Academic Rigor

How would you define "academic rigor"?  It is something I always thought I wanted for my children: academic rigor.  One of my favorite homeschool resources (WTM forums) has discussions often about Academic Rigor. It is usually seen as a good thing.  I looked up the word "rigor" on Dictionary.com, and here are some of the definitions of rigor:

1. strictness, severity, or harshness, as in dealing with people.

2. the full or extreme severity of laws, rules, etc.

3. severity of living conditions; hardship; austerity: the rigor of wartime existence.

4. a severe or harsh act, circumstance, etc.

 

Rigor even describes plants living in an unsuitable environment for growth:  inactivity, stagnation, inertia.

Rigor can mean stiffness and an inability to move.

Yikes!

I'm re-thinking this Academic Rigor idea... 

 

 

Ages and Stages

I've noticed a certain trend in learning during ages and stages of development.  Either it's genetic and that's why I see the trend, or it is a common event for a large number of children:)

Age 4-6  Learning happens naturally as a part of life.  They seem to soak things in and ask a lot of questions. For some kids, K-1st gr material will be very easy, as if they already know these things and don't really need to be formally taught.  Innocent and optimistic, the world is full of wonder to be explored.

Age 6-8  Suddenly, they seem aware of what the outside world thinks of them.  They seem hyper-sensitive to criticism and joking.  The workload gets harder and more academic, but the child doesn't quite have the study skills yet to adjust.  This new sensitivity coupled with the increasing challenge of academics creates a real rough patch in the 2nd/3rd-4th grade years.

Age 9 or 10  The "Real" Child emerges.  They come out of that volatile stage.  The parent begins to see a vision of where the child might be headed, his/her strong characteristics, interests, and natural talents. The child enters the "logic" stage, and has a deeper understanding of how things work.  He begins to question, and thinks of the world more critically, challenging ideas. 

That's all I have so far - I haven't seen anything past age 10 yet!  I'd love to hear your experience with your own children. 

Simple Equations - Horizons' Style

Basic Equations with Variables, in Horizons Math (starting 2nd or 3rd Grade)

Horizons Math teaches Equations, and I think they start this in 2nd grade.  Many math curriculum teach equations with variables, but not quite like Horizons!  I'll give an example:

Most Math curriculum will teach something like this:
x + 6 = 11;
The next step, according to other Math programs is to turn the addition problem into a subtraction problem:
11 - 6 = x;
Then 6 is subtracted from 11 to get 5
5 = x

Horizons Math shows the algebraic step missing in other programs.  Here is Horizons' method:
x + 6 = 11;
Next step is to subtract 6 on both sides of the equation.  This cancels the 6 on the left side, and gets the 6 onto the other side.  It also gets the variable alone, which is what we want;
x + 6 = 11
    -6    -6
--------------
Here, the 6s cancel on the left, and you can subtract 6 from 11 on the right.
x       =  5

I would suspect that many kids have the same reaction as my child: why do it that way?  It doesn't make sense!  I can do it the first way intuitively, and I get the answer just fine.  Why subtract from both sides?  Today I showed it with blocks, and I think it made more sense.  See the video above to see how I explained it with the blocks.  The example problem is
n + 5 = 9

Hopefully, this is enough to get the pattern.  After I explained it this way, my daughter was able to apply the whole "subtract on both sides" idea to her math problems.  Thankfully, she automatically made the connection that she'd use the opposite sign when confronted with this kind of problem:
y - 2 = 8
It seemed intuitive to her to add 2 to both sides.  Thank goodness, because I was having a hard time figuring out how I'd show that with blocks!  Looking online, the explanations get into some pretty big concepts: negative numbers and making 0.  It's not that my daughter couldn't get those concepts, I just hate to pile on too many new concepts all at once:)
Want more?  Here's a Khan Academy video that shows the same thing (without the blocks):
http://www.khanacademy.org/video/solving-one-step-equations?playlist=Developmental%20Math

Curriculum Finds

The slideshow shows all of the good deals I found at the local library. A homeschool parent must have donated the books for the library sale, and for some reason, the library accepted them (they don't usually accept textbooks). I'll list the books here:
Fallacy Detective
Story of the World Books 1 & 2
Oak Meadow 5th Gr History/English & Teacher's Guide
Apologia Exploring Creation with Biology, Exploring Creation with Chemistry (2nd ed), General Science (Chem & Gen Sci both have the answer keys booklet)
Calvert Famous Americans
Calvert Gods of Greece
Spelling Power
Vocab Classical Root Words book B
Elements in the Periodic Table
BJU Geometry Teacher's Guide 1 & 2
World Geography
Life on Earth Teacher Box & Study Guide
Last photo is some of the amazing photos from the Life on Earth Teacher box

I spent about $13 for all of these books!  I like to have a lot of resources on hand for whenever I'm inspired in any given direction.