bit lite on the teacher support.)

 

Did NOT care for Saxon's approach of little bites of instruction spread over multiple lessons spaced days apart, and emphasis on memorizing formulas to plug into problems -- often students resort to memorizing based on wording of the problems. Plus, too many little bits and pieces of too many topics in each lesson; felt like ADD skipping from one thing to another, which makes teaching more difficult (for me). (For students who connect with Saxon, it works well and makes teaching math super easy for the teacher, as those students usually pretty much self-teach through Saxon.)

 

Math U See videos are helpful in visually showing how/why behind the abstract concepts of the higher maths. And the program is a lifesaver if you have a struggling math student. But it is "lite", esp. in the problem-solving area.

 

Wished *I* could have stuck it out with Singapore's old New Elementary Math, but we only made it through half of NEM 1 because there was not enough teacher support for ME. It is fabulous for math thinking/problem-solving for those going into engineering and research areas, and if you have a self-teaching student, and access to a tutor, it's a great program.

 

I would have loved to try Art of Problem Solving, Life of Fred, Dolciani, and Lial's, but ran out of students and didn't need to add to our bookshelf of maths.  :)

 

 

PS -- ETA:

For elementary/middle school (since I just realized the OP still has younger students):

 

- Miquon -- the discovery-based aspect was fabulous for helping ME make math connections and really "getting" basic math concepts

 

- Singapore -- love the bar diagram method for visualizing solving word problems; very helpful in helping the student narrow down what they know and what they're looking for, to then fill in the dots to figure out how to get there

 

- Keys To… workbooks; really helpful to solidify foundational concepts; they come up with multiple ways of explaining things like fractions, decimals, and percents that are such a boon to the teacher -- more ways of thinking about/explaining the concept to students with different learning styles and needs

 

Again, wish Beast Academy and Life of Fred would have been available at the time we were doing those grades; those look like such great supplements.

[creekland]

Algebra (1, 2 or College Alg).  I don't particularly care what text as I can work with any of them, but I'd definitely put what our school uses (CPM Math) as low as possible on the list.  Saxon might be shortly above it (sorry Saxon lovers - it's not one I would purposely choose - but I respect that it works for others).  TT works well.  Lial's works well.  But again, I can work with any text a student brings me.

[FaithManor]

Creekland, the last time I subbed for the local PS, I was in Algebra 2 for a week with a text put out by McDougell Littel. I cannot remember the name, but it was new to the district. In my life I do not think I have ever encountered such a poorly laid out teacher's manual or student text. I was unimpressed to make an understatement.

 

The teachers HATE the text as much as the students but the district spent a truckload of money to buy it so they are stuck for a good number of years. I told the principal that they ought to peruse amazon and ebay for some decent Lial's texts for cheap. I offered to fundraise for it! They didn't take me up on my offer. Sigh....

 

I have not yet encountered CPM locally, but can only imagine that if it were anything like the MCD/Littel, I would not be pleased with it.

[kiana]

I have not yet encountered CPM locally, but can only imagine that if it were anything like the MCD/Littel, I would not be pleased with it.

 

It's worse.

[chiguirre]

What is your favorite math--by grade, subject and text to teach?

 

The one that doesn't cause an argument with my child. I went through a ton of curricula with G and ended up with Semple Math and MUS...and a tutor.

 

With T, we cruised through SM 6B and started DM 7A. I loved that book. BUT, T would argue every time I marked a problem wrong. I did realize that it wasn't the book, it was her age and the increased complexity of the material. I needed to outsource correcting the problems. I ended up with the VHSG's online at-your-own-pace Saxon Algebra 1 class. I do sit with T during the explanations and add my comments. Sometimes I pause the video and have her explain the problem herself. I show her how I want her to write out the problems in her notebook. I tell her which ones she can do mentally. It's still somewhat teacher intensive, but if she makes a dumb mistake (and that's 99% of her errors) the answer is red. It will stay red until she fixes the units, checks the negative signs, figures out she added instead of multiplied, etc. There is no arguing with the machine.

