Running two math courses...

[LisaKinVA]

I'm trying to plan this out...My oldest will be doing a 2nd year in Algebra 1, but I'd like to run it along side Geometry. Focus will be on completing Algebra 1 THIS year, and doing about half of Geometry this year, with the second half alongside Geometry.

 

I am thinking of Algebra 1, Monday, Wednesday, Friday & Saturday, with Geometry on Tuesday & Thursday & Saturday. Since this is our second time through Algebra 1 (using a different course), and my son "likes" Geometry...I don't feel like this is "too much." We school year-round, so this will be a 12 month plan vs. 9 month as well.

 

If you've had a child who did something like this, how did you work it out? Thanks.

[Kathy G]

We did something similar with algebra and Intro to Number Theory. We did MWF Algebra and T/TH number theory. It worked just fine. My DS is a mathy guy and so he liked to do several lessons in a day. If this was your 1st year in algebra I don't know if it would work, but since it is the 2nd I think you will be fine. Is your child on board with this? Our plan worked in part because it was what my DS wanted to do.

[quark]

We have done:

Dolciani Algebra 1 + AoPS Counting and Probability, then

a little of AoPS Number Theory + Jurgensen Geometry,

and now it's:

Jurgensen Geometry + reviewing Alg 1 with AoPS Intro to Algebra

 

We only "school" 4 days a week (year-round) and he does both each day.

 

I guess it would depend on:

1. How proof heavy the geometry is. Jurgensen is a proof-heavy text so he needs about 90 mins/ day. The algebra is only review and takes him about 30-40 minutes per section, or 30-40 minutes for two sections if he skips things he is sure he already knows.

2. How predictable your life is. We found that alternating days between the two did not work for us because we want to also seize other opportunities that come our way e.g. field trips, free online classes etc.

 

I think it works out fine when the kids love math.

[regentrude]

My DD has taken algebra 2 and geometry partly concurrently. We did not set a fixed schedule but rather let her choose which math she wanted to work on. there were phases when she focused more on algebra, and others when she was on a roll with geometry.

ETA: we never "schedule" math; the book is done when it is done. We require 45-60 min daily for DS, DD chooses on her own how much she wants to spend on math- it usually goes in binges.

Edited June 17, 2012 by regentrude

[KAR120C]

We've always had a primary math program (Singapore, until we switched to AoPS) and then something else going on the side, either as part of a group, or in a class, or something.... So while DS was doing Statistics at home, we were doing Zome Geometry with a group. And when we were doing Geometry at home, we were doing Competition Math in a group. Discrete Math with AoPS classes and Financial Math to go with Economics... That sort of thing.

 

It wasn't so much that we were doing two whole curricula in regular school time but that we had a side interest going along in the meantime. And really, once we've hit one topic in math, it never quite gets dropped... so as soon as he had Statistics as a class, he started using it in his science projects too... and as soon as he had had Discrete Math it got to be a more important part of competition prep.. and so forth. So even when we're doing only one thing, everything else comes back around in one way or another.

[Belacqua]

 

It wasn't so much that we were doing two whole curricula in regular school time but that we had a side interest going along in the meantime. And really, once we've hit one topic in math, it never quite gets dropped... so as soon as he had Statistics as a class, he started using it in his science projects too... and as soon as he had had Discrete Math it got to be a more important part of competition prep.. and so forth. So even when we're doing only one thing, everything else comes back around in one way or another.

 

That's pretty much what we've done, too. We'll have what we think of as regular math, following a set schedule and punctuated with tests and problem sets. Then we'll have other topics going on, as well. It's usually related to whatever was most recently covered in WOOT (an AoPS class that touches on many different topics); we'll go on what might be considered rabbit trails, if you had fairly regimented rabbits who were willing to return to their starting point every few weeks and get themselves organized. :)

 

I like how regentrude described it as going in binges.

[KAR120C]

we'll go on what might be considered rabbit trails, if you had fairly regimented rabbits who were willing to return to their starting point every few weeks and get themselves organized.

Yes... "regimented rabbits" sums it up rather well! ;)

[Colleen in SEVA]

I did this, and I do it with my older boys.

 

My freshman year of high school I went to a school that had 6 classes per day. The sequence at that school was to take Algebra 2 / Trig before Geometry, but I didn't get a good grade. I took Geometry my sophomore year, but in September we moved to another state that had 8 classes per day and students there took Geometry BEFORE Algebra 2 / Trig. Since I had to add classes, I chose to take Algebra 2 / Trig as an elective (concurrently with Geometry). I had both classes every day, but the 8th class I added was a study hall so I usually finished the homework for both classes during that. I ended up getting an A the second time through Algebra 2 / Trig, and did very well in Geometry as well. Both times through Algebra 2 / Trig were on my transcript.