 

I don't think we'll be in the annoying tween stage forever. I can already see signs of more maturity and the realization that details matter. Our year with Saxon and the computer checking has saved us both a lot of grief, though. Although Saxon isn't my first choice of curriculum, it serves its purpose. Hopefully we can do something more thoughtful when we get the basics of Algebra 1 and good math work habits firmly cemented.

 

My take away from this experience is that flexibility is golden. You may find yourself in circumstances where your dream curriculum doesn't work for your child. Whether that's forever or for a season, you'll have to go back to the drawing board. It's fun to look at all the lovely books and plan ahead, but write those plans in pencil.

[Teacher Mom]

Algebra I - II - Foersters - Grade 8 and 10. Loved it; loved the word problems.

[Lori D.]

The one that doesn't cause an argument with my child...

 

… My take away from this experience is that flexibility is golden. You may find yourself in circumstances where your dream curriculum doesn't work for your child...

 

Yes! This is so important. Alas, those pesky students really DO have to have a say in the matter if you want to succeed in teaching math; it can't just be what program is the teacher's favorite. ;)

[JanetC]

I had a blast teaching from CSMP (http://stern.buffalostate.edu/~csmp/), but I have weird taste.  It is K-6, though I started first grade with both kids.

 

Loved the games and stories, but it is a teacher intensive program (no student book, and you need to have or make manipulatives frequently), so as the girls got older (about 5th grade for each) and wanted to work faster and more independently, we moved on to other things.

 

 

 

[G5052]

Mine have done great with Saxon for pre-Algebra through Advanced Math.

 

I don't think that way at all, but they really, really know their math, and it works for them.  Not that this is everything, but they also score well on standardized tests and college testing.

[Nan in Mass]

Singapore's NEM1 and 2.  It was time consuming, but it was really good at keeping my ...creative???... students from going astray in their thinking.  The problems hit every place they might have gone wrong in their thinking so I didn't have to figure that out for myself.  I'm not a math teacher, so I really appreciated that.  I like things where I can just read the text aloud and solve the example problems and then correct their excersizes.  I don't want to have reteach the lesson.  It was very applied, so "why am I doing this" wasn't an issue.  It was more interesting than Primary Maths (which I also loved) because it was higher math.  I found it easy to teach from - just read the lesson aloud, working the problems out on paper, do the oral bits, and then have the child do the excersizes.  The language was specific enough that they didn't go astray and I didn't have to translate.  Well, except for one particular lesson, which we found confusing.  The fact that I remember that lesson tells you how much NEM's language clicked with my family's brains.  By the time we had worked through the oral part, they usually had figured out how it worked.  There were plenty of problems, so I could assign the odds and then if they were still struggling, the evens.  (I prefered the odds, though, because the answers were in the back.)  I taught it twice, once with a math-bright child and once with a math-challenged child and it worked for both.  I also have taught algebra with Dolciani and with Saxon.  Dolciani is what I had as a child and it is fine if you start at the beginning, but I am using it now with an older student for review and he hates it.  Of course, we are wailing through it at three lessons a day, which might have something to do with it.  He has no patience with the mathy language.  I'd use NEM but Dociani is much faster.  NEM takes gobs and gobs of time, at least when I do it.  We HATED Saxon.  It didn't work for us at all.  I tried it with two very different students and it worked for neither.  Too many chopped up little bits.  My children couldn't put them together.  The scary part was that they got almost all the problems right so it looked like it was working.  We also dabbled with Life of Fred.  The story was a distraction we didn't need, although I like the idea.  I've used Keys to for solidifying and it was great for that, super easy to use.  It isn't a full algebra program, though.  Youngest used and adored Miquon, but I can't say I taught it lol.  I just gave him the books and he taught himself.  I used Singpaore Primary Math 5 (or was it 6?) to teach an adult student who remembered almost no math at all and it was great because it straightened out so many of her misconceptions about how math worked.  She kept saying, "Why didn't they teach it to us this way in school?  I would have understood it if they had."

 

Nan

[MarkT]

 

Your public library probably has Susan Assouline's book 'Developing Math Talent' which also has suggestions.

The book 'Developing Math Talent' seems to be targeted at Elementary school age by the description. Is it worth reading for late starters in the after-school world?

 

 

[SilverMoon]

.

Edited May 18 by SilverMoon

[mathwonk]

30 years ago I enjoyed teaching my kids from Harold Jacobs' books Elementary Algebra, and Geometry.  More recently, with PG kids and grad students in education, I especially enjoyed teaching geometry from Euclid, with Hartshorne's Geometry: Euclid and beyond, as a guide.  I finally felt I understood Euclidean geometry, and the famous "shortcomings", but more significantly the strengths of Euclid's original approach.  Another more advanced one I have enjoyed teaching from to future mathematicians is Michael Spivak's book Calculus.

 

 I like books that are enjoyable to read and that teach me something, or make me look at the subject from a new perspective.  I like books by masters, that make me say "Of course, why didn't anyone say it that way before?  It seems so clear and simple now."  As long as something seems hard, I am not satisfied.  I want to eventually see why something should be easy, even obvious, or at least natural.

 

for example:  Archimedes says  a spherical ball should be thought of as a pyramid, where the surface of the ball is the base of the pyramid, and the center of the ball is the vertex.  If one can see that, it becomes clear why the volume of the ball is (1/3) radius, i.e. (R/3) times surface area, because the volume of a pyramid is (1/3) base times height.  So once you know the volume of a ball is (4/3)Ï€R^3, it follows that the surface area is (3/R) times that, or 4Ï€R^2.  When I was in high school, I don't recall learning the connection between those formulas.

 

To help see it as Archimedes did, start from an (upside down) ice cream cone, and imagine that as a pyramid with a rounded base.  Then let the ice cream part get wider, and the angle at the point of the cone get broader, like an umbrella being opened and then blown around backwards by the wind, until the "cone" is finally a full ball of ice cream, and the base of the "pyramid" has become the surface of the full ball of ice cream, with the point of the cone at the center.

 

 

Geometry in Euclid and Archimedes is very interconnected, so that understanding one figure leads to understanding another one.  Euclid talks about using triangles to study circles and vice versa.

 

 Archimedes goes on to cones and balls, and their similarity to pyramids.  His proof that in terms of volume, a ball plus a (double) cone equals a cylinder, is simple and  beautiful, depending only on the Pythagorean theorem. 

 

Then since the cylinder of height 2R and base πR^2 has volume 2πR^3, the cone has (1/3) that volume and the ball has 2/3 that volume or (2/3)(2πR^3) = (4/3)πR^3.

 

This simple approach was not explained in books I had seen, and I learned it from a picture Jacobs' Geometry, not that long ago.  As an old calculus professor, I was quite embarrassed not to have known how easy Archimedes made this, when I was making it look much harder in my calculus classes.

 

Another volume problem we consider very difficult in calculus classes is that of a "bicylinder", the intersection of two perpendicular cylinders, something difficult even to visualize at first.  (It looks sort of like a rounded pagoda plus its reflection in the water.)  Using Archimedes' approach it can be seen to equal a cube minus a square - based pyramid, so that again its volume is (2/3) that of the enveloping cube, exactly similar to the case of the ball.

 

 I.e. he shows that the bicylinder, the cube and the square based pyramid, are exactly analogous to the ball, the cylinder and the circular based pyramid.  So if you can do one you can do the other.  I have never seen this explained in any calculus book.

 

 

It is described in this paper, which I don't find super easy to read, but could be interesting to someone, in which Tom Apostol and a collaborator generalize Archimedes' idea to a wide class of solids..

 

https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Apostol496-508.pdf

 

There are many other amazing things, in this book by the same two authors:

 

http://www.maa.org/publications/books/new-horizons-in-geometry