 

With my kids, I do something similar. They have their main math in which they are learning things for the first time, but they also have a second math that I use one level lower that acts as review & reinforcement (different combos for different kids).

[Parker Martin]

I have never done this, but as someone who found algebra tedious but geometry delightful, I wish my school had scheduled it the way you are with your son.

[mathwonk]

please forgive me if this is way off course, but i love this combination of subjects. like Parker Martin i always liked geometry more than algebra, but found out eventually they could be combined.

 

In "algebraic geometry" ( a continuation of analytic geometry), the geometry allows visual intuition to enrich the algebra, and allows the algebra to give precision to the geometry. there is even a sort of dictionary between the two subjects. The concept of "irreducible" means "does not break into two pieces" in geometry, and means "does not factor" in algebra. But these are equivalent in a sense!

 

[OK here's where it gets technical - my apologies.]

 

I.e. the fact that the X axis is just one line in the plane corresponds to the fact that its equation Y=0 cannot be factored. By contrast the equation XY = 0, factors into X=0 and Y=0, corresponding to the fact that the solutions of the equation XY=0 is two lines, the X axis and the Y axis.

 

 

Similarly a circle has only one piece, which corresponds to the fact that its equation X^2 + Y^2 -1 = 0 cannot be factored. In this example I myself cannot readily see that the equation does not factor but I see immediately that the circle consists of only one piece. So my geometric intuition helps out my algebraic limitations.

 

The fact that a cubic equation has degree 3 corresponds to the maximum number of points in which it can meet a line, so an algebraic notion like "degree" also has a geometric meaning in terms of geometric intersections.

 

With your indulgence I add one more example. To intersect the curve with equation Y - (X^2)(X-1) = 0, with the X axis, we set Y = 0, and get X^2(X-1) = 0. Since this has a double factor of X, hence a double root at X=0, it means geometrically that the X axis meets the curve "doubly", i.e. tangentially at X=0.

 

Here the degree is three, but two of the three intersections have come together. When this happens the multiple intersection is always tangential. Thus we know these two figures must be tangent even before drawing them. This method allowed Descartes to compute tangent lines before Newton and Leibniz invented calculus.

 

This point of view thus allows one to take his strength in geometry and use it to help him gain access to algebra, or vice versa.

 

So I greatly approve of what you are doing! At a certain level many "distinct" math subjects are intimately related.

Edited June 21, 2012 by mathwonk

[LisaKinVA]

Thank you everyone for your input. I think my son will thoroughly enjoy doing these two subjects together!

[regentrude]

At a certain level many "distinct" math subjects are intimately related.

 

In other countries, the compartmentalization of math into "geometry" and "algebra" that is used in the US does not exist- they just teach "math" and teach geometric and algebraic concepts together.

 

Which has the great advantage that students do not have to wait to start algebra until they are mature enough for all the hard topics - they get introduced to simple algebra concepts earlier (linear eqs in 7th grade) and harder ones a few years later (quadratics in 9th), and geometric proofs in triangles for example are taught in 6th grade)

[mathwonk]

In euclid one can see the beginnings of geometric algebra in book 2, where essentially the product of two line segments is the rectangle they form. By sticking two segments together end to end, and A segment and a B segment, and forming the square from two copies of the combined A+B segment, one sees it decomposes into an A square, a B square and two AB rectangles, just the rule we teach in algebra as (A+B)^2 = A^2 + B^2 + 2AB.

 

I really like this way of making algebra geometrically visible. It is also why I think I now like Euclid best of all beginning math books.

 

Euclid contains what we call plane geometry, solid geometry, theory of proportion and pure number theory. They do occur in separate chapters, but they draw on and illuminate each other.

 

E.g. to him a number is a length, and rational numbers are ones that can be expressed as ratios of lengths that can be "measured" with the same unit length. So his word for "divides" is actually "measures". This helped me a lot to understand some aspects of division that had confused me.

 

For instance suppose you have two commensurable measuring sticks and you ask two questions:

 

1) what is the smallest length that can be measured using both of them, i.e. adding and subtracting them from each other.

 

2) what is the longest length that can be used to measure both of them? i.e. what is the largest unit length that divides evenly into both of them?

 

The marvelous result is that these two questions have the same answer!

 

I.e. the smallest amount of water that you can measure with two buckets, one holding 12 quarts and one holding 9 quarts,

 

is their greatest common divisor, i.e. 3 quarts, the largest number that divides both 9 and 12.

 

This is called "Euclid's algorithm".

 

An illustration of your point is the fact that Euclid apparently never uses the word geometry anywhere in his book, e.g. his book is called simply "the Elements".

Edited June 21, 2012 by mathwonk